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+The Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A System of Logic: Ratiocinative and Inductive
+       7th Edition, Vol. I
+
+Author: John Stuart Mill
+
+Release Date: February 27, 2011 [EBook #35420]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL I ***
+
+
+
+
+Produced by David Clarke, Stephen H. Sentoff and the Online
+Distributed Proofreading Team at https://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+VOL. I.
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+BEING A CONNECTED VIEW OF THE
+PRINCIPLES OF EVIDENCE
+AND THE
+METHODS OF SCIENTIFIC INVESTIGATION
+
+BY
+
+JOHN STUART MILL
+
+
+IN TWO VOLUMES
+
+VOL. I.
+
+SEVENTH EDITION
+
+
+LONDON:
+LONGMANS, GREEN, READER, AND DYER
+
+MDCCCLXVIII
+
+
+
+
+PREFACE TO THE FIRST EDITION.
+
+
+This book makes no pretence of giving to the world a new theory of the
+intellectual operations. Its claim to attention, if it possess any, is
+grounded on the fact that it is an attempt not to supersede, but to
+embody and systematize, the best ideas which have been either
+promulgated on its subject by speculative writers, or conformed to by
+accurate thinkers in their scientific inquiries.
+
+To cement together the detached fragments of a subject, never yet
+treated as a whole; to harmonize the true portions of discordant
+theories, by supplying the links of thought necessary to connect them,
+and by disentangling them from the errors with which they are always
+more or less interwoven; must necessarily require a considerable amount
+of original speculation. To other originality than this, the present
+work lays no claim. In the existing state of the cultivation of the
+sciences, there would be a very strong presumption against any one who
+should imagine that he had effected a revolution in the theory of the
+investigation of truth, or added any fundamentally new process to the
+practice of it. The improvement which remains to be effected in the
+methods of philosophizing (and the author believes that they have much
+need of improvement) can only consist in performing, more systematically
+and accurately, operations with which, at least in their elementary
+form, the human intellect in some one or other of its employments is
+already familiar.
+
+In the portion of the work which treats of Ratiocination, the author has
+not deemed it necessary to enter into technical details which may be
+obtained in so perfect a shape from the existing treatises on what is
+termed the Logic of the Schools. In the contempt entertained by many
+modern philosophers for the syllogistic art, it will be seen that he by
+no means participates; though the scientific theory on which its defence
+is usually rested appears to him erroneous: and the view which he has
+suggested of the nature and functions of the Syllogism may, perhaps,
+afford the means of conciliating the principles of the art with as much
+as is well grounded in the doctrines and objections of its assailants.
+
+The same abstinence from details could not be observed in the First
+Book, on Names and Propositions; because many useful principles and
+distinctions which were contained in the old Logic, have been gradually
+omitted from the writings of its later teachers; and it appeared
+desirable both to revive these, and to reform and rationalize the
+philosophical foundation on which they stood. The earlier chapters of
+this preliminary Book will consequently appear, to some readers,
+needlessly elementary and scholastic. But those who know in what
+darkness the nature of our knowledge, and of the processes by which it
+is obtained, is often involved by a confused apprehension of the import
+of the different classes of Words and Assertions, will not regard these
+discussions as either frivolous, or irrelevant to the topics considered
+in the later Books.
+
+On the subject of Induction, the task to be performed was that of
+generalizing the modes of investigating truth and estimating evidence,
+by which so many important and recondite laws of nature have, in the
+various sciences, been aggregated to the stock of human knowledge. That
+this is not a task free from difficulty may be presumed from the fact,
+that even at a very recent period, eminent writers (among whom it is
+sufficient to name Archbishop Whately, and the author of a celebrated
+article on Bacon in the _Edinburgh Review_) have not scrupled to
+pronounce it impossible.[1] The author has endeavoured to combat their
+theory in the manner in which Diogenes confuted the sceptical reasonings
+against the possibility of motion; remembering that Diogenes' argument
+would have been equally conclusive, though his individual perambulations
+might not have extended beyond the circuit of his own tub.
+
+Whatever may be the value of what the author has succeeded in effecting
+on this branch of his subject, it is a duty to acknowledge that for much
+of it he has been indebted to several important treatises, partly
+historical and partly philosophical, on the generalities and processes
+of physical science, which have been published within the last few
+years. To these treatises, and to their authors, he has endeavoured to
+do justice in the body of the work. But as with one of these writers,
+Dr. Whewell, he has occasion frequently to express differences of
+opinion, it is more particularly incumbent on him in this place to
+declare, that without the aid derived from the facts and ideas contained
+in that gentleman's _History of the Inductive Sciences_, the
+corresponding portion of this work would probably not have been written.
+
+The concluding Book is an attempt to contribute towards the solution of
+a question, which the decay of old opinions, and the agitation that
+disturbs European society to its inmost depths, render as important in
+the present day to the practical interests of human life, as it must at
+all times be to the completeness of our speculative knowledge: viz.
+Whether moral and social phenomena are really exceptions to the general
+certainty and uniformity of the course of nature; and how far the
+methods, by which so many of the laws of the physical world have been
+numbered among truths irrevocably acquired and universally assented to,
+can be made instrumental to the formation of a similar body of received
+doctrine in moral and political science.
+
+
+
+
+PREFACE TO THE THIRD AND FOURTH EDITIONS.
+
+
+Several criticisms, of a more or less controversial character, on this
+work, have appeared since the publication of the second edition; and Dr.
+Whewell has lately published a reply to those parts of it in which some
+of his opinions were controverted.[2]
+
+I have carefully reconsidered all the points on which my conclusions
+have been assailed. But I have not to announce a change of opinion on
+any matter of importance. Such minor oversights as have been detected,
+either by myself or by my critics, I have, in general silently,
+corrected: but it is not to be inferred that I agree with the objections
+which have been made to a passage, in every instance in which I have
+altered or cancelled it. I have often done so, merely that it might not
+remain a stumbling-block, when the amount of discussion necessary to
+place the matter in its true light would have exceeded what was suitable
+to the occasion.
+
+To several of the arguments which have been urged against me, I have
+thought it useful to reply with some degree of minuteness; not from any
+taste for controversy, but because the opportunity was favourable for
+placing my own conclusions, and the grounds of them, more clearly and
+completely before the reader. Truth, on these subjects, is militant, and
+can only establish itself by means of conflict. The most opposite
+opinions can make a plausible show of evidence while each has the
+statement of its own case; and it is only possible to ascertain which of
+them is in the right, after hearing and comparing what each can say
+against the other, and what the other can urge in its defence.
+
+Even the criticisms from which I most dissent have been of great service
+to me, by showing in what places the exposition most needed to be
+improved, or the argument strengthened. And I should have been well
+pleased if the book had undergone a much greater amount of attack; as in
+that case I should probably have been enabled to improve it still more
+than I believe I have now done.
+
+       *       *       *       *       *
+
+In the subsequent editions, the attempt to improve the work by additions
+and corrections, suggested by criticism or by thought, has been
+continued. In the present (seventh) edition, a few further corrections
+have been made, but no material additions.
+
+FOOTNOTES:
+
+[1] In the later editions of Archbishop Whately's _Logic_, he states his
+meaning to be, not that "rules" for the ascertainment of truths by
+inductive investigation cannot be laid down, or that they may not be "of
+eminent service," but that they "must always be comparatively vague and
+general, and incapable of being built up into a regular demonstrative
+theory like that of the Syllogism." (Book IV. ch. iv. § 3.) And he
+observes, that to devise a system for this purpose, capable of being
+"brought into a scientific form," would be an achievement which "he must
+be more sanguine than scientific who expects." (Book IV. ch. ii. § 4.)
+To effect this, however, being the express object of the portion of the
+present work which treats of Induction, the words in the text are no
+overstatement of the difference of opinion between Archbishop Whately
+and me on the subject.
+
+[2] Now forming a chapter in his volume on _The Philosophy of
+Discovery_.
+
+
+
+
+CONTENTS
+OF
+THE FIRST VOLUME.
+
+
+  INTRODUCTION.
+
+
+  § 1. A definition at the commencement of a subject must be
+       provisional                                                    1
+
+    2. Is logic the art and science of reasoning?                     2
+
+    3. Or the art and science of the pursuit of truth?                3
+
+    4. Logic is concerned with inferences, not with intuitive truths  5
+
+    5. Relation of logic to the other sciences                        8
+
+    6. Its utility, how shown                                        10
+
+    7. Definition of logic stated and illustrated                    11
+
+
+  BOOK I.
+
+  OF NAMES AND PROPOSITIONS.
+
+
+  CHAPTER I. _Of the Necessity of commencing with an
+  Analysis of Language._
+
+  § 1. Theory of names, why a necessary part of logic                17
+
+    2. First step in the analysis of Propositions                    18
+
+    3. Names must be studied before Things                           21
+
+
+  CHAPTER II. _Of Names._
+
+  § 1. Names are names of things, not of our ideas                   23
+
+    2. Words which are not names, but parts of names                 24
+
+    3. General and Singular names                                    26
+
+    4. Concrete and Abstract                                         29
+
+    5. Connotative and Non-connotative                               31
+
+    6. Positive and Negative                                         42
+
+    7. Relative and Absolute                                         44
+
+    8. Univocal and Æquivocal                                        47
+
+
+  CHAPTER III. _Of the Things denoted by Names._
+
+  § 1. Necessity of an enumeration of Nameable Things. The
+       Categories of Aristotle                                       49
+
+    2. Ambiguity of the most general names                           51
+
+    3. Feelings, or states of consciousness                          54
+
+    4. Feelings must be distinguished from their physical
+       antecedents. Perceptions, what                                56
+
+    5. Volitions, and Actions, what                                  58
+
+    6. Substance and Attribute                                       59
+
+    7. Body                                                          61
+
+    8. Mind                                                          67
+
+    9. Qualities                                                     69
+
+   10. Relations                                                     72
+
+   11. Resemblance                                                   74
+
+   12. Quantity                                                      78
+
+   13. All attributes of bodies are grounded on states of
+       consciousness                                                 79
+
+   14. So also all attributes of mind                                80
+
+   15. Recapitulation                                                81
+
+
+  CHAPTER IV. _Of Propositions._
+
+  § 1. Nature and office of the copula                               85
+
+    2. Affirmative and Negative propositions                         87
+
+    3. Simple and Complex                                            89
+
+    4. Universal, Particular, and Singular                           93
+
+
+  CHAPTER V. _Of the Import of Propositions._
+
+  § 1. Doctrine that a proposition is the expression of a relation
+       between two ideas                                             96
+
+    2. Doctrine that it is the expression of a relation between the
+       meanings of two names                                         99
+
+    3. Doctrine that it consists in referring something to, or
+       excluding something from, a class                            103
+
+    4. What it really is                                            107
+
+    5. It asserts (or denies) a sequence, a coexistence, a simple
+       existence, a causation                                       110
+
+    6. --or a resemblance                                           112
+
+    7. Propositions of which the terms are abstract                 115
+
+
+  CHAPTER VI. _Of Propositions merely Verbal._
+
+  § 1. Essential and Accidental propositions                        119
+
+    2. All essential propositions are identical propositions        120
+
+    3. Individuals have no essences                                 124
+
+    4. Real propositions, how distinguished from verbal             126
+
+    5. Two modes of representing the import of a Real proposition   127
+
+
+  CHAPTER VII. _Of the Nature of Classification, and
+  the Five Predicables._
+
+  § 1. Classification, how connected with Naming                    129
+
+    2. The Predicables, what                                        131
+
+    3. Genus and Species                                            131
+
+    4. Kinds have a real existence in nature                        134
+
+    5. Differentia                                                  139
+
+    6. Differentiæ for general purposes, and differentiæ for
+       special or technical purposes                                141
+
+    7. Proprium                                                     144
+
+    8. Accidens                                                     146
+
+
+  CHAPTER VIII. _Of Definition._
+
+  § 1. A definition, what                                           148
+
+    2. Every name can be defined, whose meaning is susceptible
+       of analysis                                                  150
+
+    3. Complete, how distinguished from incomplete definitions      152
+
+    4. --and from descriptions                                      154
+
+    5. What are called definitions of Things, are definitions of
+       Names with an implied assumption of the existence of
+       Things corresponding to them                                 157
+
+    6. --even when such things do not in reality exist              165
+
+    7. Definitions, though of names only, must be grounded on
+       knowledge of the corresponding Things                        167
+
+
+  BOOK II.
+
+  OF REASONING.
+
+
+  CHAPTER I. _Of Inference, or Reasoning, in general._
+
+  § 1. Retrospect of the preceding book                             175
+
+    2. Inferences improperly so called                              177
+
+    3. Inferences proper, distinguished into inductions and
+       ratiocinations                                               181
+
+
+  CHAPTER II. _Of Ratiocination, or Syllogism._
+
+  § 1. Analysis of the Syllogism                                    184
+
+    2. The _dictum de omni_ not the foundation of reasoning,
+       but a mere identical proposition                             191
+
+    3. What is the really fundamental axiom of Ratiocination        196
+
+    4. The other form of the axiom                                  199
+
+
+  CHAPTER III. _Of the Functions, and Logical Value, of the
+  Syllogism._
+
+  § 1. Is the syllogism a _petitio principii_?                      202
+
+    2. Insufficiency of the common theory                           203
+
+    3. All inference is from particulars to particulars             205
+
+    4. General propositions are a record of such inferences, and
+       the rules of the syllogism are rules for the interpretation
+       of the record                                                214
+
+    5. The syllogism not the type of reasoning, but a test of it    218
+
+    6. The true type, what                                          222
+
+    7. Relation between Induction and Deduction                     226
+
+    8. Objections answered                                          227
+
+    9. Of Formal Logic, and its relation to the Logic of Truth      231
+
+
+  CHAPTER IV. _Of Trains of Reasoning, and Deductive
+  Sciences._
+
+  § 1. For what purpose trains of reasoning exist                   234
+
+    2. A train of reasoning is a series of inductive inferences     234
+
+    3. --from particulars to particulars through marks of marks     237
+
+    4. Why there are deductive sciences                             240
+
+    5. Why other sciences still remain experimental                 244
+
+    6. Experimental sciences may become deductive by the progress
+       of experiment                                                246
+
+    7. In what manner this usually takes place                      247
+
+
+  CHAPTER V. _Of Demonstration, and Necessary Truths._
+
+  § 1. The Theorems of geometry are necessary truths only in
+       the sense of necessarily following from hypotheses           251
+
+    2. Those hypotheses are real facts with some of their
+       circumstances exaggerated or omitted                         255
+
+    3. Some of the first principles of geometry are axioms, and
+       these are not hypothetical                                   256
+
+    4. --but are experimental truths                                258
+
+    5. An objection answered                                        261
+
+    6. Dr. Whewell's opinions on axioms examined                    264
+
+
+  CHAPTER VI. _The same Subject continued._
+
+  § 1. All deductive sciences are inductive                         281
+
+    2. The propositions of the science of number are not verbal,
+       but generalizations from experience                          284
+
+    3. In what sense hypothetical                                   289
+
+    4. The characteristic property of demonstrative science is to
+       be hypothetical                                              290
+
+    5. Definition of demonstrative evidence                         292
+
+
+  CHAPTER VII. _Examination of some Opinions opposed to
+  the preceding doctrines._
+
+  § 1. Doctrine of the Universal Postulate                          294
+
+    2. The test of inconceivability does not represent the
+       aggregate of past experience                                 296
+
+    3. --nor is implied in every process of thought                 299
+
+    4. Sir W. Hamilton's opinion on the Principles of
+       Contradiction and Excluded Middle                            306
+
+
+  BOOK III.
+
+  OF INDUCTION.
+
+
+  CHAPTER I. _Preliminary Observations on Induction in general._
+
+  § 1. Importance of an Inductive Logic                             313
+
+    2. The logic of science is also that of business and life       314
+
+
+  CHAPTER II. _Of Inductions improperly so called._
+
+  § 1. Inductions distinguished from verbal transformations         319
+
+    2. --from inductions, falsely so called, in mathematics         321
+
+    3. --and from descriptions                                      323
+
+    4. Examination of Dr. Whewell's theory of Induction             326
+
+    5. Further illustration of the preceding remarks                336
+
+
+  CHAPTER III. _On the Ground of Induction._
+
+  § 1. Axiom of the uniformity of the course of nature              341
+
+    2. Not true in every sense. Induction _per enumerationem
+       simplicem_                                                   346
+
+    3. The question of Inductive Logic stated                       348
+
+
+  CHAPTER IV. _Of Laws of Nature._
+
+  § 1. The general regularity in nature is a tissue of partial
+       regularities, called laws                                    351
+
+    2. Scientific induction must be grounded on previous
+       spontaneous inductions                                       355
+
+    3. Are there any inductions fitted to be a test of all others?  357
+
+
+  CHAPTER V. _Of the Law of Universal Causation._
+
+  § 1. The universal law of successive phenomena is the Law of
+       Causation                                                    360
+
+    2. --_i.e._ the law that every consequent has an invariable
+       antecedent                                                   363
+
+    3. The cause of a phenomenon is the assemblage of its
+       conditions                                                   365
+
+    4. The distinction of agent and patient illusory                373
+
+    5. The cause is not the invariable antecedent, but the
+       _unconditional_ invariable antecedent                        375
+
+    6. Can a cause be simultaneous with its effect?                 380
+
+    7. Idea of a Permanent Cause, or original natural agent         383
+
+    8. Uniformities of coexistence between effects of different
+       permanent causes, are not laws                               386
+
+    9. Doctrine that volition is an efficient cause, examined       387
+
+
+  CHAPTER VI. _Of the Composition of Causes._
+
+  § 1. Two modes of the conjunct action of causes, the mechanical
+       and the chemical                                             405
+
+    2. The composition of causes the general rule; the other case
+       exceptional                                                  408
+
+    3. Are effects proportional to their causes?                    412
+
+
+  CHAPTER VII. _Of Observation and Experiment._
+
+  § 1. The first step of inductive inquiry is a mental analysis of
+       complex phenomena into their elements                        414
+
+    2. The next is an actual separation of those elements           416
+
+    3. Advantages of experiment over observation                    417
+
+    4. Advantages of observation over experiment                    420
+
+
+  CHAPTER VIII. _Of the Four Methods of Experimental
+  Inquiry._
+
+  § 1. Method of Agreement                                          425
+
+    2. Method of Difference                                         428
+
+    3. Mutual relation of these two methods                         429
+
+    4. Joint Method of Agreement and Difference                     433
+
+    5. Method of Residues                                           436
+
+    6. Method of Concomitant Variations                             437
+
+    7. Limitations of this last method                              443
+
+
+  CHAPTER IX. _Miscellaneous Examples of the Four Methods._
+
+  § 1. Liebig's theory of metallic poisons                          449
+
+    2. Theory of induced electricity                                453
+
+    3. Dr. Wells' theory of dew                                     457
+
+    4. Dr. Brown-Séquard's theory of cadaveric rigidity             465
+
+    5. Examples of the Method of Residues                           471
+
+    6. Dr. Whewell's objections to the Four Methods                 475
+
+
+  CHAPTER X. _Of Plurality of Causes; and of the Intermixture
+  of Effects._
+
+  § 1. One effect may have several causes                           482
+
+    2. --which is the source of a characteristic imperfection of
+       the Method of Agreement                                      483
+
+    3. Plurality of Causes, how ascertained                         487
+
+    4. Concurrence of Causes which do not compound their effects    489
+
+    5. Difficulties of the investigation, when causes compound
+       their effects                                                494
+
+    6. Three modes of investigating the laws of complex effects     499
+
+    7. The method of simple observation inapplicable                500
+
+    8. The purely experimental method inapplicable                  501
+
+
+  CHAPTER XI. _Of the Deductive Method._
+
+  § 1. First stage; ascertainment of the laws of the separate
+       causes by direct induction                                   507
+
+    2. Second stage; ratiocination from the simple laws of the
+       complex cases                                                512
+
+    3. Third stage; verification by specific experience             514
+
+
+  CHAPTER XII. _Of the Explanation of Laws of Nature._
+
+  § 1. Explanation defined                                          518
+
+    2. First mode of explanation, by resolving the law of a complex
+       effect into the laws of the concurrent causes and
+       the fact of their coexistence                                518
+
+    3. Second mode; by the detection of an intermediate link in
+       the sequence                                                 519
+
+    4. Laws are always resolved into laws more general than
+       themselves                                                   520
+
+    5. Third mode; the subsumption of less general laws under
+       a more general one                                           524
+
+    6. What the explanation of a law of nature amounts to           526
+
+
+  CHAPTER XIII. _Miscellaneous Examples of the Explanation of
+  Laws of Nature._
+
+  § 1. The general theories of the sciences                         529
+
+    2. Examples from chemical speculations                          531
+
+    3. Example from Dr. Brown-Séquard's researches on the
+       nervous system                                               533
+
+    4. Examples of following newly-discovered laws into their
+       complex manifestations                                       534
+
+    5. Examples of empirical generalizations, afterwards confirmed
+       and explained deductively                                    536
+
+    6. Example from mental science                                  538
+
+    7. Tendency of all the sciences to become deductive             539
+
+
+
+
+INTRODUCTION.
+
+
+§ 1. There is as great diversity among authors in the modes which they
+have adopted of defining logic, as in their treatment of the details of
+it. This is what might naturally be expected on any subject on which
+writers have availed themselves of the same language as a means of
+delivering different ideas. Ethics and jurisprudence are liable to the
+remark in common with logic. Almost every writer having taken a
+different view of some of the particulars which these branches of
+knowledge are usually understood to include; each has so framed his
+definition as to indicate beforehand his own peculiar tenets, and
+sometimes to beg the question in their favour.
+
+This diversity is not so much an evil to be complained of, as an
+inevitable and in some degree a proper result of the imperfect state of
+those sciences. It is not to be expected that there should be agreement
+about the definition of anything, until there is agreement about the
+thing itself. To define, is to select from among all the properties of a
+thing, those which shall be understood to be designated and declared by
+its name; and the properties must be well known to us before we can be
+competent to determine which of them are fittest to be chosen for this
+purpose. Accordingly, in the case of so complex an aggregation of
+particulars as are comprehended in anything which can be called a
+science, the definition we set out with is seldom that which a more
+extensive knowledge of the subject shows to be the most appropriate.
+Until we know the particulars themselves, we cannot fix upon the most
+correct and compact mode of circumscribing them by a general
+description. It was not until after an extensive and accurate
+acquaintance with the details of chemical phenomena, that it was found
+possible to frame a rational definition of chemistry; and the definition
+of the science of life and organization is still a matter of dispute. So
+long as the sciences are imperfect, the definitions must partake of
+their imperfection; and if the former are progressive, the latter ought
+to be so too. As much, therefore, as is to be expected from a definition
+placed at the commencement of a subject, is that it should define the
+scope of our inquiries: and the definition which I am about to offer of
+the science of logic, pretends to nothing more, than to be a statement
+of the question which I have put to myself, and which this book is an
+attempt to resolve. The reader is at liberty to object to it as a
+definition of logic; but it is at all events a correct definition of the
+subject of these volumes.
+
+
+§ 2. Logic has often been called the Art of Reasoning. A writer[1] who
+has done more than any other person to restore this study to the rank
+from which it had fallen in the estimation of the cultivated class in
+our own country, has adopted the above definition with an amendment; he
+has defined Logic to be the Science, as well as the Art, of reasoning;
+meaning by the former term, the analysis of the mental process which
+takes place whenever we reason, and by the latter, the rules, grounded
+on that analysis, for conducting the process correctly. There can be no
+doubt as to the propriety of the emendation. A right understanding of
+the mental process itself, of the conditions it depends on, and the
+steps of which it consists, is the only basis on which a system of
+rules, fitted for the direction of the process, can possibly be founded.
+Art necessarily presupposes knowledge; art, in any but its infant state,
+presupposes scientific knowledge: and if every art does not bear the
+name of a science, it is only because several sciences are often
+necessary to form the groundwork of a single art. So complicated are the
+conditions which govern our practical agency, that to enable one thing
+to be _done_, it is often requisite to _know_ the nature and properties
+of many things.
+
+Logic, then, comprises the science of reasoning, as well as an art,
+founded on that science. But the word Reasoning, again, like most other
+scientific terms in popular use, abounds in ambiguities. In one of its
+acceptations, it means syllogizing; or the mode of inference which may
+be called (with sufficient accuracy for the present purpose) concluding
+from generals to particulars. In another of its senses, to reason is
+simply to infer any assertion, from assertions already admitted: and in
+this sense induction is as much entitled to be called reasoning as the
+demonstrations of geometry.
+
+Writers on logic have generally preferred the former acceptation of the
+term: the latter, and more extensive signification is that in which I
+mean to use it. I do this by virtue of the right I claim for every
+author, to give whatever provisional definition he pleases of his own
+subject. But sufficient reasons will, I believe, unfold themselves as we
+advance, why this should be not only the provisional but the final
+definition. It involves, at all events, no arbitrary change in the
+meaning of the word; for, with the general usage of the English
+language, the wider signification, I believe, accords better than the
+more restricted one.
+
+
+§ 3. But Reasoning, even in the widest sense of which the word is
+susceptible, does not seem to comprehend all that is included, either in
+the best, or even in the most current, conception of the scope and
+province of our science. The employment of the word Logic to denote the
+theory of argumentation, is derived from the Aristotelian, or, as they
+are commonly termed, the scholastic, logicians. Yet even with them, in
+their systematic treatises, argumentation was the subject only of the
+third part: the two former treated of Terms, and of Propositions; under
+one or other of which heads were also included Definition and Division.
+By some, indeed, these previous topics were professedly introduced only
+on account of their connexion with reasoning, and as a preparation for
+the doctrine and rules of the syllogism. Yet they were treated with
+greater minuteness, and dwelt on at greater length, than was required
+for that purpose alone. More recent writers on logic have generally
+understood the term as it was employed by the able author of the Port
+Royal Logic; viz. as equivalent to the Art of Thinking. Nor is this
+acceptation confined to books, and scientific inquiries. Even in
+ordinary conversation, the ideas connected with the word Logic include
+at least precision of language, and accuracy of classification: and we
+perhaps oftener hear persons speak of a logical arrangement, or of
+expressions logically defined, than of conclusions logically deduced
+from premises. Again, a man is often called a great logician, or a man
+of powerful logic, not for the accuracy of his deductions, but for the
+extent of his command over premises; because the general propositions
+required for explaining a difficulty or refuting a sophism, copiously
+and promptly occur to him: because, in short, his knowledge, besides
+being ample, is well under his command for argumentative use. Whether,
+therefore, we conform to the practice of those who have made the subject
+their particular study, or to that of popular writers and common
+discourse, the province of logic will include several operations of the
+intellect not usually considered to fall within the meaning of the terms
+Reasoning and Argumentation.
+
+These various operations might be brought within the compass of the
+science, and the additional advantage be obtained of a very simple
+definition, if, by an extension of the term, sanctioned by high
+authorities, we were to define logic as the science which treats of the
+operations of the human understanding in the pursuit of truth. For to
+this ultimate end, naming, classification, definition, and all other
+operations over which logic has ever claimed jurisdiction, are
+essentially subsidiary. They may all be regarded as contrivances for
+enabling a person to know the truths which are needful to him, and to
+know them at the precise moment at which they are needful. Other
+purposes, indeed, are also served by these operations; for instance,
+that of imparting our knowledge to others. But, viewed with regard to
+this purpose, they have never been considered as within the province of
+the logician. The sole object of Logic is the guidance of one's own
+thoughts: the communication of those thoughts to others falls under the
+consideration of Rhetoric, in the large sense in which that art was
+conceived by the ancients; or of the still more extensive art of
+Education. Logic takes cognizance of our intellectual operations, only
+as they conduce to our own knowledge, and to our command over that
+knowledge for our own uses. If there were but one rational being in the
+universe, that being might be a perfect logician; and the science and
+art of logic would be the same for that one person as for the whole
+human race.
+
+
+§ 4. But, if the definition which we formerly examined included too
+little, that which is now suggested has the opposite fault of including
+too much.
+
+Truths are known to us in two ways: some are known directly, and of
+themselves; some through the medium of other truths. The former are the
+subject of Intuition, or Consciousness;[2] the latter, of Inference. The
+truths known by intuition are the original premises from which all
+others are inferred. Our assent to the conclusion being grounded on the
+truth of the premises, we never could arrive at any knowledge by
+reasoning, unless something could be known antecedently to all
+reasoning.
+
+Examples of truths known to us by immediate consciousness, are our own
+bodily sensations and mental feelings. I know directly, and of my own
+knowledge, that I was vexed yesterday, or that I am hungry to-day.
+Examples of truths which we know only by way of inference, are
+occurrences which took place while we were absent, the events recorded
+in history, or the theorems of mathematics. The two former we infer from
+the testimony adduced, or from the traces of those past occurrences
+which still exist; the latter, from the premises laid down in books of
+geometry, under the title of definitions and axioms. Whatever we are
+capable of knowing must belong to the one class or to the other; must
+be in the number of the primitive data, or of the conclusions which can
+be drawn from these.
+
+With the original data, or ultimate premises of our knowledge; with
+their number or nature, the mode in which they are obtained, or the
+tests by which they may be distinguished; logic, in a direct way at
+least, has, in the sense in which I conceive the science, nothing to do.
+These questions are partly not a subject of science at all, partly that
+of a very different science.
+
+Whatever is known to us by consciousness, is known beyond possibility of
+question. What one sees or feels, whether bodily or mentally, one cannot
+but be sure that one sees or feels. No science is required for the
+purpose of establishing such truths; no rules of art can render our
+knowledge of them more certain than it is in itself. There is no logic
+for this portion of our knowledge.
+
+But we may fancy that we see or feel what we in reality infer. A truth,
+or supposed truth, which is really the result of a very rapid inference,
+may seem to be apprehended intuitively. It has long been agreed by
+thinkers of the most opposite schools, that this mistake is actually
+made in so familiar an instance as that of the eyesight. There is
+nothing of which we appear to ourselves to be more directly conscious,
+than the distance of an object from us. Yet it has long been
+ascertained, that what is perceived by the eye, is at most nothing more
+than a variously coloured surface; that when we fancy we see distance,
+all we really see is certain variations of apparent size, and degrees of
+faintness of colour; that our estimate of the object's distance from us
+is the result partly of a rapid inference from the muscular sensations
+accompanying the adjustment of the focal distance of the eye to objects
+unequally remote from us, and partly of a comparison (made with so much
+rapidity that we are unconscious of making it) between the size and
+colour of the object as they appear at the time, and the size and colour
+of the same or of similar objects as they appeared when close at hand,
+or when their degree of remoteness was known by other evidence. The
+perception of distance by the eye, which seems so like intuition, is
+thus, in reality, an inference grounded on experience; an inference,
+too, which we learn to make; and which we make with more and more
+correctness as our experience increases; though in familiar cases it
+takes place so rapidly as to appear exactly on a par with those
+perceptions of sight which are really intuitive, our perceptions of
+colour.[3]
+
+Of the science, therefore, which expounds the operations of the human
+understanding in the pursuit of truth, one essential part is the
+inquiry: What are the facts which are the objects of intuition or
+consciousness, and what are those which we merely infer? But this
+inquiry has never been considered a portion of logic. Its place is in
+another and a perfectly distinct department of science, to which the
+name metaphysics more particularly belongs: that portion of mental
+philosophy which attempts to determine what part of the furniture of the
+mind belongs to it originally, and what part is constructed out of
+materials furnished to it from without. To this science appertain the
+great and much debated questions of the existence of matter; the
+existence of spirit, and of a distinction between it and matter; the
+reality of time and space, as things without the mind, and
+distinguishable from the objects which are said to exist in them. For in
+the present state of the discussion on these topics, it is almost
+universally allowed that the existence of matter or of spirit, of space
+or of time, is in its nature unsusceptible of being proved; and that if
+anything is known of them, it must be by immediate intuition. To the
+same science belong the inquiries into the nature of Conception,
+Perception, Memory, and Belief; all of which are operations of the
+understanding in the pursuit of truth; but with which, as phenomena of
+the mind, or with the possibility which may or may not exist of
+analysing any of them into simpler phenomena, the logician as such has
+no concern. To this science must also be referred the following, and all
+analogous questions: To what extent our intellectual faculties and our
+emotions are innate--to what extent the result of association: Whether
+God, and duty, are realities, the existence of which is manifest to us
+_à priori_ by the constitution of our rational faculty; or whether our
+ideas of them are acquired notions, the origin of which we are able to
+trace and explain; and the reality of the objects themselves a question
+not of consciousness or intuition, but of evidence and reasoning.
+
+The province of logic must be restricted to that portion of our
+knowledge which consists of inferences from truths previously known;
+whether those antecedent data be general propositions, or particular
+observations and perceptions. Logic is not the science of Belief, but
+the science of Proof, or Evidence. In so far as belief professes to be
+founded on proof, the office of logic is to supply a test for
+ascertaining whether or not the belief is well grounded. With the claims
+which any proposition has to belief on the evidence of consciousness,
+that is, without evidence in the proper sense of the word, logic has
+nothing to do.
+
+
+§ 5. By far the greatest portion of our knowledge, whether of general
+truths or of particular facts, being avowedly matter of inference,
+nearly the whole, not only of science, but of human conduct, is amenable
+to the authority of logic. To draw inferences has been said to be the
+great business of life. Every one has daily, hourly, and momentary need
+of ascertaining facts which he has not directly observed; not from any
+general purpose of adding to his stock of knowledge, but because the
+facts themselves are of importance to his interests or to his
+occupations. The business of the magistrate, of the military commander,
+of the navigator, of the physician, of the agriculturist, is merely to
+judge of evidence, and to act accordingly. They all have to ascertain
+certain facts, in order that they may afterwards apply certain rules,
+either devised by themselves, or prescribed for their guidance by
+others; and as they do this well or ill, so they discharge well or ill
+the duties of their several callings. It is the only occupation in
+which the mind never ceases to be engaged; and is the subject, not of
+logic, but of knowledge in general.
+
+Logic, however, is not the same thing with knowledge, though the field
+of logic is coextensive with the field of knowledge. Logic is the common
+judge and arbiter of all particular investigations. It does not
+undertake to find evidence, but to determine whether it has been found.
+Logic neither observes, nor invents, nor discovers; but judges. It is no
+part of the business of logic to inform the surgeon what appearances are
+found to accompany a violent death. This he must learn from his own
+experience and observation, or from that of others, his predecessors in
+his peculiar pursuit. But logic sits in judgment on the sufficiency of
+that observation and experience to justify his rules, and on the
+sufficiency of his rules to justify his conduct. It does not give him
+proofs, but teaches him what makes them proofs, and how he is to judge
+of them. It does not teach that any particular fact proves any other,
+but points out to what conditions all facts must conform, in order that
+they may prove other facts. To decide whether any given fact fulfils
+these conditions, or whether facts can be found which fulfil them in a
+given case, belongs exclusively to the particular art or science, or to
+our knowledge of the particular subject.
+
+It is in this sense that logic is, what Bacon so expressively called it,
+_ars artium_; the science of science itself. All science consists of
+data and conclusions from those data, of proofs and what they prove: now
+logic points out what relations must subsist between data and whatever
+can be concluded from them, between proof and everything which it can
+prove. If there be any such indispensable relations, and if these can be
+precisely determined, every particular branch of science, as well as
+every individual in the guidance of his conduct, is bound to conform to
+those relations, under the penalty of making false inferences, of
+drawing conclusions which are not grounded in the realities of things.
+Whatever has at any time been concluded justly, whatever knowledge has
+been acquired otherwise than by immediate intuition, depended on the
+observance of the laws which it is the province of logic to investigate.
+If the conclusions are just, and the knowledge real, those laws, whether
+known or not, have been observed.
+
+
+§ 6. We need not, therefore, seek any farther for a solution of the
+question, so often agitated, respecting the utility of logic. If a
+science of logic exists, or is capable of existing, it must be useful.
+If there be rules to which every mind consciously or unconsciously
+conforms in every instance in which it infers rightly, there seems
+little necessity for discussing whether a person is more likely to
+observe those rules, when he knows the rules, than when he is
+unacquainted with them.
+
+A science may undoubtedly be brought to a certain, not inconsiderable,
+stage of advancement, without the application of any other logic to it
+than what all persons, who are said to have a sound understanding,
+acquire empirically in the course of their studies. Mankind judged of
+evidence, and often correctly, before logic was a science, or they never
+could have made it one. And they executed great mechanical works before
+they understood the laws of mechanics. But there are limits both to what
+mechanicians can do without principles of mechanics, and to what
+thinkers can do without principles of logic. A few individuals, by
+extraordinary genius, or by the accidental acquisition of a good set of
+intellectual habits, may work without principles in the same way, or
+nearly the same way, in which they would have worked if they had been in
+possession of principles. But the bulk of mankind require either to
+understand the theory of what they are doing, or to have rules laid down
+for them by those who have understood the theory. In the progress of
+science from its easiest to its more difficult problems, each great step
+in advance has usually had either as its precursor, or as its
+accompaniment and necessary condition, a corresponding improvement in
+the notions and principles of logic received among the most advanced
+thinkers. And if several of the more difficult sciences are still in so
+defective a state; if not only so little is proved, but disputation has
+not terminated even about the little which seemed to be so; the reason
+perhaps is, that men's logical notions have not yet acquired the degree
+of extension, or of accuracy, requisite for the estimation of the
+evidence proper to those particular departments of knowledge.
+
+
+§ 7. Logic, then, is the science of the operations of the understanding
+which are subservient to the estimation of evidence: both the process
+itself of advancing from known truths to unknown, and all other
+intellectual operations in so far as auxiliary to this. It includes,
+therefore, the operation of Naming; for language is an instrument of
+thought, as well as a means of communicating our thoughts. It includes,
+also, Definition, and Classification. For, the use of these operations
+(putting all other minds than one's own out of consideration) is to
+serve not only for keeping our evidences and the conclusions from them
+permanent and readily accessible in the memory, but for so marshalling
+the facts which we may at any time be engaged in investigating, as to
+enable us to perceive more clearly what evidence there is, and to judge
+with fewer chances of error whether it be sufficient. These, therefore,
+are operations specially instrumental to the estimation of evidence,
+and, as such, are within the province of Logic. There are other more
+elementary processes, concerned in all thinking, such as Conception,
+Memory, and the like; but of these it is not necessary that Logic should
+take any peculiar cognizance, since they have no special connexion with
+the problem of Evidence, further than that, like all other problems
+addressed to the understanding, it presupposes them.
+
+Our object, then, will be, to attempt a correct analysis of the
+intellectual process called Reasoning or Inference, and of such other
+mental operations as are intended to facilitate this; as well as, on the
+foundation of this analysis, and _pari passu_ with it, to bring together
+or frame a set of rules or canons for testing the sufficiency of any
+given evidence to prove any given proposition.
+
+With respect to the first part of this undertaking, I do not attempt to
+decompose the mental operations in question into their ultimate
+elements. It is enough if the analysis as far as it goes is correct,
+and if it goes far enough for the practical purposes of logic considered
+as an art. The separation of a complicated phenomenon into its component
+parts is not like a connected and interdependent chain of proof. If one
+link of an argument breaks, the whole drops to the ground; but one step
+towards an analysis holds good and has an independent value, though we
+should never be able to make a second. The results which have been
+obtained by analytical chemistry are not the less valuable, though it
+should be discovered that all which we now call simple substances are
+really compounds. All other things are at any rate compounded of those
+elements: whether the elements themselves admit of decomposition, is an
+important inquiry, but does not affect the certainty of the science up
+to that point.
+
+I shall, accordingly, attempt to analyse the process of inference, and
+the processes subordinate to inference, so far only as may be requisite
+for ascertaining the difference between a correct and an incorrect
+performance of those processes. The reason for thus limiting our design,
+is evident. It has been said by objectors to logic, that we do not learn
+to use our muscles by studying their anatomy. The fact is not quite
+fairly stated; for if the action of any of our muscles were vitiated by
+local weakness, or other physical defect, a knowledge of their anatomy
+might be very necessary for effecting a cure. But we should be justly
+liable to the criticism involved in this objection, were we, in a
+treatise on logic, to carry the analysis of the reasoning process beyond
+the point at which any inaccuracy which may have crept into it must
+become visible. In learning bodily exercises (to carry on the same
+illustration) we do, and must, analyse the bodily motions so far as is
+necessary for distinguishing those which ought to be performed from
+those which ought not. To a similar extent, and no further, it is
+necessary that the logician should analyse the mental processes with
+which Logic is concerned. Logic has no interest in carrying the analysis
+beyond the point at which it becomes apparent whether the operations
+have in any individual case been rightly or wrongly performed: in the
+same manner as the science of music teaches us to discriminate between
+musical notes, and to know the combinations of which they are
+susceptible, but not what number of vibrations in a second correspond to
+each; which, though useful to be known, is useful for totally different
+purposes. The extension of Logic as a Science is determined by its
+necessities as an Art: whatever it does not need for its practical ends,
+it leaves to the larger science which may be said to correspond, not to
+any particular art, but to art in general; the science which deals with
+the constitution of the human faculties; and to which, in the part of
+our mental nature which concerns Logic, as well as in all other parts,
+it belongs to decide what are ultimate facts, and what are resolvable
+into other facts. And I believe it will be found that most of the
+conclusions arrived at in this work have no necessary connexion with any
+particular views respecting the ulterior analysis. Logic is common
+ground on which the partisans of Hartley and of Reid, of Locke and of
+Kant, may meet and join hands. Particular and detached opinions of all
+these thinkers will no doubt occasionally be controverted, since all of
+them were logicians as well as metaphysicians; but the field on which
+their principal battles have been fought, lies beyond the boundaries of
+our science.
+
+It cannot, indeed, be pretended that logical principles can be
+altogether irrelevant to those more abstruse discussions; nor is it
+possible but that the view we are led to take of the problem which logic
+proposes, must have a tendency favourable to the adoption of some one
+opinion, on these controverted subjects, rather than another. For
+metaphysics, in endeavouring to solve its own peculiar problem, must
+employ means, the validity of which falls under the cognizance of logic.
+It proceeds, no doubt, as far as possible, merely by a closer and more
+attentive interrogation of our consciousness, or more properly speaking,
+of our memory; and so far is not amenable to logic. But wherever this
+method is insufficient to attain the end of its inquiries, it must
+proceed, like other sciences, by means of evidence. Now, the moment this
+science begins to draw inferences from evidence, logic becomes the
+sovereign judge whether its inferences are well grounded, or what other
+inferences would be so.
+
+This, however, constitutes no nearer or other relation between logic
+and metaphysics, than that which exists between logic and every other
+science. And I can conscientiously affirm, that no one proposition laid
+down in this work has been adopted for the sake of establishing, or with
+any reference to its fitness for being employed in establishing,
+preconceived opinions in any department of knowledge or of inquiry on
+which the speculative world is still undecided.[4]
+
+FOOTNOTES:
+
+[1] Archbishop Whately.
+
+[2] I use these terms indiscriminately, because, for the purpose in
+view, there is no need for making any distinction between them. But
+metaphysicians usually restrict the name Intuition to the direct
+knowledge we are supposed to have of things external to our minds, and
+Consciousness to our knowledge of our own mental phenomena.
+
+[3] This important theory has of late been called in question by a
+writer of deserved reputation, Mr. Samuel Bailey; but I do not conceive
+that the grounds on which it has been admitted as an established
+doctrine for a century past, have been at all shaken by that gentleman's
+objections. I have elsewhere said what appeared to me necessary in reply
+to his arguments. (_Westminster Review_ for October 1842; reprinted in
+_Dissertations and Discussions_, vol. ii.)
+
+[4] The view taken in the text, of the definition and purpose of Logic,
+stands in marked opposition to that of the school of philosophy which,
+in this country, is represented by the writings of Sir William Hamilton
+and of his numerous pupils. Logic, as this school conceives it, is "the
+Science of the Formal Laws of Thought;" a definition framed for the
+express purpose of excluding, as irrelevant to Logic, whatever relates
+to Belief and Disbelief, or to the pursuit of truth as such, and
+restricting the science to that very limited portion of its total
+province, which has reference to the conditions, not of Truth, but of
+Consistency. What I have thought it useful to say in opposition to this
+limitation of the field of Logic, has been said at some length in a
+separate work, first published in 1865, and entitled _An Examination of
+Sir William Hamilton's Philosophy, and of the Principal Philosophical
+Questions discussed in his Writings_. For the purposes of the present
+Treatise, I am content that the justification of the larger extension
+which I give to the domain of the science, should rest on the sequel of
+the Treatise itself. Some remarks on the relation which the Logic of
+Consistency bears to the Logic of Truth, and on the place which that
+particular part occupies in the whole to which it belongs, will be found
+in the present volume (Book II. chap. iii. § 9).
+
+
+
+
+BOOK I.
+
+OF NAMES AND PROPOSITIONS.
+
+
+'La scolastique, qui produisit dans la logique, comme dans la morale,
+et dans une partie de la métaphysique, une subtilité, une précision
+d'idées, dont l'habitude inconnue aux anciens, a contribué plus qu'on ne
+croit au progrès de la bonne philosophie.'--CONDORCET, _Vie de Turgot_.
+
+'To the schoolmen the vulgar languages are principally indebted for what
+precision and analytic subtlety they possess.'--SIR W. HAMILTON,
+_Discussions in Philosophy_.
+
+
+
+
+CHAPTER I.
+
+OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.
+
+
+§ 1. It is so much the established practice of writers on logic to
+commence their treatises by a few general observations (in most cases,
+it is true, rather meagre) on Terms and their varieties, that it will,
+perhaps, scarcely be required from me in merely following the common
+usage, to be as particular in assigning my reasons, as it is usually
+expected that those should be who deviate from it.
+
+The practice, indeed, is recommended by considerations far too obvious
+to require a formal justification. Logic is a portion of the Art of
+Thinking: Language is evidently, and by the admission of all
+philosophers, one of the principal instruments or helps of thought; and
+any imperfection in the instrument, or in the mode of employing it, is
+confessedly liable, still more than in almost any other art, to confuse
+and impede the process, and destroy all ground of confidence in the
+result. For a mind not previously versed in the meaning and right use of
+the various kinds of words, to attempt the study of methods of
+philosophizing, would be as if some one should attempt to become an
+astronomical observer, having never learned to adjust the focal distance
+of his optical instruments so as to see distinctly.
+
+Since Reasoning, or Inference, the principal subject of logic, is an
+operation which usually takes place by means of words, and in
+complicated cases can take place in no other way; those who have not a
+thorough insight into the signification and purposes of words, will be
+under chances, amounting almost to certainty, of reasoning or inferring
+incorrectly. And logicians have generally felt that unless, in the very
+first stage, they removed this source of error; unless they taught their
+pupil to put away the glasses which distort the object, and to use
+those which are adapted to his purpose in such a manner as to assist,
+not perplex, his vision; he would not be in a condition to practise the
+remaining part of their discipline with any prospect of advantage.
+Therefore it is that an inquiry into language, so far as is needful to
+guard against the errors to which it gives rise, has at all times been
+deemed a necessary preliminary to the study of logic.
+
+But there is another reason, of a still more fundamental nature, why the
+import of words should be the earliest subject of the logician's
+consideration: because without it he cannot examine into the import of
+Propositions. Now this is a subject which stands on the very threshold
+of the science of logic.
+
+The object of logic, as defined in the Introductory Chapter, is to
+ascertain how we come by that portion of our knowledge (much the
+greatest portion) which is not intuitive: and by what criterion we can,
+in matters not self-evident, distinguish between things proved and
+things not proved, between what is worthy and what is unworthy of
+belief. Of the various questions which present themselves to our
+inquiring faculties, some receive an answer from direct consciousness,
+others, if resolved at all, can only be resolved by means of evidence.
+Logic is concerned with these last. But before inquiring into the mode
+of resolving questions, it is necessary to inquire what are those which
+offer themselves; what questions are conceivable; what inquiries are
+there, to which mankind have either obtained, or been able to imagine it
+possible that they should obtain, an answer. This point is best
+ascertained by a survey and analysis of Propositions.
+
+
+§ 2. The answer to every question which it is possible to frame, must be
+contained in a Proposition, or Assertion. Whatever can be an object of
+belief, or even of disbelief, must, when put into words, assume the form
+of a proposition. All truth and all error lie in propositions. What, by
+a convenient misapplication of an abstract term, we call a Truth, means
+simply a True Proposition; and errors are false propositions. To know
+the import of all possible propositions, would be to know all questions
+which can be raised, all matters which are susceptible of being either
+believed or disbelieved. How many kinds of inquiries can be propounded;
+how many kinds of judgments can be made; and how many kinds of
+propositions it is possible to frame with a meaning; are but different
+forms of one and the same question. Since, then, the objects of all
+Belief and of all Inquiry express themselves in propositions; a
+sufficient scrutiny of Propositions and of their varieties will apprize
+us what questions mankind have actually asked of themselves, and what,
+in the nature of answers to those questions, they have actually thought
+they had grounds to believe.
+
+Now the first glance at a proposition shows that it is formed by putting
+together two names. A proposition, according to the common simple
+definition, which is sufficient for our purpose, is, _discourse, in
+which something is affirmed or denied of something_. Thus, in the
+proposition, Gold is yellow, the quality _yellow_ is affirmed of the
+substance _gold_. In the proposition, Franklin was not born in England,
+the fact expressed by the words _born in England_ is denied of the man
+Franklin.
+
+Every proposition consists of three parts: the Subject, the Predicate,
+and the Copula. The predicate is the name denoting that which is
+affirmed or denied. The subject is the name denoting the person or thing
+which something is affirmed or denied of. The copula is the sign
+denoting that there is an affirmation or denial; and thereby enabling
+the hearer or reader to distinguish a proposition from any other kind of
+discourse. Thus, in the proposition, The earth is round, the Predicate
+is the word _round_, which denotes the quality affirmed, or (as the
+phrase is) predicated: _the earth_, words denoting the object which that
+quality is affirmed of, compose the Subject; the word _is_, which serves
+as the connecting mark between the subject and predicate, to show that
+one of them is affirmed of the other, is called the Copula.
+
+Dismissing, for the present, the copula, of which more will be said
+hereafter, every proposition, then, consists of at least two names;
+brings together two names, in a particular manner. This is already a
+first step towards what we are in quest of. It appears from this, that
+for an act of belief, _one_ object is not sufficient; the simplest act
+of belief supposes, and has something to do with, _two_ objects: two
+names, to say the least; and (since the names must be names of
+something) two _nameable things_. A large class of thinkers would cut
+the matter short by saying, two _ideas_. They would say, that the
+subject and predicate are both of them names of ideas; the idea of gold,
+for instance, and the idea of yellow; and that what takes place (or part
+of what takes place) in the act of belief, consists in bringing (as it
+is often expressed) one of these ideas under the other. But this we are
+not yet in a condition to say: whether such be the correct mode of
+describing the phenomenon, is an after consideration. The result with
+which for the present we must be contented, is, that in every act of
+belief _two_ objects are in some manner taken cognizance of; that there
+can be no belief claimed, or question propounded, which does not embrace
+two distinct (either material or intellectual) subjects of thought; each
+of them capable, or not, of being conceived by itself, but incapable of
+being believed by itself.
+
+I may say, for instance, "the sun." The word has a meaning, and suggests
+that meaning to the mind of any one who is listening to me. But suppose
+I ask him, Whether it is true: whether he believes it? He can give no
+answer. There is as yet nothing to believe, or to disbelieve. Now,
+however, let me make, of all possible assertions respecting the sun, the
+one which involves the least of reference to any object besides itself;
+let me say, "the sun exists." Here, at once, is something which a person
+can say he believes. But here, instead of only one, we find two distinct
+objects of conception: the sun is one object; existence is another. Let
+it not be said that this second conception, existence, is involved in
+the first; for the sun may be conceived as no longer existing. "The sun"
+does not convey all the meaning that is conveyed by "the sun exists:"
+"my father" does not include all the meaning of "my father exists," for
+he may be dead; "a round square" does not include the meaning of "a
+round square exists," for it does not and cannot exist. When I say "the
+sun," "my father," or a "round square," I do not call upon the hearer
+for any belief or disbelief, nor can either the one or the other be
+afforded me; but if I say, "the sun exists," "my father exists," or "a
+round square exists," I call for belief; and should, in the first of the
+three instances, meet with it; in the second, with belief or disbelief,
+as the case might be; in the third, with disbelief.
+
+
+§ 3. This first step in the analysis of the object of belief, which,
+though so obvious, will be found to be not unimportant, is the only one
+which we shall find it practicable to make without a preliminary survey
+of language. If we attempt to proceed further in the same path, that is,
+to analyse any further the import of Propositions; we find forced upon
+us, as a subject of previous consideration, the import of Names. For
+every proposition consists of two names; and every proposition affirms
+or denies one of these names, of the other. Now what we do, what passes
+in our mind, when we affirm or deny two names of one another, must
+depend on what they are names of; since it is with reference to that,
+and not to the mere names themselves, that we make the affirmation or
+denial. Here, therefore, we find a new reason why the signification of
+names, and the relation generally between names and the things signified
+by them, must occupy the preliminary stage of the inquiry we are engaged
+in.
+
+It may be objected that the meaning of names can guide us at most only
+to the opinions, possibly the foolish and groundless opinions, which
+mankind have formed concerning things, and that as the object of
+philosophy is truth, not opinion, the philosopher should dismiss words
+and look into things themselves, to ascertain what questions can be
+asked and answered in regard to them. This advice (which no one has it
+in his power to follow) is in reality an exhortation to discard the
+whole fruits of the labours of his predecessors, and conduct himself as
+if he were the first person who had ever turned an inquiring eye upon
+nature. What does any one's personal knowledge of Things amount to,
+after subtracting all which he has acquired by means of the words of
+other people? Even after he has learned as much as people usually do
+learn from others, will the notions of things contained in his
+individual mind afford as sufficient a basis for a _catalogue raisonné_
+as the notions which are in the minds of all mankind?
+
+In any enumeration and classification of Things, which does not set out
+from their names, no varieties of things will of course be comprehended
+but those recognised by the particular inquirer; and it will still
+remain to be established, by a subsequent examination of names, that the
+enumeration has omitted nothing which ought to have been included. But
+if we begin with names, and use them as our clue to the things, we bring
+at once before us all the distinctions which have been recognised, not
+by a single inquirer, but by all inquirers taken together. It doubtless
+may, and I believe it will, be found, that mankind have multiplied the
+varieties unnecessarily, and have imagined distinctions among things,
+where there were only distinctions in the manner of naming them. But we
+are not entitled to assume this in the commencement. We must begin by
+recognising the distinctions made by ordinary language. If some of these
+appear, on a close examination, not to be fundamental, the enumeration
+of the different kinds of realities may be abridged accordingly. But to
+impose upon the facts in the first instance the yoke of a theory, while
+the grounds of the theory are reserved for discussion in a subsequent
+stage, is not a course which a logician can reasonably adopt.
+
+
+
+
+CHAPTER II.
+
+OF NAMES.
+
+
+§ 1. "A name," says Hobbes,[1] "is a word taken at pleasure to serve for
+a mark which may raise in our mind a thought like to some thought we had
+before, and which being pronounced to others, may be to them a sign of
+what thought the speaker had[2] before in his mind." This simple
+definition of a name, as a word (or set of words) serving the double
+purpose of a mark to recall to ourselves the likeness of a former
+thought, and a sign to make it known to others, appears unexceptionable.
+Names, indeed, do much more than this; but whatever else they do, grows
+out of, and is the result of this: as will appear in its proper place.
+
+Are names more properly said to be the names of things, or of our ideas
+of things? The first is the expression in common use; the last is that
+of some metaphysicians, who conceived that in adopting it they were
+introducing a highly important distinction. The eminent thinker, just
+quoted, seems to countenance the latter opinion. "But seeing," he
+continues, "names ordered in speech (as is defined) are signs of our
+conceptions, it is manifest they are not signs of the things themselves;
+for that the sound of this word _stone_ should be the sign of a stone,
+cannot be understood in any sense but this, that he that hears it
+collects that he that pronounces it thinks of a stone."
+
+If it be merely meant that the conception alone, and not the thing
+itself, is recalled by the name, or imparted to the hearer, this of
+course cannot be denied. Nevertheless, there seems good reason for
+adhering to the common usage, and calling the word _sun_ the name of
+the sun, and not the name of our idea of the sun. For names are not
+intended only to make the hearer conceive what we conceive, but also to
+inform him what we believe. Now, when I use a name for the purpose of
+expressing a belief, it is a belief concerning the thing itself, not
+concerning my idea of it. When I say, "the sun is the cause of day," I
+do not mean that my idea of the sun causes or excites in me the idea of
+day; or in other words, that thinking of the sun makes me think of day.
+I mean, that a certain physical fact, which is called the sun's presence
+(and which, in the ultimate analysis, resolves itself into sensations,
+not ideas) causes another physical fact, which is called day. It seems
+proper to consider a word as the _name_ of that which we intend to be
+understood by it when we use it; of that which any fact that we assert
+of it is to be understood of; that, in short, concerning which, when we
+employ the word, we intend to give information. Names, therefore, shall
+always be spoken of in this work as the names of things themselves, and
+not merely of our ideas of things.
+
+But the question now arises, of what things? and to answer this it is
+necessary to take into consideration the different kinds of names.
+
+
+§ 2. It is usual, before examining the various classes into which names
+are commonly divided, to begin by distinguishing from names of every
+description, those words which are not names, but only parts of names.
+Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
+inflected cases of nouns substantive, as _me_, _him_, _John's_; and even
+adjectives, as _large_, _heavy_. These words do not express things of
+which anything can be affirmed or denied. We cannot say, Heavy fell, or
+A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
+room. Unless, indeed, we are speaking of the mere words themselves, as
+when we say, Truly is an English word, or, Heavy is an adjective. In
+that case they are complete names, viz. names of those particular
+sounds, or of those particular collections of written characters. This
+employment of a word to denote the mere letters and syllables of which
+it is composed, was termed by the schoolmen the _suppositio materialis_
+of the word. In any other sense we cannot introduce one of these words
+into the subject of a proposition, unless in combination with other
+words; as, A heavy _body_ fell, A truly _important fact_ was asserted, A
+_member_ of _parliament_ was in the room.
+
+An adjective, however, is capable of standing by itself as the predicate
+of a proposition; as when we say, Snow is white; and occasionally even
+as the subject, for we may say, White is an agreeable colour. The
+adjective is often said to be so used by a grammatical ellipsis: Snow is
+white, instead of Snow is a white object; White is an agreeable colour,
+instead of, A white colour, or, The colour white, is agreeable. The
+Greeks and Romans were allowed, by the rules of their language, to
+employ this ellipsis universally in the subject as well as in the
+predicate of a proposition. In English this cannot, generally speaking,
+be done. We may say, The earth is round; but we cannot say, Round is
+easily moved; we must say, A round object. This distinction, however, is
+rather grammatical than logical. Since there is no difference of meaning
+between _round_, and _a round object_, it is only custom which
+prescribes that on any given occasion one shall be used, and not the
+other. We shall, therefore, without scruple, speak of adjectives as
+names, whether in their own right, or as representative of the more
+circuitous forms of expression above exemplified. The other classes of
+subsidiary words have no title whatever to be considered as names. An
+adverb, or an accusative case, cannot under any circumstances (except
+when their mere letters and syllables are spoken of) figure as one of
+the terms of a proposition.
+
+Words which are not capable of being used as names, but only as parts of
+names, were called by some of the schoolmen Syncategorematic terms: from
+_σὺν_, with, and _κατηγορέω_, to predicate, because it was only _with_
+some other word that they could be predicated. A word which could be
+used either as the subject or predicate of a proposition without being
+accompanied by any other word, was termed by the same authorities a
+Categorematic term. A combination of one or more Categorematic, and one
+or more Syncategorematic words, as A heavy body, or A court of justice,
+they sometimes called a _mixed_ term; but this seems a needless
+multiplication of technical expressions. A mixed term is, in the only
+useful sense of the word, Categorematic. It belongs to the class of what
+have been called many-worded names.
+
+For, as one word is frequently not a name, but only part of a name, so a
+number of words often compose one single name, and no more. These words,
+"the place which the wisdom or policy of antiquity had destined for the
+residence of the Abyssinian princes," form in the estimation of the
+logician only one name; one Categorematic term. A mode of determining
+whether any set of words makes only one name, or more than one, is by
+predicating something of it, and observing whether, by this predication,
+we make only one assertion or several. Thus, when we say, John Nokes,
+who was the mayor of the town, died yesterday--by this predication we
+make but one assertion; whence it appears that "John Nokes, who was the
+mayor of the town," is no more than one name. It is true that in this
+proposition, besides the assertion that John Nokes died yesterday, there
+is included another assertion, namely, that John Nokes was mayor of the
+town. But this last assertion was already made: we did not make it by
+adding the predicate, "died yesterday." Suppose, however, that the words
+had been, John Nokes _and_ the mayor of the town, they would have formed
+two names instead of one. For when we say, John Nokes and the mayor of
+the town died yesterday, we make two assertions; one, that John Nokes
+died yesterday; the other, that the mayor of the town died yesterday.
+
+It being needless to illustrate at any greater length the subject of
+many-worded names, we proceed to the distinctions which have been
+established among names, not according to the words they are composed
+of, but according to their signification.
+
+
+§ 3. All names are names of something, real or imaginary; but all things
+have not names appropriated to them individually. For some individual
+objects we require, and consequently have, separate distinguishing
+names; there is a name for every person, and for every remarkable place.
+Other objects, of which we have not occasion to speak so frequently, we
+do not designate by a name of their own; but when the necessity arises
+for naming them, we do so by putting together several words, each of
+which, by itself, might be and is used for an indefinite number of other
+objects; as when I say, _this stone_: "this" and "stone" being, each of
+them, names that may be used of many other objects besides the
+particular one meant, though the only object of which they can both be
+used at the given moment, consistently with their signification, may be
+the one of which I wish to speak.
+
+Were this the sole purpose for which names, that are common to more
+things than one, could be employed; if they only served, by mutually
+limiting each other, to afford a designation for such individual objects
+as have no names of their own; they could only be ranked among
+contrivances for economizing the use of language. But it is evident that
+this is not their sole function. It is by their means that we are
+enabled to assert _general_ propositions; to affirm or deny any
+predicate of an indefinite number of things at once. The distinction,
+therefore, between _general_ names, and _individual_ or _singular_
+names, is fundamental; and may be considered as the first grand division
+of names.
+
+A general name is familiarly defined, a name which is capable of being
+truly affirmed, in the same sense, of each of an indefinite number of
+things. An individual or singular name is a name which is only capable
+of being truly affirmed, in the same sense, of one thing.
+
+Thus, _man_ is capable of being truly affirmed of John, George, Mary,
+and other persons without assignable limit; and it is affirmed of all of
+them in the same sense; for the word man expresses certain qualities,
+and when we predicate it of those persons, we assert that they all
+possess those qualities. But _John_ is only capable of being truly
+affirmed of one single person, at least in the same sense. For though
+there are many persons who bear that name, it is not conferred upon
+them to indicate any qualities, or anything which belongs to them in
+common; and cannot be said to be affirmed of them in any _sense_ at all,
+consequently not in the same sense. "The king who succeeded William the
+Conqueror," is also an individual name. For, that there cannot be more
+than one person of whom it can be truly affirmed, is implied in the
+meaning of the words. Even "_the_ king," when the occasion or the
+context defines the individual of whom it is to be understood, may
+justly be regarded as an individual name.
+
+It is not unusual, by way of explaining what is meant by a general name,
+to say that it is the name of a _class_. But this, though a convenient
+mode of expression for some purposes, is objectionable as a definition,
+since it explains the clearer of two things by the more obscure. It
+would be more logical to reverse the proposition, and turn it into a
+definition of the word _class_: "A class is the indefinite multitude of
+individuals denoted by a general name."
+
+It is necessary to distinguish _general_ from _collective_ names. A
+general name is one which can be predicated of _each_ individual of a
+multitude; a collective name cannot be predicated of each separately,
+but only of all taken together. "The 76th regiment of foot in the
+British army," which is a collective name, is not a general but an
+individual name; for though it can be predicated of a multitude of
+individual soldiers taken jointly, it cannot be predicated of them
+severally. We may say, Jones is a soldier, and Thompson is a soldier,
+and Smith is a soldier, but we cannot say, Jones is the 76th regiment,
+and Thompson is the 76th regiment, and Smith is the 76th regiment. We
+can only say, Jones, and Thompson, and Smith, and Brown, and so forth
+(enumerating all the soldiers), are the 76th regiment.
+
+"The 76th regiment" is a collective name, but not a general one: "a
+regiment" is both a collective and a general name. General with respect
+to all individual regiments, of each of which separately it can be
+affirmed; collective with respect to the individual soldiers of whom any
+regiment is composed.
+
+
+§ 4. The second general division of names is into _concrete_ and
+_abstract_. A concrete name is a name which stands for a thing; an
+abstract name is a name which stands for an attribute of a thing. Thus
+_John_, _the sea_, _this table_, are names of things. _White_, also, is
+a name of a thing, or rather of things. Whiteness, again, is the name of
+a quality or attribute of those things. Man is a name of many things;
+humanity is a name of an attribute of those things. _Old_ is a name of
+things; _old age_ is a name of one of their attributes.
+
+I have used the words concrete and abstract in the sense annexed to them
+by the schoolmen, who, notwithstanding the imperfections of their
+philosophy, were unrivalled in the construction of technical language,
+and whose definitions, in logic at least, though they never went more
+than a little way into the subject, have seldom, I think, been altered
+but to be spoiled. A practice, however, has grown up in more modern
+times, which, if not introduced by Locke, has gained currency chiefly
+from his example, of applying the expression "abstract name" to all
+names which are the result of abstraction or generalization, and
+consequently to all general names, instead of confining it to the names
+of attributes. The metaphysicians of the Condillac school,--whose
+admiration of Locke, passing over the profoundest speculations of that
+truly original genius, usually fastens with peculiar eagerness upon his
+weakest points,--have gone on imitating him in this abuse of language,
+until there is now some difficulty in restoring the word to its original
+signification. A more wanton alteration in the meaning of a word is
+rarely to be met with; for the expression _general name_, the exact
+equivalent of which exists in all languages I am acquainted with, was
+already available for the purpose to which _abstract_ has been
+misappropriated, while the misappropriation leaves that important class
+of words, the names of attributes, without any compact distinctive
+appellation. The old acceptation, however, has not gone so completely
+out of use, as to deprive those who still adhere to it of all chance of
+being understood. By _abstract_, then, I shall always, in Logic, mean
+the opposite of _concrete_: by an abstract name, the name of an
+attribute; by a concrete name, the name of an object.
+
+Do abstract names belong to the class of general, or to that of singular
+names? Some of them are certainly general. I mean those which are names
+not of one single and definite attribute, but of a class of attributes.
+Such is the word _colour_, which is a name common to whiteness, redness,
+&c. Such is even the word whiteness, in respect of the different shades
+of whiteness to which it is applied in common; the word magnitude, in
+respect of the various degrees of magnitude and the various dimensions
+of space; the word weight, in respect of the various degrees of weight.
+Such also is the word _attribute_ itself, the common name of all
+particular attributes. But when only one attribute, neither variable in
+degree nor in kind, is designated by the name; as visibleness;
+tangibleness; equality; squareness; milkwhiteness; then the name can
+hardly be considered general; for though it denotes an attribute of many
+different objects, the attribute itself is always conceived as one, not
+many.[3] To avoid needless logomachies, the best course would probably
+be to consider these names as neither general nor individual, and to
+place them in a class apart.
+
+It may be objected to our definition of an abstract name, that not only
+the names which we have called abstract, but adjectives, which we have
+placed in the concrete class, are names of attributes; that _white_, for
+example, is as much the name of the colour as _whiteness_ is. But (as
+before remarked) a word ought to be considered as the name of that which
+we intend to be understood by it when we put it to its principal use,
+that is, when we employ it in predication. When we say snow is white,
+milk is white, linen is white, we do not mean it to be understood that
+snow, or linen, or milk, is a colour. We mean that they are things
+having the colour. The reverse is the case with the word whiteness; what
+we affirm to _be_ whiteness is not snow, but the colour of snow.
+Whiteness, therefore, is the name of the colour exclusively: white is a
+name of all things whatever having the colour; a name, not of the
+quality whiteness, but of every white object. It is true, this name was
+given to all those various objects on account of the quality; and we may
+therefore say, without impropriety, that the quality forms part of its
+signification; but a name can only be said to stand for, or to be a name
+of, the things of which it can be predicated. We shall presently see
+that all names which can be said to have any signification, all names by
+applying which to an individual we give any information respecting that
+individual, may be said to _imply_ an attribute of some sort; but they
+are not names of the attribute; it has its own proper abstract name.
+
+
+§ 5. This leads to the consideration of a third great division of names,
+into _connotative_ and _non-connotative_, the latter sometimes, but
+improperly, called _absolute_. This is one of the most important
+distinctions which we shall have occasion to point out, and one of those
+which go deepest into the nature of language.
+
+A non-connotative term is one which signifies a subject only, or an
+attribute only. A connotative term is one which denotes a subject, and
+implies an attribute. By a subject is here meant anything which
+possesses attributes. Thus John, or London, or England, are names which
+signify a subject only. Whiteness, length, virtue, signify an attribute
+only. None of these names, therefore, are connotative. But _white_,
+_long_, _virtuous_, are connotative. The word white, denotes all white
+things, as snow, paper, the foam of the sea, &c., and implies, or as it
+was termed by the schoolmen, _connotes_[4], the attribute _whiteness_.
+The word white is not predicated of the attribute, but of the subjects,
+snow, &c.; but when we predicate it of them, we imply, or connote, that
+the attribute whiteness belongs to them. The same may be said of the
+other words above cited. Virtuous, for example, is the name of a class,
+which includes Socrates, Howard, the Man of Ross, and an undefinable
+number of other individuals, past, present, and to come. These
+individuals, collectively and severally, can alone be said with
+propriety to be denoted by the word: of them alone can it properly be
+said to be a name. But it is a name applied to all of them in
+consequence of an attribute which they are supposed to possess in
+common, the attribute which has received the name of virtue. It is
+applied to all beings that are considered to possess this attribute; and
+to none which are not so considered.
+
+All concrete general names are connotative. The word _man_, for example,
+denotes Peter, Jane, John, and an indefinite number of other
+individuals, of whom, taken as a class, it is the name. But it is
+applied to them, because they possess, and to signify that they possess,
+certain attributes. These seem to be, corporeity, animal life,
+rationality, and a certain external form, which for distinction we call
+the human. Every existing thing, which possessed all these attributes,
+would be called a man; and anything which possessed none of them, or
+only one, or two, or even three of them without the fourth, would not be
+so called. For example, if in the interior of Africa there were to be
+discovered a race of animals possessing reason equal to that of human
+beings, but with the form of an elephant, they would not be called men.
+Swift's Houyhnhnms would not be so called. Or if such newly-discovered
+beings possessed the form of man without any vestige of reason, it is
+probable that some other name than that of man would be found for them.
+How it happens that there can be any doubt about the matter, will appear
+hereafter. The word _man_, therefore, signifies all these attributes,
+and all subjects which possess these attributes. But it can be
+predicated only of the subjects. What we call men, are the subjects, the
+individual Stiles and Nokes; not the qualities by which their humanity
+is constituted. The name, therefore, is said to signify the subjects
+_directly_, the attributes _indirectly_; it _denotes_ the subjects, and
+implies, or involves, or indicates, or as we shall say henceforth
+_connotes_, the attributes. It is a connotative name.
+
+Connotative names have hence been also called _denominative_, because
+the subject which they denote is denominated by, or receives a name
+from, the attribute which they connote. Snow, and other objects, receive
+the name white, because they possess the attribute which is called
+whiteness; Peter, James, and others receive the name man, because they
+possess the attributes which are considered to constitute humanity. The
+attribute, or attributes, may therefore be said to denominate those
+objects, or to give them a common name.[5]
+
+It has been seen that all concrete general names are connotative. Even
+abstract names, though the names only of attributes, may in some
+instances be justly considered as connotative; for attributes themselves
+may have attributes ascribed to them; and a word which denotes
+attributes may connote an attribute of those attributes. Of this
+description, for example, is such a word as _fault_; equivalent to _bad_
+or _hurtful quality_. This word is a name common to many attributes, and
+connotes hurtfulness, an attribute of those various attributes. When,
+for example, we say that slowness, in a horse, is a fault, we do not
+mean that the slow movement, the actual change of place of the slow
+horse, is a bad thing, but that the property or peculiarity of the
+horse, from which it derives that name, the quality of being a slow
+mover, is an undesirable peculiarity.
+
+In regard to those concrete names which are not general but individual,
+a distinction must be made.
+
+Proper names are not connotative: they denote the individuals who are
+called by them; but they do not indicate or imply any attributes as
+belonging to those individuals. When we name a child by the name Paul,
+or a dog by the name Cæsar, these names are simply marks used to enable
+those individuals to be made subjects of discourse. It may be said,
+indeed, that we must have had some reason for giving them those names
+rather than any others; and this is true; but the name, once given, is
+independent of the reason. A man may have been named John, because that
+was the name of his father; a town may have been named Dartmouth,
+because it is situated at the mouth of the Dart. But it is no part of
+the signification of the word John, that the father of the person so
+called bore the same name; nor even of the word Dartmouth, to be
+situated at the mouth of the Dart. If sand should choke up the mouth of
+the river, or an earthquake change its course, and remove it to a
+distance from the town, the name of the town would not necessarily be
+changed. That fact, therefore, can form no part of the signification of
+the word; for otherwise, when the fact confessedly ceased to be true, no
+one would any longer think of applying the name. Proper names are
+attached to the objects themselves, and are not dependent on the
+continuance of any attribute of the object.
+
+But there is another kind of names, which, although they are individual
+names, that is, predicable only of one object, are really connotative.
+For, though we may give to an individual a name utterly unmeaning, which
+we call a proper name,--a word which answers the purpose of showing what
+thing it is we are talking about, but not of telling anything about it;
+yet a name peculiar to an individual is not necessarily of this
+description. It may be significant of some attribute, or some union of
+attributes, which, being possessed by no object but one, determines the
+name exclusively to that individual. "The sun" is a name of this
+description; "God," when used by a monotheist, is another. These,
+however, are scarcely examples of what we are now attempting to
+illustrate, being, in strictness of language, general, not individual
+names: for, however they may be _in fact_ predicable only of one object,
+there is nothing in the meaning of the words themselves which implies
+this: and, accordingly, when we are imagining and not affirming, we may
+speak of many suns; and the majority of mankind have believed, and still
+believe, that there are many gods. But it is easy to produce words which
+are real instances of connotative individual names. It may be part of
+the meaning of the connotative name itself, that there can exist but
+one individual possessing the attribute which it connotes: as, for
+instance, "the _only_ son of John Stiles;" "the _first_ emperor of
+Rome." Or the attribute connoted may be a connexion with some
+determinate event, and the connexion may be of such a kind as only one
+individual could have; or may at least be such as only one individual
+actually had; and this may be implied in the form of the expression.
+"The father of Socrates" is an example of the one kind (since Socrates
+could not have had two fathers); "the author of the Iliad," "the
+murderer of Henri Quatre," of the second. For, though it is conceivable
+that more persons than one might have participated in the authorship of
+the Iliad, or in the murder of Henri Quatre, the employment of the
+article _the_ implies that, in fact, this was not the case. What is here
+done by the word _the_, is done in other cases by the context: thus,
+"Cæsar's army" is an individual name, if it appears from the context
+that the army meant is that which Cæsar commanded in a particular
+battle. The still more general expressions, "the Roman army," or "the
+Christian army," may be individualized in a similar manner. Another case
+of frequent occurrence has already been noticed; it is the following.
+The name, being a many-worded one, may consist, in the first place, of a
+_general_ name, capable therefore in itself of being affirmed of more
+things than one, but which is, in the second place, so limited by other
+words joined with it, that the entire expression can only be predicated
+of one object, consistently with the meaning of the general term. This
+is exemplified in such an instance as the following: "the present prime
+minister of England." Prime Minister of England is a general name; the
+attributes which it connotes may be possessed by an indefinite number of
+persons: in succession however, not simultaneously; since the meaning of
+the name itself imports (among other things) that there can be only one
+such person at a time. This being the case, and the application of the
+name being afterwards limited by the article and the word _present_, to
+such individuals as possess the attributes at one indivisible point of
+time, it becomes applicable only to one individual. And as this appears
+from the meaning of the name, without any extrinsic proof, it is
+strictly an individual name.
+
+From the preceding observations it will easily be collected, that
+whenever the names given to objects convey any information, that is,
+whenever they have properly any meaning, the meaning resides not in what
+they _denote_, but in what they _connote_. The only names of objects
+which connote nothing are _proper_ names; and these have, strictly
+speaking, no signification.[6]
+
+If, like the robber in the Arabian Nights, we make a mark with chalk on
+a house to enable us to know it again, the mark has a purpose, but it
+has not properly any meaning. The chalk does not declare anything about
+the house; it does not mean, This is such a person's house, or This is a
+house which contains booty. The object of making the mark is merely
+distinction. I say to myself, All these houses are so nearly alike that
+if I lose sight of them I shall not again be able to distinguish that
+which I am now looking at, from any of the others; I must therefore
+contrive to make the appearance of this one house unlike that of the
+others, that I may hereafter know, when I see the mark--not indeed any
+attribute of the house--but simply that it is the same house which I am
+now looking at. Morgiana chalked all the other houses in a similar
+manner, and defeated the scheme: how? simply by obliterating the
+difference of appearance between that house and the others. The chalk
+was still there, but it no longer served the purpose of a distinctive
+mark.
+
+When we impose a proper name, we perform an operation in some degree
+analogous to what the robber intended in chalking the house. We put a
+mark, not indeed upon the object itself, but, so to speak, upon the idea
+of the object. A proper name is but an unmeaning mark which we connect
+in our minds with the idea of the object, in order that whenever the
+mark meets our eyes or occurs to our thoughts, we may think of that
+individual object. Not being attached to the thing itself, it does not,
+like the chalk, enable us to distinguish the object when we see it; but
+it enables us to distinguish it when it is spoken of, either in the
+records of our own experience, or in the discourse of others; to know
+that what we find asserted in any proposition of which it is the
+subject, is asserted of the individual thing with which we were
+previously acquainted.
+
+When we predicate of anything its proper name; when we say, pointing to
+a man, this is Brown or Smith, or pointing to a city, that it is York,
+we do not, merely by so doing, convey to the hearer any information
+about them, except that those are their names. By enabling him to
+identify the individuals, we may connect them with information
+previously possessed by him; by saying, This is York, we may tell him
+that it contains the Minster. But this is in virtue of what he has
+previously heard concerning York; not by anything implied in the name.
+It is otherwise when objects are spoken of by connotative names. When we
+say, The town is built of marble, we give the hearer what may be
+entirely new information, and this merely by the signification of the
+many-worded connotative name, "built of marble." Such names are not
+signs of the mere objects, invented because we have occasion to think
+and speak of those objects individually; but signs which accompany an
+attribute: a kind of livery in which the attribute clothes all objects
+which are recognised as possessing it. They are not mere marks, but
+more, that is to say, significant marks; and the connotation is what
+constitutes their significance.
+
+As a proper name is said to be the name of the one individual which it
+is predicated of, so (as well from the importance of adhering to
+analogy, as for the other reasons formerly assigned) a connotative name
+ought to be considered a name of all the various individuals which it is
+predicable of, or in other words _denotes_, and not of what it connotes.
+But by learning what things it is a name of, we do not learn the meaning
+of the name: for to the same thing we may, with equal propriety, apply
+many names, not equivalent in meaning. Thus, I call a certain man by the
+name Sophroniscus: I call him by another name, The father of Socrates.
+Both these are names of the same individual, but their meaning is
+altogether different; they are applied to that individual for two
+different purposes; the one, merely to distinguish him from other
+persons who are spoken of; the other to indicate a fact relating to him,
+the fact that Socrates was his son. I further apply to him these other
+expressions: a man, a Greek, an Athenian, a sculptor, an old man, an
+honest man, a brave man. All these are, or may be, names of
+Sophroniscus, not indeed of him alone, but of him and each of an
+indefinite number of other human beings. Each of these names is applied
+to Sophroniscus for a different reason, and by each whoever understands
+its meaning is apprised of a distinct fact or number of facts concerning
+him; but those who knew nothing about the names except that they were
+applicable to Sophroniscus, would be altogether ignorant of their
+meaning. It is even possible that I might know every single individual
+of whom a given name could be with truth affirmed, and yet could not be
+said to know the meaning of the name. A child knows who are its brothers
+and sisters, long before it has any definite conception of the nature of
+the facts which are involved in the signification of those words.
+
+In some cases it is not easy to decide precisely how much a particular
+word does or does not connote; that is, we do not exactly know (the case
+not having arisen) what degree of difference in the object would
+occasion a difference in the name. Thus, it is clear that the word man,
+besides animal life and rationality, connotes also a certain external
+form; but it would be impossible to say precisely what form; that is, to
+decide how great a deviation from the form ordinarily found in the
+beings whom we are accustomed to call men, would suffice in a
+newly-discovered race to make us refuse them the name of man.
+Rationality, also, being a quality which admits of degrees, it has never
+been settled what is the lowest degree of that quality which would
+entitle any creature to be considered a human being. In all such cases,
+the meaning of the general name is so far unsettled and vague; mankind
+have not come to any positive agreement about the matter. When we come
+to treat of Classification, we shall have occasion to show under what
+conditions this vagueness may exist without practical inconvenience; and
+cases will appear in which the ends of language are better promoted by
+it than by complete precision; in order that, in natural history for
+instance, individuals or species of no very marked character may be
+ranged with those more strongly characterized individuals or species to
+which, in all their properties taken together, they bear the nearest
+resemblance.
+
+But this partial uncertainty in the connotation of names can only be
+free from mischief when guarded by strict precautions. One of the chief
+sources, indeed, of lax habits of thought, is the custom of using
+connotative terms without a distinctly ascertained connotation, and with
+no more precise notion of their meaning than can be loosely collected
+from observing what objects they are used to denote. It is in this
+manner that we all acquire, and inevitably so, our first knowledge of
+our vernacular language. A child learns the meaning of the words _man_,
+or _white_, by hearing them applied to a variety of individual objects,
+and finding out, by a process of generalization and analysis which he
+could not himself describe, what those different objects have in common.
+In the case of these two words the process is so easy as to require no
+assistance from culture; the objects called human beings, and the
+objects called white, differing from all others by qualities of a
+peculiarly definite and obvious character. But in many other cases,
+objects bear a general resemblance to one another, which leads to their
+being familiarly classed together under a common name, while, without
+more analytic habits than the generality of mankind possess, it is not
+immediately apparent what are the particular attributes, upon the
+possession of which in common by them all, their general resemblance
+depends. When this is the case, people use the name without any
+recognised connotation, that is, without any precise meaning; they talk,
+and consequently think, vaguely, and remain contented to attach only the
+same degree of significance to their own words, which a child three
+years old attaches to the words brother and sister. The child at least
+is seldom puzzled by the starting up of new individuals, on whom he is
+ignorant whether or not to confer the title; because there is usually an
+authority close at hand competent to solve all doubts. But a similar
+resource does not exist in the generality of cases; and new objects are
+continually presenting themselves to men, women, and children, which
+they are called upon to class _proprio motu_. They, accordingly, do this
+on no other principle than that of superficial similarity, giving to
+each new object the name of that familiar object, the idea of which it
+most readily recalls, or which, on a cursory inspection, it seems to
+them most to resemble: as an unknown substance found in the ground will
+be called, according to its texture, earth, sand, or a stone. In this
+manner, names creep on from subject to subject, until all traces of a
+common meaning sometimes disappear, and the word comes to denote a
+number of things not only independently of any common attribute, but
+which have actually no attribute in common; or none but what is shared
+by other things to which the name is capriciously refused. Even
+scientific writers have aided in this perversion of general language
+from its purpose; sometimes because, like the vulgar, they knew no
+better; and sometimes in deference to that aversion to admit new words,
+which induces mankind, on all subjects not considered technical, to
+attempt to make the original stock of names serve with but little
+augmentation to express a constantly increasing number of objects and
+distinctions, and, consequently, to express them in a manner
+progressively more and more imperfect.
+
+To what a degree this loose mode of classing and denominating objects
+has rendered the vocabulary of mental and moral philosophy unfit for the
+purposes of accurate thinking, is best known to whoever has most
+meditated on the present condition of those branches of knowledge.
+Since, however, the introduction of a new technical language as the
+vehicle of speculations on subjects belonging to the domain of daily
+discussion, is extremely difficult to effect, and would not be free from
+inconvenience even if effected, the problem for the philosopher, and one
+of the most difficult which he has to resolve, is, in retaining the
+existing phraseology, how best to alleviate its imperfections. This can
+only be accomplished by giving to every general concrete name which
+there is frequent occasion to predicate, a definite and fixed
+connotation; in order that it may be known what attributes, when we call
+an object by that name, we really mean to predicate of the object. And
+the question of most nicety is, how to give this fixed connotation to a
+name, with the least possible change in the objects which the name is
+habitually employed to denote; with the least possible disarrangement,
+either by adding or subtraction, of the group of objects which, in
+however imperfect a manner, it serves to circumscribe and hold together;
+and with the least vitiation of the truth of any propositions which are
+commonly received as true.
+
+This desirable purpose, of giving a fixed connotation where it is
+wanting, is the end aimed at whenever any one attempts to give a
+definition of a general name already in use; every definition of a
+connotative name being an attempt either merely to declare, or to
+declare and analyse, the connotation of the name. And the fact, that no
+questions which have arisen in the moral sciences have been subjects of
+keener controversy than the definitions of almost all the leading
+expressions, is a proof how great an extent the evil to which we have
+adverted has attained.
+
+Names with indeterminate connotation are not to be confounded with names
+which have more than one connotation, that is to say, ambiguous words. A
+word may have several meanings, but all of them fixed and recognised
+ones; as the word _post_, for example, or the word _box_, the various
+senses of which it would be endless to enumerate. And the paucity of
+existing names, in comparison with the demand for them, may often render
+it advisable and even necessary to retain a name in this multiplicity
+of acceptations, distinguishing these so clearly as to prevent their
+being confounded with one another. Such a word may be considered as two
+or more names, accidentally written and spoken alike.[7]
+
+
+§ 6. The fourth principal division of names, is into _positive_ and
+_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,
+_not-tree_, _not-good_. To every positive concrete name, a corresponding
+negative one might be framed. After giving a name to any one thing, or
+to any plurality of things, we might create a second name which should
+be a name of all things whatever, except that particular thing or
+things. These negative names are employed whenever we have occasion to
+speak collectively of all things other than some thing or class of
+things. When the positive name is connotative, the corresponding
+negative name is connotative likewise; but in a peculiar way, connoting
+not the presence but the absence of an attribute. Thus, _not-white_
+denotes all things whatever except white things; and connotes the
+attribute of not possessing whiteness. For the non-possession of any
+given attribute is also an attribute, and may receive a name as such;
+and thus negative concrete names may obtain negative abstract names to
+correspond to them.
+
+Names which are positive in form are often negative in reality, and
+others are really positive though their form is negative. The word
+_inconvenient_, for example, does not express the mere absence of
+convenience; it expresses a positive attribute, that of being the cause
+of discomfort or annoyance. So the word _unpleasant_, notwithstanding
+its negative form, does not connote the mere absence of pleasantness,
+but a less degree of what is signified by the word _painful_, which, it
+is hardly necessary to say, is positive. _Idle_, on the other hand, is a
+word which, though positive in form, expresses nothing but what would be
+signified either by the phrase _not working_, or by the phrase _not
+disposed to work_; and _sober_, either by _not drunk_ or by _not
+drunken_.
+
+There is a class of names called _privative_. A privative name is
+equivalent in its signification to a positive and a negative name taken
+together; being the name of something which has once had a particular
+attribute, or for some other reason might have been expected to have it,
+but which has it not. Such is the word _blind_, which is not equivalent
+to _not seeing_, or to _not capable of seeing_, for it would not, except
+by a poetical or rhetorical figure, be applied to stocks and stones. A
+thing is not usually said to be blind, unless the class to which it is
+most familiarly referred, or to which it is referred on the particular
+occasion, be chiefly composed of things which can see, as in the case of
+a blind man, or a blind horse; or unless it is supposed for any reason
+that it ought to see; as in saying of a man, that he rushed blindly into
+an abyss, or of philosophers or the clergy that the greater part of them
+are blind guides. The names called privative, therefore, connote two
+things: the absence of certain attributes, and the presence of others,
+from which the presence also of the former might naturally have been
+expected.
+
+
+§ 7. The fifth leading division of names is into _relative_ and
+_absolute_, or let us rather say, _relative_ and _non-relative_; for the
+word absolute is put upon much too hard duty in metaphysics, not to be
+willingly spared when its services can be dispensed with. It resembles
+the word _civil_ in the language of jurisprudence, which stands for the
+opposite of criminal, the opposite of ecclesiastical, the opposite of
+military, the opposite of political--in short, the opposite of any
+positive word which wants a negative.
+
+Relative names are such as father, son; ruler, subject; like; equal;
+unlike; unequal; longer, shorter; cause, effect. Their characteristic
+property is, that they are always given in pairs. Every relative name
+which is predicated of an object, supposes another object (or objects),
+of which we may predicate either that same name or another relative name
+which is said to be the _correlative_ of the former. Thus, when we call
+any person a son, we suppose other persons who must be called parents.
+When we call any event a cause, we suppose another event which is an
+effect. When we say of any distance that it is longer, we suppose
+another distance which is shorter. When we say of any object that it is
+like, we mean that it is like some other object, which is also said to
+be like the first. In this last case both objects receive the same name;
+the relative term is its own correlative.
+
+It is evident that these words, when concrete, are, like other concrete
+general names, connotative; they denote a subject, and connote an
+attribute; and each of them has or might have a corresponding abstract
+name, to denote the attribute connoted by the concrete. Thus the
+concrete _like_ has its abstract _likeness_; the concretes, father and
+son, have, or might have, the abstracts, paternity, and filiety, or
+sonship. The concrete name connotes an attribute, and the abstract name
+which answers to it denotes that attribute. But of what nature is the
+attribute? Wherein consists the peculiarity in the connotation of a
+relative name?
+
+The attribute signified by a relative name, say some, is a relation; and
+this they give, if not as a sufficient explanation, at least as the only
+one attainable. If they are asked, What then is a relation? they do not
+profess to be able to tell. It is generally regarded as something
+peculiarly recondite and mysterious. I cannot, however, perceive in what
+respect it is more so than any other attribute; indeed, it appears to me
+to be so in a somewhat less degree. I conceive, rather, that it is by
+examining into the signification of relative names, or, in other words,
+into the nature of the attribute which they connote, that a clear
+insight may best be obtained into the nature of all attributes: of all
+that is meant by an attribute.
+
+It is obvious, in fact, that if we take any two correlative names,
+_father_ and _son_ for instance, though the objects _de_noted by the
+names are different, they both, in a certain sense, connote the same
+thing. They cannot, indeed, be said to connote the same _attribute_: to
+be a father, is not the same thing as to be a son. But when we call one
+man a father, another a son, what we mean to affirm is a set of facts,
+which are exactly the same in both cases. To predicate of A that he is
+the father of B, and of B that he is the son of A, is to assert one and
+the same fact in different words. The two propositions are exactly
+equivalent: neither of them asserts more or asserts less than the
+other. The paternity of A and the filiety of B are not two facts, but
+two modes of expressing the same fact. That fact, when analysed,
+consists of a series of physical events or phenomena, in which both A
+and B are parties concerned, and from which they both derive names. What
+those names really connote, is this series of events: that is the
+meaning, and the whole meaning, which either of them is intended to
+convey. The series of events may be said to _constitute_ the relation;
+the schoolmen called it the foundation of the relation, _fundamentum
+relationis_.
+
+In this manner any fact, or series of facts, in which two different
+objects are implicated, and which is therefore predicable of both of
+them, may be either considered as constituting an attribute of the one,
+or an attribute of the other. According as we consider it in the former,
+or in the latter aspect, it is connoted by the one or the other of the
+two correlative names. _Father_ connotes the fact, regarded as
+constituting an attribute of A: _son_ connotes the same fact, as
+constituting an attribute of B. It may evidently be regarded with equal
+propriety in either light. And all that appears necessary to account for
+the existence of relative names, is, that whenever there is a fact in
+which two individuals are concerned, an attribute grounded on that fact
+may be ascribed to either of these individuals.
+
+A name, therefore, is said to be relative, when, over and above the
+object which it denotes, it implies in its signification the existence
+of another object, also deriving a denomination from the same fact which
+is the ground of the first name. Or (to express the same meaning in
+other words) a name is relative, when, being the name of one thing, its
+signification cannot be explained but by mentioning another. Or we may
+state it thus--when the name cannot be employed in discourse so as to
+have a meaning, unless the name of some other thing than what it is
+itself the name of, be either expressed or understood. These definitions
+are all, at bottom, equivalent, being modes of variously expressing this
+one distinctive circumstance--that every other attribute of an object
+might, without any contradiction, be conceived still to exist if no
+object besides that one had ever existed;[8] but those of its
+attributes which are expressed by relative names, would on that
+supposition be swept away.
+
+
+§ 8. Names have been further distinguished into _univocal_ and
+_æquivocal_: these, however, are not two kinds of names, but two
+different modes of employing names. A name is univocal, or applied
+univocally, with respect to all things of which it can be predicated _in
+the same sense_: it is æquivocal, or applied æquivocally, as respects
+those things of which it is predicated in different senses. It is
+scarcely necessary to give instances of a fact so familiar as the double
+meaning of a word. In reality, as has been already observed, an
+æquivocal or ambiguous word is not one name, but two names, accidentally
+coinciding in sound. _File_ meaning a steel instrument, and _file_
+meaning a line of soldiers, have no more title to be considered one
+word, because written alike, than _grease_ and _Greece_ have, because
+they are pronounced alike. They are one sound, appropriated to form two
+different words.
+
+An intermediate case is that of a name used _analogically_ or
+metaphorically; that is, a name which is predicated of two things, not
+univocally, or exactly in the same signification, but in significations
+somewhat similar, and which being derived one from the other, one of
+them may be considered the primary, and the other a secondary
+signification. As when we speak of a brilliant light and a brilliant
+achievement. The word is not applied in the same sense to the light and
+to the achievement; but having been applied to the light in its original
+sense, that of brightness to the eye, it is transferred to the
+achievement in a derivative signification, supposed to be somewhat like
+the primitive one. The word, however, is just as properly two names
+instead of one, in this case, as in that of the most perfect ambiguity.
+And one of the commonest forms of fallacious reasoning arising from
+ambiguity, is that of arguing from a metaphorical expression as if it
+were literal; that is, as if a word, when applied metaphorically, were
+the same name as when taken in its original sense: which will be seen
+more particularly in its place.
+
+
+
+
+CHAPTER III.
+
+OF THE THINGS DENOTED BY NAMES.
+
+
+§ 1. Looking back now to the commencement of our inquiry, let us attempt
+to measure how far it has advanced. Logic, we found, is the Theory of
+Proof. But proof supposes something provable, which must be a
+Proposition or Assertion; since nothing but a Proposition can be an
+object of belief, or therefore of proof. A Proposition is, discourse
+which affirms or denies something of some other thing. This is one step:
+there must, it seems, be two things concerned in every act of belief.
+But what are these Things? They can be no other than those signified by
+the two names, which being joined together by a copula constitute the
+Proposition. If, therefore, we knew what all names signify, we should
+know everything which in the existing state of human knowledge, is
+capable either of being made a subject of affirmation or denial, or of
+being itself affirmed or denied of a subject. We have accordingly, in
+the preceding chapter, reviewed the various kinds of Names, in order to
+ascertain what is signified by each of them. And we have now carried
+this survey far enough to be able to take an account of its results, and
+to exhibit an enumeration of all kinds of Things which are capable of
+being made predicates, or of having anything predicated of them: after
+which to determine the import of Predication, that is, of Propositions,
+can be no arduous task.
+
+The necessity of an enumeration of Existences, as the basis of Logic,
+did not escape the attention of the schoolmen, and of their master
+Aristotle, the most comprehensive, if not also the most sagacious, of
+the ancient philosophers. The Categories, or Predicaments--the former a
+Greek word, the latter its literal translation in the Latin
+language--were intended by him and his followers as an enumeration of
+all things capable of being named; an enumeration by the _summa
+genera_, _i.e._ the most extensive classes into which things could be
+distributed; which, therefore, were so many highest Predicates, one or
+other of which was supposed capable of being affirmed with truth of
+every nameable thing whatsoever. The following are the classes into
+which, according to this school of philosophy, Things in general might
+be reduced:--
+
+  Οὐσία,       Substantia.
+  Ποσὸν,       Quantitas.
+  Ποιόν,       Qualitas.
+  Πρός τι,     Relatio.
+  Ποιεῖν,      Actio.
+  Πάσχειν,     Passio.
+  Ποῦ,         Ubi.
+  Πότε,        Quando.
+  Κεῖσθαι,     Situs.
+  Ἔχειν,       Habitus.
+
+The imperfections of this classification are too obvious to require, and
+its merits are not sufficient to reward, a minute examination. It is a
+mere catalogue of the distinctions rudely marked out by the language of
+familiar life, with little or no attempt to penetrate, by philosophic
+analysis, to the _rationale_ even of those common distinctions. Such an
+analysis, however superficially conducted, would have shown the
+enumeration to be both redundant and defective. Some objects are
+omitted, and others repeated several times under different heads. It is
+like a division of animals into men, quadrupeds, horses, asses, and
+ponies. That, for instance, could not be a very comprehensive view of
+the nature of Relation which could exclude action, passivity, and local
+situation from that category. The same observation applies to the
+categories Quando (or position in time), and Ubi (or position in space);
+while the distinction between the latter and Situs is merely verbal. The
+incongruity of erecting into a _summum genus_ the class which forms the
+tenth category is manifest. On the other hand, the enumeration takes no
+notice of anything besides substances and attributes. In what category
+are we to place sensations, or any other feelings and states of mind; as
+hope, joy, fear; sound, smell, taste; pain, pleasure; thought, judgment,
+conception, and the like? Probably all these would have been placed by
+the Aristotelian school in the categories of _actio_ and _passio_; and
+the relation of such of them as are active, to their objects, and of
+such of them as are passive, to their causes, would rightly be so
+placed; but the things themselves, the feelings or states of mind,
+wrongly. Feelings, or states of consciousness, are assuredly to be
+counted among realities, but they cannot be reckoned either among
+substances or attributes.
+
+
+§ 2. Before recommencing, under better auspices, the attempt made with
+such imperfect success by the great founder of the science of logic, we
+must take notice of an unfortunate ambiguity in all the concrete names
+which correspond to the most general of all abstract terms, the word
+Existence. When we have occasion for a name which shall be capable of
+denoting whatever exists, as contradistinguished from non-entity or
+Nothing, there is hardly a word applicable to the purpose which is not
+also, and even more familiarly, taken in a sense in which it denotes
+only substances. But substances are not all that exists; attributes, if
+such things are to be spoken of, must be said to exist; feelings
+certainly exist. Yet when we speak of an _object_, or of a _thing_, we
+are almost always supposed to mean a substance. There seems a kind of
+contradiction in using such an expression as that one _thing_ is merely
+an attribute of another thing. And the announcement of a Classification
+of Things would, I believe, prepare most readers for an enumeration like
+those in natural history, beginning with the great divisions of animal,
+vegetable, and mineral, and subdividing them into classes and orders.
+If, rejecting the word Thing, we endeavour to find another of a more
+general import, or at least more exclusively confined to that general
+import, a word denoting all that exists, and connoting only simple
+existence; no word might be presumed fitter for such a purpose than
+_being_: originally the present participle of a verb which in one of its
+meanings is exactly equivalent to the verb _exists_; and therefore
+suitable, even by its grammatical formation, to be the concrete of the
+abstract _existence_. But this word, strange as the fact may appear, is
+still more completely spoiled for the purpose which it seemed expressly
+made for, than the word Thing. _Being_ is, by custom, exactly synonymous
+with substance; except that it is free from a slight taint of a second
+ambiguity; being applied impartially to matter and to mind, while
+substance, though originally and in strictness applicable to both, is
+apt to suggest in preference the idea of matter. Attributes are never
+called Beings; nor are feelings. A Being is that which excites feelings,
+and which possesses attributes. The soul is called a Being; God and
+angels are called Beings; but if we were to say, extension, colour,
+wisdom, virtue, are beings, we should perhaps be suspected of thinking
+with some of the ancients, that the cardinal virtues are animals; or, at
+the least, of holding with the Platonic school the doctrine of
+self-existent Ideas, or with the followers of Epicurus that of Sensible
+Forms, which detach themselves in every direction from bodies, and by
+coming in contact with our organs, cause our perceptions. We should be
+supposed, in short, to believe that Attributes are Substances.
+
+In consequence of this perversion of the word Being, philosophers
+looking about for something to supply its place, laid their hands upon
+the word Entity, a piece of barbarous Latin, invented by the schoolmen
+to be used as an abstract name, in which class its grammatical form
+would seem to place it; but being seized by logicians in distress to
+stop a leak in their terminology, it has ever since been used as a
+concrete name. The kindred word _essence_, born at the same time and of
+the same parents, scarcely underwent a more complete transformation
+when, from being the abstract of the verb _to be_, it came to denote
+something sufficiently concrete to be enclosed in a glass bottle. The
+word Entity, since it settled down into a concrete name, has retained
+its universality of signification somewhat less impaired than any of the
+names before mentioned. Yet the same gradual decay to which, after a
+certain age, all the language of psychology seems liable, has been at
+work even here. If you call virtue an _entity_, you are indeed somewhat
+less strongly suspected of believing it to be a substance than if you
+called it a _being_; but you are by no means free from the suspicion.
+Every word which was originally intended to connote mere existence,
+seems, after a long time, to enlarge its connotation to _separate_
+existence, or existence freed from the condition of belonging to a
+substance; which condition being precisely what constitutes an
+attribute, attributes are gradually shut out; and along with them
+feelings, which in ninety-nine cases out of a hundred have no other name
+than that of the attribute which is grounded on them. Strange that when
+the greatest embarrassment felt by all who have any considerable number
+of thoughts to express, is to find a sufficient variety of precise words
+fitted to express them, there should be no practice to which even
+scientific thinkers are more addicted than that of taking valuable words
+to express ideas which are sufficiently expressed by other words already
+appropriated to them.
+
+When it is impossible to obtain good tools, the next best thing is to
+understand thoroughly the defects of those we have. I have therefore
+warned the reader of the ambiguity of the names which, for want of
+better, I am necessitated to employ. It must now be the writer's
+endeavour so to employ them as in no case to leave the meaning doubtful
+or obscure. No one of the above terms being altogether unambiguous, I
+shall not confine myself to any one, but shall employ on each occasion
+the word which seems least likely in the particular case to lead to
+misunderstanding; nor do I pretend to use either these or any other
+words with a rigorous adherence to one single sense. To do so would
+often leave us without a word to express what is signified by a known
+word in some one or other of its senses: unless authors had an unlimited
+licence to coin new words, together with (what it would be more
+difficult to assume) unlimited power of making readers understand them.
+Nor would it be wise in a writer, on a subject involving so much of
+abstraction, to deny himself the advantage derived from even an improper
+use of a term, when, by means of it, some familiar association is called
+up which brings the meaning home to the mind, as it were by a flash.
+
+The difficulty both to the writer and reader, of the attempt which must
+be made to use vague words so as to convey a precise meaning, is not
+wholly a matter of regret. It is not unfitting that logical treatises
+should afford an example of that, to facilitate which is among the most
+important uses of logic. Philosophical language will for a long time,
+and popular language still longer, retain so much of vagueness and
+ambiguity, that logic would be of little value if it did not, among its
+other advantages, exercise the understanding in doing its work neatly
+and correctly with these imperfect tools.
+
+After this preamble it is time to proceed to our enumeration. We shall
+commence with Feelings, the simplest class of nameable things; the term
+Feeling being of course understood in its most enlarged sense.
+
+
+I. FEELINGS, OR STATES OF CONSCIOUSNESS.
+
+§ 3. A Feeling and a State of Consciousness are, in the language of
+philosophy, equivalent expressions: everything is a feeling of which the
+mind is conscious; everything which it _feels_, or, in other words,
+which forms a part of its own sentient existence. In popular language
+Feeling is not always synonymous with State of Consciousness; being
+often taken more peculiarly for those states which are conceived as
+belonging to the sensitive, or to the emotional, phasis of our nature,
+and sometimes, with a still narrower restriction, to the emotional
+alone, as distinguished from what are conceived as belonging to the
+percipient or to the intellectual phasis. But this is an admitted
+departure from correctness of language; just as, by a popular perversion
+the exact converse of this, the word Mind is withdrawn from its rightful
+generality of signification, and restricted to the intellect. The still
+greater perversion by which Feeling is sometimes confined not only to
+bodily sensations, but to the sensations of a single sense, that of
+touch, needs not be more particularly adverted to.
+
+Feeling, in the proper sense of the term, is a genus, of which
+Sensation, Emotion, and Thought, are subordinate species. Under the word
+Thought is here to be included whatever we are internally conscious of
+when we are said to think; from the consciousness we have when we think
+of a red colour without having it before our eyes, to the most recondite
+thoughts of a philosopher or poet. Be it remembered, however, that by a
+thought is to be understood what passes in the mind itself, and not any
+object external to the mind, which the person is commonly said to be
+thinking of. He may be thinking of the sun, or of God, but the sun and
+God are not thoughts; his mental image, however, of the sun, and his
+idea of God, are thoughts; states of his mind, not of the objects
+themselves; and so also is his belief of the existence of the sun, or of
+God; or his disbelief, if the case be so. Even imaginary objects (which
+are said to exist only in our ideas) are to be distinguished from our
+ideas of them. I may think of a hobgoblin, as I may think of the loaf
+which was eaten yesterday, or of the flower which will bloom to-morrow.
+But the hobgoblin which never existed is not the same thing with my idea
+of a hobgoblin, any more than the loaf which once existed is the same
+thing with my idea of a loaf, or the flower which does not yet exist,
+but which will exist, is the same with my idea of a flower. They are
+all, not thoughts, but objects of thought; though at the present time
+all the objects are alike non-existent.
+
+In like manner, a Sensation is to be carefully distinguished from the
+object which causes the sensation; our sensation of white from a white
+object: nor is it less to be distinguished from the attribute whiteness,
+which we ascribe to the object in consequence of its exciting the
+sensation. Unfortunately for clearness and due discrimination in
+considering these subjects, our sensations seldom receive separate
+names. We have a name for the objects which produce in us a certain
+sensation: the word _white_. We have a name for the quality in those
+objects, to which we ascribe the sensation: the name _whiteness_. But
+when we speak of the sensation itself (as we have not occasion to do
+this often except in our scientific speculations), language, which
+adapts itself for the most part only to the common uses of life, has
+provided us with no single-worded or immediate designation; we must
+employ a circumlocution, and say, The sensation of white, or The
+sensation of whiteness; we must denominate the sensation either from the
+object, or from the attribute, by which it is excited. Yet the
+sensation, though it never _does_, might very well be _conceived_ to
+exist, without anything whatever to excite it. We can conceive it as
+arising spontaneously in the mind. But if it so arose, we should have no
+name to denote it which would not be a misnomer. In the case of our
+sensations of hearing we are better provided; we have the word Sound,
+and a whole vocabulary of words to denote the various kinds of sounds.
+For as we are often conscious of these sensations in the absence of any
+perceptible object, we can more easily conceive having them in the
+absence of any object whatever. We need only shut our eyes and listen to
+music, to have a conception of an universe with nothing in it except
+sounds, and ourselves hearing them: and what is easily conceived
+separately, easily obtains a separate name. But in general our names of
+sensations denote indiscriminately the sensation and the attribute.
+Thus, _colour_ stands for the sensations of white, red, &c., but also
+for the quality in the coloured object. We talk of the colours of things
+as among their _properties_.
+
+
+§ 4. In the case of sensations, another distinction has also to be kept
+in view, which is often confounded, and never without mischievous
+consequences. This is, the distinction between the sensation itself, and
+the state of the bodily organs which precedes the sensation, and which
+constitutes the physical agency by which it is produced. One of the
+sources of confusion on this subject is the division commonly made of
+feelings into Bodily and Mental. Philosophically speaking, there is no
+foundation at all for this distinction: even sensations are states of
+the sentient mind, not states of the body, as distinguished from it.
+What I am conscious of when I see the colour blue, is a feeling of blue
+colour, which is one thing; the picture on my retina, or the phenomenon
+of hitherto mysterious nature which takes place in my optic nerve or in
+my brain, is another thing, of which I am not at all conscious, and
+which scientific investigation alone could have apprised me of. These
+are states of my body; but the sensation of blue, which is the
+consequence of these states of body, is not a state of body: that which
+perceives and is conscious is called Mind. When sensations are called
+bodily feelings, it is only as being the class of feelings which are
+immediately occasioned by bodily states; whereas the other kinds of
+feelings, thoughts, for instance, or emotions, are immediately excited
+not by anything acting upon the bodily organs, but by sensations, or by
+previous thoughts. This, however, is a distinction not in our feelings,
+but in the agency which produces our feelings: all of them when actually
+produced are states of mind.
+
+Besides the affection of our bodily organs from without, and the
+sensation thereby produced in our minds, many writers admit a third link
+in the chain of phenomena, which they call a Perception, and which
+consists in the recognition of an external object as the exciting cause
+of the sensation. This perception, they say, is an _act_ of the mind,
+proceeding from its own spontaneous activity; while in a sensation the
+mind is passive, being merely acted upon by the outward object. And
+according to some metaphysicians, it is by an act of the mind, similar
+to perception, except in not being preceded by any sensation, that the
+existence of God, the soul, and other hyper-physical objects is
+recognised.
+
+These acts of what is termed perception, whatever be the conclusion
+ultimately come to respecting their nature, must, I conceive, take their
+place among the varieties of feelings or states of mind. In so classing
+them, I have not the smallest intention of declaring or insinuating any
+theory as to the law of mind in which these mental processes may be
+supposed to originate, or the conditions under which they may be
+legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
+suppose must be meant in an analogous case[9]) to indicate that as they
+are "_merely_ states of mind," it is superfluous to inquire into their
+distinguishing peculiarities. I abstain from the inquiry as irrelevant
+to the science of logic. In these so-called perceptions, or direct
+recognitions by the mind, of objects, whether physical or spiritual,
+which are external to itself, I can see only cases of belief; but of
+belief which claims to be intuitive, or independent of external
+evidence. When a stone lies before me, I am conscious of certain
+sensations which I receive from it; but if I say that these sensations
+come to me from an external object which I _perceive_, the meaning of
+these words is, that receiving the sensations, I intuitively _believe_
+that an external cause of those sensations exists. The laws of intuitive
+belief, and the conditions under which it is legitimate, are a subject
+which, as we have already so often remarked, belongs not to logic, but
+to the science of the ultimate laws of the human mind.
+
+To the same region of speculation belongs all that can be said
+respecting the distinction which the German metaphysicians and their
+French and English followers so elaborately draw between the _acts_ of
+the mind and its merely passive _states_; between what it receives from,
+and what it gives to, the crude materials of its experience. I am aware
+that with reference to the view which those writers take of the primary
+elements of thought and knowledge, this distinction is fundamental. But
+for the present purpose, which is to examine, not the original
+groundwork of our knowledge, but how we come by that portion of it which
+is not original; the difference between active and passive states of
+mind is of secondary importance. For us, they all are states of mind,
+they all are feelings; by which, let it be said once more, I mean to
+imply nothing of passivity, but simply that they are psychological
+facts, facts which take place in the mind, and are to be carefully
+distinguished from the external or physical facts with which they may be
+connected either as effects or as causes.
+
+
+§ 5. Among active states of mind, there is, however, one species which
+merits particular attention, because it forms a principal part of the
+connotation of some important classes of names. I mean _volitions_, or
+acts of the will. When we speak of sentient beings by relative names, a
+large portion of the connotation of the name usually consists of the
+actions of those beings; actions past, present, and possible or probable
+future. Take, for instance, the words Sovereign and Subject. What
+meaning do these words convey, but that of innumerable actions, done or
+to be done by the sovereign and the subjects, to or in regard to one
+another reciprocally? So with the words physician and patient, leader
+and follower, tutor and pupil. In many cases the words also connote
+actions which would be done under certain contingencies by persons other
+than those denoted: as the words mortgagor and mortgagee, obligor and
+obligee, and many other words expressive of legal relation, which
+connote what a court of justice would do to enforce the legal obligation
+if not fulfilled. There are also words which connote actions previously
+done by persons other than those denoted either by the name itself or by
+its correlative; as the word brother. From these instances, it may be
+seen how large a portion of the connotation of names consists of
+actions. Now what is an action? Not one thing, but a series of two
+things: the state of mind called a volition, followed by an effect. The
+volition or intention to produce the effect, is one thing; the effect
+produced in consequence of the intention, is another thing; the two
+together constitute the action. I form the purpose of instantly moving
+my arm; that is a state of my mind: my arm (not being tied or paralytic)
+moves in obedience to my purpose; that is a physical fact, consequent on
+a state of mind. The intention, followed by the fact, or (if we prefer
+the expression) the fact when preceded and caused by the intention, is
+called the action of moving my arm.
+
+
+§ 6. Of the first leading division of nameable things, viz. Feelings or
+States of Consciousness, we began by recognising three subdivisions;
+Sensations, Thoughts, and Emotions. The first two of these we have
+illustrated at considerable length; the third, Emotions, not being
+perplexed by similar ambiguities, does not require similar
+exemplification. And, finally, we have found it necessary to add to
+these three a fourth species, commonly known by the name Volitions.
+Without seeking to prejudge the metaphysical question whether any mental
+state or phenomenon can be found which is not included in one or other
+of these four species, it appears to me that the amount of illustration
+bestowed upon these may, so far as we are concerned, suffice for the
+whole genus. We shall, therefore, proceed to the two remaining classes
+of nameable things; all things which are external to the mind being
+considered as belonging either to the class of Substances or to that of
+Attributes.
+
+II. SUBSTANCES.
+
+Logicians have endeavoured to define Substance and Attribute; but their
+definitions are not so much attempts to draw a distinction between the
+things themselves, as instructions what difference it is customary to
+make in the grammatical structure of the sentence, according as we are
+speaking of substances or of attributes. Such definitions are rather
+lessons of English, or of Greek, Latin, or German, than of mental
+philosophy. An attribute, say the school logicians, must be the
+attribute _of_ something; colour, for example, must be the colour _of_
+something; goodness must be the goodness _of_ something: and if this
+something should cease to exist, or should cease to be connected with
+the attribute, the existence of the attribute would be at an end. A
+substance, on the contrary, is self-existent; in speaking about it, we
+need not put _of_ after its name. A stone is not the stone _of_
+anything; the moon is not the moon _of_ anything, but simply the moon.
+Unless, indeed, the name which we choose to give to the substance be a
+relative name; if so, it must be followed either by _of_, or by some
+other particle, implying, as that preposition does, a reference to
+something else: but then the other characteristic peculiarity of an
+attribute would fail; the _something_ might be destroyed, and the
+substance might still subsist. Thus, a father must be the father _of_
+something, and so far resembles an attribute, in being referred to
+something besides himself: if there were no child, there would be no
+father: but this, when we look into the matter, only means that we
+should not call him father. The man called father might still exist
+though there were no child, as he existed before there was a child: and
+there would be no contradiction in supposing him to exist, though the
+whole universe except himself were destroyed. But destroy all white
+substances, and where would be the attribute whiteness? Whiteness,
+without any white thing, is a contradiction in terms.
+
+This is the nearest approach to a solution of the difficulty, that will
+be found in the common treatises on logic. It will scarcely be thought
+to be a satisfactory one. If an attribute is distinguished from a
+substance by being the attribute _of_ something, it seems highly
+necessary to understand what is meant by _of_; a particle which needs
+explanation too much itself, to be placed in front of the explanation of
+anything else. And as for the self-existence of substance, it is very
+true that a substance may be conceived to exist without any other
+substance, but so also may an attribute without any other attribute: and
+we can no more imagine a substance without attributes than we can
+imagine attributes without a substance.
+
+Metaphysicians, however, have probed the question deeper, and given an
+account of Substance considerably more satisfactory than this.
+Substances are usually distinguished as Bodies or Minds. Of each of
+these, philosophers have at length provided us with a definition which
+seems unexceptionable.
+
+
+§ 7. A Body, according to the received doctrine of modern
+metaphysicians, may be defined, the external cause to which we ascribe
+our sensations. When I see and touch a piece of gold, I am conscious of
+a sensation of yellow colour, and sensations of hardness and weight; and
+by varying the mode of handling, I may add to these sensations many
+others completely distinct from them. The sensations are all of which I
+am directly conscious; but I consider them as produced by something not
+only existing independently of my will, but external to my bodily organs
+and to my mind. This external something I call a body.
+
+It may be asked, how come we to ascribe our sensations to any external
+cause? And is there sufficient ground for so ascribing them? It is
+known, that there are metaphysicians who have raised a controversy on
+the point; maintaining that we are not warranted in referring our
+sensations to a cause such as we understand by the word Body, or to any
+external cause whatever. Though we have no concern here with this
+controversy, nor with the metaphysical niceties on which it turns, one
+of the best ways of showing what is meant by Substance is, to consider
+what position it is necessary to take up, in order to maintain its
+existence against opponents.
+
+It is certain, then, that a part of our notion of a body consists of the
+notion of a number of sensations of our own, or of other sentient
+beings, habitually occurring simultaneously. My conception of the table
+at which I am writing is compounded of its visible form and size, which
+are complex sensations of sight; its tangible form and size, which are
+complex sensations of our organs of touch and of our muscles; its
+weight, which is also a sensation of touch and of the muscles; its
+colour, which is a sensation of sight; its hardness, which is a
+sensation of the muscles; its composition, which is another word for all
+the varieties of sensation which we receive under various circumstances
+from the wood of which it is made, and so forth. All or most of these
+various sensations frequently are, and, as we learn by experience,
+always might be, experienced simultaneously, or in many different orders
+of succession, at our own choice: and hence the thought of any one of
+them makes us think of the others, and the whole becomes mentally
+amalgamated into one mixed state of consciousness, which, in the
+language of the school of Locke and Hartley, is termed a Complex Idea.
+
+Now, there are philosophers who have argued as follows. If we conceive
+an orange to be divested of its natural colour without acquiring any new
+one; to lose its softness without becoming hard, its roundness without
+becoming square or pentagonal, or of any other regular or irregular
+figure whatever; to be deprived of size, of weight, of taste, of smell;
+to lose all its mechanical and all its chemical properties, and acquire
+no new ones; to become, in short, invisible, intangible, imperceptible
+not only by all our senses, but by the senses of all other sentient
+beings, real or possible; nothing, say these thinkers, would remain.
+For of what nature, they ask, could be the residuum? and by what token
+could it manifest its presence? To the unreflecting its existence seems
+to rest on the evidence of the senses. But to the senses nothing is
+apparent except the sensations. We know, indeed, that these sensations
+are bound together by some law; they do not come together at random, but
+according to a systematic order, which is part of the order established
+in the universe. When we experience one of these sensations, we usually
+experience the others also, or know that we have it in our power to
+experience them. But a fixed law of connexion, making the sensations
+occur together, does not, say these philosophers, necessarily require
+what is called a substratum to support them. The conception of a
+substratum is but one of many possible forms in which that connexion
+presents itself to our imagination; a mode of, as it were, realizing the
+idea. If there be such a substratum, suppose it this instant
+miraculously annihilated, and let the sensations continue to occur in
+the same order, and how would the substratum be missed? By what signs
+should we be able to discover that its existence had terminated? Should
+we not have as much reason to believe that it still existed as we now
+have? And if we should not then be warranted in believing it, how can we
+be so now? A body, therefore, according to these metaphysicians, is not
+anything intrinsically different from the sensations which the body is
+said to produce in us; it is, in short, a set of sensations, or rather,
+of possibilities of sensation, joined together according to a fixed law.
+
+The controversies to which these speculations have given rise, and the
+doctrines which have been developed in the attempt to find a conclusive
+answer to them, have been fruitful of important consequences to the
+Science of Mind. The sensations (it was answered) which we are conscious
+of, and which we receive, not at random, but joined together in a
+certain uniform manner, imply not only a law or laws of connexion, but a
+cause external to our mind, which cause, by its own laws, determines the
+laws according to which the sensations are connected and experienced.
+The schoolmen used to call this external cause by the name we have
+already employed, a _substratum_; and its attributes (as they expressed
+themselves) _inhered_, literally _stuck_, in it. To this substratum the
+name Matter is usually given in philosophical discussions. It was soon,
+however, acknowledged by all who reflected on the subject, that the
+existence of matter cannot be proved by extrinsic evidence. The answer,
+therefore, now usually made to Berkeley and his followers, is, that the
+belief is intuitive; that mankind, in all ages, have felt themselves
+compelled, by a necessity of their nature, to refer their sensations to
+an external cause: that even those who deny it in theory, yield to the
+necessity in practice, and both in speech, thought, and feeling, do,
+equally with the vulgar, acknowledge their sensations to be the effects
+of something external to them: this knowledge, therefore, it is
+affirmed, is as evidently intuitive as our knowledge of our sensations
+themselves is intuitive. And here the question merges in the fundamental
+problem of metaphysics properly so called; to which science we leave it.
+
+But although the extreme doctrine of the Idealist metaphysicians, that
+objects are nothing but our sensations and the laws which connect them,
+has not been generally adopted by subsequent thinkers; the point of most
+real importance is one on which those metaphysicians are now very
+generally considered to have made out their case: viz., that _all we
+know_ of objects is the sensations which they give us, and the order of
+the occurrence of those sensations. Kant himself, on this point, is as
+explicit as Berkeley or Locke. However firmly convinced that there
+exists an universe of "Things in themselves," totally distinct from the
+universe of phenomena, or of things as they appear to our senses; and
+even when bringing into use a technical expression (_Noumenon_) to
+denote what the thing is in itself, as contrasted with the
+_representation_ of it in our minds; he allows that this representation
+(the matter of which, he says, consists of our sensations, though the
+form is given by the laws of the mind itself) is all we know of the
+object: and that the real nature of the Thing is, and by the
+constitution of our faculties ever must remain, at least in the present
+state of existence, an impenetrable mystery to us. "Of things absolutely
+or in themselves," says Sir William Hamilton,[10] "be they external, be
+they internal, we know nothing, or know them only as incognisable; and
+become aware of their incomprehensible existence, only as this is
+indirectly and accidentally revealed to us, through certain qualities
+related to our faculties of knowledge, and which qualities, again, we
+cannot think as unconditioned, irrelative, existent in and of
+themselves. All that we know is therefore phænomenal,--phænomenal of the
+unknown."[11] The same doctrine is laid down in the clearest and
+strongest terms by M. Cousin, whose observations on the subject are the
+more worthy of attention, as, in consequence of the ultra-German and
+ontological character of his philosophy in other respects, they may be
+regarded as the admissions of an opponent.[12]
+
+There is not the slightest reason for believing that what we call the
+sensible qualities of the object are a type of anything inherent in
+itself, or bear any affinity to its own nature. A cause does not, as
+such, resemble its effects; an east wind is not like the feeling of
+cold, nor heat like the steam of boiling water. Why then should matter
+resemble our sensations? Why should the inmost nature of fire or water
+resemble the impressions made by those objects upon our senses?[13] Or
+on what principle are we authorized to deduce from the effects, anything
+concerning the cause, except that it is a cause adequate to produce
+those effects? It may, therefore, safely be laid down as a truth both
+obvious in itself, and admitted by all whom it is at present necessary
+to take into consideration, that, of the outward world, we know and can
+know absolutely nothing, except the sensations which we experience from
+it.[14]
+
+
+§ 8. Body having now been defined the external cause, and (according to
+the more reasonable opinion) the unknown external cause, to which we
+refer our sensations; it remains to frame a definition of Mind. Nor,
+after the preceding observations, will this be difficult. For, as our
+conception of a body is that of an unknown exciting cause of sensations,
+so our conception of a mind is that of an unknown recipient, or
+percipient, of them; and not of them alone, but of all our other
+feelings. As body is understood to be the mysterious something which
+excites the mind to feel, so mind is the mysterious something which
+feels and thinks. It is unnecessary to give in the case of mind, as we
+gave in the case of matter, a particular statement of the sceptical
+system by which its existence as a Thing in itself, distinct from the
+series of what are denominated its states, is called in question. But it
+is necessary to remark, that on the inmost nature (whatever be meant by
+inmost nature) of the thinking principle, as well as on the inmost
+nature of matter, we are, and with our faculties must always remain,
+entirely in the dark. All which we are aware of, even in our own minds,
+is (in the words of Mr. James Mill) a certain "thread of consciousness;"
+a series of feelings, that is, of sensations, thoughts, emotions, and
+volitions, more or less numerous and complicated. There is a something I
+call Myself, or, by another form of expression, my mind, which I
+consider as distinct from these sensations, thoughts, &c.; a something
+which I conceive to be not the thoughts, but the being that has the
+thoughts, and which I can conceive as existing for ever in a state of
+quiescence, without any thoughts at all. But what this being is, though
+it is myself, I have no knowledge, other than the series of its states
+of consciousness. As bodies manifest themselves to me only through the
+sensations of which I regard them as the causes, so the thinking
+principle, or mind, in my own nature, makes itself known to me only by
+the feelings of which it is conscious. I know nothing about myself, save
+my capacities of feeling or being conscious (including, of course,
+thinking and willing): and were I to learn anything new concerning my
+own nature, I cannot with my present faculties conceive this new
+information to be anything else, than that I have some additional
+capacities, as yet unknown to me, of feeling, thinking, or willing.
+
+Thus, then, as body is the unsentient cause to which we are naturally
+prompted to refer a certain portion of our feelings, so mind may be
+described as the sentient _subject_ (in the scholastic sense of the
+term) of all feelings; that which has or feels them. But of the nature
+of either body or mind, further than the feelings which the former
+excites, and which the latter experiences, we do not, according to the
+best existing doctrine, know anything; and if anything, logic has
+nothing to do with it, or with the manner in which the knowledge is
+acquired. With this result we may conclude this portion of our subject,
+and pass to the third and only remaining class or division of Nameable
+Things.
+
+
+III. ATTRIBUTES: AND, FIRST, QUALITIES.
+
+§ 9. From what has already been said of Substance, what is to be said of
+Attribute is easily deducible. For if we know not, and cannot know,
+anything of bodies but the sensations which they excite in us or in
+others, those sensations must be all that we can, at bottom, mean by
+their attributes; and the distinction which we verbally make between the
+properties of things and the sensations we receive from them, must
+originate in the convenience of discourse rather than in the nature of
+what is signified by the terms.
+
+Attributes are usually distributed under the three heads of Quality,
+Quantity, and Relation. We shall come to the two latter presently: in
+the first place we shall confine ourselves to the former.
+
+Let us take, then, as our example, one of what are termed the sensible
+qualities of objects, and let that example be whiteness. When we ascribe
+whiteness to any substance, as, for instance, snow; when we say that
+snow has the quality whiteness, what do we really assert? Simply, that
+when snow is present to our organs, we have a particular sensation,
+which we are accustomed to call the sensation of white. But how do I
+know that snow is present? Obviously by the sensations which I derive
+from it, and not otherwise. I infer that the object is present, because
+it gives me a certain assemblage or series of sensations. And when I
+ascribe to it the attribute whiteness, my meaning is only, that, of the
+sensations composing this group or series, that which I call the
+sensation of white colour is one.
+
+This is one view which may be taken of the subject. But there is also
+another and a different view. It may be said, that it is true we _know_
+nothing of sensible objects, except the sensations they excite in us;
+that the fact of our receiving from snow the particular sensation which
+is called a sensation of white, is the _ground_ on which we ascribe to
+that substance the quality whiteness; the sole proof of its possessing
+that quality. But because one thing may be the sole evidence of the
+existence of another thing, it does not follow that the two are one and
+the same. The attribute whiteness (it may be said) is not the fact of
+receiving the sensation, but something in the object itself; a _power_
+inherent in it; something _in virtue_ of which the object produces the
+sensation. And when we affirm that snow possesses the attribute
+whiteness, we do not merely assert that the presence of snow produces in
+us that sensation, but that it does so through, and by reason of, that
+power or quality.
+
+For the purposes of logic it is not of material importance which of
+these opinions we adopt. The full discussion of the subject belongs to
+the other department of scientific inquiry, so often alluded to under
+the name of metaphysics; but it may be said here, that for the doctrine
+of the existence of a peculiar species of entities called qualities, I
+can see no foundation except in a tendency of the human mind which is
+the cause of many delusions. I mean, the disposition, wherever we meet
+with two names which are not precisely synonymous, to suppose that they
+must be the names of two different things; whereas in reality they may
+be names of the same thing viewed in two different lights, or under
+different suppositions as to surrounding circumstances. Because
+_quality_ and _sensation_ cannot be put indiscriminately one for the
+other, it is supposed that they cannot both signify the same thing,
+namely, the impression or feeling with which we are affected through our
+senses by the presence of an object; though there is at least no
+absurdity in supposing that this identical impression or feeling may be
+called a sensation when considered merely in itself, and a quality when
+looked at in relation to any one of the numerous objects, the presence
+of which to our organs excites in our minds that among various other
+sensations or feelings. And if this be admissible as a supposition, it
+rests with those who contend for an entity _per se_ called a quality, to
+show that their opinion is preferable, or is anything in fact but a
+lingering remnant of the scholastic doctrine of occult causes; the very
+absurdity which Molière so happily ridiculed when he made one of his
+pedantic physicians account for the fact that "l'opium endormit," by the
+maxim "parcequ'il a une vertu soporifique."
+
+It is evident that when the physician stated that opium had "une vertu
+soporifique," he did not account for, but merely asserted over again,
+the fact that it _endormit_. In like manner, when we say that snow is
+white because it has the quality of whiteness, we are only re-asserting
+in more technical language the fact that it excites in us the sensation
+of white. If it be said that the sensation must have some cause, I
+answer, its cause is the presence of the assemblage of phenomena which
+is termed the object. When we have asserted that as often as the object
+is present, and our organs in their normal state, the sensation takes
+place, we have stated all that we know about the matter. There is no
+need, after assigning a certain and intelligible cause, to suppose an
+occult cause besides, for the purpose of enabling the real cause to
+produce its effect. If I am asked, why does the presence of the object
+cause this sensation in me, I cannot tell: I can only say that such is
+my nature, and the nature of the object; that the fact forms a part of
+the constitution of things. And to this we must at last come, even after
+interpolating the imaginary entity. Whatever number of links the chain
+of causes and effects may consist of, how any one link produces the one
+which is next to it, remains equally inexplicable to us. It is as easy
+to comprehend that the object should produce the sensation directly and
+at once, as that it should produce the same sensation by the aid of
+something else called the _power_ of producing it.
+
+But, as the difficulties which may be felt in adopting this view of the
+subject cannot be removed without discussions transcending the bounds of
+our science, I content myself with a passing indication, and shall, for
+the purposes of logic, adopt a language compatible with either view of
+the nature of qualities. I shall say,--what at least admits of no
+dispute,--that the quality of whiteness ascribed to the object snow, is
+_grounded_ on its exciting in us the sensation of white; and adopting
+the language already used by the school logicians in the case of the
+kind of attributes called Relations, I shall term the sensation of
+white the foundation of the quality whiteness. For logical purposes the
+sensation is the only essential part of what is meant by the word; the
+only part which we ever can be concerned in proving. When that is
+proved, the quality is proved; if an object excites a sensation, it has,
+of course, the power of exciting it.
+
+
+IV. RELATIONS.
+
+§ 10. The _qualities_ of a body, we have said, are the attributes
+grounded on the sensations which the presence of that particular body to
+our organs excites in our minds. But when we ascribe to any object the
+kind of attribute called a Relation, the foundation of the attribute
+must be something in which other objects are concerned besides itself
+and the percipient.
+
+As there may with propriety be said to be a relation between any two
+things to which two correlative names are or may be given, we may expect
+to discover what constitutes a relation in general, if we enumerate the
+principal cases in which mankind have imposed correlative names, and
+observe what these cases have in common.
+
+What, then, is the character which is possessed in common by states of
+circumstances so heterogeneous and discordant as these: one thing _like_
+another; one thing _unlike_ another; one thing _near_ another; one thing
+_far from_ another; one thing _before_, _after_, _along with_ another;
+one thing _greater_, _equal_, _less_, than another; one thing the
+_cause_ of another, the _effect_ of another; one person the _master_,
+_servant_, _child_, _parent_, _debtor_, _creditor_, _sovereign_,
+_subject_, _attorney_, _client_, of another, and so on?
+
+Omitting, for the present, the case of Resemblance, (a relation which
+requires to be considered separately,) there seems to be one thing
+common to all these cases, and only one; that in each of them there
+exists or occurs, or has existed or occurred, or may be expected to
+exist or occur, some fact or phenomenon, into which the two things which
+are said to be related to each other, both enter as parties concerned.
+This fact, or phenomenon, is what the Aristotelian logicians called the
+_fundamentum relationis_. Thus in the relation of greater and less
+between two magnitudes, the _fundamentum relationis_ is the fact that
+one of the two magnitudes could, under certain conditions, be included
+in, without entirely filling, the space occupied by the other magnitude.
+In the relation of master and servant, the _fundamentum relationis_ is
+the fact that the one has undertaken, or is compelled, to perform
+certain services for the benefit and at the bidding of the other.
+Examples might be indefinitely multiplied; but it is already obvious
+that whenever two things are said to be related, there is some fact, or
+series of facts, into which they both enter; and that whenever any two
+things are involved in some one fact, or series of facts, we may ascribe
+to those two things a mutual relation grounded on the fact. Even if they
+have nothing in common but what is common to all things, that they are
+members of the universe, we call that a relation, and denominate them
+fellow-creatures, fellow-beings, or fellow-denizens of the universe. But
+in proportion as the fact into which the two objects enter as parts is
+of a more special and peculiar, or of a more complicated nature, so also
+is the relation grounded upon it. And there are as many conceivable
+relations as there are conceivable kinds of fact in which two things can
+be jointly concerned.
+
+In the same manner, therefore, as a quality is an attribute grounded on
+the fact that a certain sensation or sensations are produced in us by
+the object, so an attribute grounded on some fact into which the object
+enters jointly with another object, is a relation between it and that
+other object. But the fact in the latter case consists of the very same
+kind of elements as the fact in the former; namely, states of
+consciousness. In the case, for example, of any legal relation, as
+debtor and creditor, principal and agent, guardian and ward, the
+_fundamentum relationis_ consists entirely of thoughts, feelings, and
+volitions (actual or contingent), either of the persons themselves or of
+other persons concerned in the same series of transactions; as, for
+instance, the intentions which would be formed by a judge, in case a
+complaint were made to his tribunal of the infringement of any of the
+legal obligations imposed by the relation; and the acts which the judge
+would perform in consequence; acts being (as we have already seen)
+another word for intentions followed by an effect, and that effect being
+but another word for sensations, or some other feelings, occasioned
+either to the agent himself or to somebody else. There is no part of
+what the names expressive of the relation imply, that is not resolvable
+into states of consciousness; outward objects being, no doubt, supposed
+throughout as the causes by which some of those states of consciousness
+are excited, and minds as the subjects by which all of them are
+experienced, but neither the external objects nor the minds making their
+existence known otherwise than by the states of consciousness.
+
+Cases of relation are not always so complicated as those to which we
+last alluded. The simplest of all cases of relation are those expressed
+by the words antecedent and consequent, and by the word simultaneous. If
+we say, for instance, that dawn preceded sunrise, the fact in which the
+two things, dawn and sunrise, were jointly concerned, consisted only of
+the two things themselves; no third thing entered into the fact or
+phenomenon at all. Unless, indeed, we choose to call the succession of
+the two objects a third thing; but their succession is not something
+added to the things themselves; it is something involved in them. Dawn
+and sunrise announce themselves to our consciousness by two successive
+sensations. Our consciousness of the succession of these sensations is
+not a third sensation or feeling added to them; we have not first the
+two feelings, and then a feeling of their succession. To have two
+feelings at all, implies having them either successively, or else
+simultaneously. Sensations, or other feelings, being given, succession
+and simultaneousness are the two conditions, to the alternative of which
+they are subjected by the nature of our faculties; and no one has been
+able, or needs expect, to analyse the matter any farther.
+
+
+§ 11. In a somewhat similar position are two other sorts of relations,
+Likeness and Unlikeness. I have two sensations; we will suppose them to
+be simple ones; two sensations of white, or one sensation of white and
+another of black. I call the first two sensations _like_; the last two
+_unlike_. What is the fact or phenomenon constituting the _fundamentum_
+of this relation? The two sensations first, and then what we call a
+feeling of resemblance, or of want of resemblance. Let us confine
+ourselves to the former case. Resemblance is evidently a feeling; a
+state of the consciousness of the observer. Whether the feeling of the
+resemblance of the two colours be a third state of consciousness, which
+I have _after_ having the two sensations of colour, or whether (like the
+feeling of their succession) it is involved in the sensations
+themselves, may be a matter of discussion. But in either case, these
+feelings of resemblance, and of its opposite dissimilarity, are parts of
+our nature; and parts so far from being capable of analysis, that they
+are presupposed in every attempt to analyse any of our other feelings.
+Likeness and unlikeness, therefore, as well as antecedence, sequence,
+and simultaneousness, must stand apart among relations, as things _sui
+generis_. They are attributes grounded on facts, that is, on states of
+consciousness, but on states which are peculiar, unresolvable, and
+inexplicable.
+
+But, though likeness or unlikeness cannot be resolved into anything
+else, complex cases of likeness or unlikeness can be resolved into
+simpler ones. When we say of two things which consist of parts, that
+they are like one another, the likeness of the wholes does admit of
+analysis; it is compounded of likenesses between the various parts
+respectively, and of likeness in their arrangement. Of how vast a
+variety of resemblances of parts must that resemblance be composed,
+which induces us to say that a portrait, or a landscape, is like its
+original. If one person mimics another with any success, of how many
+simple likenesses must the general or complex likeness be compounded:
+likeness in a succession of bodily postures; likeness in voice, or in
+the accents and intonations of the voice; likeness in the choice of
+words, and in the thoughts or sentiments expressed, whether by word,
+countenance, or gesture.
+
+All likeness and unlikeness of which we have any cognizance, resolve
+themselves into likeness and unlikeness between states of our own, or
+some other, mind. When we say that one body is like another, (since we
+know nothing of bodies but the sensations which they excite,) we mean
+really that there is a resemblance between the sensations excited by the
+two bodies, or between some portions at least of those sensations. If we
+say that two attributes are like one another, (since we know nothing of
+attributes except the sensations or states of feeling on which they are
+grounded,) we mean really that those sensations, or states of feeling,
+resemble each other. We may also say that two relations are alike. The
+fact of resemblance between relations is sometimes called _analogy_,
+forming one of the numerous meanings of that word. The relation in which
+Priam stood to Hector, namely, that of father and son, resembles the
+relation in which Philip stood to Alexander; resembles it so closely
+that they are called the same relation. The relation in which Cromwell
+stood to England resembles the relation in which Napoleon stood to
+France, though not so closely as to be called the same relation. The
+meaning in both these instances must be, that a resemblance existed
+between the facts which constituted the _fundamentum relationis_.
+
+This resemblance may exist in all conceivable gradations, from perfect
+undistinguishableness to something extremely slight. When we say, that a
+thought suggested to the mind of a person of genius is like a seed cast
+into the ground, because the former produces a multitude of other
+thoughts, and the latter a multitude of other seeds, this is saying that
+between the relation of an inventive mind to a thought contained in it,
+and the relation of a fertile soil to a seed contained in it, there
+exists a resemblance: the real resemblance being in the two _fundamenta
+relationis_, in each of which there occurs a germ, producing by its
+development a multitude of other things similar to itself. And as,
+whenever two objects are jointly concerned in a phenomenon, this
+constitutes a relation between those objects, so, if we suppose a second
+pair of objects concerned in a second phenomenon, the slightest
+resemblance between the two phenomena is sufficient to admit of its
+being said that the two relations resemble; provided, of course, the
+points of resemblance are found in those portions of the two phenomena
+respectively which are connoted by the relative names.
+
+While speaking of resemblance, it is necessary to take notice of an
+ambiguity of language, against which scarcely any one is sufficiently on
+his guard. Resemblance, when it exists in the highest degree of all,
+amounting to undistinguishableness, is often called identity, and the
+two similar things are said to be the same. I say often, not always; for
+we do not say that two visible objects, two persons for instance, are
+the same, because they are so much alike that one might be mistaken for
+the other: but we constantly use this mode of expression when speaking
+of feelings; as when I say that the sight of any object gives me the
+_same_ sensation or emotion to-day that it did yesterday, or the _same_
+which it gives to some other person. This is evidently an incorrect
+application of the word _same_; for the feeling which I had yesterday is
+gone, never to return; what I have to-day is another feeling, exactly
+like the former perhaps, but distinct from it; and it is evident that
+two different persons cannot be experiencing the same feeling, in the
+sense in which we say that they are both sitting at the same table. By a
+similar ambiguity we say, that two persons are ill of the _same_
+disease; that two persons hold the _same_ office; not in the sense in
+which we say that they are engaged in the same adventure, or sailing in
+the same ship, but in the sense that they fill offices exactly similar,
+though, perhaps, in distant places. Great confusion of ideas is often
+produced, and many fallacies engendered, in otherwise enlightened
+understandings, by not being sufficiently alive to the fact (in itself
+not always to be avoided), that they use the same name to express ideas
+so different as those of identity and undistinguishable resemblance.
+Among modern writers, Archbishop Whately stands almost alone in having
+drawn attention to this distinction, and to the ambiguity connected with
+it.
+
+Several relations, generally called by other names, are really cases of
+resemblance. As, for example, equality; which is but another word for
+the exact resemblance commonly called identity, considered as subsisting
+between things in respect of their _quantity_. And this example forms a
+suitable transition to the third and last of the three heads under
+which, as already remarked, Attributes are commonly arranged.
+
+
+V. QUANTITY.
+
+§ 12. Let us imagine two things, between which there is no difference
+(that is, no dissimilarity), except in quantity alone: for instance, a
+gallon of water, and more than a gallon of water. A gallon of water,
+like any other external object, makes its presence known to us by a set
+of sensations which it excites. Ten gallons of water are also an
+external object, making its presence known to us in a similar manner;
+and as we do not mistake ten gallons of water for a gallon of water, it
+is plain that the set of sensations is more or less different in the two
+cases. In like manner, a gallon of water, and a gallon of wine, are two
+external objects, making their presence known by two sets of sensations,
+which sensations are different from each other. In the first case,
+however, we say that the difference is in quantity; in the last there is
+a difference in quality, while the quantity of the water and of the wine
+is the same. What is the real distinction between the two cases? It is
+not the province of Logic to analyse it; nor to decide whether it is
+susceptible of analysis or not. For us the following considerations are
+sufficient. It is evident that the sensations I receive from the gallon
+of water, and those I receive from the gallon of wine, are not the same,
+that is, not precisely alike; neither are they altogether unlike: they
+are partly similar, partly dissimilar; and that in which they resemble
+is precisely that in which alone the gallon of water and the ten gallons
+do not resemble. That in which the gallon of water and the gallon of
+wine are like each other, and in which the gallon and the ten gallons of
+water are unlike each other, is called their quantity. This likeness
+and unlikeness I do not pretend to explain, no more than any other kind
+of likeness or unlikeness. But my object is to show, that when we say of
+two things that they differ in quantity, just as when we say that they
+differ in quality, the assertion is always grounded on a difference in
+the sensations which they excite. Nobody, I presume, will say, that to
+see, or to lift, or to drink, ten gallons of water, does not include in
+itself a different set of sensations from those of seeing, lifting, or
+drinking one gallon; or that to see or handle a foot-rule, and to see or
+handle a yard-measure made exactly like it, are the same sensations. I
+do not undertake to say what the difference in the sensations is.
+Everybody knows, and nobody can tell; no more than any one could tell
+what white is to a person who had never had the sensation. But the
+difference, so far as cognizable by our faculties, lies in the
+sensations. Whatever difference we say there is in the things
+themselves, is, in this as in all other cases, grounded, and grounded
+exclusively, on a difference in the sensations excited by them.
+
+
+VI. ATTRIBUTES CONCLUDED.
+
+§ 13. Thus, then, all the attributes of bodies which are classed under
+Quality or Quantity, are grounded on the sensations which we receive
+from those bodies, and may be defined, the powers which the bodies have
+of exciting those sensations. And the same general explanation has been
+found to apply to most of the attributes usually classed under the head
+of Relation. They, too, are grounded on some fact or phenomenon into
+which the related objects enter as parts; that fact or phenomenon having
+no meaning and no existence to us, except the series of sensations or
+other states of consciousness by which it makes itself known; and the
+relation being simply the power or capacity which the object possesses
+of taking part along with the correlated object in the production of
+that series of sensations or states of consciousness. We have been
+obliged, indeed, to recognise a somewhat different character in certain
+peculiar relations, those of succession and simultaneity, of likeness
+and unlikeness. These, not being grounded on any fact or phenomenon
+distinct from the related objects themselves, do not admit of the same
+kind of analysis. But these relations, though not, like other relations,
+grounded on states of consciousness, are themselves states of
+consciousness: resemblance is nothing but our feeling of resemblance;
+succession is nothing but our feeling of succession. Or, if this be
+disputed (and we cannot, without transgressing the bounds of our
+science, discuss it here), at least our knowledge of these relations,
+and even our possibility of knowledge, is confined to those which
+subsist between sensations, or other states of consciousness; for,
+though we ascribe resemblance, or succession, or simultaneity, to
+objects and to attributes, it is always in virtue of resemblance or
+succession or simultaneity in the sensations or states of consciousness
+which those objects excite, and on which those attributes are grounded.
+
+
+§ 14. In the preceding investigation we have, for the sake of
+simplicity, considered bodies only, and omitted minds. But what we have
+said, is applicable, _mutatis mutandis_, to the latter. The attributes
+of minds, as well as those of bodies, are grounded on states of feeling
+or consciousness. But in the case of a mind, we have to consider its own
+states, as well as those which it produces in other minds. Every
+attribute of a mind consists either in being itself affected in a
+certain way, or affecting other minds in a certain way. Considered in
+itself, we can predicate nothing of it but the series of its own
+feelings. When we say of any mind, that it is devout, or superstitious,
+or meditative, or cheerful, we mean that the ideas, emotions, or
+volitions implied in those words, form a frequently recurring part of
+the series of feelings, or states of consciousness, which fill up the
+sentient existence of that mind.
+
+In addition, however, to those attributes of a mind which are grounded
+on its own states of feeling, attributes may also be ascribed to it, in
+the same manner as to a body, grounded on the feelings which it excites
+in other minds. A mind does not, indeed, like a body, excite
+sensations, but it may excite thoughts or emotions. The most important
+example of attributes ascribed on this ground, is the employment of
+terms expressive of approbation or blame. When, for example, we say of
+any character, or (in other words) of any mind, that it is admirable, we
+mean that the contemplation of it excites the sentiment of admiration;
+and indeed somewhat more, for the word implies that we not only feel
+admiration, but approve that sentiment in ourselves. In some cases,
+under the semblance of a single attribute, two are really predicated:
+one of them, a state of the mind itself; the other, a state with which
+other minds are affected by thinking of it. As when we say of any one
+that he is generous. The word generosity expresses a certain state of
+mind, but being a term of praise, it also expresses that this state of
+mind excites in us another mental state, called approbation. The
+assertion made, therefore, is twofold, and of the following purport:
+Certain feelings form habitually a part of this person's sentient
+existence; and the idea of those feelings of his, excites the sentiment
+of approbation in ourselves or others.
+
+As we thus ascribe attributes to minds on the ground of ideas and
+emotions, so may we to bodies on similar grounds, and not solely on the
+ground of sensations: as in speaking of the beauty of a statue; since
+this attribute is grounded on the peculiar feeling of pleasure which the
+statue produces in our minds; which is not a sensation, but an emotion.
+
+
+VII. GENERAL RESULTS.
+
+§ 15. Our survey of the varieties of Things which have been, or which
+are capable of being, named--which have been, or are capable of being,
+either predicated of other Things, or themselves made the subject of
+predications--is now concluded.
+
+Our enumeration commenced with Feelings. These we scrupulously
+distinguished from the objects which excite them, and from the organs by
+which they are, or may be supposed to be, conveyed. Feelings are of
+four sorts: Sensations, Thoughts, Emotions, and Volitions. What are
+called Perceptions are merely a particular case of Belief, and belief is
+a kind of thought. Actions are merely volitions followed by an effect.
+If there be any other kind of mental state not included under these
+subdivisions, we did not think it necessary or proper in this place to
+discuss its existence, or the rank which ought to be assigned to it.
+
+After Feelings we proceeded to Substances. These are either Bodies or
+Minds. Without entering into the grounds of the metaphysical doubts
+which have been raised concerning the existence of Matter and Mind as
+objective realities, we stated as sufficient for us the conclusion in
+which the best thinkers are now for the most part agreed, that all we
+can know of Matter is the sensations which it gives us, and the order of
+occurrence of those sensations; and that while the substance Body is the
+unknown cause of our sensations, the substance Mind is the unknown
+recipient.
+
+The only remaining class of Nameable Things is Attributes; and these are
+of three kinds, Quality, Relation, and Quantity. Qualities, like
+substances, are known to us no otherwise than by the sensations or other
+states of consciousness which they excite: and while, in compliance with
+common usage, we have continued to speak of them as a distinct class of
+Things, we showed that in predicating them no one means to predicate
+anything but those sensations or states of consciousness, on which they
+may be said to be grounded, and by which alone they can be defined or
+described. Relations, except the simple cases of likeness and
+unlikeness, succession and simultaneity, are similarly grounded on some
+fact or phenomenon, that is, on some series of sensations or states of
+consciousness, more or less complicated. The third species of Attribute,
+Quantity, is also manifestly grounded on something in our sensations or
+states of feeling, since there is an indubitable difference in the
+sensations excited by a larger and a smaller bulk, or by a greater or a
+less degree of intensity, in any object of sense or of consciousness.
+All attributes, therefore, are to us nothing but either our sensations
+and other states of feeling, or something inextricably involved
+therein; and to this even the peculiar and simple relations just
+adverted to are not exceptions. Those peculiar relations, however, are
+so important, and, even if they might in strictness be classed among
+states of consciousness, are so fundamentally distinct from any other of
+those states, that it would be a vain subtlety to bring them under that
+common description, and it is necessary that they should be classed
+apart.
+
+As the result, therefore, of our analysis, we obtain the following as an
+enumeration and classification of all Nameable Things:--
+
+1st. Feelings, or States of Consciousness.
+
+2nd. The Minds which experience those feelings.
+
+3rd. The Bodies, or external objects, which excite certain of those
+feelings, together with the powers or properties whereby they excite
+them; these last being included rather in compliance with common
+opinion, and because their existence is taken for granted in the common
+language from which I cannot prudently deviate, than because the
+recognition of such powers or properties as real existences appears to
+be warranted by a sound philosophy.
+
+4th, and last. The Successions and Co-existences, the Likenesses and
+Unlikenesses, between feelings or states of consciousness. Those
+relations, when considered as subsisting between other things, exist in
+reality only between the states of consciousness which those things, if
+bodies, excite, if minds, either excite or experience.
+
+This, until a better can be suggested, may serve as a substitute for the
+abortive Classification of Existences, termed the Categories of
+Aristotle. The practical application of it will appear when we commence
+the inquiry into the Import of Propositions; in other words, when we
+inquire what it is which the mind actually believes, when it gives what
+is called its assent to a proposition.
+
+These four classes comprising, if the classification be correct, all
+Nameable Things, these or some of them must of course compose the
+signification of all names; and of these, or some of them, is made up
+whatever we call a fact.
+
+For distinction's sake, every fact which is solely composed of feelings
+or states of consciousness considered as such, is often called a
+Psychological or Subjective fact; while every fact which is composed,
+either wholly or in part, of something different from these, that is, of
+substances and attributes, is called an Objective fact. We may say,
+then, that every objective fact is grounded on a corresponding
+subjective one; and has no meaning to us, (apart from the subjective
+fact which corresponds to it,) except as a name for the unknown and
+inscrutable process by which that subjective or psychological fact is
+brought to pass.
+
+
+
+
+CHAPTER IV.
+
+OF PROPOSITIONS.
+
+
+§ 1. In treating of Propositions, as already in treating of Names, some
+considerations of a comparatively elementary nature respecting their
+form and varieties must be premised, before entering upon that analysis
+of the import conveyed by them, which is the real subject and purpose of
+this preliminary book.
+
+A proposition, we have before said, is a portion of discourse in which a
+predicate is affirmed or denied of a subject. A predicate and a subject
+are all that is necessarily required to make up a proposition: but as we
+cannot conclude from merely seeing two names put together, that they are
+a predicate and a subject, that is, that one of them is intended to be
+affirmed or denied of the other, it is necessary that there should be
+some mode or form of indicating that such is the intention; some sign to
+distinguish a predication from any other kind of discourse. This is
+sometimes done by a slight alteration of one of the words, called an
+_inflection_; as when we say, Fire burns; the change of the second word
+from _burn_ to _burns_ showing that we mean to affirm the predicate burn
+of the subject fire. But this function is more commonly fulfilled by the
+word _is_, when an affirmation is intended, _is not_, when a negation;
+or by some other part of the verb _to be_. The word which thus serves
+the purpose of a sign of predication is called, as we formerly observed,
+the _copula_. It is important that there should be no indistinctness in
+our conception of the nature and office of the copula; for confused
+notions respecting it are among the causes which have spread mysticism
+over the field of logic, and perverted its speculations into
+logomachies.
+
+It is apt to be supposed that the copula is something more than a mere
+sign of predication; that it also signifies existence. In the
+proposition, Socrates is just, it may seem to be implied not only that
+the quality _just_ can be affirmed of Socrates, but moreover that
+Socrates _is_, that is to say, exists. This, however, only shows that
+there is an ambiguity in the word _is_; a word which not only performs
+the function of the copula in affirmations, but has also a meaning of
+its own, in virtue of which it may itself be made the predicate of a
+proposition. That the employment of it as a copula does not necessarily
+include the affirmation of existence, appears from such a proposition as
+this, A centaur is a fiction of the poets; where it cannot possibly be
+implied that a centaur exists, since the proposition itself expressly
+asserts that the thing has no real existence.
+
+Many volumes might be filled with the frivolous speculations concerning
+the nature of Being, (_το ὄν_, _οὐσία_, Ens, Entitas, Essentia, and the
+like) which have arisen from overlooking this double meaning of the word
+_to be_; from supposing that when it signifies _to exist_, and when it
+signifies to _be_ some specified thing, as to _be_ a man, to _be_
+Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a
+nonentity, it must still, at bottom, answer to the same idea; and that a
+meaning must be found for it which shall suit all these cases. The fog
+which rose from this narrow spot diffused itself at an early period over
+the whole surface of metaphysics. Yet it becomes us not to triumph over
+the great intellects of Plato and Aristotle because we are now able to
+preserve ourselves from many errors into which they, perhaps inevitably,
+fell. The fire-teazer of a modern steam-engine produces by his exertions
+far greater effects than Milo of Crotona could, but he is not therefore
+a stronger man. The Greeks seldom knew any language but their own. This
+rendered it far more difficult for them than it is for us, to acquire a
+readiness in detecting ambiguities. One of the advantages of having
+accurately studied a plurality of languages, especially of those
+languages which eminent thinkers have used as the vehicle of their
+thoughts, is the practical lesson we learn respecting the ambiguities of
+words, by finding that the same word in one language corresponds, on
+different occasions, to different words in another. When not thus
+exercised, even the strongest understandings find it difficult to
+believe that things which have a common name, have not in some respect
+or other a common nature; and often expend much labour very unprofitably
+(as was frequently done by the two philosophers just mentioned) in vain
+attempts to discover in what this common nature consists. But, the habit
+once formed, intellects much inferior are capable of detecting even
+ambiguities which are common to many languages: and it is surprising
+that the one now under consideration, though it exists in the modern
+languages as well as in the ancient, should have been overlooked by
+almost all authors. The quantity of futile speculation which had been
+caused by a misapprehension of the nature of the copula, was hinted at
+by Hobbes; but Mr. James Mill[15] was, I believe, the first who
+distinctly characterized the ambiguity, and pointed out how many errors
+in the received systems of philosophy it has had to answer for. It has
+indeed misled the moderns scarcely less than the ancients, though their
+mistakes, because our understandings are not yet so completely
+emancipated from their influence, do not appear equally irrational.
+
+We shall now briefly review the principal distinctions which exist among
+propositions, and the technical terms most commonly in use to express
+those distinctions.
+
+
+§ 2. A proposition being a portion of discourse in which something is
+affirmed or denied of something, the first division of propositions is
+into affirmative and negative. An affirmative proposition is that in
+which the predicate is _affirmed_ of the subject; as, Cæsar is dead. A
+negative proposition is that in which the predicate is _denied_ of the
+subject; as, Cæsar is not dead. The copula, in this last species of
+proposition, consists of the words _is not_, which are the sign of
+negation; _is_ being the sign of affirmation.
+
+Some logicians, among whom may be mentioned Hobbes, state this
+distinction differently; they recognise only one form of copula, _is_,
+and attach the negative sign to the predicate. "Cæsar is dead," and
+"Cæsar is not dead," according to these writers, are propositions
+agreeing not in the subject and predicate, but in the subject only. They
+do not consider "dead," but "not dead," to be the predicate of the
+second proposition, and they accordingly define a negative proposition
+to be one in which the predicate is a negative name. The point, though
+not of much practical moment, deserves notice as an example (not
+unfrequent in logic) where by means of an apparent simplification, but
+which is merely verbal, matters are made more complex than before. The
+notion of these writers was, that they could get rid of the distinction
+between affirming and denying, by treating every case of denying as the
+affirming of a negative name. But what is meant by a negative name? A
+name expressive of the _absence_ of an attribute. So that when we affirm
+a negative name, what we are really predicating is absence and not
+presence; we are asserting not that anything is, but that something is
+not; to express which operation no word seems so proper as the word
+denying. The fundamental distinction is between a fact and the
+non-existence of that fact; between seeing something and not seeing it,
+between Cæsar's being dead and his not being dead; and if this were a
+merely verbal distinction, the generalization which brings both within
+the same form of assertion would be a real simplification: the
+distinction, however, being real, and in the facts, it is the
+generalization confounding the distinction that is merely verbal; and
+tends to obscure the subject, by treating the difference between two
+kinds of truths as if it were only a difference between two kinds of
+words. To put things together, and to put them or keep them asunder,
+will remain different operations, whatever tricks we may play with
+language.
+
+A remark of a similar nature may be applied to most of those
+distinctions among propositions which are said to have reference to
+their _modality_; as, difference of tense or time; the sun _did_ rise,
+the sun _is_ rising, the sun _will_ rise. These differences, like that
+between affirmation and negation, might be glossed over by considering
+the incident of time as a mere modification of the predicate: thus, The
+sun is _an object having risen_, The sun is _an object now rising_, The
+sun is _an object to rise hereafter_. But the simplification would be
+merely verbal. Past, present, and future, do not constitute so many
+different kinds of rising; they are designations belonging to the event
+asserted, to the _sun's_ rising to-day. They affect, not the predicate,
+but the applicability of the predicate to the particular subject. That
+which we affirm to be past, present, or future, is not what the subject
+signifies, nor what the predicate signifies, but specifically and
+expressly what the predication signifies; what is expressed only by the
+proposition as such, and not by either or both of the terms. Therefore
+the circumstance of time is properly considered as attaching to the
+copula, which is the sign of predication, and not to the predicate. If
+the same cannot be said of such modifications as these, Cæsar _may_ be
+dead; Cæsar is _perhaps_ dead; it is _possible_ that Cæsar is dead; it
+is only because these fall altogether under another head, being properly
+assertions not of anything relating to the fact itself, but of the state
+of our own mind in regard to it; namely, our absence of disbelief of it.
+Thus "Cæsar may be dead" means "I am not sure that Cæsar is alive."
+
+
+§ 3. The next division of propositions is into Simple and Complex. A
+simple proposition is that in which one predicate is affirmed or denied
+of one subject. A complex proposition is that in which there is more
+than one predicate, or more than one subject, or both.
+
+At first sight this division has the air of an absurdity; a solemn
+distinction of things into one and more than one; as if we were to
+divide horses into single horses and teams of horses. And it is true
+that what is called a complex proposition is often not a proposition at
+all, but several propositions, held together by a conjunction. Such, for
+example, is this: Cæsar is dead, and Brutus is alive: or even this,
+Cæsar is dead, _but_ Brutus is alive. There are here two distinct
+assertions; and we might as well call a street a complex house, as
+these two propositions a complex proposition. It is true that the
+syncategorematic words _and_ and _but_ have a meaning; but that meaning
+is so far from making the two propositions one, that it adds a third
+proposition to them. All particles are abbreviations, and generally
+abbreviations of propositions; a kind of short-hand, whereby something
+which, to be expressed fully, would have required a proposition or a
+series of propositions, is suggested to the mind at once. Thus the
+words, Cæsar is dead and Brutus is alive, are equivalent to these: Cæsar
+is dead; Brutus is alive; it is desired that the two preceding
+propositions should be thought of together. If the words were, Cæsar is
+dead _but_ Brutus is alive, the sense would be equivalent to the same
+three propositions together with a fourth; "between the two preceding
+propositions there exists a contrast:" viz. either between the two facts
+themselves, or between the feelings with which it is desired that they
+should be regarded.
+
+In the instances cited the two propositions are kept visibly distinct,
+each subject having its separate predicate, and each predicate its
+separate subject. For brevity, however, and to avoid repetition, the
+propositions are often blended together: as in this, "Peter and James
+preached at Jerusalem and in Galilee," which contains four propositions:
+Peter preached at Jerusalem, Peter preached in Galilee, James preached
+at Jerusalem, James preached in Galilee.
+
+We have seen that when the two or more propositions comprised in what is
+called a complex proposition are stated absolutely, and not under any
+condition or proviso, it is not a proposition at all, but a plurality of
+propositions; since what it expresses is not a single assertion, but
+several assertions, which, if true when joined, are true also when
+separated. But there is a kind of proposition which, though it contains
+a plurality of subjects and of predicates, and may be said in one sense
+of the word to consist of several propositions, contains but one
+assertion; and its truth does not at all imply that of the simple
+propositions which compose it. An example of this is, when the simple
+propositions are connected by the particle _or_; as, Either A is B or C
+is D; or by the particle _if_; as, A is B if C is D. In the former case,
+the proposition is called _disjunctive_, in the latter, _conditional_:
+the name _hypothetical_ was originally common to both. As has been well
+remarked by Archbishop Whately and others, the disjunctive form is
+resolvable into the conditional; every disjunctive proposition being
+equivalent to two or more conditional ones. "Either A is B or C is D,"
+means, "if A is not B, C is D; and if C is not D, A is B." All
+hypothetical propositions, therefore, though disjunctive in form, are
+conditional in meaning; and the words hypothetical and conditional may
+be, as indeed they generally are, used synonymously. Propositions in
+which the assertion is not dependent on a condition, are said, in the
+language of logicians, to be _categorical_.
+
+An hypothetical proposition is not, like the pretended complex
+propositions which we previously considered, a mere aggregation of
+simple propositions. The simple propositions which form part of the
+words in which it is couched, form no part of the assertion which it
+conveys. When we say, If the Koran comes from God, Mahomet is the
+prophet of God, we do not intend to affirm either that the Koran does
+come from God, or that Mahomet is really his prophet. Neither of these
+simple propositions may be true, and yet the truth of the hypothetical
+proposition may be indisputable. What is asserted is not the truth of
+either of the propositions, but the inferribility of the one from the
+other. What, then, is the subject, and what the predicate of the
+hypothetical proposition? "The Koran" is not the subject of it, nor is
+"Mahomet:" for nothing is affirmed or denied either of the Koran or of
+Mahomet. The real subject of the predication is the entire proposition,
+"Mahomet is the prophet of God;" and the affirmation is, that this is a
+legitimate inference from the proposition, "The Koran comes from God."
+The subject and predicate, therefore, of an hypothetical proposition are
+names of propositions. The subject is some one proposition. The
+predicate is a general relative name applicable to propositions; of this
+form--"an inference from so and so." A fresh instance is here afforded
+of the remark, that particles are abbreviations; since "_If_ A is B, C
+is D," is found to be an abbreviation of the following: "The proposition
+C is D, is a legitimate inference from the proposition A is B."
+
+The distinction, therefore, between hypothetical and categorical
+propositions, is not so great as it at first appears. In the
+conditional, as well as in the categorical form, one predicate is
+affirmed of one subject, and no more: but a conditional proposition is a
+proposition concerning a proposition; the subject of the assertion is
+itself an assertion. Nor is this a property peculiar to hypothetical
+propositions. There are other classes of assertions concerning
+propositions. Like other things, a proposition has attributes which may
+be predicated of it. The attribute predicated of it in an hypothetical
+proposition, is that of being an inference from a certain other
+proposition. But this is only one of many attributes that might be
+predicated. We may say, That the whole is greater than its part, is an
+axiom in mathematics: That the Holy Ghost proceeds from the Father
+alone, is a tenet of the Greek Church: The doctrine of the divine right
+of kings was renounced by Parliament at the Revolution: The
+infallibility of the Pope has no countenance from Scripture. In all
+these cases the subject of the predication is an entire proposition.
+That which these different predicates are affirmed of, is _the
+proposition_, "the whole is greater than its part;" _the proposition_,
+"the Holy Ghost proceeds from the Father alone;" _the proposition_,
+"kings have a divine right;" _the proposition_, "the Pope is
+infallible."
+
+Seeing, then, that there is much less difference between hypothetical
+propositions and any others, than one might be led to imagine from their
+form, we should be at a loss to account for the conspicuous position
+which they have been selected to fill in treatises on logic, if we did
+not remember that what they predicate of a proposition, namely, its
+being an inference from something else, is precisely that one of its
+attributes with which most of all a logician is concerned.
+
+
+§ 4. The next of the common divisions of Propositions is into
+Universal, Particular, Indefinite, and Singular: a distinction founded
+on the degree of generality in which the name, which is the subject of
+the proposition, is to be understood. The following are examples:
+
+  _All men_ are mortal--       Universal.
+  _Some men_ are mortal--      Particular.
+  _Man_ is mortal--            Indefinite.
+  _Julius Cæsar_ is mortal--   Singular.
+
+The proposition is Singular, when the subject is an individual name. The
+individual name needs not be a proper name. "The Founder of Christianity
+was crucified," is as much a singular proposition as "Christ was
+crucified."
+
+When the name which is the subject of the proposition is a general name,
+we may intend to affirm or deny the predicate, either of all the things
+that the subject denotes, or only of some. When the predicate is
+affirmed or denied of all and each of the things denoted by the subject,
+the proposition is universal; when of some undefined portion of them
+only, it is particular. Thus, All men are mortal; Every man is mortal;
+are universal propositions. No man is immortal, is also an universal
+proposition, since the predicate, immortal, is denied of each and every
+individual denoted by the term man; the negative proposition being
+exactly equivalent to the following, Every man is not-immortal. But
+"some men are wise," "some men are not wise," are particular
+propositions; the predicate _wise_ being in the one case affirmed and in
+the other denied not of each and every individual denoted by the term
+man, but only of each and every one of some portion of those
+individuals, without specifying what portion; for if this were
+specified, the proposition would be changed either into a singular
+proposition, or into an universal proposition with a different subject;
+as, for instance, "all _properly instructed_ men are wise." There are
+other forms of particular propositions; as, "_Most_ men are imperfectly
+educated:" it being immaterial how large a portion of the subject the
+predicate is asserted of, as long as it is left uncertain how that
+portion is to be distinguished from the rest.
+
+When the form of the expression does not clearly show whether the
+general name which is the subject of the proposition is meant to stand
+for all the individuals denoted by it, or only for some of them, the
+proposition is, by some logicians, called Indefinite; but this, as
+Archbishop Whately observes, is a solecism, of the same nature as that
+committed by some grammarians when in their list of genders they
+enumerate the _doubtful_ gender. The speaker must mean to assert the
+proposition either as an universal or as a particular proposition,
+though he has failed to declare which: and it often happens that though
+the words do not show which of the two he intends, the context, or the
+custom of speech, supplies the deficiency. Thus, when it is affirmed
+that "Man is mortal," nobody doubts that the assertion is intended of
+all human beings; and the word indicative of universality is commonly
+omitted, only because the meaning is evident without it. In the
+proposition, "Wine is good," it is understood with equal readiness,
+though for somewhat different reasons, that the assertion is not
+intended to be universal, but particular.[16]
+
+When a general name stands for each and every individual which it is a
+name of, or in other words, which it denotes, it is said by logicians to
+be _distributed_, or taken distributively. Thus, in the proposition, All
+men are mortal, the subject, Man, is distributed, because mortality is
+affirmed of each and every man. The predicate, Mortal, is not
+distributed, because the only mortals who are spoken of in the
+proposition are those who happen to be men; while the word may, for
+aught that appears, and in fact does, comprehend within it an indefinite
+number of objects besides men. In the proposition, Some men are mortal,
+both the predicate and the subject are undistributed. In the following,
+No men have wings, both the predicate and the subject are distributed.
+Not only is the attribute of having wings denied of the entire class
+Man, but that class is severed and cast out from the whole of the class
+Winged, and not merely from some part of that class.
+
+This phraseology, which is of great service in stating and
+demonstrating the rules of the syllogism, enables us to express very
+concisely the definitions of an universal and a particular proposition.
+An universal proposition is that of which the subject is distributed; a
+particular proposition is that of which the subject is undistributed.
+
+There are many more distinctions among propositions than those we have
+here stated, some of them of considerable importance. But, for
+explaining and illustrating these, more suitable opportunities will
+occur in the sequel.
+
+
+
+
+CHAPTER V.
+
+OF THE IMPORT OF PROPOSITIONS.
+
+
+§ 1. An inquiry into the nature of propositions must have one of two
+objects: to analyse the state of mind called Belief, or to analyse what
+is believed. All language recognises a difference between a doctrine or
+opinion, and the fact of entertaining the opinion; between assent, and
+what is assented to.
+
+Logic, according to the conception here formed of it, has no concern
+with the nature of the act of judging or believing; the consideration of
+that act, as a phenomenon of the mind, belongs to another science.
+Philosophers, however, from Descartes downwards, and especially from the
+era of Leibnitz and Locke, have by no means observed this distinction;
+and would have treated with great disrespect any attempt to analyse the
+import of Propositions, unless founded on an analysis of the act of
+Judgment. A proposition, they would have said, is but the expression in
+words of a Judgment. The thing expressed, not the mere verbal
+expression, is the important matter. When the mind assents to a
+proposition, it judges. Let us find out what the mind does when it
+judges, and we shall know what propositions mean, and not otherwise.
+
+Conformably to these views, almost all the writers on Logic in the last
+two centuries, whether English, German, or French, have made their
+theory of Propositions, from one end to the other, a theory of
+Judgments. They considered a Proposition, or a Judgment, for they used
+the two words indiscriminately, to consist in affirming or denying one
+_idea_ of another. To judge, was to put two ideas together, or to bring
+one idea under another, or to compare two ideas, or to perceive the
+agreement or disagreement between two ideas: and the whole doctrine of
+Propositions, together with the theory of Reasoning, (always necessarily
+founded on the theory of Propositions,) was stated as if Ideas, or
+Conceptions, or whatever other term the writer preferred as a name for
+mental representations generally, constituted essentially the subject
+matter and substance of those operations.
+
+It is, of course, true, that in any case of judgment, as for instance
+when we judge that gold is yellow, a process takes place in our minds,
+of which some one or other of these theories is a partially correct
+account. We must have the idea of gold and the idea of yellow, and these
+two ideas must be brought together in our mind. But in the first place,
+it is evident that this is only a part of what takes place; for we may
+put two ideas together without any act of belief; as when we merely
+imagine something, such as a golden mountain; or when we actually
+disbelieve: for in order even to disbelieve that Mahomet was an apostle
+of God, we must put the idea of Mahomet and that of an apostle of God
+together. To determine what it is that happens in the case of assent or
+dissent besides putting two ideas together, is one of the most intricate
+of metaphysical problems. But whatever the solution may be, we may
+venture to assert that it can have nothing whatever to do with the
+import of propositions; for this reason, that propositions (except
+sometimes when the mind itself is the subject treated of) are not
+assertions respecting our ideas of things, but assertions respecting the
+things themselves. In order to believe that gold is yellow, I must,
+indeed, have the idea of gold, and the idea of yellow, and something
+having reference to those ideas must take place in my mind; but my
+belief has not reference to the ideas, it has reference to the things.
+What I believe, is a fact relating to the outward thing, gold, and to
+the impression made by that outward thing upon the human organs; not a
+fact relating to my conception of gold, which would be a fact in my
+mental history, not a fact of external nature. It is true, that in order
+to believe this fact in external nature, another fact must take place in
+my mind, a process must be performed upon my ideas; but so it must in
+everything else that I do. I cannot dig the ground unless I have the
+idea of the ground, and of a spade, and of all the other things I am
+operating upon, and unless I put those ideas together.[17] But it would
+be a very ridiculous description of digging the ground to say that it is
+putting one idea into another. Digging is an operation which is
+performed upon the things themselves, though it cannot be performed
+unless I have in my mind the ideas of them. And in like manner,
+believing is an act which has for its subject the facts themselves,
+though a previous mental conception of the facts is an indispensable
+condition. When I say that fire causes heat, do I mean that my idea of
+fire causes my idea of heat? No: I mean that the natural phenomenon,
+fire, causes the natural phenomenon, heat. When I mean to assert
+anything respecting the ideas, I give them their proper name, I call
+them ideas: as when I say, that a child's idea of a battle is unlike the
+reality, or that the ideas entertained of the Deity have a great effect
+on the characters of mankind.
+
+The notion that what is of primary importance to the logician in a
+proposition, is the relation between the two _ideas_ corresponding to
+the subject and predicate, (instead of the relation between the two
+_phenomena_ which they respectively express,) seems to me one of the
+most fatal errors ever introduced into the philosophy of Logic; and the
+principal cause why the theory of the science has made such
+inconsiderable progress during the last two centuries. The treatises on
+Logic, and on the branches of Mental Philosophy connected with Logic,
+which have been produced since the intrusion of this cardinal error,
+though sometimes written by men of extraordinary abilities and
+attainments, almost always tacitly imply a theory that the investigation
+of truth consists in contemplating and handling our ideas, or
+conceptions of things, instead of the things themselves: a doctrine
+tantamount to the assertion, that the only mode of acquiring knowledge
+of nature is to study it at second hand, as represented in our own
+minds. Meanwhile, inquiries into every kind of natural phenomena were
+incessantly establishing great and fruitful truths on most important
+subjects, by processes upon which these views of the nature of Judgment
+and Reasoning threw no light, and in which they afforded no assistance
+whatever. No wonder that those who knew by practical experience how
+truths are arrived at, should deem a science futile, which consisted
+chiefly of such speculations. What has been done for the advancement of
+Logic since these doctrines came into vogue, has been done not by
+professed logicians, but by discoverers in the other sciences; in whose
+methods of investigation many principles of logic, not previously
+thought of, have successively come forth into light, but who have
+generally committed the error of supposing that nothing whatever was
+known of the art of philosophizing by the old logicians, because their
+modern interpreters have written to so little purpose respecting it.
+
+We have to inquire, then, on the present occasion, not into Judgment,
+but judgments; not into the act of believing, but into the thing
+believed. What is the immediate object of belief in a Proposition? What
+is the matter of fact signified by it? What is it to which, when I
+assert the proposition, I give my assent, and call upon others to give
+theirs? What is that which is expressed by the form of discourse called
+a Proposition, and the conformity of which to fact constitutes the truth
+of the proposition?
+
+
+§ 2. One of the clearest and most consecutive thinkers whom this country
+or the world has produced, I mean Hobbes, has given the following answer
+to this question. In every proposition (says he) what is signified is,
+the belief of the speaker that the predicate is a name of the same thing
+of which the subject is a name; and if it really is so, the proposition
+is true. Thus the proposition, All men are living beings (he would say)
+is true, because _living being_ is a name of everything of which _man_
+is a name. All men are six feet high, is not true, because _six feet
+high_ is not a name of everything (though it is of some things) of which
+_man_ is a name.
+
+What is stated in this theory as the definition of a true proposition,
+must be allowed to be a property which all true propositions possess.
+The subject and predicate being both of them names of things, if they
+were names of quite different things the one name could not,
+consistently with its signification, be predicated of the other. If it
+be true that some men are copper-coloured, it must be true--and the
+proposition does really assert--that among the individuals denoted by
+the name man, there are some who are also among those denoted by the
+name copper-coloured. If it be true that all oxen ruminate, it must be
+true that all the individuals denoted by the name ox are also among
+those denoted by the name ruminating; and whoever asserts that all oxen
+ruminate, undoubtedly does assert that this relation subsists between
+the two names.
+
+The assertion, therefore, which, according to Hobbes, is the only one
+made in any proposition, really is made in every proposition: and his
+analysis has consequently one of the requisites for being the true one.
+We may go a step farther; it is the only analysis that is rigorously
+true of all propositions without exception. What he gives as the meaning
+of propositions, is part of the meaning of all propositions, and the
+whole meaning of some. This, however, only shows what an extremely
+minute fragment of meaning it is quite possible to include within the
+logical formula of a proposition. It does not show that no proposition
+means more. To warrant us in putting together two words with a copula
+between them, it is really enough that the thing or things denoted by
+one of the names should be capable, without violation of usage, of being
+called by the other name also. If, then, this be all the meaning
+necessarily implied in the form of discourse called a Proposition, why
+do I object to it as the scientific definition of what a proposition
+means? Because, though the mere collocation which makes the proposition
+a proposition, conveys no more than this scanty amount of meaning, that
+same collocation combined with other circumstances, that _form_
+combined with other _matter_, does convey more, and much more.
+
+The only propositions of which Hobbes' principle is a sufficient
+account, are that limited and unimportant class in which both the
+predicate and the subject are proper names. For, as has already been
+remarked, proper names have strictly no meaning; they are mere marks for
+individual objects: and when a proper name is predicated of another
+proper name, all the signification conveyed is, that both the names are
+marks for the same object. But this is precisely what Hobbes produces as
+a theory of predication in general. His doctrine is a full explanation
+of such predications as these: Hyde was Clarendon, or, Tully is Cicero.
+It exhausts the meaning of those propositions. But it is a sadly
+inadequate theory of any others. That it should ever have been thought
+of as such, can be accounted for only by the fact, that Hobbes, in
+common with the other Nominalists, bestowed little or no attention upon
+the _connotation_ of words; and sought for their meaning exclusively in
+what they _denote_: as if all names had been (what none but proper names
+really are) marks put upon individuals; and as if there were no
+difference between a proper and a general name, except that the first
+denotes only one individual, and the last a greater number.
+
+It has been seen, however, that the meaning of all names, except proper
+names and that portion of the class of abstract names which are not
+connotative, resides in the connotation. When, therefore, we are
+analysing the meaning of any proposition in which the predicate and the
+subject, or either of them, are connotative names, it is to the
+connotation of those terms that we must exclusively look, and not to
+what they _denote_, or in the language of Hobbes (language so far
+correct) are names of.
+
+In asserting that the truth of a proposition depends on the conformity
+of import between its terms, as, for instance, that the proposition,
+Socrates is wise, is a true proposition, because Socrates and wise are
+names applicable to, or, as he expresses it, names of, the same person;
+it is very remarkable that so powerful a thinker should not have asked
+himself the question, But how came they to be names of the same person?
+Surely not because such was the intention of those who invented the
+words. When mankind fixed the meaning of the word wise, they were not
+thinking of Socrates, nor, when his parents gave him the name of
+Socrates, were they thinking of wisdom. The names _happen_ to fit the
+same person because of a certain _fact_, which fact was not known, nor
+in being, when the names were invented. If we want to know what the fact
+is, we shall find the clue to it in the _connotation_ of the names.
+
+A bird or a stone, a man, or a wise man, means simply, an object having
+such and such attributes. The real meaning of the word man, is those
+attributes, and not Smith, Brown, and the remainder of the individuals.
+The word _mortal_, in like manner connotes a certain attribute or
+attributes; and when we say, All men are mortal, the meaning of the
+proposition is, that all beings which possess the one set of attributes,
+possess also the other. If, in our experience, the attributes connoted
+by _man_ are always accompanied by the attribute connoted by _mortal_,
+it will follow as a consequence, that the class _man_ will be wholly
+included in the class _mortal_, and that _mortal_ will be a name of all
+things of which _man_ is a name: but why? Those objects are brought
+under the name, by possessing the attributes connoted by it: but their
+possession of the attributes is the real condition on which the truth of
+the proposition depends; not their being called by the name. Connotative
+names do not precede, but follow, the attributes which they connote. If
+one attribute happens to be always found in conjunction with another
+attribute, the concrete names which answer to those attributes will of
+course be predicable of the same subjects, and may be said, in Hobbes'
+language, (in the propriety of which on this occasion I fully concur,)
+to be two names for the same things. But the possibility of a concurrent
+application of the two names, is a mere consequence of the conjunction
+between the two attributes, and was, in most cases, never thought of
+when the names were introduced and their signification fixed. That the
+diamond is combustible, was a proposition certainly not dreamt of when
+the words Diamond and Combustible first received their meaning; and
+could not have been discovered by the most ingenious and refined
+analysis of the signification of those words. It was found out by a very
+different process, namely, by exerting the senses, and learning from
+them, that the attribute of combustibility existed in the diamonds upon
+which the experiment was tried; the number or character of the
+experiments being such, that what was true of those individuals might be
+concluded to be true of all substances "called by the name," that is, of
+all substances possessing the attributes which the name connotes. The
+assertion, therefore, when analysed, is, that wherever we find certain
+attributes, there will be found a certain other attribute: which is not
+a question of the signification of names, but of laws of nature; the
+order existing among phenomena.
+
+
+§ 3. Although Hobbes' theory of Predication has not, in the terms in
+which he stated it, met with a very favourable reception from subsequent
+thinkers, a theory virtually identical with it, and not by any means so
+perspicuously expressed, may almost be said to have taken the rank of an
+established opinion. The most generally received notion of Predication
+decidedly is that it consists in referring something to a class, _i.e._,
+either placing an individual under a class, or placing one class under
+another class. Thus, the proposition, Man is mortal, asserts, according
+to this view of it, that the class man is included in the class mortal.
+"Plato is a philosopher," asserts that the individual Plato is one of
+those who compose the class philosopher. If the proposition is negative,
+then instead of placing something in a class, it is said to exclude
+something from a class. Thus, if the following be the proposition, The
+elephant is not carnivorous; what is asserted (according to this theory)
+is, that the elephant is excluded, from the class carnivorous, or is not
+numbered among the things comprising that class. There is no real
+difference, except in language, between this theory of Predication and
+the theory of Hobbes. For a class _is_ absolutely nothing but an
+indefinite number of individuals denoted by a general name. The name
+given to them in common, is what makes them a class. To refer anything
+to a class, therefore, is to look upon it as one of the things which are
+to be called by that common name. To exclude it from a class, is to say
+that the common name is not applicable to it.
+
+How widely these views of predication have prevailed, is evident from
+this, that they are the basis of the celebrated _dictum de omni et
+nullo_. When the syllogism is resolved, by all who treat of it, into an
+inference that what is true of a class is true of all things whatever
+that belong to the class; and when this is laid down by almost all
+professed logicians as the ultimate principle to which all reasoning
+owes its validity; it is clear that in the general estimation of
+logicians, the propositions of which reasonings are composed can be the
+expression of nothing but the process of dividing things into classes,
+and referring everything to its proper class.
+
+This theory appears to me a signal example of a logical error very often
+committed in logic, that of _ὕστερον προτέρον_, or explaining a thing by
+something which presupposes it. When I say that snow is white, I may and
+ought to be thinking of snow as a class, because I am asserting a
+proposition as true of all snow: but I am certainly not thinking of
+white objects as a class; I am thinking of no white object whatever
+except snow, but only of that, and of the sensation of white which it
+gives me. When, indeed, I have judged, or assented to the propositions,
+that snow is white, and that several other things are also white, I
+gradually begin to think of white objects as a class, including snow and
+those other things. But this is a conception which followed, not
+preceded, those judgments, and therefore cannot be given as an
+explanation of them. Instead of explaining the effect by the cause, this
+doctrine explains the cause by the effect, and is, I conceive, founded
+on a latent misconception of the nature of classification.
+
+There is a sort of language very generally prevalent in these
+discussions, which seems to suppose that classification is an
+arrangement and grouping of definite and known individuals: that when
+names were imposed, mankind took into consideration all the individual
+objects in the universe, distributed them into parcels or lists, and
+gave to the objects of each list a common name, repeating this operation
+_toties quoties_ until they had invented all the general names of which
+language consists; which having been once done, if a question
+subsequently arises whether a certain general name can be truly
+predicated of a certain particular object, we have only (as it were) to
+read the roll of the objects upon which that name was conferred, and see
+whether the object about which the question arises is to be found among
+them. The framers of language (it would seem to be supposed) have
+predetermined all the objects that are to compose each class, and we
+have only to refer to the record of an antecedent decision.
+
+So absurd a doctrine will be owned by nobody when thus nakedly stated;
+but if the commonly received explanations of classification and naming
+do not imply this theory, it requires to be shown how they admit of
+being reconciled with any other.
+
+General names are not marks put upon definite objects; classes are not
+made by drawing a line round a given number of assignable individuals.
+The objects which compose any given class are perpetually fluctuating.
+We may frame a class without knowing the individuals, or even any of the
+individuals, of which it may be composed; we may do so while believing
+that no such individuals exist. If by the _meaning_ of a general name
+are to be understood the things which it is the name of, no general
+name, except by accident, has a fixed meaning at all, or ever long
+retains the same meaning. The only mode in which any general name has a
+definite meaning, is by being a name of an indefinite variety of things;
+namely, of all things, known or unknown, past, present, or future, which
+possess certain definite attributes. When, by studying not the meaning
+of words, but the phenomena of nature, we discover that these attributes
+are possessed by some object not previously known to possess them, (as
+when chemists found that the diamond was combustible), we include this
+new object in the class; but it did not already belong to the class. We
+place the individual in the class because the proposition is true; the
+proposition is not true because the object is placed in the class.
+
+It will appear hereafter, in treating of reasoning, how much the theory
+of that intellectual process has been vitiated by the influence of these
+erroneous notions, and by the habit which they exemplify of assimilating
+all the operations of the human understanding which have truth for their
+object, to processes of mere classification and naming. Unfortunately,
+the minds which have been entangled in this net are precisely those
+which have escaped the other cardinal error commented upon in the
+beginning of the present chapter. Since the revolution which dislodged
+Aristotle from the schools, logicians may almost be divided into those
+who have looked upon reasoning as essentially an affair of Ideas, and
+those who have looked upon it as essentially an affair of Names.
+
+Although, however, Hobbes' theory of Predication, according to the
+well-known remark of Leibnitz, and the avowal of Hobbes himself,[18]
+renders truth and falsity completely arbitrary, with no standard but the
+will of men, it must not be concluded that either Hobbes, or any of the
+other thinkers who have in the main agreed with him, did in fact
+consider the distinction between truth and error as less real, or
+attached less importance to it, than other people. To suppose that they
+did so would argue total unacquaintance with their other speculations.
+But this shows how little hold their doctrine possessed over their own
+minds. No person, at bottom, ever imagined that there was nothing more
+in truth than propriety of expression; than using language in conformity
+to a previous convention. When the inquiry was brought down from
+generals to a particular case, it has always been acknowledged that
+there is a distinction between verbal and real questions; that some
+false propositions are uttered from ignorance of the meaning of words,
+but that in others the source of the error is a misapprehension of
+things; that a person who has not the use of language at all may form
+propositions mentally, and that they may be untrue, that is, he may
+believe as matters of fact what are not really so. This last admission
+cannot be made in stronger terms than it is by Hobbes himself;[19]
+though he will not allow such erroneous belief to be called falsity, but
+only error. And he has himself laid down, in other places, doctrines in
+which the true theory of predication is by implication contained. He
+distinctly says that general names are given to things on account of
+their attributes, and that abstract names are the names of those
+attributes. "Abstract is that which in any subject denotes the cause of
+the concrete name.... And these causes of names are the same with the
+causes of our conceptions, namely, some power of action, or affection,
+of the thing conceived, which some call the manner by which anything
+works upon our senses, but by most men they are called _accidents_."[20]
+It is strange that having gone so far, he should not have gone one step
+farther, and seen that what he calls the cause of the concrete name, is
+in reality the meaning of it; and that when we predicate of any subject
+a name which is given _because_ of an attribute (or, as he calls it, an
+accident), our object is not to affirm the name, but, by means of the
+name, to affirm the attribute.
+
+
+§ 4. Let the predicate be, as we have said, a connotative term; and to
+take the simplest case first, let the subject be a proper name: "The
+summit of Chimborazo is white." The word white connotes an attribute
+which is possessed by the individual object designated by the words
+"summit of Chimborazo;" which attribute consists in the physical fact,
+of its exciting in human beings the sensation which we call a sensation
+of white. It will be admitted that, by asserting the proposition, we
+wish to communicate information of that physical fact, and are not
+thinking of the names, except as the necessary means of making that
+communication. The meaning of the proposition, therefore, is, that the
+individual thing denoted by the subject, has the attributes connoted by
+the predicate.
+
+If we now suppose the subject also to be a connotative name, the meaning
+expressed by the proposition has advanced a step farther in
+complication. Let us first suppose the proposition to be universal, as
+well as affirmative: "All men are mortal." In this case, as in the last,
+what the proposition asserts (or expresses a belief of) is, of course,
+that the objects denoted by the subject (man) possess the attributes
+connoted by the predicate (mortal). But the characteristic of this case
+is, that the objects are no longer _individually_ designated. They are
+pointed out only by some of their attributes: they are the objects
+called men, that is, possessing the attributes connoted by the name man;
+and the only thing known of them may be those attributes: indeed, as the
+proposition is general, and the objects denoted by the subject are
+therefore indefinite in number, most of them are not known individually
+at all. The assertion, therefore, is not, as before, that the attributes
+which the predicate connotes are possessed by any given individual, or
+by any number of individuals previously known as John, Thomas, &c., but
+that those attributes are possessed by each and every individual
+possessing certain other attributes; that whatever has the attributes
+connoted by the subject, has also those connoted by the predicate; that
+the latter set of attributes _constantly accompany_ the former set.
+Whatever has the attributes of man has the attribute of mortality;
+mortality constantly accompanies the attributes of man.[21]
+
+If it be remembered that every attribute is _grounded_ on some fact or
+phenomenon, either of outward sense or of inward consciousness, and that
+to _possess_ an attribute is another phrase for being the cause of, or
+forming part of, the fact or phenomenon upon which the attribute is
+grounded; we may add one more step to complete the analysis. The
+proposition which asserts that one attribute always accompanies another
+attribute, really asserts thereby no other thing than this, that one
+phenomenon always accompanies another phenomenon; insomuch that where we
+find the one, we have assurance of the existence of the other. Thus, in
+the proposition, All men are mortal, the word man connotes the
+attributes which we ascribe to a certain kind of living creatures, on
+the ground of certain phenomena which they exhibit, and which are partly
+physical phenomena, namely the impressions made on our senses by their
+bodily form and structure, and partly mental phenomena, namely the
+sentient and intellectual life which they have of their own. All this is
+understood when we utter the word man, by any one to whom the meaning of
+the word is known. Now, when we say, Man is mortal, we mean that
+wherever these various physical and mental phenomena are all found,
+there we have assurance that the other physical and mental phenomenon,
+called death, will not fail to take place. The proposition does not
+affirm _when_; for the connotation of the word _mortal_ goes no farther
+than to the occurrence of the phenomenon at some time or other, leaving
+the precise time undecided.
+
+
+§ 5. We have already proceeded far enough, not only to demonstrate the
+error of Hobbes, but to ascertain the real import of by far the most
+numerous class of propositions. The object of belief in a proposition,
+when it asserts anything more than the meaning of words, is generally,
+as in the cases which we have examined, either the co-existence or the
+sequence of two phenomena. At the very commencement of our inquiry, we
+found that every act of belief implied two Things: we have now
+ascertained what, in the most frequent case, these two things are,
+namely two Phenomena, in other words, two states of consciousness; and
+what it is which the proposition affirms (or denies) to subsist between
+them, namely either succession or co-existence. And this case includes
+innumerable instances which no one, previous to reflection, would think
+of referring to it. Take the following example: A generous person is
+worthy of honour. Who would expect to recognise here a case of
+co-existence between phenomena? But so it is. The attribute which causes
+a person to be termed generous, is ascribed to him on the ground of
+states of his mind, and particulars of his conduct: both are phenomena:
+the former are facts of internal consciousness; the latter, so far as
+distinct from the former, are physical facts, or perceptions of the
+senses. Worthy of honour admits of a similar analysis. Honour, as here
+used, means a state of approving and admiring emotion, followed on
+occasion by corresponding outward acts. "Worthy of honour" connotes all
+this, together with our approval of the act of showing honour. All these
+are phenomena; states of internal consciousness, accompanied or followed
+by physical facts. When we say, A generous person is worthy of honour,
+we affirm co-existence between the two complicated phenomena connoted by
+the two terms respectively. We affirm, that wherever and whenever the
+inward feelings and outward facts implied in the word generosity have
+place, then and there the existence and manifestation of an inward
+feeling, honour, would be followed in our minds by another inward
+feeling, approval.
+
+After the analysis, in a former chapter, of the import of names, many
+examples are not needed to illustrate the import of propositions. When
+there is any obscurity, or difficulty, it does not lie in the meaning of
+the proposition, but in the meaning of the names which compose it; in
+the extremely complicated connotation of many words; the immense
+multitude and prolonged series of facts which often constitute the
+phenomenon connoted by a name. But where it is seen what the phenomenon
+is, there is seldom any difficulty in seeing that the assertion conveyed
+by the proposition is, the co-existence of one such phenomenon with
+another; or the succession of one such phenomenon to another: their
+_conjunction_, in short, so that where the one is found, we may
+calculate on finding both.
+
+This, however, though the most common, is not the only meaning which
+propositions are ever intended to convey. In the first place, sequences
+and co-existences are not only asserted respecting Phenomena; we make
+propositions also respecting those hidden causes of phenomena, which are
+named substances and attributes. A substance, however, being to us
+nothing but either that which causes, or that which is conscious of,
+phenomena; and the same being true, _mutatis mutandis_, of attributes;
+no assertion can be made, at least with a meaning, concerning these
+unknown and unknowable entities, except in virtue of the Phenomena by
+which alone they manifest themselves to our faculties. When we say,
+Socrates was cotemporary with the Peloponnesian war, the foundation of
+this assertion, as of all assertions concerning substances, is an
+assertion concerning the phenomena which they exhibit,--namely, that the
+series of facts by which Socrates manifested himself to mankind, and the
+series of mental states which constituted his sentient existence, went
+on simultaneously with the series of facts known by the name of the
+Peloponnesian war. Still, the proposition does not assert that alone; it
+asserts that the Thing in itself, the _noumenon_ Socrates, was existing,
+and doing or experiencing those various facts during the same time.
+Co-existence and sequence, therefore, may be affirmed or denied not only
+between phenomena, but between noumena, or between a noumenon and
+phenomena. And both of noumena and of phenomena we may affirm simple
+existence. But what is a noumenon? An unknown cause. In affirming,
+therefore, the existence of a noumenon, we affirm causation. Here,
+therefore, are two additional kinds of fact, capable of being asserted
+in a proposition. Besides the propositions which assert Sequence or
+Coexistence, there are some which assert simple Existence; and others
+assert Causation, which, subject to the explanations which will follow
+in the Third Book, must be considered provisionally as a distinct and
+peculiar kind of assertion.
+
+
+§ 6. To these four kinds of matter-of-fact or assertion, must be added a
+fifth, Resemblance. This was a species of attribute which we found it
+impossible to analyse; for which no _fundamentum_, distinct from the
+objects themselves, could be assigned. Besides propositions which assert
+a sequence or co-existence between two phenomena, there are therefore
+also propositions which assert resemblance between them: as, This colour
+is like that colour;--The heat of to-day is _equal_ to the heat of
+yesterday. It is true that such an assertion might with some
+plausibility be brought within the description of an affirmation of
+sequence, by considering it as an assertion that the simultaneous
+contemplation of the two colours is _followed_ by a specific feeling
+termed the feeling of resemblance. But there would be nothing gained by
+encumbering ourselves, especially in this place, with a generalization
+which may be looked upon as strained. Logic does not undertake to
+analyse mental facts into their ultimate elements. Resemblance between
+two phenomena is more intelligible in itself than any explanation could
+make it, and under any classification must remain specifically distinct
+from the ordinary cases of sequence and co-existence.
+
+It is sometimes said, that all propositions whatever, of which the
+predicate is a general name, do, in point of fact, affirm or deny
+resemblance. All such propositions affirm that a thing belongs to a
+class; but things being classed together according to their resemblance,
+everything is of course classed with the things which it is supposed to
+resemble most; and thence, it may be said, when we affirm that Gold is a
+metal, or that Socrates is a man, the affirmation intended is, that
+gold resembles other metals, and Socrates other men, more nearly than
+they resemble the objects contained in any other of the classes
+co-ordinate with these.
+
+There is some slight degree of foundation for this remark, but no more
+than a slight degree. The arrangement of things into classes, such as
+the class _metal_, or the class _man_, is grounded indeed on a
+resemblance among the things which are placed in the same class, but not
+on a mere general resemblance: the resemblance it is grounded on
+consists in the possession by all those things, of certain common
+peculiarities; and those peculiarities it is which the terms connote,
+and which the propositions consequently assert; not the resemblance: for
+though when I say, Gold is a metal, I say by implication that if there
+be any other metals it must resemble them, yet if there were no other
+metals I might still assert the proposition with the same meaning as at
+present, namely, that gold has the various properties implied in the
+word metal; just as it might be said, Christians are men, even if there
+were no men who were not Christians. Propositions, therefore, in which
+objects are referred to a class because they possess the attributes
+constituting the class, are so far from asserting nothing but
+resemblance, that they do not, properly speaking, assert resemblance at
+all.
+
+But we remarked some time ago (and the reasons of the remark will be
+more fully entered into in a subsequent Book[22]) that there is
+sometimes a convenience in extending the boundaries of a class so as to
+include things which possess in a very inferior degree, if in any, some
+of the characteristic properties of the class,--provided they resemble
+that class more than any other, insomuch that the general propositions
+which are true of the class, will be nearer to being true of those
+things than any other equally general propositions. For instance, there
+are substances called metals which have very few of the properties by
+which metals are commonly recognised; and almost every great family of
+plants or animals has a few anomalous genera or species on its borders,
+which are admitted into it by a sort of courtesy, and concerning which
+it has been matter of discussion to what family they properly belonged.
+Now when the class-name is predicated of any object of this description,
+we do, by so predicating it, affirm resemblance and nothing more. And in
+order to be scrupulously correct it ought to be said, that in every case
+in which we predicate a general name, we affirm, not absolutely that the
+object possesses the properties designated by the name, but that it
+_either_ possesses those properties, or if it does not, at any rate
+resembles the things which do so, more than it resembles any other
+things. In most cases, however, it is unnecessary to suppose any such
+alternative, the latter of the two grounds being very seldom that on
+which the assertion is made: and when it is, there is generally some
+slight difference in the form of the expression, as, This species (or
+genus) is _considered_, or _may be ranked_, as belonging to such and
+such a family: we should hardly say positively that it does belong to
+it, unless it possessed unequivocally the properties of which the
+class-name is scientifically significant.
+
+There is still another exceptional case, in which, though the predicate
+is the name of a class, yet in predicating it we affirm nothing but
+resemblance, the class being founded not on resemblance in any given
+particular, but on general unanalysable resemblance. The classes in
+question are those into which our simple sensations, or other simple
+feelings, are divided. Sensations of white, for instance, are classed
+together, not because we can take them to pieces, and say they are alike
+in this, and not alike in that, but because we feel them to be alike
+altogether, though in different degrees. When, therefore, I say, The
+colour I saw yesterday was a white colour, or, The sensation I feel is
+one of tightness, in both cases the attribute I affirm of the colour or
+of the other sensation is mere resemblance--simple _likeness_ to
+sensations which I have had before, and which have had those names
+bestowed upon them. The names of feelings, like other concrete general
+names, are connotative; but they connote a mere resemblance. When
+predicated of any individual feeling, the information they convey is
+that of its likeness to the other feelings which we have been accustomed
+to call by the same name. Thus much may suffice in illustration of the
+kind of propositions in which the matter-of-fact asserted (or denied) is
+simple Resemblance.
+
+Existence, Coexistence, Sequence, Causation, Resemblance: one or other
+of these is asserted (or denied) in every proposition which is not
+merely verbal. This five-fold division is an exhaustive classification
+of matters-of-fact; of all things that can be believed, or tendered for
+belief; of all questions that can be propounded, and all answers that
+can be returned to them. Instead of Coexistence and Sequence, we shall
+sometimes say, for greater particularity, Order in Place, and Order in
+Time: Order in Place being the specific mode of coexistence, not
+necessary to be more particularly analysed here; while the mere fact of
+coexistence, or simultaneousness, may be classed, together with
+Sequence, under the head of Order in Time.
+
+
+§ 7. In the foregoing inquiry into the import of Propositions, we have
+thought it necessary to analyse directly those alone, in which the terms
+of the proposition (or the predicate at least) are concrete terms. But,
+in doing so, we have indirectly analysed those in which the terms are
+abstract. The distinction between an abstract term and its corresponding
+concrete, does not turn upon any difference in what they are appointed
+to signify; for the real signification of a concrete general name is, as
+we have so often said, its connotation; and what the concrete term
+connotes, forms the entire meaning of the abstract name. Since there is
+nothing in the import of an abstract name which is not in the import of
+the corresponding concrete, it is natural to suppose that neither can
+there be anything in the import of a proposition of which the terms are
+abstract, but what there is in some proposition which can be framed of
+concrete terms.
+
+And this presumption a closer examination will confirm. An abstract name
+is the name of an attribute, or combination of attributes. The
+corresponding concrete is a name given to things, because of, and in
+order to express, their possessing that attribute, or that combination
+of attributes. When, therefore, we predicate of anything a concrete
+name, the attribute is what we in reality predicate of it. But it has
+now been shown that in all propositions of which the predicate is a
+concrete name, what is really predicated is one of five things:
+Existence, Coexistence, Causation, Sequence, or Resemblance. An
+attribute, therefore, is necessarily either an existence, a coexistence,
+a causation, a sequence, or a resemblance. When a proposition consists
+of a subject and predicate which are abstract terms, it consists of
+terms which must necessarily signify one or other of these things. When
+we predicate of anything an abstract name, we affirm of the thing that
+it is one or other of these five things; that it is a case of Existence,
+or of Coexistence, or of Causation, or of Sequence, or of Resemblance.
+
+It is impossible to imagine any proposition expressed in abstract terms,
+which cannot be transformed into a precisely equivalent proposition in
+which the terms are concrete; namely, either the concrete names which
+connote the attributes themselves, or the names of the _fundamenta_ of
+those attributes; the facts or phenomena on which they are grounded. To
+illustrate the latter case, let us take this proposition, of which the
+subject only is an abstract name, "Thoughtlessness is dangerous."
+Thoughtlessness is an attribute, grounded on the facts which we call
+thoughtless actions; and the proposition is equivalent to this,
+Thoughtless actions are dangerous. In the next example the predicate as
+well as the subject are abstract names: "Whiteness is a colour;" or "The
+colour of snow is a whiteness." These attributes being grounded on
+sensations, the equivalent propositions in the concrete would be, The
+sensation of white is one of the sensations called those of colour,--The
+sensation of sight, caused by looking at snow, is one of the sensations
+called sensations of white. In these propositions, as we have before
+seen, the matter-of-fact asserted is a Resemblance. In the following
+examples, the concrete terms are those which directly correspond to the
+abstract names; connoting the attribute which these denote. "Prudence
+is a virtue:" this may be rendered, "All prudent persons, _in so far as_
+prudent, are virtuous:" "Courage is deserving of honour," thus, "All
+courageous persons are deserving of honour _in so far_ as they are
+courageous:" which is equivalent to this--"All courageous persons
+deserve an addition to the honour, or a diminution of the disgrace,
+which would attach to them on other grounds."
+
+In order to throw still further light upon the import of propositions of
+which the terms are abstract, we will subject one of the examples given
+above to a minuter analysis. The proposition we shall select is the
+following:--"Prudence is a virtue." Let us substitute for the word
+virtue an equivalent but more definite expression, such as "a mental
+quality beneficial to society," or "a mental quality pleasing to God,"
+or whatever else we adopt as the definition of virtue. What the
+proposition asserts is a sequence, accompanied with causation; namely,
+that benefit to society, or that the approval of God, is consequent on,
+and caused by, prudence. Here is a sequence; but between what? We
+understand the consequent of the sequence, but we have yet to analyse
+the antecedent. Prudence is an attribute; and, in connexion with it, two
+things besides itself are to be considered; prudent persons, who are the
+_subjects_ of the attribute, and prudential conduct, which may be called
+the _foundation_ of it. Now is either of these the antecedent? and,
+first, is it meant, that the approval of God, or benefit to society, is
+attendant upon all prudent _persons_? No; except _in so far_ as they are
+prudent; for prudent persons who are scoundrels can seldom on the whole
+be beneficial to society, nor can they be acceptable to a good being. Is
+it upon prudential _conduct_, then, that divine approbation and benefit
+to mankind are supposed to be invariably consequent? Neither is this the
+assertion meant, when it is said that prudence is a virtue; except with
+the same reservation as before, and for the same reason, namely, that
+prudential conduct, although in _so far as_ it is prudential it is
+beneficial to society, may yet, by reason of some other of its
+qualities, be productive of an injury outweighing the benefit, and
+deserve a displeasure exceeding the approbation which would be due to
+the prudence. Neither the substance, therefore, (viz. the person,) nor
+the phenomenon, (the conduct,) is an antecedent on which the other term
+of the sequence is universally consequent. But the proposition,
+"Prudence is a virtue," is an universal proposition. What is it, then,
+upon which the proposition affirms the effects in question to be
+universally consequent? Upon that in the person, and in the conduct,
+which causes them to be called prudent, and which is equally in them
+when the action, though prudent, is wicked; namely, a correct foresight
+of consequences, a just estimation of their importance to the object in
+view, and repression of any unreflecting impulse at variance with the
+deliberate purpose. These, which are states of the person's mind, are
+the real antecedent in the sequence, the real cause in the causation,
+asserted by the proposition. But these are also the real ground, or
+foundation, of the attribute Prudence; since wherever these states of
+mind exist we may predicate prudence, even before we know whether any
+conduct has followed. And in this manner every assertion respecting an
+attribute, may be transformed into an assertion exactly equivalent
+respecting the fact or phenomenon which is the ground of the attribute.
+And no case can be assigned, where that which is predicated of the fact
+or phenomenon, does not belong to one or other of the five species
+formerly enumerated: it is either simple Existence, or it is some
+Sequence, Coexistence, Causation, or Resemblance.
+
+And as these five are the only things which can be affirmed, so are they
+the only things which can be denied. "No horses are web-footed" denies
+that the attributes of a horse ever coexist with web-feet. It is
+scarcely necessary to apply the same analysis to Particular affirmations
+and negations. "Some birds are web-footed," affirms that, with the
+attributes connoted by _bird_, the phenomenon web-feet is sometimes
+co-existent: "Some birds are not web-footed," asserts that there are
+other instances in which this coexistence does not have place. Any
+further explanation of a thing which, if the previous exposition has
+been assented to, is so obvious, may here be spared.
+
+
+
+
+CHAPTER VI.
+
+OF PROPOSITIONS MERELY VERBAL.
+
+
+§ 1. As a preparation for the inquiry which is the proper object of
+Logic, namely, in what manner propositions are to be proved, we have
+found it necessary to inquire what they contain which requires, or is
+susceptible of, proof; or (which is the same thing) what they assert. In
+the course of this preliminary investigation into the import of
+Propositions, we examined the opinion of the Conceptualists, that a
+proposition is the expression of a relation between two ideas; and the
+doctrine of the Nominalists, that it is the expression of an agreement
+or disagreement between the meanings of two names. We decided that, as
+general theories, both of these are erroneous; and that, though
+propositions may be made both respecting names and respecting ideas,
+neither the one nor the other are the subject-matter of Propositions
+considered generally. We then examined the different kinds of
+Propositions, and found that, with the exception of those which are
+merely verbal, they assert five different kinds of matters of fact,
+namely, Existence, Order in Place, Order in Time, Causation, and
+Resemblance; that in every proposition one of these five is either
+affirmed, or denied, of some fact or phenomenon, or of some object the
+unknown source of a fact or phenomenon.
+
+In distinguishing, however, the different kinds of matters of fact
+asserted in propositions, we reserved one class of propositions, which
+do not relate to any matter of fact, in the proper sense of the term, at
+all, but to the meaning of names. Since names and their signification
+are entirely arbitrary, such propositions are not, strictly speaking,
+susceptible of truth or falsity, but only of conformity or disconformity
+to usage or convention; and all the proof they are capable of, is proof
+of usage; proof that the words have been employed by others in the
+acceptation in which the speaker or writer desires to use them. These
+propositions occupy, however, a conspicuous place in philosophy; and
+their nature and characteristics are of as much importance in logic, as
+those of any of the other classes of propositions previously adverted
+to.
+
+If all propositions respecting the signification of words were as simple
+and unimportant as those which served us for examples when examining
+Hobbes' theory of predication, viz. those of which the subject and
+predicate are proper names, and which assert only that those names have,
+or that they have not, been conventionally assigned to the same
+individual, there would be little to attract to such propositions the
+attention of philosophers. But the class of merely verbal propositions
+embraces not only much more than these, but much more than any
+propositions which at first sight present themselves as verbal;
+comprehending a kind of assertions which have been regarded not only as
+relating to things, but as having actually a more intimate relation with
+them than any other propositions whatever. The student in philosophy
+will perceive that I allude to the distinction on which so much stress
+was laid by the schoolmen, and which has been retained either under the
+same or under other names by most metaphysicians to the present day,
+viz. between what were called _essential_, and what were called
+_accidental_, propositions, and between essential and accidental
+properties or attributes.
+
+
+§ 2. Almost all metaphysicians prior to Locke, as well as many since his
+time, have made a great mystery of Essential Predication, and of
+predicates which are said to be of the _essence_ of the subject. The
+essence of a thing, they said, was that without which the thing could
+neither be, nor be conceived to be. Thus, rationality was of the essence
+of man, because without rationality, man could not be conceived to
+exist. The different attributes which made up the essence of the thing
+were called its essential properties; and a proposition in which any of
+these were predicated of it was called an Essential Proposition, and was
+considered to go deeper into the nature of the thing, and to convey more
+important information respecting it, than any other proposition could
+do. All properties, not of the essence of the thing, were called its
+accidents; were supposed to have nothing at all, or nothing
+comparatively, to do with its inmost nature; and the propositions in
+which any of these were predicated of it were called Accidental
+Propositions. A connexion may be traced between this distinction, which
+originated with the schoolmen, and the well-known dogmas of _substantiæ
+secundæ_ or general substances, and _substantial forms_, doctrines which
+under varieties of language pervaded alike the Aristotelian and the
+Platonic schools, and of which more of the spirit has come down to
+modern times than might be conjectured from the disuse of the
+phraseology. The false views of the nature of classification and
+generalization which prevailed among the schoolmen, and of which these
+dogmas were the technical expression, afford the only explanation which
+can be given of their having misunderstood the real nature of those
+Essences which held so conspicuous a place in their philosophy. They
+said, truly, that _man_ cannot be conceived without rationality. But
+though _man_ cannot, a being may be conceived exactly like a man in all
+points except that one quality, and those others which are the
+conditions or consequences of it. All therefore which is really true in
+the assertion that man cannot be conceived without rationality, is only,
+that if he had not rationality, he would not be reputed a man. There is
+no impossibility in conceiving the _thing_, nor, for aught we know, in
+its existing: the impossibility is in the conventions of language, which
+will not allow the thing, even if it exist, to be called by the name
+which is reserved for rational beings. Rationality, in short, is
+involved in the meaning of the word man: is one of the attributes
+connoted by the name. The essence of man, simply means the whole of the
+attributes connoted by the word; and any one of those attributes taken
+singly, is an essential property of man.
+
+But these reflections, so easy to us, would have been difficult to
+persons who thought, as most of the later Aristotelians did, that
+objects were made what they were called, that gold (for instance) was
+made gold, not by the possession of certain properties to which mankind
+have chosen to attach that name, but by participation in the nature of
+a certain general substance, called gold in general, which substance,
+together with all the properties that belonged to it, _inhered_ in every
+individual piece of gold.[23] As they did not consider these universal
+substances to be attached to all general names, but only to some, they
+thought that an object borrowed only a part of its properties from an
+universal substance, and that the rest belonged to it individually: the
+former they called its essence, and the latter its accidents. The
+scholastic doctrine of essences long survived the theory on which it
+rested, that of the existence of real entities corresponding to general
+terms; and it was reserved for Locke at the end of the seventeenth
+century, to convince philosophers that the supposed essences of classes
+were merely the signification of their names; nor, among the signal
+services which his writings rendered to philosophy, was there one more
+needful or more valuable.
+
+Now, as the most familiar of the general names by which an object is
+designated usually connotes not one only, but several attributes of the
+object, each of which attributes separately forms also the bond of union
+of some class, and the meaning of some general name; we may predicate of
+a name which connotes a variety of attributes, another name which
+connotes only one of these attributes, or some smaller number of them
+than all. In such cases, the universal affirmative proposition will be
+true; since whatever possesses the whole of any set of attributes, must
+possess any part of that same set. A proposition of this sort, however,
+conveys no information to any one who previously understood the whole
+meaning of the terms. The propositions, Every man is a corporeal being,
+Every man is a living creature, Every man is rational, convey no
+knowledge to any one who was already aware of the entire meaning of the
+word _man_, for the meaning of the word includes all this: and that
+every _man_ has the attributes connoted by all these predicates, is
+already asserted when he is called a man. Now, of this nature are all
+the propositions which have been called essential. They are, in fact,
+identical propositions.
+
+It is true that a proposition which predicates any attribute, even
+though it be one implied in the name, is in most cases understood to
+involve a tacit assertion that there _exists_ a thing corresponding to
+the name, and possessing the attributes connoted by it; and this implied
+assertion may convey information, even to those who understood the
+meaning of the name. But all information of this sort, conveyed by all
+the essential propositions of which man can be made the subject, is
+included in the assertion, Men exist. And this assumption of real
+existence is, after all, the result of an imperfection of language. It
+arises from the ambiguity of the copula, which, in addition to its
+proper office of a mark to show that an assertion is made, is also, as
+formerly remarked, a concrete word connoting existence. The actual
+existence of the subject of the proposition is therefore only
+apparently, not really, implied in the predication, if an essential one:
+we may say, A ghost is a disembodied spirit, without believing in
+ghosts. But an accidental, or non-essential, affirmation, does imply the
+real existence of the subject, because in the case of a non-existent
+subject there is nothing for the proposition to assert. Such a
+proposition as, The ghost of a murdered person haunts the couch of the
+murderer, can only have a meaning if understood as implying a belief in
+ghosts; for since the signification of the word ghost implies nothing of
+the kind, the speaker either means nothing, or means to assert a thing
+which he wishes to be believed to have really taken place.
+
+It will be hereafter seen that when any important consequences seem to
+follow, as in mathematics, from an essential proposition, or, in other
+words, from a proposition involved in the meaning of a name, what they
+really flow from is the tacit assumption of the real existence of the
+objects so named. Apart from this assumption of real existence, the
+class of propositions in which the predicate is of the essence of the
+subject (that is, in which the predicate connotes the whole or part of
+what the subject connotes, but nothing besides) answer no purpose but
+that of unfolding the whole or some part of the meaning of the name, to
+those who did not previously know it. Accordingly, the most useful, and
+in strictness the only useful kind of essential propositions, are
+Definitions: which, to be complete, should unfold the whole of what is
+involved in the meaning of the word defined; that is, (when it is a
+connotative word,) the whole of what it connotes. In defining a name,
+however, it is not usual to specify its entire connotation, but so much
+only as is sufficient to mark out the objects usually denoted by it from
+all other known objects. And sometimes a merely accidental property, not
+involved in the meaning of the name, answers this purpose equally well.
+The various kinds of definition which these distinctions give rise to,
+and the purposes to which they are respectively subservient, will be
+minutely considered in the proper place.
+
+
+§ 3. According to the above view of essential propositions, no
+proposition can be reckoned such which relates to an individual by name,
+that is, in which the subject is a proper name. Individuals have no
+essences. When the schoolmen talked of the essence of an individual,
+they did not mean the properties implied in its name, for the names of
+individuals imply no properties. They regarded as of the essence of an
+individual, whatever was of the essence of the species in which they
+were accustomed to place that individual; _i.e._ of the class to which
+it was most familiarly referred, and to which, therefore, they conceived
+that it by nature belonged. Thus, because the proposition Man is a
+rational being, was an essential proposition, they affirmed the same
+thing of the proposition, Julius Cæsar is a rational being. This
+followed very naturally if genera and species were to be considered as
+entities, distinct from, but _inhering_ in, the individuals composing
+them. If _man_ was a substance inhering in each individual man, the
+_essence_ of man (whatever that might mean) was naturally supposed to
+accompany it; to inhere in John Thompson, and to form the _common
+essence_ of Thompson and Julius Cæsar. It might then be fairly said,
+that rationality, being of the essence of Man, was of the essence also
+of Thompson. But if Man altogether be only the individual men and a name
+bestowed upon them in consequence of certain common properties, what
+becomes of John Thompson's essence?
+
+A fundamental error is seldom expelled from philosophy by a single
+victory. It retreats slowly, defends every inch of ground, and often,
+after it has been driven from the open country, retains a footing in
+some remote fastness. The essences of individuals were an unmeaning
+figment arising from a misapprehension of the essences of classes, yet
+even Locke, when he extirpated the parent error, could not shake himself
+free from that which was its fruit. He distinguished two sorts of
+essences, Real and Nominal. His nominal essences were the essences of
+classes, explained nearly as we have now explained them. Nor is anything
+wanting to render the third book of Locke's Essay a nearly
+unexceptionable treatise on the connotation of names, except to free its
+language from the assumption of what are called Abstract Ideas, which
+unfortunately is involved in the phraseology, though not necessarily
+connected with the thoughts contained in that immortal Third Book.[24]
+But, besides nominal essences, he admitted real essences, or essences of
+individual objects, which he supposed to be the causes of the sensible
+properties of those objects. We know not (said he) what these are; (and
+this acknowledgment rendered the fiction comparatively innocuous;) but
+if we did, we could, from them alone, demonstrate the sensible
+properties of the object, as the properties of the triangle are
+demonstrated from the definition of the triangle. I shall have occasion
+to revert to this theory in treating of Demonstration, and of the
+conditions under which one property of a thing admits of being
+demonstrated from another property. It is enough here to remark that,
+according to this definition, the real essence of an object has, in the
+progress of physics, come to be conceived as nearly equivalent, in the
+case of bodies, to their corpuscular structure: what it is now supposed
+to mean in the case of any other entities, I would not take upon myself
+to define.
+
+
+§ 4. An essential proposition, then, is one which is purely verbal;
+which asserts of a thing under a particular name, only what is asserted
+of it in the fact of calling it by that name; and which therefore either
+gives no information, or gives it respecting the name, not the thing.
+Non-essential, or accidental propositions, on the contrary, may be
+called Real Propositions, in opposition to Verbal. They predicate of a
+thing some fact not involved in the signification of the name by which
+the proposition speaks of it; some attribute not connoted by that name.
+Such are all propositions concerning things individually designated, and
+all general or particular propositions in which the predicate connotes
+any attribute not connoted by the subject. All these, if true, add to
+our knowledge: they convey information, not already involved in the
+names employed. When I am told that all, or even that some objects,
+which have certain qualities, or which stand in certain relations, have
+also certain other qualities, or stand in certain other relations, I
+learn from this proposition a new fact; a fact not included in my
+knowledge of the meaning of the words, nor even of the existence of
+Things answering to the signification of those words. It is this class
+of propositions only which are in themselves instructive, or from which
+any instructive propositions can be inferred.[25]
+
+Nothing has probably contributed more to the opinion so long prevalent
+of the futility of the school logic, than the circumstance that almost
+all the examples used in the common school books to illustrate the
+doctrine of predication and that of the syllogism, consist of essential
+propositions. They were usually taken either from the branches or from
+the main trunk of the Predicamental Tree, which included nothing but
+what was of the _essence_ of the species: _Omne corpus est substantia_,
+_Omne animal est corpus_, _Omnis homo est corpus_, _Omnis homo est
+animal_, _Omnis homo est rationalis_, and so forth. It is far from
+wonderful that the syllogistic art should have been thought to be of no
+use in assisting correct reasoning, when almost the only propositions
+which, in the hands of its professed teachers, it was employed to prove,
+were such as every one assented to without proof the moment he
+comprehended the meaning of the words; and stood exactly on a level, in
+point of evidence, with the premises from which they were drawn. I have,
+therefore, throughout this work, avoided the employment of essential
+propositions as examples, except where the nature of the principle to be
+illustrated specifically required them.
+
+
+§ 5. With respect to propositions which do convey information--which
+assert something of a Thing, under a name that does not already
+presuppose what is about to be asserted; there are two different aspects
+in which these, or rather such of them as are general propositions, may
+be considered: we may either look at them as portions of speculative
+truth, or as memoranda for practical use. According as we consider
+propositions in one or the other of these lights, their import may be
+conveniently expressed in one or in the other of two formulas.
+
+According to the formula which we have hitherto employed, and which is
+best adapted to express the import of the proposition as a portion of
+our theoretical knowledge, All men are mortal, means that the attributes
+of man are always accompanied by the attribute mortality: No men are
+gods, means that the attributes of man are never accompanied by the
+attributes, or at least never by all the attributes, signified by the
+word god. But when the proposition is considered as a memorandum for
+practical use, we shall find a different mode of expressing the same
+meaning better adapted to indicate the office which the proposition
+performs. The practical use of a proposition is, to apprise or remind us
+what we have to expect, in any individual case which comes within the
+assertion contained in the proposition. In reference to this purpose,
+the proposition, All men are mortal, means that the attributes of man
+are _evidence of_, are a _mark_ of, mortality; an indication by which
+the presence of that attribute is made manifest. No men are gods, means
+that the attributes of man are a mark or evidence that some or all of
+the attributes understood to belong to a god are not there; that where
+the former are, we need not expect to find the latter.
+
+These two forms of expression are at bottom equivalent; but the one
+points the attention more directly to what a proposition means, the
+latter to the manner in which it is to be used.
+
+Now it is to be observed that Reasoning (the subject to which we are
+next to proceed) is a process into which propositions enter not as
+ultimate results, but as means to the establishment of other
+propositions. We may expect, therefore, that the mode of exhibiting the
+import of a general proposition which shows it in its application to
+practical use, will best express the function which propositions perform
+in Reasoning. And accordingly, in the theory of Reasoning, the mode of
+viewing the subject which considers a Proposition as asserting that one
+fact or phenomenon is a _mark_ or _evidence_ of another fact or
+phenomenon, will be found almost indispensable. For the purposes of that
+Theory, the best mode of defining the import of a proposition is not the
+mode which shows most clearly what it is in itself, but that which most
+distinctly suggests the manner in which it may be made available for
+advancing from it to other propositions.
+
+
+
+
+CHAPTER VII.
+
+OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
+
+
+§ 1. In examining into the nature of general propositions, we have
+adverted much less than is usual with logicians to the ideas of a Class,
+and Classification; ideas which, since the Realist doctrine of General
+Substances went out of vogue, have formed the basis of almost every
+attempt at a philosophical theory of general terms and general
+propositions. We have considered general names as having a meaning,
+quite independently of their being the names of classes. That
+circumstance is in truth accidental, it being wholly immaterial to the
+signification of the name whether there are many objects, or only one,
+to which it happens to be applicable, or whether there be any at all.
+God is as much a general term to the Christian or Jew as to the
+Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much
+so as if real objects existed, corresponding to those names. Every name
+the signification of which is constituted by attributes, is potentially
+a name of an indefinite number of objects; but it needs not be actually
+the name of any; and if of any, it may be the name of only one. As soon
+as we employ a name to connote attributes, the things, be they more or
+fewer, which happen to possess those attributes, are constituted _ipso
+facto_ a class. But in predicating the name we predicate only the
+attributes; and the fact of belonging to a class does not, in many
+cases, come into view at all.
+
+Although, however, Predication does not presuppose Classification, and
+though the theory of Names and of Propositions is not cleared up, but
+only encumbered, by intruding the idea of classification into it, there
+is nevertheless a close connexion between Classification and the
+employment of General Names. By every general name which we introduce,
+we create a class, if there be any things, real or imaginary, to compose
+it; that is, any Things corresponding to the signification of the name.
+Classes, therefore, mostly owe their existence to general language. But
+general language, also, though that is not the most common case,
+sometimes owes its existence to classes. A general, which is as much as
+to say a significant, name, is indeed mostly introduced because we have
+a signification to express by it; because we need a word by means of
+which to predicate the attributes which it connotes. But it is also true
+that a name is sometimes introduced because we have found it convenient
+to create a class; because we have thought it useful for the regulation
+of our mental operations, that a certain group of objects should be
+thought of together. A naturalist, for purposes connected with his
+particular science, sees reason to distribute the animal or vegetable
+creation into certain groups rather than into any others, and he
+requires a name to bind, as it were, each of his groups together. It
+must not however be supposed that such names, when introduced, differ in
+any respect, as to their mode of signification, from other connotative
+names. The classes which they denote are, as much as any other classes,
+constituted by certain common attributes, and their names are
+significant of those attributes, and of nothing else. The names of
+Cuvier's classes and orders, _Plantigrades_, _Digitigrades_, &c., are as
+much the expression of attributes as if those names had preceded,
+instead of grown out of, his classification of animals. The only
+peculiarity of the case is, that the convenience of classification was
+here the primary motive for introducing the names; while in other cases
+the name is introduced as a means of predication, and the formation of a
+class denoted by it is only an indirect consequence.
+
+The principles which ought to regulate Classification as a logical
+process subservient to the investigation of truth, cannot be discussed
+to any purpose until a much later stage of our inquiry. But, of
+Classification as resulting from, and implied in, the fact of employing
+general language, we cannot forbear to treat here, without leaving the
+theory of general names and of their employment in predication,
+mutilated and formless.
+
+
+§ 2. This portion of the theory of general language is the subject of
+what is termed the doctrine of the Predicables; a set of distinctions
+handed down from Aristotle, and his follower Porphyry, many of which
+have taken a firm root in scientific, and some of them even in popular,
+phraseology. The predicables are a five-fold division of General Names,
+not grounded as usual on a difference in their meaning, that is, in the
+attribute which they connote, but on a difference in the kind of class
+which they denote. We may predicate of a thing five different varieties
+of class-name:--
+
+  A _genus_ of the thing  (_γὲνος_).
+  A _species_             (_εἶδος_).
+  A _differentia_         (_διαφορὰ_).
+  A _proprium_            (_ἴδιόν_).
+  An _accidens_           (_συμβεβηκός_).
+
+It is to be remarked of these distinctions, that they express, not what
+the predicate is in its own meaning, but what relation it bears to the
+subject of which it happens on the particular occasion to be predicated.
+There are not some names which are exclusively genera, and others which
+are exclusively species, or differentiæ; but the same name is referred
+to one or another predicable, according to the subject of which it is
+predicated on the particular occasion. _Animal_, for instance, is a
+genus with respect to man, or John; a species with respect to Substance,
+or Being. _Rectangular_ is one of the Differentiæ of a geometrical
+square; it is merely one of the Accidentia of the table at which I am
+writing. The words genus, species, &c. are therefore relative terms;
+they are names applied to certain predicates, to express the relation
+between them and some given subject: a relation grounded, as we shall
+see, not on what the predicate connotes, but on the class which it
+denotes, and on the place which, in some given classification, that
+class occupies relatively to the particular subject.
+
+
+§ 3. Of these five names, two, Genus and Species, are not only used by
+naturalists in a technical acceptation not precisely agreeing with their
+philosophical meaning, but have also acquired a popular acceptation,
+much more general than either. In this popular sense any two classes,
+one of which includes the whole of the other and more, may be called a
+Genus and a Species. Such, for instance, are Animal and Man; Man and
+Mathematician. Animal is a Genus; Man and Brute are its two species; or
+we may divide it into a greater number of species, as man, horse, dog,
+&c. _Biped_, or _two-footed animal_, may also be considered a genus, of
+which man and bird are two species. _Taste_ is a genus, of which sweet
+taste, sour taste, salt taste, &c. are species. _Virtue_ is a genus;
+justice, prudence, courage, fortitude, generosity, &c. are its species.
+
+The same class which is a genus with reference to the sub-classes or
+species included in it, may be itself a species with reference to a more
+comprehensive, or, as it is often called, a superior genus. Man is a
+species with reference to animal, but a genus with reference to the
+species Mathematician. Animal is a genus, divided into two species, man
+and brute; but animal is also a species, which, with another species,
+vegetable, makes up the genus, organized being. Biped is a genus with
+reference to man and bird, but a species with respect to the superior
+genus, animal. Taste is a genus divided into species, but also a species
+of the genus sensation. Virtue, a genus with reference to justice,
+temperance, &c., is one of the species of the genus, mental quality.
+
+In this popular sense the words Genus and Species have passed into
+common discourse. And it should be observed that in ordinary parlance,
+not the name of the class, but the class itself, is said to be the genus
+or species; not, of course, the class in the sense of each individual of
+the class, but the individuals collectively, considered as an aggregate
+whole; the name by which the class is designated being then called not
+the genus or species, but the generic or specific name. And this is an
+admissible form of expression; nor is it of any importance which of the
+two modes of speaking we adopt, provided the rest of our language is
+consistent with it; but, if we call the class itself the genus, we must
+not talk of predicating the genus. We predicate of man the _name_
+mortal; and by predicating the name, we may be said, in an intelligible
+sense, to predicate what the name expresses, the _attribute_ mortality;
+but in no allowable sense of the word predication do we predicate of man
+the _class_ mortal. We predicate of him the fact of belonging to the
+class.
+
+By the Aristotelian logicians, the terms genus and species were used in
+a more restricted sense. They did not admit every class which could be
+divided into other classes to be a genus, or every class which could be
+included in a larger class to be a species. Animal was by them
+considered a genus; man and brute co-ordinate species under that genus:
+_biped_, however, would not have been admitted to be a genus with
+reference to man, but a _proprium_ or _accidens_ only. It was requisite,
+according to their theory, that genus and species should be of the
+_essence_ of the subject. Animal was of the essence of man; biped was
+not. And in every classification they considered some one class as the
+lowest or _infima_ species. Man, for instance, was a lowest species. Any
+further divisions into which the class might be capable of being broken
+down, as man into white, black, and red man, or into priest and layman,
+they did not admit to be species.
+
+It has been seen, however, in the preceding chapter, that the
+distinction between the essence of a class, and the attributes or
+properties which are not of its essence--a distinction which has given
+occasion to so much abstruse speculation, and to which so mysterious a
+character was formerly, and by many writers is still, attached,--amounts
+to nothing more than the difference between those attributes of the
+class which are, and those which are not, involved in the signification
+of the class-name. As applied to individuals, the word Essence, we
+found, has no meaning, except in connexion with the exploded tenets of
+the Realists; and what the schoolmen chose to call the essence of an
+individual, was simply the essence of the class to which that individual
+was most familiarly referred.
+
+Is there no difference, then, save this merely verbal one, between the
+classes which the schoolmen admitted to be genera or species, and those
+to which they refused the title? Is it an error to regard some of the
+differences which exist among objects as differences _in kind_ (_genere_
+or _specie_), and others only as differences in the accidents? Were the
+schoolmen right or wrong in giving to some of the classes into which
+things may be divided, the name of _kinds_, and considering others as
+secondary divisions, grounded on differences of a comparatively
+superficial nature? Examination will show that the Aristotelians did
+mean something by this distinction, and something important; but which,
+being but indistinctly conceived, was inadequately expressed by the
+phraseology of essences, and the various other modes of speech to which
+they had recourse.
+
+
+§ 4. It is a fundamental principle in logic, that the power of framing
+classes is unlimited, as long as there is any (even the smallest)
+difference to found a distinction upon. Take any attribute whatever, and
+if some things have it, and others have not, we may ground on the
+attribute a division of all things into two classes; and we actually do
+so, the moment we create a name which connotes the attribute. The number
+of possible classes, therefore, is boundless; and there are as many
+actual classes (either of real or of imaginary things) as there are
+general names, positive and negative together.
+
+But if we contemplate any one of the classes so formed, such as the
+class animal or plant, or the class sulphur or phosphorus, or the class
+white or red, and consider in what particulars the individuals included
+in the class differ from those which do not come within it, we find a
+very remarkable diversity in this respect between some classes and
+others. There are some classes, the things contained in which differ
+from other things only in certain particulars which may be numbered,
+while others differ in more than can be numbered, more even than we need
+ever expect to know. Some classes have little or nothing in common to
+characterize them by, except precisely what is connoted by the name:
+white things, for example, are not distinguished by any common
+properties, except whiteness; or if they are, it is only by such as are
+in some way dependent on, or connected with, whiteness. But a hundred
+generations have not exhausted the common properties of animals or of
+plants, of sulphur or of phosphorus; nor do we suppose them to be
+exhaustible, but proceed to new observations and experiments, in the
+full confidence of discovering new properties which were by no means
+implied in those we previously knew. While, if any one were to propose
+for investigation the common properties of all things which are of the
+same colour, the same shape, or the same specific gravity, the absurdity
+would be palpable. We have no ground to believe that any such common
+properties exist, except such as may be shown to be involved in the
+supposition itself, or to be derivable from it by some law of causation.
+It appears, therefore, that the properties, on which we ground our
+classes, sometimes exhaust all that the class has in common, or contain
+it all by some mode of implication; but in other instances we make a
+selection of a few properties from among not only a greater number, but
+a number inexhaustible by us, and to which as we know no bounds, they
+may, so far as we are concerned, be regarded as infinite.
+
+There is no impropriety in saying that, of these two classifications,
+the one answers to a much more radical distinction in the things
+themselves, than the other does. And if any one even chooses to say that
+the one classification is made by nature, the other by us for our
+convenience, he will be right; provided he means no more than this:
+Where a certain apparent difference between things (though perhaps in
+itself of little moment) answers to we know not what number of other
+differences, pervading not only their known properties, but properties
+yet undiscovered, it is not optional but imperative to recognise this
+difference as the foundation of a specific distinction; while, on the
+contrary, differences that are merely finite and determinate, like those
+designated by the words white, black, or red, may be disregarded if the
+purpose for which the classification is made does not require attention
+to those particular properties. The differences, however, are made by
+nature, in both cases; while the recognition of those differences as
+grounds of classification and of naming, is, equally in both cases, the
+act of man: only in the one case, the ends of language and of
+classification would be subverted if no notice were taken of the
+difference, while in the other case, the necessity of taking notice of
+it depends on the importance or unimportance of the particular qualities
+in which the difference happens to consist.
+
+Now, these classes, distinguished by unknown multitudes of properties,
+and not solely by a few determinate ones--which are parted off from one
+another by an unfathomable chasm, instead of a mere ordinary ditch with
+a visible bottom--are the only classes which, by the Aristotelian
+logicians, were considered as genera or species. Differences which
+extended only to a certain property or properties, and there terminated,
+they considered as differences only in the _accidents_ of things; but
+where any class differed from other things by an infinite series of
+differences, known and unknown, they considered the distinction as one
+of _kind_, and spoke of it as being an _essential_ difference, which is
+also one of the current meanings of that vague expression at the present
+day.
+
+Conceiving the schoolmen to have been justified in drawing a broad line
+of separation between these two kinds of classes and of
+class-distinctions, I shall not only retain the division itself, but
+continue to express it in their language. According to that language,
+the proximate (or lowest) Kind to which any individual is referrible, is
+called its species. Conformably to this, Sir Isaac Newton would be said
+to be of the species man. There are indeed numerous sub-classes included
+in the class man, to which Newton also belongs; for example, Christian,
+and Englishman, and Mathematician. But these, though distinct classes,
+are not, in our sense of the term, distinct Kinds of men. A Christian,
+for example, differs from other human beings; but he differs only in the
+attribute which the word expresses, namely, belief in Christianity, and
+whatever else that implies, either as involved in the fact itself, or
+connected with it through some law of cause and effect. We should never
+think of inquiring what properties, unconnected with Christianity either
+as cause or effect, are common to all Christians and peculiar to them;
+while in regard to all Men, physiologists are perpetually carrying on
+such an inquiry; nor is the answer ever likely to be completed. Man,
+therefore, we may call a species; Christian, or Mathematician, we
+cannot.
+
+Note here, that it is by no means intended to imply that there may not
+be different Kinds, or logical species, of man. The various races and
+temperaments, the two sexes, and even the various ages, may be
+differences of kind, within our meaning of the term. I do not say that
+they are so. For in the progress of physiology it may almost be said to
+be made out, that the differences which really exist between different
+races, sexes, &c., follow as consequences, under laws of nature, from a
+small number of primary differences which can be precisely determined,
+and which, as the phrase is, _account for_ all the rest. If this be so,
+these are not distinctions in kind; no more than Christian, Jew,
+Mussulman, and Pagan, a difference which also carries many consequences
+along with it. And in this way classes are often mistaken for real
+Kinds, which are afterwards proved not to be so. But if it turned out
+that the differences were not capable of being thus accounted for, then
+Caucasian, Mongolian, Negro, &c. would be really different Kinds of
+human beings, and entitled to be ranked as species by the logician;
+though not by the naturalist. For (as already noticed) the word species
+is used in a different signification in logic and in natural history. By
+the naturalist, organized beings are not usually said to be of different
+species, if it is supposed that they could possibly have descended from
+the same stock. That, however, is a sense artificially given to the
+word, for the technical purposes of a particular science. To the
+logician, if a negro and a white man differ in the same manner (however
+less in degree) as a horse and a camel do, that is, if their differences
+are inexhaustible, and not referrible to any common cause, they are
+different species, whether they are descended from common ancestors or
+not. But if their differences can all be traced to climate and habits,
+or to some one or a few special differences in structure, they are not,
+in the logician's view, specially distinct.
+
+When the _infima species_, or proximate Kind, to which an individual
+belongs, has been ascertained, the properties common to that Kind
+include necessarily the whole of the common properties of every other
+real Kind to which the individual can be referrible. Let the individual,
+for example, be Socrates, and the proximate Kind, man. Animal, or living
+creature, is also a real Kind, and includes Socrates; but, since it
+likewise includes man, or in other words, since all men are animals, the
+properties common to animals form a portion of the common properties of
+the sub-class, man. And if there be any class which includes Socrates
+without including man, that class is not a real Kind. Let the class for
+example, be _flat-nosed_; that being a class which includes Socrates,
+without including all men. To determine whether it is a real Kind, we
+must ask ourselves this question: Have all flat-nosed animals, in
+addition to whatever is implied in their flat noses, any common
+properties, other than those which are common to all animals whatever?
+If they had; if a flat nose were a mark or index to an indefinite number
+of other peculiarities, not deducible from the former by an
+ascertainable law, then out of the class man we might cut another class,
+flat-nosed man, which according to our definition, would be a Kind. But
+if we could do this, man would not be, as it was assumed to be, the
+proximate Kind. Therefore, the properties of the proximate Kind do
+comprehend those (whether known or unknown) of all other Kinds to which
+the individual belongs; which was the point we undertook to prove. And
+hence, every other Kind which is predicable of the individual, will be
+to the proximate Kind in the relation of a genus, according to even the
+popular acceptation of the terms genus and species; that is, it will be
+a larger class, including it and more.
+
+We are now able to fix the logical meaning of these terms. Every class
+which is a real Kind, that is, which is distinguished from all other
+classes by an indeterminate multitude of properties not derivable from
+one another, is either a genus or a species. A Kind which is not
+divisible into other Kinds, cannot be a genus, because it has no
+species under it; but it is itself a species, both with reference to the
+individuals below and to the genera above (Species Prædicabilis and
+Species Subjicibilis.) But every Kind which admits of division into real
+Kinds (as animal into mammal, bird, fish, &c., or bird into various
+species of birds) is a genus to all below it, a species to all genera in
+which it is itself included. And here we may close this part of the
+discussion, and pass to the three remaining predicables, Differentia,
+Proprium, and Accidens.
+
+
+§ 5. To begin with Differentia. This word is correlative with the words
+genus and species, and as all admit, it signifies the attribute which
+distinguishes a given species from every other species of the same
+genus. This is so far clear: but we may still ask, which of the
+distinguishing attributes it signifies. For we have seen that every Kind
+(and a species must be a Kind) is distinguished from other Kinds not by
+any one attribute, but by an indefinite number. Man, for instance, is a
+species of the genus animal: Rational (or rationality, for it is of no
+consequence here whether we use the concrete or the abstract form) is
+generally assigned by logicians as the Differentia; and doubtless this
+attribute serves the purpose of distinction: but it has also been
+remarked of man, that he is a cooking animal; the only animal that
+dresses its food. This, therefore, is another of the attributes by which
+the species man is distinguished from other species of the same genus:
+would this attribute serve equally well for a differentia? The
+Aristotelians say No; having laid it down that the differentia must,
+like the genus and species, be of the _essence_ of the subject.
+
+And here we lose even that vestige of a meaning grounded in the nature
+of the things themselves, which may be supposed to be attached to the
+word essence when it is said that genus and species must be of the
+essence of the thing. There can be no doubt that when the schoolmen
+talked of the essences of things as opposed to their accidents, they had
+confusedly in view the distinction between differences of kind, and the
+differences which are not of kind; they meant to intimate that genera
+and species must be Kinds. Their notion of the essence of a thing was a
+vague notion of a something which makes it what it is, _i. e._ which
+makes it the Kind of thing that it is--which causes it to have all that
+variety of properties which distinguish its Kind. But when the matter
+came to be looked at more closely, nobody could discover what caused the
+thing to have all those properties, nor even that there was anything
+which caused it to have them. Logicians, however, not liking to admit
+this, and being unable to detect what made the thing to be what it was,
+satisfied themselves with what made it to be what it was called. Of the
+innumerable properties, known and unknown, that are common to the class
+man, a portion only, and of course a very small portion, are connoted by
+its name; these few, however, will naturally have been thus
+distinguished from the rest either for their greater obviousness, or for
+greater supposed importance. These properties, then, which were connoted
+by the name, logicians seized upon, and called them the essence of the
+species; and not stopping there, they affirmed them, in the case of the
+_infima species_, to be the essence of the individual too; for it was
+their maxim, that the species contained the "whole essence" of the
+thing. Metaphysics, that fertile field of delusion propagated by
+language, does not afford a more signal instance of such delusion. On
+this account it was that rationality, being connoted by the name man,
+was allowed to be a differentia of the class; but the peculiarity of
+cooking their food, not being connoted, was relegated to the class of
+accidental properties.
+
+The distinction, therefore, between Differentia, Proprium, and Accidens,
+is not grounded in the nature of things, but in the connotation of
+names; and we must seek it there, if we wish to find what it is.
+
+From the fact that the genus includes the species, in other words
+_de_notes more than the species, or is predicable of a greater number of
+individuals, it follows that the species must connote more than the
+genus. It must connote all the attributes which the genus connotes, or
+there would be nothing to prevent it from denoting individuals not
+included in the genus. And it must connote something besides, otherwise
+it would include the whole genus. Animal denotes all the individuals
+denoted by man, and many more. Man, therefore, must connote all that
+animal connotes, otherwise there might be men who are not animals; and
+it must connote something more than animal connotes, otherwise all
+animals would be men. This surplus of connotation--this which the
+species connotes over and above the connotation of the genus--is the
+Differentia, or specific difference; or, to state the same proposition
+in other words, the Differentia is that which must be added to the
+connotation of the genus, to complete the connotation of the species.
+
+The word man, for instance, exclusively of what it connotes in common
+with animal, also connotes rationality, and at least some approximation
+to that external form which we all know, but which as we have no name
+for it considered in itself, we are content to call the human. The
+Differentia, or specific difference, therefore, of man, as referred to
+the genus animal, is that outward form and the possession of reason. The
+Aristotelians said, the possession of reason, without the outward form.
+But if they adhered to this, they would have been obliged to call the
+Houyhnhnms men. The question never arose, and they were never called
+upon to decide how such a case would have affected their notion of
+essentiality. However this may be, they were satisfied with taking such
+a portion of the differentia as sufficed to distinguish the species from
+all other _existing_ things, though by so doing they might not exhaust
+the connotation of the name.
+
+
+§ 6. And here, to prevent the notion of differentia from being
+restricted within too narrow limits, it is necessary to remark, that a
+species, even as referred to the same genus, will not always have the
+same differentia, but a different one, according to the principle and
+purpose which preside over the particular classification. For example, a
+naturalist surveys the various kinds of animals, and looks out for the
+classification of them most in accordance with the order in which, for
+zoological purposes, he considers it desirable that we should think of
+them. With this view he finds it advisable that one of his fundamental
+divisions should be into warm-blooded and cold-blooded animals; or into
+animals which breathe with lungs and those which breathe with gills; or
+into carnivorous, and frugivorous or graminivorous; or into those which
+walk on the flat part and those which walk on the extremity of the foot,
+a distinction on which two of Cuvier's families are founded. In doing
+this, the naturalist creates as many new classes; which are by no means
+those to which the individual animal is familiarly and spontaneously
+referred; nor should we ever think of assigning to them so prominent a
+position in our arrangement of the animal kingdom, unless for a
+preconceived purpose of scientific convenience. And to the liberty of
+doing this there is no limit. In the examples we have given, most of the
+classes are real Kinds, since each of the peculiarities is an index to a
+multitude of properties belonging to the class which it characterizes:
+but even if the case were otherwise--if the other properties of those
+classes could all be derived, by any process known to us, from the one
+peculiarity on which the class is founded--even then, if these
+derivative properties were of primary importance for the purposes of the
+naturalist, he would be warranted in founding his primary divisions on
+them.
+
+If, however, practical convenience is a sufficient warrant for making
+the main demarcations in our arrangement of objects run in lines not
+coinciding with any distinction of Kind, and so creating genera and
+species in the popular sense which are not genera or species in the
+rigorous sense at all, _à fortiori_ must we be warranted, when our
+genera and species _are_ real genera and species, in marking the
+distinction between them by those of their properties which
+considerations of practical convenience most strongly recommend. If we
+cut a species out of a given genus--the species man, for instance, out
+of the genus animal--with an intention on our part that the peculiarity
+by which we are to be guided in the application of the name man should
+be rationality, then rationality is the differentia of the species man.
+Suppose, however, that being naturalists, we, for the purposes of our
+particular study, cut out of the genus animal the same species man, but
+with an intention that the distinction between man and all other species
+of animal should be, not rationality, but the possession of "four
+incisors in each jaw, tusks solitary, and erect posture." It is evident
+that the word man, when used by us as naturalists, no longer connotes
+rationality, but connotes the three other properties specified; for that
+which we have expressly in view when we impose a name, assuredly forms
+part of the meaning of that name. We may, therefore, lay it down as a
+maxim, that wherever there is a Genus, and a Species marked out from
+that genus by an assignable differentia, the name of the species must be
+connotative, and must connote the differentia; but the connotation may
+be special--not involved in the signification of the term as ordinarily
+used, but given to it when employed as a term of art or science. The
+word Man in common use, connotes rationality and a certain form, but
+does not connote the number or character of the teeth; in the Linnæan
+system it connotes the number of incisor and canine teeth, but does not
+connote rationality nor any particular form. The word _man_ has,
+therefore, two different meanings; though not commonly considered as
+ambiguous, because it happens in both cases to _de_note the same
+individual objects. But a case is conceivable in which the ambiguity
+would become evident: we have only to imagine that some new kind of
+animal were discovered, having Linnæus's three characteristics of
+humanity, but not rational, or not of the human form. In ordinary
+parlance, these animals would not be called men; but in natural history
+they must still be called so by those, if any there be, who adhere to
+the Linnæan classification; and the question would arise, whether the
+word should continue to be used in two senses, or the classification be
+given up, and the technical sense of the term be abandoned along with
+it.
+
+Words not otherwise connotative may, in the mode just adverted to,
+acquire a special or technical connotation. Thus the word whiteness, as
+we have so often remarked, connotes nothing; it merely denotes the
+attribute corresponding to a certain sensation: but if we are making a
+classification of colours, and desire to justify, or even merely to
+point out, the particular place assigned to whiteness in our
+arrangement, we may define it "the colour produced by the mixture of all
+the simple rays;" and this fact, though by no means implied in the
+meaning of the word whiteness as ordinarily used, but only known by
+subsequent scientific investigation, is part of its meaning in the
+particular essay or treatise, and becomes the differentia of the
+species.[26]
+
+The differentia, therefore, of a species may be defined to be, that part
+of the connotation of the specific name, whether ordinary or special and
+technical, which distinguishes the species in question from all other
+species of the genus to which on the particular occasion we are
+referring it.
+
+
+§ 7. Having disposed of Genus, Species, and Differentia, we shall not
+find much difficulty in attaining a clear conception of the distinction
+between the other two predicables, as well as between them and the first
+three.
+
+In the Aristotelian phraseology, Genus and Differentia are of the
+_essence_ of the subject; by which, as we have seen, is really meant
+that the properties signified by the genus and those signified by the
+differentia, form part of the connotation of the name denoting the
+species. Proprium and Accidens, on the other hand, form no part of the
+essence, but are predicated of the species only _accidentally_. Both are
+Accidents, in the wider sense in which the accidents of a thing are
+opposed to its essence; though, in the doctrine of the Predicables,
+Accidens is used for one sort of accident only, Proprium being another
+sort. Proprium, continue the schoolmen, is predicated _accidentally_,
+indeed, but _necessarily_; or, as they further explain it, signifies an
+attribute which is not indeed part of the essence, but which flows from,
+or is a consequence of, the essence, and is, therefore, inseparably
+attached to the species; _e. g._ the various properties of a triangle,
+which, though no part of its definition, must necessarily be possessed
+by whatever comes under that definition. Accidens, on the contrary, has
+no connexion whatever with the essence, but may come and go, and the
+species still remain what it was before. If a species could exist
+without its Propria, it must be capable of existing without that on
+which its Propria are necessarily consequent, and therefore without its
+essence, without that which constitutes it a species. But an Accidens,
+whether separable or inseparable from the species in actual experience,
+may be supposed separated, without the necessity of supposing any other
+alteration; or at least, without supposing any of the essential
+properties of the species to be altered, since with them an Accidens has
+no connexion.
+
+A Proprium, therefore, of the species, may be defined, any attribute
+which belongs to all the individuals included in the species, and which,
+though not connoted by the specific name, (either ordinarily if the
+classification we are considering be for ordinary purposes, or specially
+if it be for a special purpose,) yet follows from some attribute which
+the name either ordinarily or specially connotes.
+
+One attribute may follow from another in two ways; and there are
+consequently two kinds of Proprium. It may follow as a conclusion
+follows premises, or it may follow as an effect follows a cause. Thus,
+the attribute of having the opposite sides equal, which is not one of
+those connoted by the word Parallelogram, nevertheless follows from
+those connoted by it, namely, from having the opposite sides straight
+lines and parallel, and the number of sides four. The attribute,
+therefore, of having the opposite sides equal, is a Proprium of the
+class parallelogram; and a Proprium of the first kind, which follows
+from the connoted attributes by way of _demonstration_. The attribute of
+being capable of understanding language, is a Proprium of the species
+man, since without being connoted by the word, it follows from an
+attribute which the word does connote, viz. from the attribute of
+rationality. But this is a Proprium of the second kind, which follows by
+way of _causation_. How it is that one property of a thing follows, or
+can be inferred, from another; under what conditions this is possible,
+and what is the exact meaning of the phrase; are among the questions
+which will occupy us in the two succeeding Books. At present it needs
+only be said, that whether a Proprium follows by demonstration or by
+causation, it follows _necessarily_; that is to say, its not following
+would be inconsistent with some law which we regard as a part of the
+constitution either of our thinking faculty or of the universe.
+
+
+§ 8. Under the remaining predicable, Accidens, are included all
+attributes of a thing which are neither involved in the signification of
+the name (whether ordinarily or as a term of art), nor have, so far as
+we know, any necessary connexion with attributes which are so involved.
+They are commonly divided into Separable and Inseparable Accidents.
+Inseparable accidents are those which--although we know of no connexion
+between them and the attributes constitutive of the species, and
+although, therefore, so far as we are aware, they might be absent
+without making the name inapplicable and the species a different
+species--are yet never in fact known to be absent. A concise mode of
+expressing the same meaning is, that inseparable accidents are
+properties which are universal to the species, but not necessary to it.
+Thus, blackness is an attribute of a crow, and, as far as we know, an
+universal one. But if we were to discover a race of white birds, in
+other respects resembling crows, we should not say, These are not crows;
+we should say, These are white crows. Crow, therefore, does not connote
+blackness; nor, from any of the attributes which it does connote,
+whether as a word in popular use or as a term of art, could blackness be
+inferred. Not only, therefore, can we conceive a white crow, but we know
+of no reason why such an animal should not exist. Since, however, none
+but black crows are known to exist, blackness, in the present state of
+our knowledge, ranks as an accident, but an inseparable accident, of
+the species crow.
+
+Separable Accidents are those which are found, in point of fact, to be
+sometimes absent from the species; which are not only not necessary, but
+not even universal. They are such as do not belong to every individual
+of the species, but only to some individuals; or if to all, not at all
+times. Thus the colour of an European is one of the separable accidents
+of the species man, because it is not an attribute of all human
+creatures. Being born, is also (speaking in the logical sense) a
+separable accident of the species man, because, though an attribute of
+all human beings, it is so only at one particular time. _À fortiori_
+those attributes which are not constant even in the same individual, as,
+to be in one or in another place, to be hot or cold, sitting or walking,
+must be ranked as separable accidents.
+
+
+
+
+CHAPTER VIII.
+
+OF DEFINITION.
+
+
+§ 1. One necessary part of the theory of Names and of Propositions
+remains to be treated of in this place: the theory of Definitions. As
+being the most important of the class of propositions which we have
+characterized as purely verbal, they have already received some notice
+in the chapter preceding the last. But their fuller treatment was at
+that time postponed, because definition is so closely connected with
+classification, that, until the nature of the latter process is in some
+measure understood, the former cannot be discussed to much purpose.
+
+The simplest and most correct notion of a Definition is, a proposition
+declaratory of the meaning of a word; namely, either the meaning which
+it bears in common acceptation, or that which the speaker or writer, for
+the particular purposes of his discourse, intends to annex to it.
+
+The definition of a word being the proposition which enunciates its
+meaning, words which have no meaning are unsusceptible of definition.
+Proper names, therefore, cannot be defined. A proper name being a mere
+mark put upon an individual, and of which it is the characteristic
+property to be destitute of meaning, its meaning cannot of course be
+declared; though we may indicate by language, as we might indicate still
+more conveniently by pointing with the finger, upon what individual that
+particular mark has been, or is intended to be, put. It is no definition
+of "John Thomson" to say he is "the son of General Thomson;" for the
+name John Thomson does not express this. Neither is it any definition of
+"John Thomson" to say he is "the man now crossing the street." These
+propositions may serve to make known who is the particular man to whom
+the name belongs, but that may be done still more unambiguously by
+pointing to him, which, however, has not been esteemed one of the modes
+of definition.
+
+In the case of connotative names, the meaning, as has been so often
+observed, is the connotation; and the definition of a connotative name,
+is the proposition which declares its connotation. This might be done
+either directly or indirectly. The direct mode would be by a proposition
+in this form: "Man" (or whatsoever the word may be) "is a name connoting
+such and such attributes," or "is a name which, when predicated of
+anything, signifies the possession of such and such attributes by that
+thing." Or thus: Man is everything which possesses such and such
+attributes: Man is everything which possesses corporeity, organization,
+life, rationality, and certain peculiarities of external form.
+
+This form of definition is the most precise and least equivocal of any;
+but it is not brief enough, and is besides too technical for common
+discourse. The more usual mode of declaring the connotation of a name,
+is to predicate of it another name or names of known signification,
+which connote the same aggregation of attributes. This may be done
+either by predicating of the name intended to be defined, another
+connotative name exactly synonymous, as, "Man is a human being," which
+is not commonly accounted a definition at all; or by predicating two or
+more connotative names, which make up among them the whole connotation
+of the name to be defined. In this last case, again, we may either
+compose our definition of as many connotative names as there are
+attributes, each attribute being connoted by one, as, Man is a
+corporeal, organized, animated, rational being, shaped so and so; or we
+may employ names which connote several of the attributes at once, as,
+Man is a rational _animal_, shaped so and so.
+
+The definition of a name, according to this view of it, is the sum total
+of all the _essential_ propositions which can be framed with that name
+for their subject. All propositions the truth of which is implied in the
+name, all those which we are made aware of by merely hearing the name,
+are included in the definition, if complete, and may be evolved from it
+without the aid of any other premises; whether the definition expresses
+them in two or three words, or in a larger number. It is, therefore, not
+without reason that Condillac and other writers have affirmed a
+definition to be an _analysis_. To resolve any complex whole into the
+elements of which it is compounded, is the meaning of analysis: and this
+we do when we replace one word which connotes a set of attributes
+collectively, by two or more which connote the same attributes singly,
+or in smaller groups.
+
+
+§ 2. From this, however, the question naturally arises, in what manner
+are we to define a name which connotes only a single attribute: for
+instance, "white," which connotes nothing but whiteness; "rational,"
+which connotes nothing but the possession of reason. It might seem that
+the meaning of such names could only be declared in two ways; by a
+synonymous term, if any such can be found; or in the direct way already
+alluded to: "White is a name connoting the attribute whiteness." Let us
+see, however, whether the analysis of the meaning of the name, that is,
+the breaking down of that meaning into several parts, admits of being
+carried farther. Without at present deciding this question as to the
+word _white_, it is obvious that in the case of _rational_ some further
+explanation may be given of its meaning than is contained in the
+proposition, "Rational is that which possesses the attribute of reason;"
+since the attribute reason itself admits of being defined. And here we
+must turn our attention to the definitions of attributes, or rather of
+the names of attributes, that is, of abstract names.
+
+In regard to such names of attributes as are connotative, and express
+attributes of those attributes, there is no difficulty: like other
+connotative names they are defined by declaring their connotation. Thus,
+the word _fault_ may be defined, "a quality productive of evil or
+inconvenience." Sometimes, again, the attribute to be defined is not one
+attribute, but an union of several: we have only, therefore, to put
+together the names of all the attributes taken separately, and we obtain
+the definition of the name which belongs to them all taken together; a
+definition which will correspond exactly to that of the corresponding
+concrete name. For, as we define a concrete name by enumerating the
+attributes which it connotes, and as the attributes connoted by a
+concrete name form the entire signification of the corresponding
+abstract name, the same enumeration will serve for the definition of
+both. Thus, if the definition of _a human being_ be this, "a being,
+corporeal, animated, rational, shaped so and so," the definition of
+_humanity_ will be corporeity and animal life, combined with
+rationality, and with such and such a shape.
+
+When, on the other hand, the abstract name does not express a
+complication of attributes, but a single attribute, we must remember
+that every attribute is grounded on some fact or phenomenon, from which,
+and which alone, it derives its meaning. To that fact or phenomenon,
+called in a former chapter the foundation of the attribute, we must,
+therefore, have recourse for its definition. Now, the foundation of the
+attribute may be a phenomenon of any degree of complexity, consisting of
+many different parts, either coexistent or in succession. To obtain a
+definition of the attribute, we must analyse the phenomenon into these
+parts. Eloquence, for example, is the name of one attribute only; but
+this attribute is grounded on external effects of a complicated nature,
+flowing from acts of the person to whom we ascribed the attribute; and
+by resolving this phenomenon of causation into its two parts, the cause
+and the effect, we obtain a definition of eloquence, viz. the power of
+influencing the feelings by speech or writing.
+
+A name, therefore, whether concrete or abstract, admits of definition,
+provided we are able to analyse, that is, to distinguish into parts, the
+attribute or set of attributes which constitute the meaning both of the
+concrete name and of the corresponding abstract: if a set of attributes,
+by enumerating them; if a single attribute, by dissecting the fact or
+phenomenon (whether of perception or of internal consciousness) which is
+the foundation of the attribute. But, further, even when the fact is one
+of our simple feelings or states of consciousness, and therefore
+unsusceptible of analysis, the names both of the object and of the
+attribute still admit of definition: or rather, would do so if all our
+simple feelings had names. Whiteness may be defined, the property or
+power of exciting the sensation of white. A white object may be defined,
+an object which excites the sensation of white. The only names which are
+unsusceptible of definition, because their meaning is unsusceptible of
+analysis, are the names of the simple feelings themselves. These are in
+the same condition as proper names. They are not indeed, like proper
+names, unmeaning; for the words _sensation of white_ signify, that the
+sensation which I so denominate resembles other sensations which I
+remember to have had before, and to have called by that name. But as we
+have no words by which to recal those former sensations, except the very
+word which we seek to define, or some other which, being exactly
+synonymous with it, requires definition as much, words cannot unfold the
+signification of this class of names; and we are obliged to make a
+direct appeal to the personal experience of the individual whom we
+address.
+
+
+§ 3. Having stated what seems to be the true idea of a Definition, we
+proceed to examine some opinions of philosophers, and some popular
+conceptions on the subject, which conflict more or less with that idea.
+
+The only adequate definition of a name is, as already remarked, one
+which declares the facts, and the whole of the facts, which the name
+involves in its signification. But with most persons the object of a
+definition does not embrace so much; they look for nothing more, in a
+definition, than a guide to the correct use of the term--a protection
+against applying it in a manner inconsistent with custom and convention.
+Anything, therefore, is to them a sufficient definition of a term, which
+will serve as a correct index to what the term denotes; though not
+embracing the whole, and sometimes, perhaps, not even any part, of what
+it connotes. This gives rise to two sorts of imperfect, or unscientific
+definition; Essential but incomplete Definitions, and Accidental
+Definitions, or Descriptions. In the former, a connotative name is
+defined by a part only of its connotation; in the latter, by something
+which forms no part of the connotation at all.
+
+An example of the first kind of imperfect definitions is the
+following:--Man is a rational animal. It is impossible to consider this
+as a complete definition of the word Man, since (as before remarked) if
+we adhered to it we should be obliged to call the Houyhnhnms men; but as
+there happen to be no Houyhnhnms, this imperfect definition is
+sufficient to mark out and distinguish from all other things, the
+objects at present denoted by "man;" all the beings actually known to
+exist, of whom the name is predicable. Though the word is defined by
+some only among the attributes which it connotes, not by all, it happens
+that all known objects which possess the enumerated attributes, possess
+also those which are omitted; so that the field of predication which the
+word covers, and the employment of it which is conformable to usage, are
+as well indicated by the inadequate definition as by an adequate one.
+Such definitions, however, are always liable to be overthrown by the
+discovery of new objects in nature.
+
+Definitions of this kind are what logicians have had in view, when they
+laid down the rule, that the definition of a species should be _per
+genus et differentiam_. Differentia being seldom taken to mean the whole
+of the peculiarities constitutive of the species, but some one of those
+peculiarities only, a complete definition would be _per genus et
+differentias_, rather than _differentiam_. It would include, with the
+name of the superior genus, not merely _some_ attribute which
+distinguishes the species intended to be defined from all other species
+of the same genus, but _all_ the attributes implied in the name of the
+species, which the name of the superior genus has not already implied.
+The assertion, however, that a definition must of necessity consist of a
+genus and differentiæ, is not tenable. It was early remarked by
+logicians, that the _summum genus_ in any classification, having no
+genus superior to itself, could not be defined in this manner. Yet we
+have seen that all names, except those of our elementary feelings, are
+susceptible of definition in the strictest sense; by setting forth in
+words the constituent parts of the fact or phenomenon, of which the
+connotation of every word is ultimately composed.
+
+
+§ 4. Although the first kind of imperfect definition, (which defines a
+connotative term by a part only of what it connotes, but a part
+sufficient to mark out correctly the boundaries of its denotation,) has
+been considered by the ancients, and by logicians in general, as a
+complete definition; it has always been deemed necessary that the
+attributes employed should really form part of the connotation; for the
+rule was that the definition must be drawn from the _essence_ of the
+class; and this would not have been the case if it had been in any
+degree made up of attributes not connoted by the name. The second kind
+of imperfect definition, therefore, in which the name of a class is
+defined by any of its accidents,--that is, by attributes which are not
+included in its connotation,--has been rejected from the rank of genuine
+Definition by all logicians, and has been termed Description.
+
+This kind of imperfect definition, however, takes its rise from the same
+cause as the other, namely, the willingness to accept as a definition
+anything which, whether it expounds the meaning of the name or not,
+enables us to discriminate the things denoted by the name from all other
+things, and consequently to employ the term in predication without
+deviating from established usage. This purpose is duly answered by
+stating any (no matter what) of the attributes which are common to the
+whole of the class, and peculiar to it; or any combination of attributes
+which happens to be peculiar to it, though separately each of those
+attributes may be common to it with some other things. It is only
+necessary that the definition (or description) thus formed, should be
+_convertible_ with the name which it professes to define; that is,
+should be exactly co-extensive with it, being predicable of everything
+of which it is predicable, and of nothing of which it is not predicable;
+though the attributes specified may have no connexion with those which
+mankind had in view when they formed or recognised the class, and gave
+it a name. The following are correct definitions of Man, according to
+this test: Man is a mammiferous animal, having (by nature) two hands
+(for the human species answers to this description, and no other animal
+does): Man is an animal who cooks his food: Man is a featherless biped.
+
+What would otherwise be a mere description, may be raised to the rank of
+a real definition by the peculiar purpose which the speaker or writer
+has in view. As was seen in the preceding chapter, it may, for the ends
+of a particular art or science, or for the more convenient statement of
+an author's particular doctrines, be advisable to give to some general
+name, without altering its denotation, a special connotation, different
+from its ordinary one. When this is done, a definition of the name by
+means of the attributes which make up the special connotation, though in
+general a mere accidental definition or description, becomes on the
+particular occasion and for the particular purpose a complete and
+genuine definition. This actually occurs with respect to one of the
+preceding examples, "Man is a mammiferous animal having two hands,"
+which is the scientific definition of man, considered as one of the
+species in Cuvier's distribution of the animal kingdom.
+
+In cases of this sort, though the definition is still a declaration of
+the meaning which in the particular instance the name is appointed to
+convey, it cannot be said that to state the meaning of the word is the
+purpose of the definition. The purpose is not to expound a name, but a
+classification. The special meaning which Cuvier assigned to the word
+Man, (quite foreign to its ordinary meaning, though involving no change
+in the denotation of the word,) was incidental to a plan of arranging
+animals into classes on a certain principle, that is, according to a
+certain set of distinctions. And since the definition of Man according
+to the ordinary connotation of the word, though it would have answered
+every other purpose of a definition, would not have pointed out the
+place which the species ought to occupy in that particular
+classification; he gave the word a special connotation, that he might be
+able to define it by the kind of attributes on which, for reasons of
+scientific convenience, he had resolved to found his division of
+animated nature.
+
+Scientific definitions, whether they are definitions of scientific
+terms, or of common terms used in a scientific sense, are almost always
+of the kind last spoken of: their main purpose is to serve as the
+landmarks of scientific classification. And since the classifications in
+any science are continually modified as scientific knowledge advances,
+the definitions in the sciences are also constantly varying. A striking
+instance is afforded by the words Acid and Alkali, especially the
+former. As experimental discovery advanced, the substances classed with
+acids have been constantly multiplying, and by a natural consequence the
+attributes connoted by the word have receded and become fewer. At first
+it connoted the attributes, of combining with an alkali to form a
+neutral substance (called a salt); being compounded of a base and
+oxygen; causticity to the taste and touch; fluidity, &c. The true
+analysis of muriatic acid, into chlorine and hydrogen, caused the second
+property, composition from a base and oxygen, to be excluded from the
+connotation. The same discovery fixed the attention of chemists upon
+hydrogen as an important element in acids; and more recent discoveries
+having led to the recognition of its presence in sulphuric, nitric, and
+many other acids, where its existence was not previously suspected,
+there is now a tendency to include the presence of this element in the
+connotation of the word. But carbonic acid, silica, sulphurous acid,
+have no hydrogen in their composition; that property cannot therefore be
+connoted by the term, unless those substances are no longer to be
+considered acids. Causticity and fluidity have long since been excluded
+from the characteristics of the class, by the inclusion of silica and
+many other substances in it; and the formation of neutral bodies by
+combination with alkalis, together with such electro-chemical
+peculiarities as this is supposed to imply, are now the only
+_differentiæ_ which form the fixed connotation of the word Acid, as a
+term of chemical science.
+
+What is true of the definition of any term of science, is of course true
+of the definition of a science itself: and accordingly, (as observed in
+the Introductory Chapter of this work,) the definition of a science must
+necessarily be progressive and provisional. Any extension of knowledge
+or alteration in the current opinions respecting the subject matter, may
+lead to a change more or less extensive in the particulars included in
+the science; and its composition being thus altered, it may easily
+happen that a different set of characteristics will be found better
+adapted as differentiæ for defining its name.
+
+In the same manner in which a special or technical definition has for
+its object to expound the artificial classification out of which it
+grows; the Aristotelian logicians seem to have imagined that it was also
+the business of ordinary definition to expound the ordinary, and what
+they deemed the natural, classification of things, namely, the division
+of them into Kinds; and to show the place which each Kind occupies, as
+superior, collateral, or subordinate, among other Kinds. This notion
+would account for the rule that all definition must necessarily be _per
+genus et differentiam_, and would also explain why a single differentia
+was deemed sufficient. But to expound, or express in words, a
+distinction of Kind, has already been shown to be an impossibility: the
+very meaning of a Kind is, that the properties which distinguish it do
+not grow out of one another, and cannot therefore be set forth in words,
+even by implication, otherwise than by enumerating them all: and all are
+not known, nor are ever likely to be so. It is idle, therefore, to look
+to this as one of the purposes of a definition: while, if it be only
+required that the definition of a Kind should indicate what Kinds
+include it or are included by it, any definitions which expound the
+connotation of the names will do this: for the name of each class must
+necessarily connote enough of its properties to fix the boundaries of
+the class. If the definition, therefore, be a full statement of the
+connotation, it is all that a definition can be required to be.
+
+
+§ 5. Of the two incomplete and popular modes of definition, and in what
+they differ from the complete or philosophical mode, enough has now been
+said. We shall next examine an ancient doctrine, once generally
+prevalent and still by no means exploded, which I regard as the source
+of a great part of the obscurity hanging over some of the most important
+processes of the understanding in the pursuit of truth. According to
+this, the definitions of which we have now treated are only one of two
+sorts into which definitions may be divided, viz. definitions of names,
+and definitions of things. The former are intended to explain the
+meaning of a term; the latter, the nature of a thing; the last being
+incomparably the most important.
+
+This opinion was held by the ancient philosophers, and by their
+followers, with the exception of the Nominalists; but as the spirit of
+modern metaphysics, until a recent period, has been on the whole a
+Nominalist spirit, the notion of definitions of things has been to a
+certain extent in abeyance, still continuing, however, to breed
+confusion in logic, by its consequences indeed rather than by itself.
+Yet the doctrine in its own proper form now and then breaks out, and has
+appeared (among other places) where it was scarcely to be expected, in a
+justly admired work, Archbishop Whately's _Logic_.[27] In a review of
+that work published by me in the _Westminster Review_ for January 1828,
+and containing some opinions which I no longer entertain, I find the
+following observations on the question now before us; observations with
+which my present view of that question is still sufficiently in
+accordance.
+
+"The distinction between nominal and real definitions, between
+definitions of words and what are called definitions of things, though
+conformable to the ideas of most of the Aristotelian logicians, cannot,
+as it appears to us, be maintained. We apprehend that no definition is
+ever intended to 'explain and unfold the nature of a thing.' It is some
+confirmation of our opinion, that none of those writers who have thought
+that there were definitions of things, have ever succeeded in
+discovering any criterion by which the definition of a thing can be
+distinguished from any other proposition relating to the thing. The
+definition, they say, unfolds the nature of the thing: but no definition
+can unfold its whole nature; and every proposition in which any quality
+whatever is predicated of the thing, unfolds some part of its nature.
+The true state of the case we take to be this. All definitions are of
+names, and of names only; but, in some definitions, it is clearly
+apparent, that nothing is intended except to explain the meaning of the
+word; while in others, besides explaining the meaning of the word, it is
+intended to be implied that there exists a thing, corresponding to the
+word. Whether this be or be not implied in any given case, cannot be
+collected from the mere form of the expression. 'A centaur is an animal
+with the upper parts of a man and the lower parts of a horse,' and 'A
+triangle is a rectilineal figure with three sides,' are, in form,
+expressions precisely similar; although in the former it is not implied
+that any _thing_, conformable to the term, really exists, while in the
+latter it is; as may be seen by substituting, in both definitions, the
+word _means_ for _is_. In the first expression, 'A centaur means an
+animal,' &c., the sense would remain unchanged: in the second, 'A
+triangle means,' &c., the meaning would be altered, since it would be
+obviously impossible to deduce any of the truths of geometry from a
+proposition expressive only of the manner in which we intend to employ a
+particular sign.
+
+"There are, therefore, expressions, commonly passing for definitions,
+which include in themselves more than the mere explanation of the
+meaning of a term. But it is not correct to call an expression of this
+sort a peculiar kind of definition. Its difference from the other kind
+consists in this, that it is not a definition, but a definition and
+something more. The definition above given of a triangle, obviously
+comprises not one, but two propositions, perfectly distinguishable. The
+one is, 'There may exist a figure, bounded by three straight lines;' the
+other, 'And this figure may be termed a triangle.' The former of these
+propositions is not a definition at all: the latter is a mere nominal
+definition, or explanation of the use and application of a term. The
+first is susceptible of truth or falsehood, and may therefore be made
+the foundation of a train of reasoning. The latter can neither be true
+nor false; the only character it is susceptible of is that of conformity
+or disconformity to the ordinary usage of language."
+
+There is a real distinction, then, between definitions of names, and
+what are erroneously called definitions of things; but it is, that the
+latter, along with the meaning of a name, covertly asserts a matter of
+fact. This covert assertion is not a definition, but a postulate. The
+definition is a mere identical proposition, which gives information only
+about the use of language, and from which no conclusions affecting
+matters of fact can possibly be drawn. The accompanying postulate, on
+the other hand, affirms a fact, which may lead to consequences of every
+degree of importance. It affirms the actual or possible existence of
+Things possessing the combination of attributes set forth in the
+definition; and this, if true, may be foundation sufficient on which to
+build a whole fabric of scientific truth.
+
+We have already made, and shall often have to repeat, the remark, that
+the philosophers who overthrew Realism by no means got rid of the
+consequences of Realism, but retained long afterwards, in their own
+philosophy, numerous propositions which could only have a rational
+meaning as part of a Realistic system. It had been handed down from
+Aristotle, and probably from earlier times, as an obvious truth, that
+the science of Geometry is deduced from definitions. This, so long as a
+definition was considered to be a proposition "unfolding the nature of
+the thing," did well enough. But Hobbes followed, and rejected utterly
+the notion that a definition declares the nature of the thing, or does
+anything but state the meaning of a name; yet he continued to affirm as
+broadly as any of his predecessors, that the _ἀρχαὶ_, _principia_, or
+original premises of mathematics, and even of all science, are
+definitions; producing the singular paradox, that systems of scientific
+truth, nay, all truths whatever at which we arrive by reasoning, are
+deduced from the arbitrary conventions of mankind concerning the
+signification of words.
+
+To save the credit of the doctrine that definitions are the premises of
+scientific knowledge, the proviso is sometimes added, that they are so
+only under a certain condition, namely, that they be framed conformably
+to the phenomena of nature; that is, that they ascribe such meanings to
+terms as shall suit objects actually existing. But this is only an
+instance of the attempt so often made, to escape from the necessity of
+abandoning old language after the ideas which it expresses have been
+exchanged for contrary ones. From the meaning of a name (we are told) it
+is possible to infer physical facts, provided the name has corresponding
+to it an existing thing. But if this proviso be necessary, from which of
+the two is the inference really drawn? From the existence of a thing
+having the properties, or from the existence of a name meaning them?
+
+Take, for instance, any of the definitions laid down as premises in
+Euclid's Elements; the definition, let us say, of a circle. This, being
+analysed, consists of two propositions; the one an assumption with
+respect to a matter of fact, the other a genuine definition. "A figure
+may exist, having all the points in the line which bounds it equally
+distant from a single point within it:" "Any figure possessing this
+property is called a circle." Let us look at one of the demonstrations
+which are said to depend on this definition, and observe to which of the
+two propositions contained in it the demonstration really appeals.
+"About the centre A, describe the circle B C D." Here is an assumption
+that a figure, such as the definition expresses, _may_ be described;
+which is no other than the postulate, or covert assumption, involved in
+the so-called definition. But whether that figure be called a circle or
+not is quite immaterial. The purpose would be as well answered, in all
+respects except brevity, were we to say, "Through the point B, draw a
+line returning into itself, of which every point shall be at an equal
+distance from the point A." By this the definition of a circle would be
+got rid of, and rendered needless; but not the postulate implied in it;
+without that the demonstration could not stand. The circle being now
+described, let us proceed to the consequence. "Since B C D is a circle,
+the radius B A is equal to the radius C A." B A is equal to C A, not
+because B C D is a circle, but because B C D is a figure with the radii
+equal. Our warrant for assuming that such a figure about the centre A,
+with the radius B A, may be made to exist, is the postulate. Whether the
+admissibility of these postulates rests on intuition, or on proof, may
+be a matter of dispute; but in either case they are the premises on
+which the theorems depend; and while these are retained it would make no
+difference in the certainty of geometrical truths, though every
+definition in Euclid, and every technical term therein defined, were
+laid aside.
+
+It is, perhaps, superfluous to dwell at so much length on what is so
+nearly self-evident; but when a distinction, obvious as it may appear,
+has been confounded, and by powerful intellects, it is better to say too
+much than too little for the purpose of rendering such mistakes
+impossible in future. I will, therefore, detain the reader while I point
+out one of the absurd consequences flowing from the supposition that
+definitions, as such, are the premises in any of our reasonings, except
+such as relate to words only. If this supposition were true, we might
+argue correctly from true premises, and arrive at a false conclusion. We
+should only have to assume as a premise the definition of a nonentity;
+or rather of a name which has no entity corresponding to it. Let this,
+for instance, be our definition:
+
+  A dragon is a serpent breathing flame.
+
+This proposition, considered only as a definition, is indisputably
+correct. A dragon _is_ a serpent breathing flame: the word _means_ that.
+The tacit assumption, indeed, (if there were any such understood
+assertion), of the existence of an object with properties corresponding
+to the definition, would, in the present instance, be false. Out of this
+definition we may carve the premises of the following syllogism:
+
+  A dragon is a thing which breathes flame:
+  A dragon is a serpent:
+
+From which the conclusion is,
+
+  Therefore some serpent or serpents breathe flame:--
+
+an unexceptionable syllogism in the first mode of the third figure, in
+which both premises are true and yet the conclusion false; which every
+logician knows to be an absurdity. The conclusion being false and the
+syllogism correct, the premises cannot be true. But the premises,
+considered as parts of a definition, are true. Therefore, the premises
+considered as parts of a definition cannot be the real ones. The real
+premises must be--
+
+  A dragon is a _really existing_ thing which breathes flame:
+  A dragon is a _really existing_ serpent:
+
+which implied premises being false, the falsity of the conclusion
+presents no absurdity.
+
+If we would determine what conclusion follows from the same ostensible
+premises when the tacit assumption of real existence is left out, let
+us, according to the recommendation in a previous page, substitute
+_means_ for _is_. We then have--
+
+  Dragon is _a word meaning_ a thing which breathes flame:
+  Dragon is _a word meaning_ a serpent:
+
+From which the conclusion is,
+
+  Some _word or words which mean_ a serpent, also mean a thing which
+  breathes flame:
+
+where the conclusion (as well as the premises) is true, and is the only
+kind of conclusion which can ever follow from a definition, namely, a
+proposition relating to the meaning of words.
+
+There is still another shape into which we may transform this syllogism.
+We may suppose the middle term to be the designation neither of a thing
+nor of a name, but of an idea. We then have--
+
+  The _idea of_ a dragon is _an idea of_ a thing which breathes
+    flame:
+  The _idea of_ a dragon is _an idea of_ a serpent:
+  Therefore, there is _an idea of_ a serpent, which is _an idea of_
+    a thing breathing flame.
+
+Here the conclusion is true, and also the premises; but the premises are
+not definitions. They are propositions affirming that an idea existing
+in the mind, includes certain ideal elements. The truth of the
+conclusion follows from the existence of the psychological phenomenon
+called the idea of a dragon; and therefore still from the tacit
+assumption of a matter of fact.[28]
+
+When, as in this last syllogism, the conclusion is a proposition
+respecting an idea, the assumption on which it depends may be merely
+that of the existence of an idea. But when the conclusion is a
+proposition concerning a Thing, the postulate involved in the definition
+which stands as the apparent premise, is the existence of a thing
+conformable to the definition, and not merely of an idea conformable to
+it. This assumption of real existence will always convey the impression
+that we intend to make, when we profess to define any name which is
+already known to be a name of really existing objects. On this account
+it is, that the assumption was not necessarily implied in the definition
+of a dragon, while there was no doubt of its being included in the
+definition of a circle.
+
+
+§ 6. One of the circumstances which have contributed to keep up the
+notion, that demonstrative truths follow from definitions rather than
+from the postulates implied in those definitions, is, that the
+postulates, even in those sciences which are considered to surpass all
+others in demonstrative certainty, are not always exactly true. It is
+not true that a circle exists, or can be described, which has all its
+radii _exactly_ equal. Such accuracy is ideal only; it is not found in
+nature, still less can it be realized by art. People had a difficulty,
+therefore, in conceiving that the most certain of all conclusions could
+rest on premises which, instead of being certainly true, are certainly
+not true to the full extent asserted. This apparent paradox will be
+examined when we come to treat of Demonstration; where we shall be able
+to show that as much of the postulate is true, as is required to support
+as much as is true of the conclusion. Philosophers, however, to whom
+this view had not occurred, or whom it did not satisfy, have thought it
+indispensable that there should be found in definitions something _more_
+certain, or at least more accurately true, than the implied postulate of
+the real existence of a corresponding object. And this something they
+flattered themselves they had found, when they laid it down that a
+definition is a statement and analysis not of the mere meaning of a
+word, nor yet of the nature of a thing, but of an idea. Thus, the
+proposition, "A circle is a plane figure bounded by a line all the
+points of which are at an equal distance from a given point within it,"
+was considered by them, not as an assertion that any real circle has
+that property, (which would not be exactly true,) but that we _conceive_
+a circle as having it; that our abstract idea of a circle is an idea of
+a figure with its radii exactly equal.
+
+Conformably to this it is said, that the subject-matter of mathematics,
+and of every other demonstrative science, is not things as they really
+exist, but abstractions of the mind. A geometrical line is a line
+without breadth; but no such line exists in nature; it is a notion
+merely suggested to the mind by its experience of nature. The definition
+(it is said) is a definition of this mental line, not of any actual
+line: and it is only of the mental line, not of any line existing in
+nature, that the theorems of geometry are accurately true.
+
+Allowing this doctrine respecting the nature of demonstrative truth to
+be correct (which, in a subsequent place, I shall endeavour to prove
+that it is not;) even on that supposition, the conclusions which seem to
+follow from a definition, do not follow from the definition as such, but
+from an implied postulate. Even if it be true that there is no object in
+nature answering to the definition of a line, and that the geometrical
+properties of lines are not true of any lines in nature, but only of the
+idea of a line; the definition, at all events, postulates the real
+existence of such an idea: it assumes that the mind can frame, or rather
+has framed, the notion of length without breadth, and without any other
+sensible property whatever. To me, indeed, it appears that the mind
+cannot form any such notion; it cannot conceive length without breadth;
+it can only, in contemplating objects, attend to their length,
+exclusively of their other sensible qualities, and so determine what
+properties may be predicated of them in virtue of their length alone. If
+this be true, the postulate involved in the geometrical definition of a
+line, is the real existence, not of length without breadth, but merely
+of length, that is, of long objects. This is quite enough to support all
+the truths of geometry, since every property of a geometrical line is
+really a property of all physical objects in so far as possessing
+length. But even what I hold to be the false doctrine on the subject,
+leaves the conclusion that our reasonings are grounded on the matters of
+fact postulated in definitions, and not on the definitions themselves,
+entirely unaffected; and accordingly this conclusion is one which I have
+in common with Dr. Whewell, in his _Philosophy of the Inductive
+Sciences_: though, on the nature of demonstrative truth, Dr. Whewell's
+opinions are greatly at variance with mine. And here, as in many other
+instances, I gladly acknowledge that his writings are eminently
+serviceable in clearing from confusion the initial steps in the analysis
+of the mental processes, even where his views respecting the ultimate
+analysis are such as (though with unfeigned respect) I cannot but regard
+as fundamentally erroneous.
+
+
+§ 7. Although, according to the opinion here presented, Definitions are
+properly of names only, and not of things, it does not follow from this
+that definitions are arbitrary. How to define a name, may not only be an
+inquiry of considerable difficulty and intricacy, but may involve
+considerations going deep into the nature of the things which are
+denoted by the name. Such, for instance, are the inquiries which form
+the subjects of the most important of Plato's Dialogues; as, "What is
+rhetoric?" the topic of the Gorgias, or "What is justice?" that of the
+Republic. Such, also, is the question scornfully asked by Pilate, "What
+is truth?" and the fundamental question with speculative moralists in
+all ages, "What is virtue?"
+
+It would be a mistake to represent these difficult and noble inquiries
+as having nothing in view beyond ascertaining the conventional meaning
+of a name. They are inquiries not so much to determine what is, as what
+should be, the meaning of a name; which, like other practical questions
+of terminology, requires for its solution that we should enter, and
+sometimes enter very deeply, into the properties not merely of names but
+of the things named.
+
+Although the meaning of every concrete general name resides in the
+attributes which it connotes, the objects were named before the
+attributes; as appears from the fact that in all languages, abstract
+names are mostly compounds or other derivatives of the concrete names
+which correspond to them. Connotative names, therefore, were, after
+proper names, the first which were used: and in the simpler cases, no
+doubt, a distinct connotation was present to the minds of those who
+first used the name, and was distinctly intended by them to be conveyed
+by it. The first person who used the word white, as applied to snow or
+to any other object, knew, no doubt, very well what quality he intended
+to predicate, and had a perfectly distinct conception in his mind of the
+attribute signified by the name.
+
+But where the resemblances and differences on which our classifications
+are founded are not of this palpable and easily determinable kind;
+especially where they consist not in any one quality but in a number of
+qualities, the effects of which being blended together are not very
+easily discriminated, and referred each to its true source; it often
+happens that names are applied to nameable objects, with no distinct
+connotation present to the minds of those who apply them. They are only
+influenced by a general resemblance between the new object and all or
+some of the old familiar objects which they have been accustomed to call
+by that name. This, as we have seen, is the law which even the mind of
+the philosopher must follow, in giving names to the simple elementary
+feelings of our nature: but, where the things to be named are complex
+wholes, a philosopher is not content with noticing a general
+resemblance; he examines what the resemblance consists in: and he only
+gives the same name to things which resemble one another in the same
+definite particulars. The philosopher, therefore, habitually employs his
+general names with a definite connotation. But language was not made,
+and can only in some small degree be mended, by philosophers. In the
+minds of the real arbiters of language, general names, especially where
+the classes they denote cannot be brought before the tribunal of the
+outward senses to be identified and discriminated, connote little more
+than a vague gross resemblance to the things which they were earliest,
+or have been most, accustomed to call by those names. When, for
+instance, ordinary persons predicate the words _just_ or _unjust_ of any
+action, _noble_ or _mean_ of any sentiment, expression, or demeanour,
+_statesman_ or _charlatan_ of any personage figuring in politics, do
+they mean to affirm of those various subjects any determinate
+attributes, of whatever kind? No: they merely recognise, as they think,
+some likeness, more or less vague and loose, between these and some
+other things which they have been accustomed to denominate or to hear
+denominated by those appellations.
+
+Language, as Sir James Mackintosh used to say of governments, "is not
+made, but grows." A name is not imposed at once and by previous purpose
+upon a _class_ of objects, but is first applied to one thing, and then
+extended by a series of transitions to another and another. By this
+process (as has been remarked by several writers, and illustrated with
+great force and clearness by Dugald Stewart in his Philosophical Essays)
+a name not unfrequently passes by successive links of resemblance from
+one object to another, until it becomes applied to things having nothing
+in common with the first things to which the name was given; which,
+however, do not, for that reason, drop the name; so that it at last
+denotes a confused huddle of objects, having nothing whatever in common;
+and connotes nothing, not even a vague and general resemblance. When a
+name has fallen into this state, in which by predicating it of any
+object we assert literally nothing about the object, it has become unfit
+for the purposes either of thought or of the communication of thought;
+and can only be made serviceable by stripping it of some part of its
+multifarious denotation, and confining it to objects possessed of some
+attributes in common, which it may be made to connote. Such are the
+inconveniences of a language which "is not made, but grows." Like the
+governments which are in a similar case, it may be compared to a road
+which is not made but has made itself: it requires continual mending in
+order to be passable.
+
+From this it is already evident, why the question respecting the
+definition of an abstract name is often one of so much difficulty. The
+question, What is justice? is, in other words, What is the attribute
+which mankind mean to predicate when they call an action just? To which
+the first answer is, that having come to no precise agreement on the
+point, they do not mean to predicate distinctly any attribute at all.
+Nevertheless, all believe that there is some common attribute belonging
+to all the actions which they are in the habit of calling just. The
+question then must be, whether there is any such common attribute? and,
+in the first place, whether mankind agree sufficiently with one another
+as to the particular actions which they do or do not call just, to
+render the inquiry, what quality those actions have in common, a
+possible one: if so, whether the actions really have any quality in
+common; and if they have, what it is. Of these three, the first alone is
+an inquiry into usage and convention; the other two are inquiries into
+matters of fact. And if the second question (whether the actions form a
+class at all) has been answered negatively, there remains a fourth,
+often more arduous than all the rest, namely, how best to form a class
+artificially, which the name may denote.
+
+And here it is fitting to remark, that the study of the spontaneous
+growth of languages is of the utmost importance to those who would
+logically remodel them. The classifications rudely made by established
+language, when retouched, as they almost all require to be, by the hands
+of the logician, are often in themselves excellently suited to his
+purposes. As compared with the classifications of a philosopher, they
+are like the customary law of a country, which has grown up as it were
+spontaneously, compared with laws methodized and digested into a code:
+the former are a far less perfect instrument than the latter; but being
+the result of a long, though unscientific, course of experience, they
+contain a mass of materials which may be made very usefully available in
+the formation of the systematic body of written law. In like manner, the
+established grouping of objects under a common name, even when founded
+only on a gross and general resemblance, is evidence, in the first
+place, that the resemblance is obvious, and therefore considerable;
+and, in the next place, that it is a resemblance which has struck great
+numbers of persons during a series of years and ages. Even when a name,
+by successive extensions, has come to be applied to things among which
+there does not exist this gross resemblance common to them all, still at
+every step in its progress we shall find such a resemblance. And these
+transitions of the meaning of words are often an index to real
+connexions between the things denoted by them, which might otherwise
+escape the notice of thinkers; of those at least who, from using a
+different language, or from any difference in their habitual
+associations, have fixed their attention in preference on some other
+aspect of the things. The history of philosophy abounds in examples of
+such oversights, committed for want of perceiving the hidden link that
+connected together the seemingly disparate meanings of some ambiguous
+word.[29]
+
+Whenever the inquiry into the definition of the name of any real object
+consists of anything else than a mere comparison of authorities, we
+tacitly assume that a meaning must be found for the name, compatible
+with its continuing to denote, if possible all, but at any rate the
+greater or the more important part, of the things of which it is
+commonly predicated. The inquiry, therefore, into the definition, is an
+inquiry into the resemblances and differences among those things:
+whether there be any resemblance running through them all; if not,
+through what portion of them such a general resemblance can be traced:
+and finally, what are the common attributes, the possession of which
+gives to them all, or to that portion of them, the character of
+resemblance which has led to their being classed together. When these
+common attributes have been ascertained and specified, the name which
+belongs in common to the resembling objects acquires a distinct instead
+of a vague connotation; and by possessing this distinct connotation,
+becomes susceptible of definition.
+
+In giving a distinct connotation to the general name, the philosopher
+will endeavour to fix upon such attributes as, while they are common to
+all the things usually denoted by the name, are also of greatest
+importance in themselves; either directly, or from the number, the
+conspicuousness, or the interesting character, of the consequences to
+which they lead. He will select, as far as possible, such _differentiæ_
+as lead to the greatest number of interesting _propria_. For these,
+rather than the more obscure and recondite qualities on which they often
+depend, give that general character and aspect to a set of objects,
+which determine the groups into which they naturally fall. But to
+penetrate to the more hidden agreement on which these obvious and
+superficial agreements depend, is often one of the most difficult of
+scientific problems. As it is among the most difficult, so it seldom
+fails to be among the most important. And since upon the result of this
+inquiry respecting the causes of the properties of a class of things,
+there incidentally depends the question what shall be the meaning of a
+word; some of the most profound and most valuable investigations which
+philosophy presents to us, have been introduced by, and have offered
+themselves under the guise of, inquiries into the definition of a name.
+
+FOOTNOTES:
+
+[1] _Computation or Logic_, chap. ii.
+
+[2] In the original "had, _or had not_." These last words, as involving
+a subtlety foreign to our present purpose, I have forborne to quote.
+
+[3] Vide infra, note at the end of § 3, book ii. ch. ii.
+
+[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one
+thing _with_ or _in addition to_ another.
+
+[5] Archbishop Whately, who, in the later editions of his _Elements of
+Logic_, aided in reviving the important distinction treated of in the
+text, proposes the term "Attributive" as a substitute for "Connotative"
+(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it
+has not the advantage of being connected with any verb, of so markedly
+distinctive a character as "to connote," it is not, I think, fitted to
+supply the place of the word Connotative in scientific use.
+
+[6] A writer who entitles his book _Philosophy; or, the Science of
+Truth_, charges me in his very first page (referring at the foot of it
+to this passage) with asserting that _general_ names have properly no
+signification. And he repeats this statement many times in the course of
+his volume, with comments, not at all flattering, thereon. It is well to
+be now and then reminded to how great a length perverse misquotation
+(for, strange as it appears, I do not believe that the writer is
+dishonest) can sometimes go. It is a warning to readers, when they see
+an author accused, with volume and page referred to, and the apparent
+guarantee of inverted commas, of maintaining something more than
+commonly absurd, not to give implicit credence to the assertion without
+verifying the reference.
+
+[7] Before quitting the subject of connotative names, it is proper to
+observe, that the first writer who, in our times, has adopted from the
+schoolmen the word _to connote_, Mr. James Mill, in his _Analysis of the
+Phenomena of the Human Mind_, employs it in a signification different
+from that in which it is here used. He uses the word in a sense
+coextensive with its etymology, applying it to every case in which a
+name, while pointing directly to one thing, (which is consequently
+termed its signification,) includes also a tacit reference to some other
+thing. In the case considered in the text, that of concrete general
+names, his language and mine are the converse of one another.
+Considering (very justly) the signification of the name to lie in the
+attribute, he speaks of the word as _noting_ the attribute, and
+_connoting_ the things possessing the attribute. And he describes
+abstract names as being properly concrete names with their connotation
+dropped: whereas, in my view, it is the _de_notation which would be said
+to be dropped, what was previously connoted becoming the whole
+signification.
+
+In adopting a phraseology at variance with that which so high an
+authority, and one which I am less likely than any other person to
+undervalue, has deliberately sanctioned, I have been influenced by the
+urgent necessity for a term exclusively appropriated to express the
+manner in which a concrete general name serves to mark the attributes
+which are involved in its signification. This necessity can scarcely be
+felt in its full force by any one who has not found by experience how
+vain is the attempt to communicate clear ideas on the philosophy of
+language without such a word. It is hardly an exaggeration to say, that
+some of the most prevalent of the errors with which logic has been
+infected, and a large part of the cloudiness and confusion of ideas
+which have enveloped it, would, in all probability, have been avoided,
+if a term had been in common use to express exactly what I have
+signified by the term to connote. And the schoolmen, to whom we are
+indebted for the greater part of our logical language, gave us this
+also, and in this very sense. For though some of their general
+expressions countenance the use of the word in the more extensive and
+vague acceptation in which it is taken by Mr. Mill, yet when they had to
+define it specifically as a technical term, and to fix its meaning as
+such, with that admirable precision which always characterizes their
+definitions, they clearly explained that nothing was said to be connoted
+except _forms_, which word may generally, in their writings, be
+understood as synonymous with _attributes_.
+
+Now, if the word _to connote_, so well suited to the purpose to which
+they applied it, be diverted from that purpose by being taken to fulfil
+another, for which it does not seem to me to be at all required; I am
+unable to find any expression to replace it, but such as are commonly
+employed in a sense so much more general, that it would be useless
+attempting to associate them peculiarly with this precise idea. Such are
+the words, to involve, to imply, &c. By employing these, I should fail
+of attaining the object for which alone the name is needed, namely, to
+distinguish this particular kind of involving and implying from all
+other kinds, and to assure to it the degree of habitual attention which
+its importance demands.
+
+[8] Or rather, all objects except itself and the percipient mind; for,
+as we shall see hereafter, to ascribe any attribute to an object,
+necessarily implies a mind to perceive it.
+
+The simple and clear explanation given in the text, of relation and
+relative names, a subject so long the opprobrium of metaphysics, was
+given (as far as I know) for the first time, by Mr. James Mill, in his
+Analysis of the Phenomena of the Human Mind.
+
+[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.
+
+[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.
+
+[11] It is to be regretted that Sir William Hamilton, though he often
+strenuously insists on this doctrine, and though, in the passage quoted,
+he states it with a comprehensiveness and force which leave nothing to
+be desired, did not consistently adhere to his own doctrine, but
+maintained along with it opinions with which it is utterly
+irreconcileable. See the third and other chapters of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous
+ne pouvons expliquer nos perceptions sans les rattacher à des causes
+distinctes de nous-mêmes; nous savons de plus que ces causes, dont nous
+ne connaissons pas d'ailleurs l'essence, produisent les effets les plus
+variables, les plus divers, et même les plus contraires, selon qu'elles
+rencontrent telle nature ou telle disposition du sujet. Mais savons-nous
+quelque chose de plus? et même, vu le caractère indéterminé des causes
+que nous concevons dans les corps, y a-t-il quelque chose de plus à
+savoir? Y a-t-il lieu de nous enquérir si nous percevons les choses
+telles qu'elles sont? Non évidemment.... Je ne dis pas que le problème
+est insoluble, _je dis qu'il est absurde et enferme une contradiction_.
+Nous _ne savons pas ce que ces causes sont en elles-mêmes_, et la raison
+nous défend de chercher à le connaître: mais il est bien évident _à
+priori_, qu'_elles ne sont pas en elles-mêmes ce qu'elles sont par
+rapport à nous_, puisque la présence du sujet modifie nécessairement
+leur action. Supprimez tout sujet sentant, il est certain que ces causes
+agiraient encore puisqu'elles continueraient d'exister; mais elles
+agiraient autrement; elles seraient encore des qualités et des
+propriétés, mais qui ne ressembleraient à rien de ce que nous
+connaissons. Le feu ne manifesterait plus aucune des propriétés que nous
+lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.
+_C'est d'ailleurs peut-être un problème qui ne répugne pas seulement à
+la nature de notre esprit, mais à l'essence même des choses._ Quand même
+en effet on supprimerait par la pensée tous les sujets sentants, il
+faudrait encore admettre que nul corps ne manifesterait ses propriétés
+autrement qu'en relation avec un sujet quelconque, et dans ce cas _ses
+propriétés ne seraient encore que relatives_: en sorte qu'il me paraît
+fort raisonnable d'admettre que les propriétés déterminées des corps
+n'existent pas indépendamment d'un sujet quelconque, et que quand on
+demande si les propriétés de la matière sont telles que nous les
+percevons, il faudrait voir auparavant si elles sont en tant que
+déterminées, et dans quel sens il est vrai de dire qu'elles
+sont."--_Cours d'Histoire de la Philosophie Morale au 18me siècle_, 8me
+leçon.
+
+[13] An attempt, indeed, has been made by Reid and others, to establish
+that although some of the properties we ascribe to objects exist only in
+our sensations, others exist in the things themselves, being such as
+cannot possibly be copies of any impression upon the senses; and they
+ask, from what sensations our notions of extension and figure have been
+derived? The gauntlet thrown down by Reid was taken up by Brown, who,
+applying greater powers of analysis than had previously been applied to
+the notions of extension and figure, pointed out that the sensations
+from which those notions are derived, are sensations of touch, combined
+with sensations of a class previously too little adverted to by
+metaphysicians, those which have their seat in our muscular frame. His
+analysis, which was adopted and followed up by James Mill, has been
+further and greatly improved upon in Professor Bain's profound work,
+_The Senses and the Intellect_, and in the chapters on "Perception" of a
+work of eminent analytic power, Mr. Herbert Spencer's _Principles of
+Psychology_.
+
+On this point M. Cousin may again be cited in favour of the better
+doctrine. M. Cousin recognises, in opposition to Reid, the essential
+subjectivity of our conceptions of what are called the primary qualities
+of matter, as extension, solidity, &c., equally with those of colour,
+heat, and the remainder of the so-called secondary qualities.--_Cours_,
+ut supra, 9me leçon.
+
+[14] This doctrine, which is the most complete form of the philosophical
+theory known as the Relativity of Human Knowledge, has, since the recent
+revival in this country of an active interest in metaphysical
+speculation, been the subject of a greatly increased amount of
+discussion and controversy; and dissentients have manifested themselves
+in considerably greater number than I had any knowledge of when the
+passage in the text was written. The doctrine has been attacked from two
+sides. Some thinkers, among whom are the late Professor Ferrier, in his
+_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio
+Philosophica_, appear to deny altogether the reality of Noumena, or
+Things in themselves--of an unknowable substratum or support for the
+sensations which we experience, and which, according to the theory,
+constitute all our knowledge of an external world. It seems to me,
+however, that in Professor Grote's case at least, the denial of Noumena
+is only apparent, and that he does not essentially differ from the other
+class of objectors, including Mr. Bailey in his valuable _Letters on the
+Philosophy of the Human Mind_, and (in spite of the striking passage
+quoted in the text) also Sir William Hamilton, who contend for a direct
+knowledge by the human mind of more than the sensations--of certain
+attributes or properties as they exist not in us, but in the Things
+themselves.
+
+With the first of these opinions, that which denies Noumena, I have, as
+a metaphysician, no quarrel; but, whether it be true or false, it is
+irrelevant to Logic. And since all the forms of language are in
+contradiction to it, nothing but confusion could result from its
+unnecessary introduction into a treatise, every essential doctrine of
+which could stand equally well with the opposite and accredited opinion.
+The other and rival doctrine, that of a direct perception or intuitive
+knowledge of the outward object as it is in itself, considered as
+distinct from the sensations we receive from it, is of far greater
+practical moment. But even this question, depending on the nature and
+laws of Intuitive Knowledge, is not within the province of Logic. For
+the grounds of my own opinion concerning it, I must content myself with
+referring to a work already mentioned--_An Examination of Sir William
+Hamilton's Philosophy_; several chapters of which are devoted to a full
+discussion of the questions and theories relating to the supposed direct
+perception of external objects.
+
+[15] _Analysis of the Human Mind_, i. 126 et seq.
+
+[16] It may, however, be considered as equivalent to an universal
+proposition with a different predicate, viz. "All wine is good _quâ_
+wine," or "is good in respect of the qualities which constitute it
+wine."
+
+[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
+statement, and asks, "Are we to say that a mole cannot dig the ground,
+except he has an idea of the ground, and of the snout and paws with
+which he digs it?" I do not know what passes in a mole's mind, nor what
+amount of mental apprehension may or may not accompany his instinctive
+actions. But a human being does not use a spade by instinct; and he
+certainly could not use it unless he had knowledge of a spade, and of
+the earth which he uses it upon.
+
+[18] "From hence also this may be deduced, that the first truths were
+arbitrarily made by those that first of all imposed names upon things,
+or received them from the imposition of others. For it is true (for
+example) that _man is a living creature_, but it is for this reason,
+that it pleased men to impose both these names on the same
+thing."--_Computation or Logic_, ch. iii. sect. 8.
+
+[19] "Men are subject to err not only in affirming and denying, but also
+in perception, and in silent cogitation.... Tacit errors, or the errors
+of sense and cogitation, are made by passing from one imagination to the
+imagination of another different thing; or by feigning that to be past,
+or future, which never was, nor ever shall be; as when by seeing the
+image of the sun in water, we imagine the sun itself to be there; or by
+seeing swords, that there has been, or shall be, fighting, because it
+uses to be so for the most part; or when from promises we feign the mind
+of the promiser to be such and such; or, lastly, when from any sign we
+vainly imagine something to be signified which is not. And errors of
+this sort are common to all things that have sense."--_Computation or
+Logic_, ch. v. sect. 1.
+
+[20] Ch. iii. sect. 3.
+
+[21] To the preceding statement it has been objected, that "we naturally
+construe the subject of a proposition in its extension, and the
+predicate (which therefore may be an adjective) in its intension,
+(connotation): and that consequently coexistence of attributes does not,
+any more than the opposite theory of equation of groups, correspond with
+the living processes of thought and language." I acknowledge the
+distinction here drawn, which, indeed, I had myself laid down and
+exemplified a few pages back (p. 104). But though it is true that we
+naturally "construe the subject of a proposition in its extension," this
+extension, or in other words, the extent of the class denoted by the
+name, is not apprehended or indicated directly. It is both apprehended
+and indicated solely through the attributes. In the "living processes of
+thought and language" the extension, though in this case really thought
+of (which in the case of the predicate it is not), is thought of only
+through the medium of what my acute and courteous critic terms the
+"intension."
+
+For further illustrations of this subject, see _Examination of Sir
+William Hamilton's Philosophy_, ch. xxii.
+
+[22] Book iv. ch. vii.
+
+[23] The doctrines which prevented the real meaning of Essences from
+being understood, had not assumed so settled a shape in the time of
+Aristotle and his immediate followers, as was afterwards given to them
+by the Realists of the middle ages. Aristotle himself (in his Treatise
+on the Categories) expressly denies that the _δεύτεραι οὔσιαι_, or
+Substantiæ Secundæ, inhere in a subject. They are only, he says,
+predicated of it.
+
+[24] The always acute and often profound author of _An Outline of
+Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more
+intelligible if, in the majority of places, we substitute 'the knowledge
+of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms
+on Locke's use of the word Idea, this is the one which, as it appears to
+me, most nearly hits the mark; and I quote it for the additional reason
+that it precisely expresses the point of difference respecting the
+import of Propositions, between my view and what I have spoken of as the
+Conceptualist view of them. Where a Conceptualist says that a name or a
+proposition expresses our Idea of a thing, I should generally say
+(instead of our Idea) our Knowledge, or Belief, concerning the thing
+itself.
+
+[25] This distinction corresponds to that which is drawn by Kant and
+other metaphysicians between what they term _analytic_, and _synthetic_,
+judgments; the former being those which can be evolved from the meaning
+of the terms used.
+
+[26] If we allow a differentia to what is not really a species. For the
+distinction of Kinds, in the sense explained by us, not being in any way
+applicable to attributes, it of course follows that although attributes
+may be put into classes, those classes can be admitted to be genera or
+species only by courtesy.
+
+[27] In the fuller discussion which Archbishop Whately has given to this
+subject in his later editions, he almost ceases to regard the
+definitions of names and those of things as, in any important sense,
+distinct. He seems (9th ed. p. 145) to limit the notion of a Real
+Definition to one which "explains anything _more_ of the nature of the
+thing than is implied in the name;" (including under the word "implied,"
+not only what the name connotes, but everything which can be deduced by
+reasoning from the attributes connoted). Even this, as he adds, is
+usually called, not a Definition, but a Description; and (as it seems to
+me) rightly so called. A Description, I conceive, can only be ranked
+among Definitions, when taken (as in the case of the zoological
+definition of man) to fulfil the true office of a Definition, by
+declaring the connotation given to a word in some special use, as a term
+of science or art: which special connotation of course would not be
+expressed by the proper definition of the word in its ordinary
+employment.
+
+Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
+understands by a Real Definition one which contains _less_ than the
+Nominal Definition, provided only that what it contains is sufficient
+for distinction. "By _real_ definition I mean such an explanation of the
+word, be it the whole of the meaning or only part, as will be sufficient
+to separate the things contained under that word from all others. Thus
+the following, I believe, is a complete definition of an elephant: An
+animal which naturally drinks by drawing the water into its nose, and
+then spurting it into its mouth."--_Formal Logic_, p. 36. Mr. De
+Morgan's general proposition and his example are at variance; for the
+peculiar mode of drinking of the elephant certainly forms no part of the
+meaning of the word elephant. It could not be said, because a person
+happened to be ignorant of this property, that he did not know what an
+elephant means.
+
+[28] In the only attempt which, so far as I know, has been made to
+refute the preceding argumentation, it is maintained that in the first
+form of the syllogism,
+
+  A dragon is a thing which breathes flame,
+  A dragon is a serpent,
+  Therefore some serpent or serpents breathe flame,
+
+"there is just as much truth in the conclusion as there is in the
+premises, or rather, no more in the latter than in the former. If the
+general name serpent includes both real and imaginary serpents, there is
+no falsity in the conclusion; if not, there is falsity in the minor
+premise."
+
+Let us, then, try to set out the syllogism on the hypothesis that the
+name serpent includes imaginary serpents. We shall find that it is now
+necessary to alter the predicates; for it cannot be asserted that an
+imaginary creature breathes flame: in predicating of it such a fact, we
+assert by the most positive implication that it is real and not
+imaginary. The conclusion must run thus, "Some serpent or serpents
+either do or are _imagined_ to breathe flame." And to prove this
+conclusion by the instance of dragons, the premises must be, A dragon is
+_imagined_ as breathing flame, A dragon is a (real or imaginary)
+serpent: from which it undoubtedly follows, that there are serpents
+which are imagined to breathe flame; but the major premise is not a
+definition, nor part of a definition; which is all that I am concerned
+to prove.
+
+Let us now examine the other assertion--that if the word serpent stands
+for none but real serpents, the minor premise (a dragon is a serpent) is
+false. This is exactly what I have myself said of the premise,
+considered as a statement of fact: but it is not false as part of the
+definition of a dragon; and since the premises, or one of them, must be
+false, (the conclusion being so,) the real premise cannot be the
+definition, which is true, but the statement of fact, which is false.
+
+[29] "Few people" (I have said in another place) "have reflected how
+great a knowledge of Things is required to enable a man to affirm that
+any given argument turns wholly upon words. There is, perhaps, not one
+of the leading terms of philosophy which is not used in almost
+innumerable shades of meaning, to express ideas more or less widely
+different from one another. Between two of these ideas a sagacious and
+penetrating mind will discern, as it were intuitively, an unobvious link
+of connexion, upon which, though perhaps unable to give a logical
+account of it, he will found a perfectly valid argument, which his
+critic, not having so keen an insight into the Things, will mistake for
+a fallacy turning on the double meaning of a term. And the greater the
+genius of him who thus safely leaps over the chasm, the greater will
+probably be the crowing and vain-glory of the mere logician, who,
+hobbling after him, evinces his own superior wisdom by pausing on its
+brink, and giving up as desperate his proper business of bridging it
+over."
+
+
+
+
+BOOK II.
+
+OF REASONING.
+
+
+Διωρισμένων δε τούτων λέγωμεν ἤδη, διὰ τίνων, καὶ πότε, καὶ πῶς γίνεται
+πᾶς συλλογισμός ὕστερον δὲ λεκτέον περὶ ἀποδείξεως. Πρότερον γὰρ περὶ
+συλλογισμοῦ λεκτέον, ἢ περὶ ἀποδείξεως, διὰ τὸ καθόλου μᾶλλον εἰναὶ τὸν
+συλλογισμόν. Ἡ μὲν γὰρ ἀπόδειξις, συλλογισμός τις; ὁ συλλογισμός δὲ οὐ
+πᾶς, ἀπόδειξις.
+
+                    ARIST. _Analyt. Prior._ l. i. cap. 4.
+
+
+
+
+CHAPTER I.
+
+OF INFERENCE, OR REASONING, IN GENERAL.
+
+
+§ 1. In the preceding Book, we have been occupied not with the nature of
+Proof, but with the nature of Assertion: the import conveyed by a
+Proposition, whether that Proposition be true or false; not the means by
+which to discriminate true from false Propositions. The proper subject,
+however, of Logic is Proof. Before we could understand what Proof is, it
+was necessary to understand what that is to which proof is applicable;
+what that is which can be a subject of belief or disbelief, of
+affirmation or denial; what, in short, the different kinds of
+Propositions assert.
+
+This preliminary inquiry we have prosecuted to a definite result.
+Assertion, in the first place, relates either to the meaning of words,
+or to some property of the things which words signify. Assertions
+respecting the meaning of words, among which definitions are the most
+important, hold a place, and an indispensable one, in philosophy; but as
+the meaning of words is essentially arbitrary, this class of assertions
+are not susceptible of truth or falsity, nor therefore of proof or
+disproof. Assertions respecting Things, or what may be called Real
+Propositions, in contradistinction to verbal ones, are of various sorts.
+We have analysed the import of each sort, and have ascertained the
+nature of the things they relate to, and the nature of what they
+severally assert respecting those things. We found that whatever be the
+form of the proposition, and whatever its nominal subject or predicate,
+the real subject of every proposition is some one or more facts or
+phenomena of consciousness, or some one or more of the hidden causes or
+powers to which we ascribe those facts; and that what is predicated or
+asserted, either in the affirmative or negative, of those phenomena or
+those powers, is always either Existence, Order in Place, Order in Time,
+Causation, or Resemblance. This, then, is the theory of the Import of
+Propositions, reduced to its ultimate elements: but there is another and
+a less abstruse expression for it, which, though stopping short in an
+earlier stage of the analysis, is sufficiently scientific for many of
+the purposes for which such a general expression is required. This
+expression recognises the commonly received distinction between Subject
+and Attribute, and gives the following as the analysis of the meaning of
+propositions:--Every Proposition asserts, that some given subject does
+or does not possess some attribute; or that some attribute is or is not
+(either in all or in some portion of the subjects in which it is met
+with) conjoined with some other attribute.
+
+We shall now for the present take our leave of this portion of our
+inquiry, and proceed to the peculiar problem of the Science of Logic,
+namely, how the assertions, of which we have analysed the import, are
+proved or disproved; such of them, at least, as, not being amenable to
+direct consciousness or intuition, are appropriate subjects of proof.
+
+We say of a fact or statement, that it is proved, when we believe its
+truth by reason of some other fact or statement from which it is said to
+_follow_. Most of the propositions, whether affirmative or negative,
+universal, particular, or singular, which we believe, are not believed
+on their own evidence, but on the ground of something previously
+assented to, from which they are said to be _inferred_. To infer a
+proposition from a previous proposition or propositions; to give
+credence to it, or claim credence for it, as a conclusion from something
+else; is to _reason_, in the most extensive sense of the term. There is
+a narrower sense, in which the name reasoning is confined to the form of
+inference which is termed ratiocination, and of which the syllogism is
+the general type. The reasons for not conforming to this restricted use
+of the term were stated in an earlier stage of our inquiry, and
+additional motives will be suggested by the considerations on which we
+are now about to enter.
+
+
+§ 2. In proceeding to take into consideration the cases in which
+inferences can legitimately be drawn, we shall first mention some cases
+in which the inference is apparent, not real; and which require notice
+chiefly that they may not be confounded with cases of inference properly
+so called. This occurs when the proposition ostensibly inferred from
+another, appears on analysis to be merely a repetition of the same, or
+part of the same, assertion, which was contained in the first. All the
+cases mentioned in books of Logic as examples of æquipollency or
+equivalence of propositions, are of this nature. Thus, if we were to
+argue, No man is incapable of reason, for every man is rational; or, All
+men are mortal, for no man is exempt from death; it would be plain that
+we were not proving the proposition, but only appealing to another mode
+of wording it, which may or may not be more readily comprehensible by
+the hearer, or better adapted to suggest the real proof, but which
+contains in itself no shadow of proof.
+
+Another case is where, from an universal proposition, we affect to infer
+another which differs from it only in being particular: as All A is B,
+therefore Some A is B: No A is B, therefore Some A is not B. This, too,
+is not to conclude one proposition from another, but to repeat a second
+time something which had been asserted at first; with the difference,
+that we do not here repeat the whole of the previous assertion, but only
+an indefinite part of it.
+
+A third case is where, the antecedent having affirmed a predicate of a
+given subject, the consequent affirms of the same subject something
+already connoted by the former predicate: as, Socrates is a man,
+therefore Socrates is a living creature; where all that is connoted by
+living creature was affirmed of Socrates when he was asserted to be a
+man. If the propositions are negative, we must invert their order, thus:
+Socrates is not a living creature, therefore he is not a man; for if we
+deny the less, the greater, which includes it, is already denied by
+implication. These, therefore, are not really cases of inference; and
+yet the trivial examples by which, in manuals of Logic, the rules of the
+syllogism are illustrated, are often of this ill-chosen kind; formal
+demonstrations of conclusions to which whoever understands the terms
+used in the statement of the data, has already, and consciously,
+assented.
+
+The most complex case of this sort of apparent inference is what is
+called the Conversion of propositions; which consists in turning the
+predicate into a subject, and the subject into a predicate, and framing
+out of the same terms thus reversed, another proposition, which must be
+true if the former is true. Thus, from the particular affirmative
+proposition, Some A is B, we may infer that Some B is A. From the
+universal negative, No A is B, we may conclude that No B is A. From the
+universal affirmative proposition, All A is B, it cannot be inferred
+that all B is A; though all water is liquid, it is not implied that all
+liquid is water; but it is implied that some liquid is so; and hence the
+proposition, All A is B, is legitimately convertible into Some B is A.
+This process, which converts an universal proposition into a particular,
+is termed conversion _per accidens_. From the proposition, Some A is not
+B, we cannot even infer that some B is not A; though some men are not
+Englishmen, it does not follow that some Englishmen are not men. The
+only mode usually recognised of converting a particular negative
+proposition, is in the form, Some A is not B, therefore, something which
+is not B is A; and this is termed conversion by contraposition. In this
+case, however, the predicate and subject are not merely reversed, but
+one of them is changed. Instead of [A] and [B], the terms of the new
+proposition are [a thing which is not B], and [A]. The original
+proposition, Some A _is not_ B, is first changed into a proposition
+æquipollent with it, Some A _is_ "a thing which is not B;" and the
+proposition, being now no longer a particular negative, but a particular
+affirmative, _admits_ of conversion in the first mode, or as it is
+called, _simple_ conversion.[1]
+
+In all these cases there is not really any inference; there is in the
+conclusion no new truth, nothing but what was already asserted in the
+premises, and obvious to whoever apprehends them. The fact asserted in
+the conclusion is either the very same fact, or part of the fact
+asserted in the original proposition. This follows from our previous
+analysis of the Import of Propositions. When we say, for example, that
+some lawful sovereigns are tyrants, what is the meaning of the
+assertion? That the attributes connoted by the term "lawful sovereign,"
+and the attributes connoted by the term "tyrant," sometimes coexist in
+the same individual. Now this is also precisely what we mean, when we
+say that some tyrants are lawful sovereigns; which, therefore, is not a
+second proposition inferred from the first, any more than the English
+translation of Euclid's Elements is a collection of theorems different
+from, and consequences of, those contained in the Greek original. Again,
+if we assert that no great general is a rash man, we mean that the
+attributes connoted by "great general," and those connoted by "rash,"
+never coexist in the same subject; which is also the exact meaning which
+would be expressed by saying, that no rash man is a great general. When
+we say that all quadrupeds are warm-blooded, we assert, not only that
+the attributes connoted by "quadruped" and those connoted by
+"warm-blooded" sometimes coexist, but that the former never exist
+without the latter: now the proposition, Some warm-blooded creatures are
+quadrupeds, expresses the first half of this meaning, dropping the
+latter half; and therefore has been already affirmed in the antecedent
+proposition, All quadrupeds are warm-blooded. But that _all_
+warm-blooded creatures are quadrupeds, or, in other words, that the
+attributes connoted by "warm-blooded" never exist without those connoted
+by "quadruped," has not been asserted, and cannot be inferred. In order
+to reassert, in an inverted form, the whole of what was affirmed in the
+proposition, All quadrupeds are warm-blooded, we must convert it by
+contraposition, thus, Nothing which is not warm-blooded is a quadruped.
+This proposition, and the one from which it is derived, are exactly
+equivalent, and either of them may be substituted for the other; for,
+to say that when the attributes of a quadruped are present, those of a
+warm-blooded creature are present, is to say that when the latter are
+absent the former are absent.
+
+In a manual for young students, it would be proper to dwell at greater
+length on the conversion and æquipollency of propositions. For, though
+that cannot be called reasoning or inference which is a mere reassertion
+in different words of what had been asserted before, there is no more
+important intellectual habit, nor any the cultivation of which falls
+more strictly within the province of the art of logic, than that of
+discerning rapidly and surely the identity of an assertion when
+disguised under diversity of language. That important chapter in logical
+treatises which relates to the Opposition of Propositions, and the
+excellent technical language which logic provides for distinguishing the
+different kinds or modes of opposition, are of use chiefly for this
+purpose. Such considerations as these, that contrary propositions may
+both be false, but cannot both be true; that subcontrary propositions
+may both be true, but cannot both be false; that of two contradictory
+propositions one must be true and the other false; that of two
+subalternate propositions the truth of the universal proves the truth of
+the particular, and the falsity of the particular proves the falsity of
+the universal, but not _vice versâ_;[2] are apt to appear, at first
+sight, very technical and mysterious, but when explained, seem almost
+too obvious to require so formal a statement, since the same amount of
+explanation which is necessary to make the principles intelligible,
+would enable the truths which they convey to be apprehended in any
+particular case which can occur. In this respect, however, these axioms
+of logic are on a level with those of mathematics. That things which are
+equal to the same thing are equal to one another, is as obvious in any
+particular case as it is in the general statement: and if no such
+general maxim had ever been laid down, the demonstrations in Euclid
+would never have halted for any difficulty in stepping across the gap
+which this axiom at present serves to bridge over. Yet no one has ever
+censured writers on geometry, for placing a list of these elementary
+generalizations at the head of their treatises, as a first exercise to
+the learner of the faculty which will be required in him at every step,
+that of apprehending a _general_ truth. And the student of logic, in the
+discussion even of such truths as we have cited above, acquires habits
+of circumspect interpretation of words, and of exactly measuring the
+length and breadth of his assertions, which are among the most
+indispensable conditions of any considerable mental attainment, and
+which it is one of the primary objects of logical discipline to
+cultivate.
+
+
+§ 3. Having noticed, in order to exclude from the province of Reasoning
+or Inference properly so called, the cases in which the progression from
+one truth to another is only apparent, the logical consequent being a
+mere repetition of the logical antecedent; we now pass to those which
+are cases of inference in the proper acceptation of the term, those in
+which we set out from known truths, to arrive at others really distinct
+from them.
+
+Reasoning, in the extended sense in which I use the term, and in which
+it is synonymous with Inference, is popularly said to be of two kinds:
+reasoning from particulars to generals, and reasoning from generals to
+particulars; the former being called Induction, the latter Ratiocination
+or Syllogism. It will presently be shown that there is a third species
+of reasoning, which falls under neither of these descriptions, and
+which, nevertheless, is not only valid, but is the foundation of both
+the others.
+
+It is necessary to observe, that the expressions, reasoning from
+particulars to generals, and reasoning from generals to particulars, are
+recommended by brevity rather than by precision, and do not adequately
+mark, without the aid of a commentary, the distinction between Induction
+(in the sense now adverted to) and Ratiocination. The meaning intended
+by these expressions is, that Induction is inferring a proposition from
+propositions _less general_ than itself, and Ratiocination is inferring
+a proposition from propositions _equally_ or _more_ general. When, from
+the observation of a number of individual instances, we ascend to a
+general proposition, or when, by combining a number of general
+propositions, we conclude from them another proposition still more
+general, the process, which is substantially the same in both instances,
+is called Induction. When from a general proposition, not alone (for
+from a single proposition nothing can be concluded which is not involved
+in the terms), but by combining it with other propositions, we infer a
+proposition of the same degree of generality with itself, or a less
+general proposition, or a proposition merely individual, the process is
+Ratiocination. When, in short, the conclusion is more general than the
+largest of the premises, the argument is commonly called Induction; when
+less general, or equally general, it is Ratiocination.
+
+As all experience begins with individual cases, and proceeds from them
+to generals, it might seem most conformable to the natural order of
+thought that Induction should be treated of before we touch upon
+Ratiocination. It will, however, be advantageous, in a science which
+aims at tracing our acquired knowledge to its sources, that the inquirer
+should commence with the latter rather than with the earlier stages of
+the process of constructing our knowledge; and should trace derivative
+truths backward to the truths from which they are deduced, and on which
+they depend for their evidence, before attempting to point out the
+original spring from which both ultimately take their rise. The
+advantages of this order of proceeding in the present instance will
+manifest themselves as we advance, in a manner superseding the necessity
+of any further justification or explanation.
+
+Of Induction, therefore, we shall say no more at present, than that it
+at least is, without doubt, a process of real inference. The conclusion
+in an induction embraces more than is contained in the premises. The
+principle or law collected from particular instances, the general
+proposition in which we embody the result of our experience, covers a
+much larger extent of ground than the individual experiments which form
+its basis. A principle ascertained by experience, is more than a mere
+summing up of what has been specifically observed in the individual
+cases which have been examined; it is a generalization grounded on those
+cases, and expressive of our belief, that what we there found true is
+true in an indefinite number of cases which we have not examined, and
+are never likely to examine. The nature and grounds of this inference,
+and the conditions necessary to make it legitimate, will be the subject
+of discussion in the Third Book: but that such inference really takes
+place is not susceptible of question. In every induction we proceed from
+truths which we knew, to truths which we did not know; from facts
+certified by observation, to facts which we have not observed, and even
+to facts not capable of being now observed; future facts, for example;
+but which we do not hesitate to believe on the sole evidence of the
+induction itself.
+
+Induction, then, is a real process of Reasoning or Inference. Whether,
+and in what sense, as much can be said of the Syllogism, remains to be
+determined by the examination into which we are about to enter.
+
+
+
+
+CHAPTER II.
+
+OF RATIOCINATION, OR SYLLOGISM.
+
+
+§ 1. The analysis of the Syllogism has been so accurately and fully
+performed in the common manuals of Logic, that in the present work,
+which is not designed as a manual, it is sufficient to recapitulate,
+_memoriæ causâ_, the leading results of that analysis, as a foundation
+for the remarks to be afterwards made on the functions of the syllogism,
+and the place which it holds in science.
+
+To a legitimate syllogism it is essential that there should be three,
+and no more than three, propositions, namely, the conclusion, or
+proposition to be proved, and two other propositions which together
+prove it, and which are called the premises. It is essential that there
+should be three, and no more than three, terms, namely, the subject and
+predicate of the conclusion, and another called the middleterm, which
+must be found in both premises, since it is by means of it that the
+other two terms are to be connected together. The predicate of the
+conclusion is called the major term of the syllogism; the subject of the
+conclusion is called the minor term. As there can be but three terms,
+the major and minor terms must each be found in one, and only one, of
+the premises, together with the middleterm which is in them both. The
+premise which contains the middleterm and the major term is called the
+major premise; that which contains the middleterm and the minor term is
+called the minor premise.
+
+Syllogisms are divided by some logicians into three _figures_, by others
+into four, according to the position of the middleterm, which may either
+be the subject in both premises, the predicate in both, or the subject
+in one and the predicate in the other. The most common case is that in
+which the middleterm is the subject of the major premise and the
+predicate of the minor. This is reckoned as the first figure. When the
+middleterm is the predicate in both premises, the syllogism belongs to
+the second figure; when it is the subject in both, to the third. In the
+fourth figure the middleterm is the subject of the minor premise and the
+predicate of the major. Those writers who reckon no more than three
+figures, include this case in the first.
+
+Each figure is divided into _moods_, according to what are called the
+_quantity_ and _quality_ of the propositions, that is, according as they
+are universal or particular, affirmative or negative. The following are
+examples of all the legitimate moods, that is, all those in which the
+conclusion correctly follows from the premises. A is the minor term, C
+the major, B the middleterm.
+
+FIRST FIGURE.
+
+  All B is C    No B is C     All B is C     No B is C
+  All A is B    All A is B    Some A is B    Some A is B
+    therefore     therefore     therefore      therefore
+  All A is C    No A is C     Some A is C    Some A is not C
+
+SECOND FIGURE.
+
+  No C is B     All C is B    No C is B         All C is B
+  All A is B    No A is B     Some A is B       Some A is not B
+    therefore     therefore     therefore         therefore
+  No A is C     No A is C     Some A is not C   Some A is not C
+
+THIRD FIGURE.
+
+  All B is C   No B is C    Some B is C  All B is C   Some B      No B is C
+                                                        is not C
+  All B is A   All B is A   All B is A   Some B is A  All B is A  Some B is A
+    therefore    therefore    therefore    therefore    therefore   therefore
+  Some A is C  Some A       Some A is C  Some A is C  Some A      Some A
+                 is not C                               is not C    is not C
+
+FOURTH FIGURE.
+
+  All C is B   All C is B       Some C is B  No C is B        No C is B
+  All B is A   No B is A        All B is A   All B is A       Some B is A
+    therefore    therefore        therefore    therefore        therefore
+  Some A is C  Some A is not C  Some A is C  Some A is not C  Some A is not C
+
+In these exemplars, or blank forms for making syllogisms, no place is
+assigned to _singular_ propositions; not, of course, because such
+propositions are not used in ratiocination, but because, their predicate
+being affirmed or denied of the whole of the subject, they are ranked,
+for the purposes of the syllogism, with universal propositions. Thus,
+these two syllogisms--
+
+  All men are mortal,      All men are mortal,
+  All kings are men,       Socrates is a man,
+    therefore                therefore
+  All kings are mortal,    Socrates is mortal,
+
+are arguments precisely similar, and are both ranked in the first mood
+of the first figure.
+
+The reasons why syllogisms in any of the above forms are legitimate,
+that is, why, if the premises are true, the conclusion must inevitably
+be so, and why this is not the case in any other possible mood, (that
+is, in any other combination of universal and particular, affirmative
+and negative propositions,) any person taking interest in these
+inquiries may be presumed to have either learned from the common school
+books of the syllogistic logic, or to be capable of discovering for
+himself. The reader may, however, be referred, for every needful
+explanation, to Archbishop Whately's _Elements of Logic_, where he will
+find stated with philosophical precision, and explained with remarkable
+perspicuity, the whole of the common doctrine of the syllogism.
+
+All valid ratiocination; all reasoning by which, from general
+propositions previously admitted, other propositions equally or less
+general are inferred; may be exhibited in some of the above forms. The
+whole of Euclid, for example, might be thrown without difficulty into a
+series of syllogisms, regular in mood and figure.
+
+Though a syllogism framed according to any of these formulæ is a valid
+argument, all correct ratiocination admits of being stated in syllogisms
+of the first figure alone. The rules for throwing an argument in any of
+the other figures into the first figure, are called rules for the
+_reduction_ of syllogisms. It is done by the _conversion_ of one or
+other, or both, of the premises. Thus an argument in the first mood of
+the second figure, as--
+
+  No C is B
+  All A is B
+    therefore
+  No A is C,
+
+may be reduced as follows. The proposition, No C is B, being an
+universal negative, admits of simple conversion, and may be changed into
+No B is C, which, as we showed, is the very same assertion in other
+words--the same fact differently expressed. This transformation having
+been effected, the argument assumes the following form:--
+
+  No B is C
+  All A is B
+    therefore
+  No A is C,
+
+which is a good syllogism in the second mood of the first figure. Again,
+an argument in the first mood of the third figure must resemble the
+following:--
+
+  All B is C
+  All B is A
+    therefore
+  Some A is C,
+
+where the minor premise, All B is A, conformably to what was laid down
+in the last chapter respecting universal affirmatives, does not admit of
+simple conversion, but may be converted _per accidens_, thus, Some A is
+B; which, though it does not express the whole of what is asserted in
+the proposition All B is A, expresses, as was formerly shown, part of
+it, and must therefore be true if the whole is true. We have, then, as
+the result of the reduction, the following syllogism in the third mood
+of the first figure:--
+
+  All B is C
+  Some A is B,
+
+from which it obviously follows, that
+
+  Some A is C.
+
+In the same manner, or in a manner on which after these examples it is
+not necessary to enlarge, every mood of the second, third, and fourth
+figures may be reduced to some one of the four moods of the first. In
+other words, every conclusion which can be proved in any of the last
+three figures, may be proved in the first figure from the same premises,
+with a slight alteration in the mere manner of expressing them. Every
+valid ratiocination, therefore, may be stated in the first figure, that
+is, in one of the following forms:--
+
+  Every B is C            No B is C
+  All A   }  is B,        All A   } is B,
+  Some A  }               Some A  }
+      therefore               therefore
+  All A   }  is C.        No A is        }  C.
+  Some A  }               Some A is not  }
+
+Or if more significant symbols are preferred:--
+
+To prove an affirmative, the argument must admit of being stated in this
+form:--
+
+  All animals are mortal;
+  All men   }
+  Some men  }  are animals;
+  Socrates  }
+        therefore
+  All men   }
+  Some men  }  are mortal.
+  Socrates  }
+
+To prove a negative, the argument must be capable of being expressed in
+this form:--
+
+  No one who is capable of self-control is necessarily vicious;
+  All negroes   }
+  Some negroes  }  are capable of self-control;
+  Mr. A's negro }
+        therefore
+  No negroes are        }
+  Some negroes are not  }  necessarily vicious.
+  Mr. A's negro is not  }
+
+Though all ratiocination admits of being thrown into one or the other of
+these forms, and sometimes gains considerably by the transformation,
+both in clearness and in the obviousness of its consequence; there are,
+no doubt, cases in which the argument falls more naturally into one of
+the other three figures, and in which its conclusiveness is more
+apparent at the first glance in those figures, than when reduced to the
+first. Thus, if the proposition were that pagans may be virtuous, and
+the evidence to prove it were the example of Aristides; a syllogism in
+the third figure,
+
+  Aristides was virtuous,
+  Aristides was a pagan,
+       therefore
+  Some pagan was virtuous,
+
+would be a more natural mode of stating the argument, and would carry
+conviction more instantly home, than the same ratiocination strained
+into the first figure, thus--
+
+  Aristides was virtuous,
+  Some pagan was Aristides,
+       therefore
+  Some pagan was virtuous.
+
+A German philosopher, Lambert, whose _Neues Organon_ (published in the
+year 1764) contains among other things one of the most elaborate and
+complete expositions which had ever been made of the syllogistic
+doctrine, has expressly examined what sort of arguments fall most
+naturally and suitably into each of the four figures; and his
+investigation is characterized by great ingenuity and clearness of
+thought.[3] The argument, however, is one and the same, in whichever
+figure it is expressed; since, as we have already seen, the premises of
+a syllogism in the second, third, or fourth figure, and those of the
+syllogism in the first figure to which it may be reduced, are the same
+premises in everything except language, or, at least, as much of them as
+contributes to the proof of the conclusion is the same. We are
+therefore at liberty, in conformity with the general opinion of
+logicians, to consider the two elementary forms of the first figure as
+the universal types of all correct ratiocination; the one, when the
+conclusion to be proved is affirmative, the other, when it is negative;
+even though certain arguments may have a tendency to clothe themselves
+in the forms of the second, third, and fourth figures; which, however,
+cannot possibly happen with the only class of arguments which are of
+first-rate scientific importance, those in which the conclusion is an
+universal affirmative, such conclusions being susceptible of proof in
+the first figure alone.[4]
+
+
+§ 2. On examining, then, these two general formulæ, we find that in
+both of them, one premise, the major, is an universal proposition; and
+according as this is affirmative or negative, the conclusion is so too.
+All ratiocination, therefore, starts from a _general_ proposition,
+principle, or assumption: a proposition in which a predicate is
+affirmed or denied of an entire class; that is, in which some attribute,
+or the negation of some attribute, is asserted of an indefinite number
+of objects distinguished by a common characteristic, and designated in
+consequence, by a common name.
+
+The other premise is always affirmative, and asserts that something
+(which may be either an individual, a class, or part of a class)
+belongs to, or is included in, the class respecting which something was
+affirmed or denied in the major premise. It follows that the attribute
+affirmed or denied of the entire class may (if that affirmation or
+denial was correct) be affirmed or denied of the object or objects
+alleged to be included in the class: and this is precisely the assertion
+made in the conclusion.
+
+Whether or not the foregoing is an adequate account of the constituent
+parts of the syllogism, will be presently considered; but as far as it
+goes it is a true account. It has accordingly been generalized, and
+erected into a logical maxim, on which all ratiocination is said to be
+founded, insomuch that to reason, and to apply the maxim, are supposed
+to be one and the same thing. The maxim is, That whatever can be
+affirmed (or denied) of a class, may be affirmed (or denied) of
+everything included in the class. This axiom, supposed to be the basis
+of the syllogistic theory, is termed by logicians the _dictum de omni et
+nullo_.
+
+This maxim, however, when considered as a principle of reasoning,
+appears suited to a system of metaphysics once indeed generally
+received, but which for the last two centuries has been considered as
+finally abandoned, though there have not been wanting in our own day
+attempts at its revival. So long as what are termed Universals were
+regarded as a peculiar kind of substances, having an objective existence
+distinct from the individual objects classed under them, the _dictum de
+omni_ conveyed an important meaning; because it expressed the
+intercommunity of nature, which it was necessary on that theory that we
+should suppose to exist between those general substances and the
+particular substances which were subordinated to them. That everything
+predicable of the universal was predicable of the various individuals
+contained under it, was then no identical proposition, but a statement
+of what was conceived as a fundamental law of the universe. The
+assertion that the entire nature and properties of the _substantia
+secunda_ formed part of the nature and properties of each of the
+individual substances called by the same name; that the properties of
+Man, for example, were properties of all men; was a proposition of real
+significance when man did not _mean_ all men, but something inherent in
+men, and vastly superior to them in dignity. Now, however, when it is
+known that a class, an universal, a genus or species, is not an entity
+_per se_, but neither more nor less than the individual substances
+themselves which are placed in the class, and that there is nothing real
+in the matter except those objects, a common name given to them, and
+common attributes indicated by the name; what, I should be glad to know,
+do we learn by being told, that whatever can be affirmed of a class, may
+be affirmed of every object contained in the class? The class is nothing
+but the objects contained in it: and the _dictum de omni_ merely amounts
+to the identical proposition, that whatever is true of certain objects,
+is true of each of those objects. If all ratiocination were no more than
+the application of this maxim to particular cases, the syllogism would
+indeed be, what it has so often been declared to be, solemn trifling.
+The _dictum de omni_ is on a par with another truth, which in its time
+was also reckoned of great importance, "Whatever is, is." To give any
+real meaning to the _dictum de omni_, we must consider it not as an
+axiom, but as a definition; we must look upon it as intended to explain,
+in a circuitous and paraphrastic manner, the meaning of the word,
+_class_.
+
+An error which seemed finally refuted and dislodged from thought, often
+needs only put on a new suit of phrases, to be welcomed back to its old
+quarters, and allowed to repose unquestioned for another cycle of ages.
+Modern philosophers have not been sparing in their contempt for the
+scholastic dogma that genera and species are a peculiar kind of
+substances, which general substances being the only permanent things,
+while the individual substances comprehended under them are in a
+perpetual flux, knowledge, which necessarily imports stability, can only
+have relation to those general substances or universals, and not to the
+facts or particulars included under them. Yet, though nominally
+rejected, this very doctrine, whether disguised under the Abstract Ideas
+of Locke (whose speculations, however, it has less vitiated than those
+of perhaps any other writer who has been infected with it), under the
+ultra-nominalism of Hobbes and Condillac, or the ontology of the later
+Kantians, has never ceased to poison philosophy. Once accustomed to
+consider scientific investigation as essentially consisting in the study
+of universals, men did not drop this habit of thought when they ceased
+to regard universals as possessing an independent existence: and even
+those who went the length of considering them as mere names, could not
+free themselves from the notion that the investigation of truth
+consisted entirely or partly in some kind of conjuration or juggle with
+those names. When a philosopher adopted fully the Nominalist view of the
+signification of general language, retaining along with it the _dictum
+de omni_ as the foundation of all reasoning, two such premises fairly
+put together were likely, if he was a consistent thinker, to land him in
+rather startling conclusions. Accordingly it has been seriously held, by
+writers of deserved celebrity, that the process of arriving at new
+truths by reasoning consists in the mere substitution of one set of
+arbitrary signs for another; a doctrine which they suppose to derive
+irresistible confirmation from the example of algebra. If there were any
+process in sorcery or necromancy more preternatural than this, I should
+be much surprised. The culminating point of this philosophy is the noted
+aphorism of Condillac, that a science is nothing, or scarcely anything,
+but _une langue bien faite_; in other words, that the one sufficient
+rule for discovering the nature and properties of objects is to name
+them properly: as if the reverse were not the truth, that it is
+impossible to name them properly except in proportion as we are already
+acquainted with their nature and properties. Can it be necessary to say,
+that none, not even the most trivial knowledge with respect to Things,
+ever was or could be originally got at by any conceivable manipulation
+of mere names, as such; and that what can be learned from names, is only
+what somebody who used the names knew before? Philosophical analysis
+confirms the indication of common sense, that the function of names is
+but that of enabling us to _remember_ and to _communicate_ our thoughts.
+That they also strengthen, even to an incalculable extent, the power of
+thought itself, is most true: but they do this by no intrinsic and
+peculiar virtue; they do it by the power inherent in an artificial
+memory, an instrument of which few have adequately considered the
+immense potency. As an artificial memory, language truly is, what it has
+so often been called, an instrument of thought; but it is one thing to
+be the instrument, and another to be the exclusive subject upon which
+the instrument is exercised. We think, indeed, to a considerable extent,
+by means of names, but what we think of, are the things called by those
+names; and there cannot be a greater error than to imagine that thought
+can be carried on with nothing in our mind but names, or that we can
+make the names think for us.
+
+
+§ 3. Those who considered the _dictum de omni_ as the foundation of the
+syllogism, looked upon arguments in a manner corresponding to the
+erroneous view which Hobbes took of propositions. Because there are some
+propositions which are merely verbal, Hobbes, in order apparently that
+his definition might be rigorously universal, defined a proposition as
+if no propositions declared anything except the meaning of words. If
+Hobbes was right; if no further account than this could be given of the
+import of propositions; no theory could be given but the commonly
+received one, of the combination of propositions in a syllogism. If the
+minor premise asserted nothing more than that something belongs to a
+class, and if the major premise asserted nothing of that class except
+that it is included in another class, the conclusion would only be that
+what was included in the lower class is included in the higher, and the
+result, therefore, nothing except that the classification is consistent
+with itself. But we have seen that it is no sufficient account of the
+meaning of a proposition, to say that it refers something to, or
+excludes something from, a class. Every proposition which conveys real
+information asserts a matter of fact, dependent on the laws of nature,
+and not on classification. It asserts that a given object does or does
+not possess a given attribute; or it asserts that two attributes, or
+sets of attributes, do or do not (constantly or occasionally) coexist.
+Since such is the purport of all propositions which convey any real
+knowledge, and since ratiocination is a mode of acquiring real
+knowledge, any theory of ratiocination which does not recognise this
+import of propositions, cannot, we may be sure, be the true one.
+
+Applying this view of propositions to the two premises of a syllogism,
+we obtain the following results. The major premise, which, as already
+remarked, is always universal, asserts, that all things which have a
+certain attribute (or attributes) have or have not along with it, a
+certain other attribute (or attributes). The minor premise asserts that
+the thing or set of things which are the subject of that premise, have
+the first-mentioned attribute; and the conclusion is, that they have (or
+that they have not) the second. Thus in our former example,
+
+  All men are mortal,
+  Socrates is a man,
+        therefore
+  Socrates is mortal,
+
+the subject and predicate of the major premise are connotative terms,
+denoting objects and connoting attributes. The assertion in the major
+premise is, that along with one of the two sets of attributes, we always
+find the other: that the attributes connoted by "man" never exist unless
+conjoined with the attribute called mortality. The assertion in the
+minor premise is that the individual named Socrates possesses the former
+attributes; and it is concluded that he possesses also the attribute
+mortality. Or if both the premises are general propositions, as
+
+  All men are mortal,
+  All kings are men,
+        therefore
+  All kings are mortal,
+
+the minor premise asserts that the attributes denoted by kingship only
+exist in conjunction with those signified by the word man. The major
+asserts as before, that the last-mentioned attributes are never found
+without the attribute of mortality. The conclusion is, that wherever the
+attributes of kingship are found, that of mortality is found also.
+
+If the major premise were negative, as, No men are omnipotent, it would
+assert, not that the attributes connoted by "man" never exist without,
+but that they never exist with, those connoted by "omnipotent:" from
+which, together with the minor premise, it is concluded, that the same
+incompatibility exists between the attribute omnipotence and those
+constituting a king. In a similar manner we might analyse any other
+example of the syllogism.
+
+If we generalize this process, and look out for the principle or law
+involved in every such inference, and presupposed in every syllogism,
+the propositions of which are anything more than merely verbal; we find,
+not the unmeaning _dictum de omni et nullo_, but a fundamental
+principle, or rather two principles, strikingly resembling the axioms of
+mathematics. The first, which is the principle of affirmative
+syllogisms, is, that things which coexist with the same thing, coexist
+with one another. The second is the principle of negative syllogisms,
+and is to this effect: that a thing which coexists with another thing,
+with which other a third thing does not coexist, is not coexistent with
+that third thing. These axioms manifestly relate to facts, and not to
+conventions; and one or other of them is the ground of the legitimacy of
+every argument in which facts and not conventions are the matter treated
+of.[5]
+
+
+§ 4. It remains to translate this exposition of the syllogism from the
+one into the other of the two languages in which we formerly
+remarked[6] that all propositions, and of course therefore all
+combinations of propositions, might be expressed. We observed that a
+proposition might be considered in two different lights; as a portion of
+our knowledge of nature, or as a memorandum for our guidance. Under the
+former, or speculative aspect, an affirmative general proposition is an
+assertion of a speculative truth, viz. that whatever has a certain
+attribute has a certain other attribute. Under the other aspect, it is
+to be regarded not as a part of our knowledge, but as an aid for our
+practical exigencies, by enabling us, when we see or learn that an
+object possesses one of the two attributes, to infer that it possesses
+the other; thus employing the first attribute as a mark or evidence of
+the second. Thus regarded, every syllogism comes within the following
+general formula:--
+
+  Attribute A is a mark of attribute B,
+  The given object has the mark A,
+              therefore
+  The given object has the attribute B.
+
+Referred to this type, the arguments which we have lately cited as
+specimens of the syllogism, will express themselves in the following
+manner:--
+
+  The attributes of man are a mark of the attribute mortality,
+  Socrates has the attributes of man,
+              therefore
+  Socrates has the attribute mortality.
+
+And again,
+
+  The attributes of man are a mark of the attribute mortality,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the attribute mortality.
+
+And, lastly,
+
+  The attributes of man are a mark of the absence of
+    the attribute omnipotence,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the absence of
+    the attribute signified by the word omnipotent
+    (or, are evidence of the absence of that attribute).
+
+To correspond with this alteration in the form of the syllogisms, the
+axioms on which the syllogistic process is founded must undergo a
+corresponding transformation. In this altered phraseology, both those
+axioms may be brought under one general expression; namely, that
+whatever has any mark, has that which it is a mark of. Or, when the
+minor premise as well as the major is universal, we may state it thus:
+Whatever is a mark of any mark, is a mark of that which this last is a
+mark of. To trace the identity of these axioms with those previously
+laid down, may be left to the intelligent reader. We shall find, as we
+proceed, the great convenience of the phraseology into which we have
+last thrown them, and which is better adapted than any I am acquainted
+with, to express with precision and force what is aimed at, and actually
+accomplished, in every case of the ascertainment of a truth by
+ratiocination.
+
+
+
+
+CHAPTER III.
+
+OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.
+
+
+§ 1. We have shown what is the real nature of the truths with which the
+Syllogism is conversant, in contradistinction to the more superficial
+manner in which their import is conceived in the common theory; and what
+are the fundamental axioms on which its probative force or
+conclusiveness depends. We have now to inquire, whether the syllogistic
+process, that of reasoning from generals to particulars, is, or is not,
+a process of inference; a progress from the known to the unknown: a
+means of coming to a knowledge of something which we did not know
+before.
+
+Logicians have been remarkably unanimous in their mode of answering this
+question. It is universally allowed that a syllogism is vicious if there
+be anything more in the conclusion than was assumed in the premises. But
+this is, in fact, to say, that nothing ever was, or can be, proved by
+syllogism, which was not known, or assumed to be known, before. Is
+ratiocination, then, not a process of inference? And is the syllogism,
+to which the word reasoning has so often been represented to be
+exclusively appropriate, not really entitled to be called reasoning at
+all? This seems an inevitable consequence of the doctrine, admitted by
+all writers on the subject, that a syllogism can prove no more than is
+involved in the premises. Yet the acknowledgment so explicitly made, has
+not prevented one set of writers from continuing to represent the
+syllogism as the correct analysis of what the mind actually performs in
+discovering and proving the larger half of the truths, whether of
+science or of daily life, which we believe; while those who have avoided
+this inconsistency, and followed out the general theorem respecting the
+logical value of the syllogism to its legitimate corollary, have been
+led to impute uselessness and frivolity to the syllogistic theory
+itself, on the ground of the _petitio principii_ which they allege to be
+inherent in every syllogism. As I believe both these opinions to be
+fundamentally erroneous, I must request the attention of the reader to
+certain considerations, without which any just appreciation of the true
+character of the syllogism, and the functions it performs in philosophy,
+appears to me impossible; but which seem to have been either overlooked,
+or insufficiently adverted to, both by the defenders of the syllogistic
+theory and by its assailants.
+
+
+§ 2. It must be granted that in every syllogism, considered as an
+argument to prove the conclusion, there is a _petitio principii_. When
+we say,
+
+  All men are mortal,
+  Socrates is a man,
+      therefore
+  Socrates is mortal;
+
+it is unanswerably urged by the adversaries of the syllogistic theory,
+that the proposition, Socrates is mortal, is presupposed in the more
+general assumption, All men are mortal: that we cannot be assured of the
+mortality of all men, unless we are already certain of the mortality of
+every individual man: that if it be still doubtful whether Socrates, or
+any other individual we choose to name, be mortal or not, the same
+degree of uncertainty must hang over the assertion, All men are mortal:
+that the general principle, instead of being given as evidence of the
+particular case, cannot itself be taken for true without exception,
+until every shadow of doubt which could affect any case comprised with
+it, is dispelled by evidence _aliundè_; and then what remains for the
+syllogism to prove? That, in short, no reasoning from generals to
+particulars can, as such, prove anything: since from a general principle
+we cannot infer any particulars, but those which the principle itself
+assumes as known.
+
+This doctrine appears to me irrefragable; and if logicians, though
+unable to dispute it, have usually exhibited a strong disposition to
+explain it away, this was not because they could discover any flaw in
+the argument itself, but because the contrary opinion seemed to rest on
+arguments equally indisputable. In the syllogism last referred to, for
+example, or in any of those which we previously constructed, is it not
+evident that the conclusion may, to the person to whom the syllogism is
+presented, be actually and _bonâ fide_ a new truth? Is it not matter of
+daily experience that truths previously unthought of, facts which have
+not been, and cannot be, directly observed, are arrived at by way of
+general reasoning? We believe that the Duke of Wellington is mortal. We
+do not know this by direct observation, so long as he is not yet dead.
+If we were asked how, this being the case, we know the duke to be
+mortal, we should probably answer, Because all men are so. Here,
+therefore, we arrive at the knowledge of a truth not (as yet)
+susceptible of observation, by a reasoning which admits of being
+exhibited in the following syllogism:--
+
+  All men are mortal,
+  The Duke of Wellington is a man,
+              therefore
+  The Duke of Wellington is mortal.
+
+And since a large portion of our knowledge is thus acquired, logicians
+have persisted in representing the syllogism as a process of inference
+or proof; though none of them has cleared up the difficulty which arises
+from the inconsistency between that assertion, and the principle, that
+if there be anything in the conclusion which was not already asserted in
+the premises, the argument is vicious. For it is impossible to attach
+any serious scientific value to such a mere salvo, as the distinction
+drawn between being involved _by implication_ in the premises, and being
+directly asserted in them. When Archbishop Whately says[7] that the
+object of reasoning is "merely to expand and unfold the assertions wrapt
+up, as it were, and implied in those with which we set out, and to bring
+a person to perceive and acknowledge the full force of that which he
+has admitted," he does not, I think, meet the real difficulty requiring
+to be explained, namely, how it happens that a science, like geometry,
+_can_ be all "wrapt up" in a few definitions and axioms. Nor does this
+defence of the syllogism differ much from what its assailants urge
+against it as an accusation, when they charge it with being of no use
+except to those who seek to press the consequences of an admission into
+which a person has been entrapped without having considered and
+understood its full force. When you admitted the major premise, you
+asserted the conclusion; but, says Archbishop Whately, you asserted it
+by implication merely: this, however, can here only mean that you
+asserted it unconsciously; that you did not know you were asserting it;
+but, if so, the difficulty revives in this shape--Ought you not to have
+known? Were you warranted in asserting the general proposition without
+having satisfied yourself of the truth of everything which it fairly
+includes? And if not, is not the syllogistic art _primâ facie_ what its
+assailants affirm it to be, a contrivance for catching you in a trap,
+and holding you fast in it?[8]
+
+
+§ 3. From this difficulty there appears to be but one issue. The
+proposition that the Duke of Wellington is mortal, is evidently an
+inference; it is got at as a conclusion from something else; but do we,
+in reality, conclude it from the proposition, All men are mortal? I
+answer, no.
+
+The error committed is, I conceive, that of overlooking the distinction
+between two parts of the process of philosophizing, the inferring part,
+and the registering part; and ascribing to the latter the functions of
+the former. The mistake is that of referring a person to his own notes
+for the origin of his knowledge. If a person is asked a question, and is
+at the moment unable to answer it, he may refresh his memory by turning
+to a memorandum which he carries about with him. But if he were asked,
+how the fact came to his knowledge, he would scarcely answer, because it
+was set down in his note-book: unless the book was written, like the
+Koran, with a quill from the wing of the angel Gabriel.
+
+Assuming that the proposition, The Duke of Wellington is mortal, is
+immediately an inference from the proposition, All men are mortal;
+whence do we derive our knowledge of that general truth? Of course from
+observation. Now, all which man can observe are individual cases. From
+these all general truths must be drawn, and into these they may be again
+resolved; for a general truth is but an aggregate of particular truths;
+a comprehensive expression, by which an indefinite number of individual
+facts are affirmed or denied at once. But a general proposition is not
+merely a compendious form for recording and preserving in the memory a
+number of particular facts, all of which have been observed.
+Generalization is not a process of mere naming, it is also a process of
+inference. From instances which we have observed, we feel warranted in
+concluding, that what we found true in those instances, holds in all
+similar ones, past, present, and future, however numerous they may be.
+We then, by that valuable contrivance of language which enables us to
+speak of many as if they were one, record all that we have observed,
+together with all that we infer from our observations, in one concise
+expression; and have thus only one proposition, instead of an endless
+number, to remember or to communicate. The results of many observations
+and inferences, and instructions for making innumerable inferences in
+unforeseen cases, are compressed into one short sentence.
+
+When, therefore, we conclude from the death of John and Thomas, and
+every other person we ever heard of in whose case the experiment had
+been fairly tried, that the Duke of Wellington is mortal like the rest;
+we may, indeed, pass through the generalization, All men are mortal, as
+an intermediate stage; but it is not in the latter half of the process,
+the descent from all men to the Duke of Wellington, that the _inference_
+resides. The inference is finished when we have asserted that all men
+are mortal. What remains to be performed afterwards is merely
+decyphering our own notes.
+
+Archbishop Whately has contended that syllogizing, or reasoning from
+generals to particulars, is not, agreeably to the vulgar idea, a
+peculiar _mode_ of reasoning, but the philosophical analysis of _the_
+mode in which all men reason, and must do so if they reason at all. With
+the deference due to so high an authority, I cannot help thinking that
+the vulgar notion is, in this case, the more correct. If, from our
+experience of John, Thomas, &c., who once were living, but are now dead,
+we are entitled to conclude that all human beings are mortal, we might
+surely without any logical inconsequence have concluded at once from
+those instances, that the Duke of Wellington is mortal. The mortality of
+John, Thomas, and company is, after all, the whole evidence we have for
+the mortality of the Duke of Wellington. Not one iota is added to the
+proof by interpolating a general proposition. Since the individual cases
+are all the evidence we can possess, evidence which no logical form into
+which we choose to throw it can make greater than it is; and since that
+evidence is either sufficient in itself, or, if insufficient for the one
+purpose, cannot be sufficient for the other; I am unable to see why we
+should be forbidden to take the shortest cut from these sufficient
+premises to the conclusion, and constrained to travel the "high priori
+road," by the arbitrary fiat of logicians. I cannot perceive why it
+should be impossible to journey from one place to another unless we
+"march up a hill, and then march down again." It may be the safest road,
+and there may be a resting-place at the top of the hill, affording a
+commanding view of the surrounding country; but for the mere purpose of
+arriving at our journey's end, our taking that road is perfectly
+optional; it is a question of time, trouble, and danger.
+
+Not only _may_ we reason from particulars to particulars without passing
+through generals, but we perpetually do so reason. All our earliest
+inferences are of this nature. From the first dawn of intelligence we
+draw inferences, but years elapse before we learn the use of general
+language. The child, who, having burnt his fingers, avoids to thrust
+them again into the fire, has reasoned or inferred, though he has never
+thought of the general maxim, Fire burns. He knows from memory that he
+has been burnt, and on this evidence believes, when he sees a candle,
+that if he puts his finger into the flame of it, he will be burnt again.
+He believes this in every case which happens to arise; but without
+looking, in each instance, beyond the present case. He is not
+generalizing; he is inferring a particular from particulars. In the same
+way, also, brutes reason. There is no ground for attributing to any of
+the lower animals the use of signs, of such a nature as to render
+general propositions possible. But those animals profit by experience,
+and avoid what they have found to cause them pain, in the same manner,
+though not always with the same skill, as a human creature. Not only the
+burnt child, but the burnt dog, dreads the fire.
+
+I believe that, in point of fact, when drawing inferences from our
+personal experience, and not from maxims handed down to us by books or
+tradition, we much oftener conclude from particulars to particulars
+directly, than through the intermediate agency of any general
+proposition. We are constantly reasoning from ourselves to other people,
+or from one person to another, without giving ourselves the trouble to
+erect our observations into general maxims of human or external nature.
+When we conclude that some person will, on some given occasion, feel or
+act so and so, we sometimes judge from an enlarged consideration of the
+manner in which human beings in general, or persons of some particular
+character, are accustomed to feel and act: but much oftener from merely
+recollecting the feelings and conduct of the same person in some
+previous instance, or from considering how we should feel or act
+ourselves. It is not only the village matron, who, when called to a
+consultation upon the case of a neighbour's child, pronounces on the
+evil and its remedy simply on the recollection and authority of what she
+accounts the similar case of her Lucy. We all, where we have no definite
+maxims to steer by, guide ourselves in the same way: and if we have an
+extensive experience, and retain its impressions strongly, we may
+acquire in this manner a very considerable power of accurate judgment,
+which we may be utterly incapable of justifying or of communicating to
+others. Among the higher order of practical intellects there have been
+many of whom it was remarked how admirably they suited their means to
+their ends, without being able to give any sufficient reasons for what
+they did; and applied, or seemed to apply, recondite principles which
+they were wholly unable to state. This is a natural consequence of
+having a mind stored with appropriate particulars, and having been long
+accustomed to reason at once from these to fresh particulars, without
+practising the habit of stating to oneself or to others the
+corresponding general propositions. An old warrior, on a rapid glance at
+the outlines of the ground, is able at once to give the necessary orders
+for a skilful arrangement of his troops; though if he has received
+little theoretical instruction, and has seldom been called upon to
+answer to other people for his conduct, he may never have had in his
+mind a single general theorem respecting the relation between ground and
+array. But his experience of encampments, in circumstances more or less
+similar, has left a number of vivid, unexpressed, ungeneralized
+analogies in his mind, the most appropriate of which, instantly
+suggesting itself, determines him to a judicious arrangement.
+
+The skill of an uneducated person in the use of weapons, or of tools,
+is of a precisely similar nature. The savage who executes unerringly the
+exact throw which brings down his game, or his enemy, in the manner most
+suited to his purpose, under the operation of all the conditions
+necessarily involved, the weight and form of the weapon, the direction
+and distance of the object, the action of the wind, &c., owes this power
+to a long series of previous experiments, the results of which he
+certainly never framed into any verbal theorems or rules. The same thing
+may generally be said of any other extraordinary manual dexterity. Not
+long ago a Scotch manufacturer procured from England, at a high rate of
+wages, a working dyer, famous for producing very fine colours, with the
+view of teaching to his other workmen the same skill. The workman came;
+but his mode of proportioning the ingredients, in which lay the secret
+of the effects he produced, was by taking them up in handfuls, while the
+common method was to weigh them. The manufacturer sought to make him
+turn his handling system into an equivalent weighing system, that the
+general principle of his peculiar mode of proceeding might be
+ascertained. This, however, the man found himself quite unable to do,
+and therefore could impart his skill to nobody. He had, from the
+individual cases of his own experience, established a connexion in his
+mind between fine effects of colour, and tactual perceptions in handling
+his dyeing materials; and from these perceptions he could, in any
+particular case, infer the means to be employed, and the effects which
+would be produced, but could not put others in possession of the grounds
+on which he proceeded, from having never generalized them in his own
+mind, or expressed them in language.
+
+Almost every one knows Lord Mansfield's advice to a man of practical
+good sense, who, being appointed governor of a colony, had to preside in
+its court of justice, without previous judicial practice or legal
+education. The advice was to give his decision boldly, for it would
+probably be right; but never to venture on assigning reasons, for they
+would almost infallibly be wrong. In cases like this, which are of no
+uncommon occurrence, it would be absurd to suppose that the bad reason
+was the source of the good decision. Lord Mansfield knew that if any
+reason were assigned it would be necessarily an afterthought, the judge
+being _in fact_ guided by impressions from past experience, without the
+circuitous process of framing general principles from them, and that if
+he attempted to frame any such he would assuredly fail. Lord Mansfield,
+however, would not have doubted that a man of equal experience who had
+also a mind stored with general propositions derived by legitimate
+induction from that experience, would have been greatly preferable as a
+judge, to one, however sagacious, who could not be trusted with the
+explanation and justification of his own judgments. The cases of men of
+talent performing wonderful things they know not how, are examples of
+the rudest and most spontaneous form of the operations of superior
+minds. It is a defect in them, and often a source of errors, not to have
+generalized as they went on; but generalization, though a help, the most
+important indeed of all helps, is not an essential.
+
+Even the scientifically instructed, who possess, in the form of general
+propositions, a systematic record of the results of the experience of
+mankind, need not always revert to those general propositions in order
+to apply that experience to a new case. It is justly remarked by Dugald
+Stewart, that though the reasonings in mathematics depend entirely on
+the axioms, it is by no means necessary to our seeing the conclusiveness
+of the proof, that the axioms should be expressly adverted to. When it
+is inferred that AB is equal to CD because each of them is equal to EF,
+the most uncultivated understanding, as soon as the propositions were
+understood, would assent to the inference, without having ever heard of
+the general truth that "things which are equal to the same thing are
+equal to one another." This remark of Stewart, consistently followed
+out, goes to the root, as I conceive, of the philosophy of
+ratiocination; and it is to be regretted that he himself stopt short at
+a much more limited application of it. He saw that the general
+propositions on which a reasoning is said to depend, may, in certain
+cases, be altogether omitted, without impairing its probative force.
+But he imagined this to be a peculiarity belonging to axioms; and argued
+from it, that axioms are not the foundations or first principles of
+geometry, from which all the other truths of the science are
+synthetically deduced (as the laws of motion and of the composition of
+forces in dynamics, the equal mobility of fluids in hydrostatics, the
+laws of reflection and refraction in optics, are the first principles of
+those sciences); but are merely necessary assumptions, self-evident
+indeed, and the denial of which would annihilate all demonstration, but
+from which, as premises, nothing can be demonstrated. In the present, as
+in many other instances, this thoughtful and elegant writer has
+perceived an important truth, but only by halves. Finding, in the case
+of geometrical axioms, that general names have not any talismanic virtue
+for conjuring new truths out of the well where they lie hid, and not
+seeing that this is equally true in every other case of generalization,
+he contended that axioms are in their nature barren of consequences, and
+that the really fruitful truths, the real first principles of geometry,
+are the definitions; that the definition, for example, of the circle is
+to the properties of the circle, what the laws of equilibrium and of the
+pressure of the atmosphere are to the rise of the mercury in the
+Torricellian tube. Yet all that he had asserted respecting the function
+to which the axioms are confined in the demonstrations of geometry,
+holds equally true of the definitions. Every demonstration in Euclid
+might be carried on without them. This is apparent from the ordinary
+process of proving a proposition of geometry by means of a diagram. What
+assumption, in fact, do we set out from, to demonstrate by a diagram any
+of the properties of the circle? Not that in all circles the radii are
+equal, but only that they are so in the circle ABC. As our warrant for
+assuming this, we appeal, it is true, to the definition of a circle in
+general; but it is only necessary that the assumption be granted in the
+case of the particular circle supposed. From this, which is not a
+general but a singular proposition, combined with other propositions of
+a similar kind, some of which _when generalized_ are called definitions,
+and others axioms, we prove that a certain conclusion is true, not of
+all circles, but of the particular circle ABC; or at least would be so,
+if the facts precisely accorded with our assumptions. The enunciation,
+as it is called, that is, the general theorem which stands at the head
+of the demonstration, is not the proposition actually demonstrated. One
+instance only is demonstrated: but the process by which this is done, is
+a process which, when we consider its nature, we perceive might be
+exactly copied in an indefinite number of other instances; in every
+instance which conforms to certain conditions. The contrivance of
+general language furnishing us with terms which connote these
+conditions, we are able to assert this indefinite multitude of truths in
+a single expression, and this expression is the general theorem. By
+dropping the use of diagrams, and substituting, in the demonstrations,
+general phrases for the letters of the alphabet, we might prove the
+general theorem directly, that is, we might demonstrate all the cases at
+once; and to do this we must, of course, employ as our premises, the
+axioms and definitions in their general form. But this only means, that
+if we can prove an individual conclusion by assuming an individual fact,
+then in whatever case we are warranted in making an exactly similar
+assumption, we may draw an exactly similar conclusion. The definition is
+a sort of notice to ourselves and others, what assumptions we think
+ourselves entitled to make. And so in all cases, the general
+propositions, whether called definitions, axioms, or laws of nature,
+which we lay down at the beginning of our reasonings, are merely
+abridged statements, in a kind of short-hand, of the particular facts,
+which, as occasion arises, we either think we may proceed on as proved,
+or intend to assume. In any one demonstration it is enough if we assume
+for a particular case suitably selected, what by the statement of the
+definition or principle we announce that we intend to assume in all
+cases which may arise. The definition of the circle, therefore, is to
+one of Euclid's demonstrations, exactly what, according to Stewart, the
+axioms are; that is, the demonstration does not depend on it, but yet if
+we deny it the demonstration fails. The proof does not rest on the
+general assumption, but on a similar assumption confined to the
+particular case: that case, however, being chosen as a specimen or
+paradigm of the whole class of cases included in the theorem, there can
+be no ground for making the assumption in that case which does not exist
+in every other; and to deny the assumption as a general truth, is to
+deny the right of making it in the particular instance.
+
+There are, undoubtedly, the most ample reasons for stating both the
+principles and the theorems in their general form, and these will be
+explained presently, so far as explanation is requisite. But, that
+unpractised learners, even in making use of one theorem to demonstrate
+another, reason rather from particular to particular than from the
+general proposition, is manifest from the difficulty they find in
+applying a theorem to a case in which the configuration of the diagram
+is extremely unlike that of the diagram by which the original theorem
+was demonstrated. A difficulty which, except in cases of unusual mental
+power, long practice can alone remove, and removes chiefly by rendering
+us familiar with all the configurations consistent with the general
+conditions of the theorem.
+
+
+§ 4. From the considerations now adduced, the following conclusions seem
+to be established. All inference is from particulars to particulars:
+General propositions are merely registers of such inferences already
+made, and short formulæ for making more: The major premise of a
+syllogism, consequently, is a formula of this description: and the
+conclusion is not an inference drawn _from_ the formula, but an
+inference drawn _according_ to the formula: the real logical antecedent,
+or premise, being the particular facts from which the general
+proposition was collected by induction. Those facts, and the individual
+instances which supplied them, may have been forgotten: but a record
+remains, not indeed descriptive of the facts themselves, but showing how
+those cases may be distinguished, respecting which the facts, when
+known, were considered to warrant a given inference. According to the
+indications of this record we draw our conclusion; which is, to all
+intents and purposes, a conclusion from the forgotten facts. For this
+it is essential that we should read the record correctly: and the rules
+of the syllogism are a set of precautions to ensure our doing so.
+
+This view of the functions of the syllogism is confirmed by the
+consideration of precisely those cases which might be expected to be
+least favourable to it, namely, those in which ratiocination is
+independent of any previous induction. We have already observed that the
+syllogism, in the ordinary course of our reasoning, is only the latter
+half of the process of travelling from premises to a conclusion. There
+are, however, some peculiar cases in which it is the whole process.
+Particulars alone are capable of being subjected to observation; and all
+knowledge which is derived from observation, begins, therefore, of
+necessity, in particulars; but our knowledge may, in cases of certain
+descriptions, be conceived as coming to us from other sources than
+observation. It may present itself as coming from testimony, which, on
+the occasion and for the purpose in hand, is accepted as of an
+authoritative character: and the information thus communicated, may be
+conceived to comprise not only particular facts but general
+propositions, as when a scientific doctrine is accepted without
+examination on the authority of writers, or a theological doctrine on
+that of Scripture. Or the generalization may not be, in the ordinary
+sense, an assertion at all, but a command; a law, not in the
+philosophical, but in the moral and political sense of the term: an
+expression of the desire of a superior, that we, or any number of other
+persons, shall conform our conduct to certain general instructions. So
+far as this asserts a fact, namely, a volition of the legislator, that
+fact is an individual fact, and the proposition, therefore, is not a
+general proposition. But the description therein contained of the
+conduct which it is the will of the legislator that his subjects should
+observe, is general. The proposition asserts, not that all men _are_
+anything, but that all men _shall_ do something.
+
+In both these cases the generalities are the original data, and the
+particulars are elicited from them by a process which correctly resolves
+itself into a series of syllogisms. The real nature, however, of the
+supposed deductive process, is evident enough. The only point to be
+determined is, whether the authority which declared the general
+proposition, intended to include this case in it; and whether the
+legislator intended his command to apply to the present case among
+others, or not. This is ascertained by examining whether the case
+possesses the marks by which, as those authorities have signified, the
+cases which they meant to certify or to influence may be known. The
+object of the inquiry is to make out the witness's or the legislator's
+intention, through the indication given by their words. This is a
+question, as the Germans express it, of hermeneutics. The operation is
+not a process of inference, but a process of interpretation.
+
+In this last phrase we have obtained an expression which appears to me
+to characterize, more aptly than any other, the functions of the
+syllogism in all cases. When the premises are given by authority, the
+function of Reasoning is to ascertain the testimony of a witness, or the
+will of a legislator, by interpreting the signs in which the one has
+intimated his assertion and the other his command. In like manner, when
+the premises are derived from observation, the function of Reasoning is
+to ascertain what we (or our predecessors) formerly thought might be
+inferred from the observed facts, and to do this by interpreting a
+memorandum of ours, or of theirs. The memorandum reminds us, that from
+evidence, more or less carefully weighed, it formerly appeared that a
+certain attribute might be inferred wherever we perceive a certain mark.
+The proposition, All men are mortal (for instance) shows that we have
+had experience from which we thought it followed that the attributes
+connoted by the term man, are a mark of mortality. But when we conclude
+that the Duke of Wellington is mortal, we do not infer this from the
+memorandum, but from the former experience. All that we infer from the
+memorandum is our own previous belief, (or that of those who transmitted
+to us the proposition), concerning the inferences which that former
+experience would warrant.
+
+This view of the nature of the syllogism renders consistent and
+intelligible what otherwise remains obscure and confused in the theory
+of Archbishop Whately and other enlightened defenders of the syllogistic
+doctrine, respecting the limits to which its functions are confined.
+They affirm in as explicit terms as can be used, that the sole office of
+general reasoning is to prevent inconsistency in our opinions; to
+prevent us from assenting to anything, the truth of which would
+contradict something to which we had previously on good grounds given
+our assent. And they tell us, that the sole ground which a syllogism
+affords for assenting to the conclusion, is that the supposition of its
+being false, combined with the supposition that the premises are true,
+would lead to a contradiction in terms. Now this would be but a lame
+account of the real grounds which we have for believing the facts which
+we learn from reasoning, in contradistinction to observation. The true
+reason why we believe that the Duke of Wellington will die, is that his
+fathers, and our fathers, and all other persons who were cotemporary
+with them, have died. Those facts are the real premises of the
+reasoning. But we are not led to infer the conclusion from those
+premises, by the necessity of avoiding any verbal inconsistency. There
+is no contradiction in supposing that all those persons have died, and
+that the Duke of Wellington may, notwithstanding, live for ever. But
+there would be a contradiction if we first, on the ground of those same
+premises, made a general assertion including and covering the case of
+the Duke of Wellington, and then refused to stand to it in the
+individual case. There is an inconsistency to be avoided between the
+memorandum we make of the inferences which may be justly drawn in future
+cases, and the inferences we actually draw in those cases when they
+arise. With this view we interpret our own formula, precisely as a judge
+interprets a law: in order that we may avoid drawing any inferences not
+conformable to our former intention, as a judge avoids giving any
+decision not conformable to the legislator's intention. The rules for
+this interpretation are the rules of the syllogism: and its sole purpose
+is to maintain consistency between the conclusions we draw in every
+particular case, and the previous general directions for drawing them;
+whether those general directions were framed by ourselves as the result
+of induction, or were received by us from an authority competent to give
+them.
+
+
+§ 5. In the above observations it has, I think, been shown, that, though
+there is always a process of reasoning or inference where a syllogism is
+used, the syllogism is not a correct analysis of that process of
+reasoning or inference; which is, on the contrary, (when not a mere
+inference from testimony) an inference from particulars to particulars;
+authorized by a previous inference from particulars to generals, and
+substantially the same with it; of the nature, therefore, of Induction.
+But while these conclusions appear to me undeniable, I must yet enter a
+protest, as strong as that of Archbishop Whately himself, against the
+doctrine that the syllogistic art is useless for the purposes of
+reasoning. The reasoning lies in the act of generalization, not in
+interpreting the record of that act; but the syllogistic form is an
+indispensable collateral security for the correctness of the
+generalization itself.
+
+It has already been seen, that if we have a collection of particulars
+sufficient for grounding an induction, we need not frame a general
+proposition; we may reason at once from those particulars to other
+particulars. But it is to be remarked withal, that whenever, from a set
+of particular cases, we can legitimately draw any inference, we may
+legitimately make our inference a general one. If, from observation and
+experiment, we can conclude to one new case, so may we to an indefinite
+number. If that which has held true in our past experience will
+therefore hold in time to come, it will hold not merely in some
+individual case, but in all cases of some given description. Every
+induction, therefore, which suffices to prove one fact, proves an
+indefinite multitude of facts: the experience which justifies a single
+prediction must be such as will suffice to bear out a general theorem.
+This theorem it is extremely important to ascertain and declare, in its
+broadest form of generality; and thus to place before our minds, in its
+full extent, the whole of what our evidence must prove if it proves
+anything.
+
+This throwing of the whole body of possible inferences from a given set
+of particulars, into one general expression, operates as a security for
+their being just inferences, in more ways than one. First, the general
+principle presents a larger object to the imagination than any of the
+singular propositions which it contains. A process of thought which
+leads to a comprehensive generality, is felt as of greater importance
+than one which terminates in an insulated fact; and the mind is, even
+unconsciously, led to bestow greater attention upon the process, and to
+weigh more carefully the sufficiency of the experience appealed to, for
+supporting the inference grounded upon it. There is another, and a more
+important, advantage. In reasoning from a course of individual
+observations to some new and unobserved case, which we are but
+imperfectly acquainted with (or we should not be inquiring into it), and
+in which, since we are inquiring into it, we probably feel a peculiar
+interest; there is very little to prevent us from giving way to
+negligence, or to any bias which may affect our wishes or our
+imagination, and, under that influence, accepting insufficient evidence
+as sufficient. But if, instead of concluding straight to the particular
+case, we place before ourselves an entire class of facts--the whole
+contents of a general proposition, every tittle of which is legitimately
+inferrible from our premises, if that one particular conclusion is so;
+there is then a considerable likelihood that if the premises are
+insufficient, and the general inference, therefore, groundless, it will
+comprise within it some fact or facts the reverse of which we already
+know to be true; and we shall thus discover the error in our
+generalization by a _reductio ad impossibile_.
+
+Thus if, during the reign of Marcus Aurelius, a subject of the Roman
+empire, under the bias naturally given to the imagination and
+expectations by the lives and characters of the Antonines, had been
+disposed to expect that Commodus would be a just ruler; supposing him to
+stop there, he might only have been undeceived by sad experience. But if
+he reflected that this expectation could not be justifiable unless from
+the same evidence he was warranted in concluding some general
+proposition, as, for instance, that all Roman emperors are just rulers;
+he would immediately have thought of Nero, Domitian, and other
+instances, which, showing the falsity of the general conclusion, and
+therefore the insufficiency of the premises, would have warned him that
+those premises could not prove in the instance of Commodus, what they
+were inadequate to prove in any collection of cases in which his was
+included.
+
+The advantage, in judging whether any controverted inference is
+legitimate, of referring to a parallel case, is universally
+acknowledged. But by ascending to the general proposition, we bring
+under our view not one parallel case only, but all possible parallel
+cases at once; all cases to which the same set of evidentiary
+considerations are applicable.
+
+When, therefore, we argue from a number of known cases to another case
+supposed to be analogous, it is always possible, and generally
+advantageous, to divert our argument into the circuitous channel of an
+induction from those known cases to a general proposition, and a
+subsequent application of that general proposition to the unknown case.
+This second part of the operation, which, as before observed, is
+essentially a process of interpretation, will be resolvable into a
+syllogism or a series of syllogisms, the majors of which will be general
+propositions embracing whole classes of cases; every one of which
+propositions must be true in all its extent, if the argument is
+maintainable. If, therefore, any fact fairly coming within the range of
+one of these general propositions, and consequently asserted by it, is
+known or suspected to be other than the proposition asserts it to be,
+this mode of stating the argument causes us to know or to suspect that
+the original observations, which are the real grounds of our conclusion,
+are not sufficient to support it. And in proportion to the greater
+chance of our detecting the inconclusiveness of our evidence, will be
+the increased reliance we are entitled to place in it if no such
+evidence of defect shall appear.
+
+The value, therefore, of the syllogistic form, and of the rules for
+using it correctly, does not consist in their being the form and the
+rules according to which our reasonings are necessarily, or even
+usually, made; but in their furnishing us with a mode in which those
+reasonings may always be represented, and which is admirably calculated,
+if they are inconclusive, to bring their inconclusiveness to light. An
+induction from particulars to generals, followed by a syllogistic
+process from those generals to other particulars, is a form in which we
+may always state our reasonings if we please. It is not a form in which
+we _must_ reason, but it is a form in which we _may_ reason, and into
+which it is indispensable to throw our reasoning, when there is any
+doubt of its validity: though when the case is familiar and little
+complicated, and there is no suspicion of error, we may, and do, reason
+at once from the known particular cases to unknown ones.[9]
+
+These are the uses of syllogism, as a mode of verifying any given
+argument. Its ulterior uses, as respects the general course of our
+intellectual operations, hardly require illustration, being in fact the
+acknowledged uses of general language. They amount substantially to
+this, that the inductions may be made once for all: a single careful
+interrogation of experience may suffice, and the result may be
+registered in the form of a general proposition, which is committed to
+memory or to writing, and from which afterwards we have only to
+syllogize. The particulars of our experiments may then be dismissed from
+the memory, in which it would be impossible to retain so great a
+multitude of details; while the knowledge which those details afforded
+for future use, and which would otherwise be lost as soon as the
+observations were forgotten, or as their record became too bulky for
+reference, is retained in a commodious and immediately available shape
+by means of general language.
+
+Against this advantage is to be set the countervailing inconvenience,
+that inferences originally made on insufficient evidence, become
+consecrated, and, as it were, hardened into general maxims; and the mind
+cleaves to them from habit, after it has outgrown any liability to be
+misled by similar fallacious appearances if they were now for the first
+time presented; but having forgotten the particulars, it does not think
+of revising its own former decision. An inevitable drawback, which,
+however considerable in itself, forms evidently but a small set-off
+against the immense benefits of general language.
+
+The use of the syllogism is in truth no other than the use of general
+propositions in reasoning. We _can_ reason without them; in simple and
+obvious cases we habitually do so; minds of great sagacity can do it in
+cases not simple and obvious, provided their experience supplies them
+with instances essentially similar to every combination of circumstances
+likely to arise. But other minds, and the same minds where they have not
+the same pre-eminent advantages of personal experience, are quite
+helpless without the aid of general propositions, wherever the case
+presents the smallest complication; and if we made no general
+propositions, few persons would get much beyond those simple inferences
+which are drawn by the more intelligent of the brutes. Though not
+necessary to reasoning, general propositions are necessary to any
+considerable progress in reasoning. It is, therefore, natural and
+indispensable to separate the process of investigation into two parts;
+and obtain general formulæ for determining what inferences may be drawn,
+before the occasion arises for drawing the inferences. The work of
+drawing them is then that of applying the formulæ; and the rules of
+syllogism are a system of securities for the correctness of the
+application.
+
+
+§ 6. To complete the series of considerations connected with the
+philosophical character of the syllogism, it is requisite to consider,
+since the syllogism is not the universal type of the reasoning process,
+what is the real type. This resolves itself into the question, what is
+the nature of the minor premise, and in what manner it contributes to
+establish the conclusion: for as to the major, we now fully understand,
+that the place which it nominally occupies in our reasonings, properly
+belongs to the individual facts or observations of which it expresses
+the general result; the major itself being no real part of the argument,
+but an intermediate halting-place for the mind, interposed by an
+artifice of language between the real premises and the conclusion, by
+way of a security, which it is in a most material degree, for the
+correctness of the process. The minor, however, being an indispensable
+part of the syllogistic expression of an argument, without doubt either
+is, or corresponds to, an equally indispensable part of the argument
+itself, and we have only to inquire what part.
+
+It is perhaps worth while to notice here a speculation of a philosopher
+to whom mental science is much indebted, but who, though a very
+penetrating, was a very hasty thinker, and whose want of due
+circumspection rendered him fully as remarkable for what he did not see,
+as for what he saw. I allude to Dr. Thomas Brown, whose theory of
+ratiocination is peculiar. He saw the _petitio principii_ which is
+inherent in every syllogism, if we consider the major to be itself the
+evidence by which the conclusion is proved, instead of being, what in
+fact it is, an assertion of the existence of evidence sufficient to
+prove any conclusion of a given description. Seeing this, Dr. Brown not
+only failed to see the immense advantage, in point of security for
+correctness, which is gained by interposing this step between the real
+evidence and the conclusion; but he thought it incumbent on him to
+strike out the major altogether from the reasoning process, without
+substituting anything else, and maintained that our reasonings consist
+only of the minor premise and the conclusion, Socrates is a man,
+therefore Socrates is mortal: thus actually suppressing, as an
+unnecessary step in the argument, the appeal to former experience. The
+absurdity of this was disguised from him by the opinion he adopted, that
+reasoning is merely analysing our own general notions, or abstract
+ideas; and that the proposition, Socrates is mortal, is evolved from the
+proposition, Socrates is a man, simply by recognising the notion of
+mortality as already contained in the notion we form of a man.
+
+After the explanations so fully entered into on the subject of
+propositions, much further discussion cannot be necessary to make the
+radical error of this view of ratiocination apparent. If the word man
+connoted mortality; if the meaning of "mortal" were involved in the
+meaning of "man;" we might, undoubtedly, evolve the conclusion from the
+minor alone, because the minor would have already asserted it. But if,
+as is in fact the case, the word man does not connote mortality, how
+does it appear that in the mind of every person who admits Socrates to
+be a man, the idea of man must include the idea of mortality? Dr. Brown
+could not help seeing this difficulty, and in order to avoid it, was
+led, contrary to his intention, to re-establish, under another name,
+that step in the argument which corresponds to the major, by affirming
+the necessity of _previously perceiving_ the relation between the idea
+of man and the idea of mortal. If the reasoner has not previously
+perceived this relation, he will not, says Dr. Brown, infer because
+Socrates is a man, that Socrates is mortal. But even this admission,
+though amounting to a surrender of the doctrine that an argument
+consists of the minor and the conclusion alone, will not save the
+remainder of Dr. Brown's theory. The failure of assent to the argument
+does not take place merely because the reasoner, for want of due
+analysis, does not perceive that his idea of man includes the idea of
+mortality; it takes place, much more commonly, because in his mind that
+relation between the two ideas has never existed. And in truth it never
+does exist, except as the result of experience. Consenting, for the sake
+of the argument, to discuss the question on a supposition of which we
+have recognised the radical incorrectness, namely, that the meaning of a
+proposition relates to the ideas of the things spoken of, and not to
+the things themselves; I must yet observe, that the idea of man, as an
+universal idea, the common property of all rational creatures, cannot
+involve anything but what is strictly implied in the name. If any one
+includes in his own private idea of man, as no doubt is always the case,
+some other attributes, such for instance as mortality, he does so only
+as the consequence of experience, after having satisfied himself that
+all men possess that attribute: so that whatever the idea contains, in
+any person's mind, beyond what is included in the conventional
+signification of the word, has been added to it as the result of assent
+to a proposition; while Dr. Brown's theory requires us to suppose, on
+the contrary, that assent to the proposition is produced by evolving,
+through an analytic process, this very element out of the idea. This
+theory, therefore, may be considered as sufficiently refuted; and the
+minor premise must be regarded as totally insufficient to prove the
+conclusion, except with the assistance of the major, or of that which
+the major represents, namely, the various singular propositions
+expressive of the series of observations, of which the generalization
+called the major premise is the result.
+
+In the argument, then, which proves that Socrates is mortal, one
+indispensable part of the premises will be as follows: "My father, and
+my father's father, A, B, C, and an indefinite number of other persons,
+were mortal;" which is only an expression in different words of the
+observed fact that they have died. This is the major premise divested of
+the _petitio principii_, and cut down to as much as is really known by
+direct evidence.
+
+In order to connect this proposition with the conclusion Socrates is
+mortal, the additional link necessary is such a proposition as the
+following: "Socrates resembles my father, and my father's father, and
+the other individuals specified." This proposition we assert when we say
+that Socrates is a man. By saying so we likewise assert in what respect
+he resembles them, namely, in the attributes connoted by the word man.
+And we conclude that he further resembles them in the attribute
+mortality.
+
+
+§ 7. We have thus obtained what we were seeking, an universal type of
+the reasoning process. We find it resolvable in all cases into the
+following elements: Certain individuals have a given attribute; an
+individual or individuals resemble the former in certain other
+attributes; therefore they resemble them also in the given attribute.
+This type of ratiocination does not claim, like the syllogism, to be
+conclusive, from the mere form of the expression; nor can it possibly be
+so. That one proposition does or does not assert the very fact which was
+already asserted in another, may appear from the form of the expression,
+that is, from a comparison of the language; but when the two
+propositions assert facts which are _bonâ fide_ different, whether the
+one fact proves the other or not can never appear from the language, but
+must depend on other considerations. Whether, from the attributes in
+which Socrates resembles those men who have heretofore died, it is
+allowable to infer that he resembles them also in being mortal, is a
+question of Induction; and is to be decided by the principles or canons
+which we shall hereafter recognise as tests of the correct performance
+of that great mental operation.
+
+Meanwhile, however, it is certain, as before remarked, that if this
+inference can be drawn as to Socrates, it can be drawn as to all others
+who resemble the observed individuals in the same attributes in which he
+resembles them; that is (to express the thing concisely) of all mankind.
+If, therefore, the argument be admissible in the case of Socrates, we
+are at liberty, once for all, to treat the possession of the attributes
+of man as a mark, or satisfactory evidence, of the attribute of
+mortality. This we do by laying down the universal proposition, All men
+are mortal, and interpreting this, as occasion arises, in its
+application to Socrates and others. By this means we establish a very
+convenient division of the entire logical operation into two steps;
+first, that of ascertaining what attributes are marks of mortality; and,
+secondly, whether any given individuals possess those marks. And it will
+generally be advisable, in our speculations on the reasoning process, to
+consider this double operation as in fact taking place, and all
+reasoning as carried on in the form into which it must necessarily be
+thrown to enable us to apply to it any test of its correct performance.
+
+Although, therefore, all processes of thought in which the ultimate
+premises are particulars, whether we conclude from particulars to a
+general formula, or from particulars to other particulars according to
+that formula, are equally Induction: we shall yet, conformably to usage,
+consider the name Induction as more peculiarly belonging to the process
+of establishing the general proposition, and the remaining operation,
+which is substantially that of interpreting the general proposition, we
+shall call by its usual name, Deduction. And we shall consider every
+process by which anything is inferred respecting an unobserved case, as
+consisting of an Induction followed by a Deduction; because, although
+the process needs not necessarily be carried on in this form, it is
+always susceptible of the form, and must be thrown into it when
+assurance of scientific accuracy is needed and desired.
+
+
+§ 8. The theory of the syllogism, laid down in the preceding pages, has
+obtained, among other important adhesions, three of peculiar value;
+those of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir
+John Herschel considering the doctrine, though not strictly "a
+discovery,"[13] to be "one of the greatest steps which have yet been
+made in the philosophy of Logic." "When we consider" (to quote the
+further words of the same authority) "the inveteracy of the habits and
+prejudices which it has cast to the winds," there is no cause for
+misgiving in the fact that other thinkers, no less entitled to
+consideration, have formed a very different estimate of it. Their
+principal objection cannot be better or more succinctly stated than by
+borrowing a sentence from Archbishop Whately.[14] "In every case where
+an inference is drawn from Induction (unless that name is to be given to
+a mere random guess without any grounds at all) we must form a judgment
+that the instance or instances adduced are _sufficient_ to authorize the
+conclusion; that it is _allowable_ to take these instances as a sample
+warranting an inference respecting the whole class;" and the expression
+of this judgment in words (it has been said by several of my critics)
+_is_ the major premise.
+
+I quite admit that the major is an affirmation of the sufficiency of the
+evidence on which the conclusion rests. That it is so, is the very
+essence of my own theory. And whoever admits that the major premise is
+_only_ this, adopts the theory in its essentials.
+
+But I cannot concede that this recognition of the sufficiency of the
+evidence--that is, of the correctness of the induction--is a part of the
+induction itself; unless we ought to say that it is a part of everything
+we do, to satisfy ourselves that it has been done rightly. We conclude
+from known instances to unknown by the impulse of the generalizing
+propensity; and (until after a considerable amount of practice and
+mental discipline) the question of the sufficiency of the evidence is
+only raised by a retrospective act, turning back upon our own footsteps,
+and examining whether we were warranted in doing what we have already
+done. To speak of this reflex operation as part of the original one,
+requiring to be expressed in words in order that the verbal formula may
+correctly represent the psychological process, appears to me false
+psychology.[15] We review our syllogistic as well as our inductive
+processes, and recognise that they have been correctly performed; but
+logicians do not add a third premise to the syllogism, to express this
+act of recognition. A careful copyist verifies his transcript by
+collating it with the original; and if no error appears, he recognises
+that the transcript has been correctly made. But we do not call the
+examination of the copy a part of the act of copying.
+
+The conclusion in an induction is inferred from the evidence itself, and
+not from a recognition of the sufficiency of the evidence; as I infer
+that my friend is walking towards me because I see him, and not because
+I recognise that my eyes are open, and that eyesight is a means of
+knowledge. In all operations which require care, it is good to assure
+ourselves that the process has been performed accurately; but the
+testing of the process is not the process itself; and, besides, may have
+been omitted altogether, and yet the process be correct. It is precisely
+because that operation is omitted in ordinary unscientific reasoning,
+that there is anything gained in certainty by throwing reasoning into
+the syllogistic form. To make sure, as far as possible, that it shall
+not be omitted, we make the testing operation a part of the reasoning
+process itself. We insist that the inference from particulars to
+particulars shall pass through a general proposition. But this is a
+security for good reasoning, not a condition of all reasoning; and in
+some cases not even a security. Our most familiar inferences are all
+made before we learn the use of general propositions; and a person of
+untutored sagacity will skilfully apply his acquired experience to
+adjacent cases, though he would bungle grievously in fixing the limits
+of the appropriate general theorem. But though he may conclude rightly,
+he never, properly speaking, knows whether he has done so or not; he has
+not tested his reasoning. Now, this is precisely what forms of reasoning
+do for us. We do not need them to enable us to reason, but to enable us
+to know whether we reason correctly.
+
+In still further answer to the objection, it may be added that, even
+when the test has been applied, and the sufficiency of the evidence
+recognised,--if it is sufficient to support the general proposition, it
+is sufficient also to support an inference from particulars to
+particulars without passing through the general proposition. The
+inquirer who has logically satisfied himself that the conditions of
+legitimate induction were realized in the cases A, B, C, would be as
+much justified in concluding directly to the Duke of Wellington as in
+concluding to all men. The general conclusion is never legitimate,
+unless the particular one would be so too; and in no sense, intelligible
+to me, can the particular conclusion be said to be drawn from the
+general one. Whenever there is ground for drawing any conclusion at all
+from particular instances, there is ground for a general conclusion; but
+that this general conclusion should be actually drawn, however useful,
+cannot be an indispensable condition of the validity of the inference in
+the particular case. A man gives away sixpence by the same power by
+which he disposes of his whole fortune; but it is not necessary to the
+legality of the smaller act, that he should make a formal assertion of
+his right to the greater one.
+
+Some additional remarks, in reply to minor objections, are appended.[16]
+
+
+§ 9. The preceding considerations enable us to understand the true
+nature of what is termed, by recent writers, Formal Logic, and the
+relation between it and Logic in the widest sense. Logic, as I conceive
+it, is the entire theory of the ascertainment of reasoned or inferred
+truth. Formal Logic, therefore, which Sir William Hamilton from his own
+point of view, and Archbishop Whately from his, have represented as the
+whole of Logic properly so called, is really a very subordinate part of
+it, not being directly concerned with the process of Reasoning or
+Inference in the sense in which that process is a part of the
+Investigation of Truth. What, then, is Formal Logic? The name seems to
+be properly applied to all that portion of doctrine which relates to the
+equivalence of different modes of expression; the rules for determining
+when assertions in a given form imply or suppose the truth or falsity of
+other assertions. This includes the theory of the Import of
+Propositions, and of their Conversion, Æquipollence, and Opposition; of
+those falsely called Inductions (to be hereafter spoken of[17]), in
+which the apparent generalization is a mere abridged statement of cases
+known individually; and finally, of the syllogism: while the theory of
+Naming, and of (what is inseparably connected with it) Definition,
+though belonging still more to the other and larger kind of logic than
+to this, is a necessary preliminary to this. The end aimed at by Formal
+Logic, and attained by the observance of its precepts, is not truth, but
+consistency. It has been seen that this is the only direct purpose of
+the rules of the syllogism; the intention and effect of which is simply
+to keep our inferences or conclusions in complete consistency with our
+general formulæ or directions for drawing them. The Logic of Consistency
+is a necessary auxiliary to the logic of truth, not only because what is
+inconsistent with itself or with other truths cannot be true, but also
+because truth can only be successfully pursued by drawing inferences
+from experience, which, if warrantable at all, admit of being
+generalized, and, to test their warrantableness, require to be exhibited
+in a generalized form; after which the correctness of their application
+to particular cases is a question which specially concerns the Logic of
+Consistency. This Logic, not requiring any preliminary knowledge of the
+processes or conclusions of the various sciences, may be studied with
+benefit in a much earlier stage of education than the Logic of Truth:
+and the practice which has empirically obtained of teaching it apart,
+through elementary treatises which do not attempt to include anything
+else, though the reasons assigned for the practice are in general very
+far from philosophical, admits of a philosophical justification.
+
+
+
+
+CHAPTER IV.
+
+OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
+
+
+§ 1. In our analysis of the syllogism, it appeared that the minor
+premise always affirms a resemblance between a new case and some cases
+previously known; while the major premise asserts something which,
+having been found true of those known cases, we consider ourselves
+warranted in holding true of any other case resembling the former in
+certain given particulars.
+
+If all ratiocinations resembled, as to the minor premise, the examples
+which were exclusively employed in the preceding chapter; if the
+resemblance, which that premise asserts, were obvious to the senses, as
+in the proposition "Socrates is a man," or were at once ascertainable by
+direct observation; there would be no necessity for trains of reasoning,
+and Deductive or Ratiocinative Sciences would not exist. Trains of
+reasoning exist only for the sake of extending an induction founded, as
+all inductions must be, on observed cases, to other cases in which we
+not only cannot directly observe what is to be proved, but cannot
+directly observe even the mark which is to prove it.
+
+
+§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is
+before me is a cow, therefore it ruminates. The minor, if true at all,
+is obviously so: the only premise the establishment of which requires
+any anterior process of inquiry, is the major; and provided the
+induction of which that premise is the expression was correctly
+performed, the conclusion respecting the animal now present will be
+instantly drawn; because, as soon as she is compared with the formula,
+she will be identified as being included in it. But suppose the
+syllogism to be the following:--All arsenic is poisonous, the substance
+which is before me is arsenic, therefore it is poisonous. The truth of
+the minor may not here be obvious at first sight; it may not be
+intuitively evident, but may itself be known only by inference. It may
+be the conclusion of another argument, which, thrown into the
+syllogistic form, would stand thus:--Whatever when lighted produces a
+dark spot on a piece of white porcelain held in the flame, which spot is
+soluble in hypochlorite of calcium, is arsenic; the substance before me
+conforms to this condition; therefore it is arsenic. To establish,
+therefore, the ultimate conclusion, The substance before me is
+poisonous, requires a process, which, in order to be syllogistically
+expressed, stands in need of two syllogisms; and we have a Train of
+Reasoning.
+
+When, however, we thus add syllogism to syllogism, we are really adding
+induction to induction. Two separate inductions must have taken place to
+render this chain of inference possible; inductions founded, probably,
+on different sets of individual instances, but which converge in their
+results, so that the instance which is the subject of inquiry comes
+within the range of them both. The record of these inductions is
+contained in the majors of the two syllogisms. First, we, or others for
+us, have examined various objects which yielded under the given
+circumstances a dark spot with the given property, and found that they
+possessed the properties connoted by the word arsenic; they were
+metallic, volatile, their vapour had a smell of garlic, and so forth.
+Next, we, or others for us, have examined various specimens which
+possessed this metallic and volatile character, whose vapour had this
+smell, &c., and have invariably found that they were poisonous. The
+first observation we judge that we may extend to all substances whatever
+which yield that particular kind of dark spot; the second, to all
+metallic and volatile substances resembling those we examined; and
+consequently, not to those only which are seen to be such, but to those
+which are concluded to be such by the prior induction. The substance
+before us is only seen to come within one of these inductions; but by
+means of this one, it is brought within the other. We are still, as
+before, concluding from particulars to particulars; but we are now
+concluding from particulars observed, to other particulars which are
+not, as in the simple case, _seen_ to resemble them in the material
+points, but _inferred_ to do so, because resembling them in something
+else, which we have been led by quite a different set of instances to
+consider as a mark of the former resemblance.
+
+This first example of a train of reasoning is still extremely simple,
+the series consisting of only two syllogisms. The following is somewhat
+more complicated:--No government, which earnestly seeks the good of its
+subjects, is likely to be overthrown; some particular government
+earnestly seeks the good of its subjects, therefore it is not likely to
+be overthrown. The major premise in this argument we shall suppose not
+to be derived from considerations _à priori_, but to be a generalization
+from history, which, whether correct or erroneous, must have been
+founded on observation of governments concerning whose desire of the
+good of their subjects there was no doubt. It has been found, or thought
+to be found, that these were not easily overthrown, and it has been
+deemed that those instances warranted an extension of the same predicate
+to any and every government which resembles them in the attribute of
+desiring earnestly the good of its subjects. But _does_ the government
+in question thus resemble them? This may be debated _pro_ and _con_ by
+many arguments, and must, in any case, be proved by another induction;
+for we cannot directly observe the sentiments and desires of the persons
+who carry on the government. To prove the minor, therefore, we require
+an argument in this form: Every government which acts in a certain
+manner, desires the good of its subjects; the supposed government acts
+in that particular manner, therefore it desires the good of its
+subjects. But is it true that the government acts in the manner
+supposed? This minor also may require proof; still another induction, as
+thus:--What is asserted by intelligent and disinterested witnesses, may
+be believed to be true; that the government acts in this manner, is
+asserted by such witnesses, therefore it may be believed to be true. The
+argument hence consists of three steps. Having the evidence of our
+senses that the case of the government under consideration resembles a
+number of former cases, in the circumstance of having something asserted
+respecting it by intelligent and disinterested witnesses, we infer,
+first, that, as in those former instances, so in this instance, the
+assertion is true. Secondly, what was asserted of the government being
+that it acts in a particular manner, and other governments or persons
+having been observed to act in the same manner, the government in
+question is brought into known resemblance with those other governments
+or persons; and since they were known to desire the good of the people,
+it is thereupon, by a second induction, inferred that the particular
+government spoken of, desires the good of the people. This brings that
+government into known resemblance with the other governments which were
+thought likely to escape revolution, and thence, by a third induction,
+it is concluded that this particular government is also likely to
+escape. This is still reasoning from particulars to particulars, but we
+now reason to the new instance from three distinct sets of former
+instances: to one only of those sets of instances do we directly
+perceive the new one to be similar; but from that similarity we
+inductively infer that it has the attribute by which it is assimilated
+to the next set, and brought within the corresponding induction; after
+which by a repetition of the same operation we infer it to be similar to
+the third set, and hence a third induction conducts us to the ultimate
+conclusion.
+
+
+§ 3. Notwithstanding the superior complication of these examples,
+compared with those by which in the preceding chapter we illustrated the
+general theory of reasoning, every doctrine which we then laid down
+holds equally true in these more intricate cases. The successive general
+propositions are not steps in the reasoning, are not intermediate links
+in the chain of inference, between the particulars observed and those to
+which we apply the observation. If we had sufficiently capacious
+memories, and a sufficient power of maintaining order among a huge mass
+of details, the reasoning could go on without any general propositions;
+they are mere formulæ for inferring particulars from particulars. The
+principle of general reasoning is (as before explained), that if from
+observation of certain known particulars, what was seen to be true of
+them can be inferred to be true of any others, it may be inferred of all
+others which are of a certain description. And in order that we may
+never fail to draw this conclusion in a new case when it can be drawn
+correctly, and may avoid drawing it when it cannot, we determine once
+for all what are the distinguishing marks by which such cases may be
+recognised. The subsequent process is merely that of identifying an
+object, and ascertaining it to have those marks; whether we identify it
+by the very marks themselves, or by others which we have ascertained
+(through another and a similar process) to be marks of those marks. The
+real inference is always from particulars to particulars, from the
+observed instances to an unobserved one: but in drawing this inference,
+we conform to a formula which we have adopted for our guidance in such
+operations, and which is a record of the criteria by which we thought we
+had ascertained that we might distinguish when the inference could, and
+when it could not, be drawn. The real premises are the individual
+observations, even though they may have been forgotten, or, being the
+observations of others and not of ourselves, may, to us, never have been
+known: but we have before us proof that we or others once thought them
+sufficient for an induction, and we have marks to show whether any new
+case is one of those to which, if then known, the induction would have
+been deemed to extend. These marks we either recognise at once, or by
+the aid of other marks, which by another previous induction we collected
+to be marks of the first. Even these marks of marks may only be
+recognised through a third set of marks; and we may have a train of
+reasoning, of any length, to bring a new case within the scope of an
+induction grounded on particulars its similarity to which is only
+ascertained in this indirect manner.
+
+Thus, in the preceding example, the ultimate inductive inference was,
+that a certain government was not likely to be overthrown; this
+inference was drawn according to a formula in which desire of the public
+good was set down as a mark of not being likely to be overthrown; a mark
+of this mark was, acting in a particular manner; and a mark of acting in
+that manner was, being asserted to do so by intelligent and
+disinterested witnesses: this mark, the government under discussion was
+recognised by the senses as possessing. Hence that government fell
+within the last induction, and by it was brought within all the others.
+The perceived resemblance of the case to one set of observed particular
+cases, brought it into known resemblance with another set, and that with
+a third.
+
+In the more complex branches of knowledge, the deductions seldom
+consist, as in the examples hitherto exhibited, of a single chain, _a_ a
+mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They
+consist (to carry on the same metaphor) of several chains united at the
+extremity, as thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_
+of _n_, therefore _a b c_ a mark of _n_. Suppose, for example, the
+following combination of circumstances; 1st, rays of light impinging on
+a reflecting surface; 2nd, that surface parabolic; 3rd, those rays
+parallel to each other and to the axis of the surface. It is to be
+proved that the concourse of these three circumstances is a mark that
+the reflected rays will pass through the focus of the parabolic surface.
+Now, each of the three circumstances is singly a mark of something
+material to the case. Rays of light impinging on a reflecting surface,
+are a mark that those rays will be reflected at an angle equal to the
+angle of incidence. The parabolic form of the surface is a mark that,
+from any point of it, a line drawn to the focus and a line parallel to
+the axis will make equal angles with the surface. And finally, the
+parallelism of the rays to the axis is a mark that their angle of
+incidence coincides with one of these equal angles. The three marks
+taken together are therefore a mark of all these three things united.
+But the three united are evidently a mark that the angle of reflection
+must coincide with the other of the two equal angles, that formed by a
+line drawn to the focus; and this again, by the fundamental axiom
+concerning straight lines, is a mark that the reflected rays pass
+through the focus. Most chains of physical deduction are of this more
+complicated type; and even in mathematics such are abundant, as in all
+propositions where the hypothesis includes numerous conditions: "_If_ a
+circle be taken, and _if_ within that circle a point be taken, not the
+centre, and _if_ straight lines be drawn from that point to the
+circumference, then," &c.
+
+
+§ 4. The considerations now stated remove a serious difficulty from the
+view we have taken of reasoning; which view might otherwise have seemed
+not easily reconcileable with the fact that there are Deductive or
+Ratiocinative Sciences. It might seem to follow, if all reasoning be
+induction, that the difficulties of philosophical investigation must lie
+in the inductions exclusively, and that when these were easy, and
+susceptible of no doubt or hesitation, there could be no science, or, at
+least, no difficulties in science. The existence, for example, of an
+extensive Science of Mathematics, requiring the highest scientific
+genius in those who contributed to its creation, and calling for a most
+continued and vigorous exertion of intellect in order to appropriate it
+when created, may seem hard to be accounted for on the foregoing theory.
+But the considerations more recently adduced remove the mystery, by
+showing, that even when the inductions themselves are obvious, there may
+be much difficulty in finding whether the particular case which is the
+subject of inquiry comes within them; and ample room for scientific
+ingenuity in so combining various inductions, as, by means of one within
+which the case evidently falls, to bring it within others in which it
+cannot be directly seen to be included.
+
+When the more obvious of the inductions which can be made in any science
+from direct observations, have been made, and general formulas have been
+framed, determining the limits within which these inductions are
+applicable; as often as a new case can be at once seen to come within
+one of the formulas, the induction is applied to the new case, and the
+business is ended. But new cases are continually arising, which do not
+obviously come within any formula whereby the question we want solved in
+respect of them could be answered. Let us take an instance from
+geometry: and as it is taken only for illustration, let the reader
+concede to us for the present, what we shall endeavour to prove in the
+next chapter, that the first principles of geometry are results of
+induction. Our example shall be the fifth proposition of the first book
+of Euclid. The inquiry is, Are the angles at the base of an isosceles
+triangle equal or unequal? The first thing to be considered is, what
+inductions we have, from which we can infer equality or inequality. For
+inferring equality we have the following formulæ:--Things which being
+applied to each other coincide, are equals. Things which are equal to
+the same thing are equals. A whole and the sum of its parts are equals.
+The sums of equal things are equals. The differences of equal things are
+equals. There are no other original formulæ to prove equality. For
+inferring inequality we have the following:--A whole and its parts are
+unequals. The sums of equal things and unequal things are unequals. The
+differences of equal things and unequal things are unequals. In all,
+eight formulæ. The angles at the base of an isosceles triangle do not
+obviously come within any of these. The formulæ specify certain marks of
+equality and of inequality, but the angles cannot be perceived
+intuitively to have any of those marks. On examination it appears that
+they have; and we ultimately succeed in bringing them within the
+formula, "The differences of equal things are equal." Whence comes the
+difficulty of recognising these angles as the differences of equal
+things? Because each of them is the difference not of one pair only, but
+of innumerable pairs of angles; and out of these we had to imagine and
+select two, which could either be intuitively perceived to be equals, or
+possessed some of the marks of equality set down in the various formulæ.
+By an exercise of ingenuity, which, on the part of the first inventor,
+deserves to be regarded as considerable, two pairs of angles were hit
+upon, which united these requisites. First, it could be perceived
+intuitively that their differences were the angles at the base; and,
+secondly, they possessed one of the marks of equality, namely,
+coincidence when applied to one another. This coincidence, however, was
+not perceived intuitively, but inferred, in conformity to another
+formula.
+
+For greater clearness, I subjoin an analysis of the demonstration.
+Euclid, it will be remembered, demonstrates his fifth proposition by
+means of the fourth. This it is not allowable for us to do, because we
+are undertaking to trace deductive truths not to prior deductions, but
+to their original inductive foundation. We must therefore use the
+premises of the fourth proposition instead of its conclusion, and prove
+the fifth directly from first principles. To do so requires six
+formulas. (We must begin, as in Euclid, by prolonging the equal sides
+AB, AC, to equal distances, and joining the extremities BE, DC.)
+
+[Illustration]
+
+FIRST FORMULA. _The sums of equals are equal._
+
+AD and AE are sums of equals by the supposition. Having that mark of
+equality, they are concluded by this formula to be equal.
+
+SECOND FORMULA. _Equal straight lines being applied to one another
+coincide._
+
+AC, AB, are within this formula by supposition; AD, AE, have been
+brought within it by the preceding step. Both these pairs of straight
+lines have the property of equality; which, according to the second
+formula, is a mark that, if applied to each other, they will coincide.
+Coinciding altogether means coinciding in every part, and of course at
+their extremities, D, E, and B, C.
+
+THIRD FORMULA. _Straight lines, having their extremities coincident,
+coincide._
+
+BE and CD have been brought within this formula by the preceding
+induction; they will, therefore, coincide.
+
+FOURTH FORMULA. _Angles, having their sides coincident, coincide._
+
+The third induction having shown that BE and CD coincide, and the second
+that AB, AC, coincide, the angles ABE and ACD are thereby brought within
+the fourth formula, and accordingly coincide.
+
+FIFTH FORMULA. _Things which coincide are equal._
+
+The angles ABE and ACD are brought within this formula by the induction
+immediately preceding. This train of reasoning being also applicable,
+_mutatis mutandis_, to the angles EBC, DCB, these also are brought
+within the fifth formula. And, finally,
+
+SIXTH FORMULA. _The differences of equals are equal._
+
+The angle ABC being the difference of ABE, CBE, and the angle ACB being
+the difference of ACD, DCB; which have been proved to be equals; ABC and
+ACB are brought within the last formula by the whole of the previous
+process.
+
+The difficulty here encountered is chiefly that of figuring to ourselves
+the two angles at the base of the triangle ABC as remainders made by
+cutting one pair of angles out of another, while each pair shall be
+corresponding angles of triangles which have two sides and the
+intervening angle equal. It is by this happy contrivance that so many
+different inductions are brought to bear upon the same particular case.
+And this not being at all an obvious thought, it may be seen from an
+example so near the threshold of mathematics, how much scope there may
+well be for scientific dexterity in the higher branches of that and
+other sciences, in order so to combine a few simple inductions, as to
+bring within each of them innumerable cases which are not obviously
+included in it; and how long, and numerous, and complicated may be the
+processes necessary for bringing the inductions together, even when each
+induction may itself be very easy and simple. All the inductions
+involved in all geometry are comprised in those simple ones, the formulæ
+of which are the Axioms, and a few of the so-called Definitions. The
+remainder of the science is made up of the processes employed for
+bringing unforeseen cases within these inductions; or (in syllogistic
+language) for proving the minors necessary to complete the syllogisms;
+the majors being the definitions and axioms. In those definitions and
+axioms are laid down the whole of the marks, by an artful combination of
+which it has been found possible to discover and prove all that is
+proved in geometry. The marks being so few, and the inductions which
+furnish them being so obvious and familiar; the connecting of several of
+them together, which constitutes Deductions, or Trains of Reasoning,
+forms the whole difficulty of the science, and with a trifling
+exception, its whole bulk; and hence Geometry is a Deductive Science.
+
+
+§ 5. It will be seen hereafter[18] that there are weighty scientific
+reasons for giving to every science as much of the character of a
+Deductive Science as possible; for endeavouring to construct the science
+from the fewest and the simplest possible inductions, and to make these,
+by any combinations however complicated, suffice for proving even such
+truths, relating to complex cases, as could be proved, if we chose, by
+inductions from specific experience. Every branch of natural philosophy
+was originally experimental; each generalization rested on a special
+induction, and was derived from its own distinct set of observations and
+experiments. From being sciences of pure experiment, as the phrase is,
+or, to speak more correctly, sciences in which the reasonings mostly
+consist of no more than one step, and are expressed by single
+syllogisms, all these sciences have become to some extent, and some of
+them in nearly the whole of their extent, sciences of pure reasoning;
+whereby multitudes of truths, already known by induction from as many
+different sets of experiments, have come to be exhibited as deductions
+or corollaries from inductive propositions of a simpler and more
+universal character. Thus mechanics, hydrostatics, optics, acoustics,
+thermology, have successively been rendered mathematical; and astronomy
+was brought by Newton within the laws of general mechanics. Why it is
+that the substitution of this circuitous mode of proceeding for a
+process apparently much easier and more natural, is held, and justly, to
+be the greatest triumph of the investigation of nature, we are not, in
+this stage of our inquiry, prepared to examine. But it is necessary to
+remark, that although, by this progressive transformation, all sciences
+tend to become more and more Deductive, they are not, therefore, the
+less Inductive; every step in the Deduction is still an Induction. The
+opposition is not between the terms Deductive and Inductive, but between
+Deductive and Experimental. A science is experimental, in proportion as
+every new case, which presents any peculiar features, stands in need of
+a new set of observations and experiments--a fresh induction. It is
+deductive, in proportion as it can draw conclusions, respecting cases of
+a new kind, by processes which bring those cases under old inductions;
+by ascertaining that cases which cannot be observed to have the
+requisite marks, have, however, marks of those marks.
+
+We can now, therefore, perceive what is the generic distinction between
+sciences which can be made Deductive, and those which must as yet remain
+Experimental. The difference consists in our having been able, or not
+yet able, to discover marks of marks. If by our various inductions we
+have been able to proceed no further than to such propositions as these,
+_a_ a mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of
+_d_, or _c_ and _d_ marks of one another, without anything to connect
+_a_ or _b_ with _c_ or _d_; we have a science of detached and mutually
+independent generalizations, such as these, that acids redden vegetable
+blues, and that alkalies colour them green; from neither of which
+propositions could we, directly or indirectly, infer the other: and a
+science, so far as it is composed of such propositions, is purely
+experimental. Chemistry, in the present state of our knowledge, has not
+yet thrown off this character. There are other sciences, however, of
+which the propositions are of this kind: _a_ a mark of _b_, _b_ a mark
+of _c_, _c_ of _d_, _d_ of _e_, &c. In these sciences we can mount the
+ladder from _a_ to _e_ by a process of ratiocination; we can conclude
+that _a_ is a mark of _e_, and that every object which has the mark _a_
+has the property _e_, although, perhaps, we never were able to observe
+_a_ and _e_ together, and although even _d_, our only direct mark of
+_e_, may not be perceptible in those objects, but only inferrible. Or,
+varying the first metaphor, we may be said to get from _a_ to _e_
+underground: the marks _b_, _c_, _d_, which indicate the route, must all
+be possessed somewhere by the objects concerning which we are inquiring;
+but they are below the surface: _a_ is the only mark that is visible,
+and by it we are able to trace in succession all the rest.
+
+
+§ 6. We can now understand how an experimental may transform itself into
+a deductive science by the mere progress of experiment. In an
+experimental science, the inductions, as we have said, lie detached, as,
+_a_ a mark of _b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now,
+a new set of instances, and a consequent new induction, may at any time
+bridge over the interval between two of these unconnected arches; _b_,
+for example, may be ascertained to be a mark of _c_, which enables us
+thenceforth to prove deductively that _a_ is a mark of _c_. Or, as
+sometimes happens, some comprehensive induction may raise an arch high
+in the air, which bridges over hosts of them at once: _b_, _d_, _f_, and
+all the rest, turning out to be marks of some one thing, or of things
+between which a connexion has already been traced. As when Newton
+discovered that the motions, whether regular or apparently anomalous, of
+all the bodies of the solar system, (each of which motions had been
+inferred by a separate logical operation, from separate marks,) were all
+marks of moving round a common centre, with a centripetal force varying
+directly as the mass, and inversely as the square of the distance from
+that centre. This is the greatest example which has yet occurred of the
+transformation, at one stroke, of a science which was still to a great
+degree merely experimental, into a deductive science.
+
+Transformations of the same nature, but on a smaller scale, continually
+take place in the less advanced branches of physical knowledge, without
+enabling them to throw off the character of experimental sciences. Thus
+with regard to the two unconnected propositions before cited, namely,
+Acids redden vegetable blues, Alkalies make them green; it is remarked
+by Liebig, that all blue colouring matters which are reddened by acids
+(as well as, reciprocally, all red colouring matters which are rendered
+blue by alkalies) contain nitrogen: and it is quite possible that this
+circumstance may one day furnish a bond of connexion between the two
+propositions in question, by showing that the antagonistic action of
+acids and alkalies in producing or destroying the colour blue, is the
+result of some one, more general, law. Although this connecting of
+detached generalizations is so much gain, it tends but little to give a
+deductive character to any science as a whole; because the new courses
+of observation and experiment, which thus enable us to connect together
+a few general truths, usually make known to us a still greater number of
+unconnected new ones. Hence chemistry, though similar extensions and
+simplifications of its generalizations are continually taking place, is
+still in the main an experimental science; and is likely so to continue
+unless some comprehensive induction should be hereafter arrived at,
+which, like Newton's, shall connect a vast number of the smaller known
+inductions together, and change the whole method of the science at once.
+Chemistry has already one great generalization, which, though relating
+to one of the subordinate aspects of chemical phenomena, possesses
+within its limited sphere this comprehensive character; the principle of
+Dalton, called the atomic theory, or the doctrine of chemical
+equivalents: which by enabling us to a certain extent to foresee the
+proportions in which two substances will combine, before the experiment
+has been tried, constitutes undoubtedly a source of new chemical truths
+obtainable by deduction, as well as a connecting principle for all
+truths of the same description previously obtained by experiment.
+
+
+§ 7. The discoveries which change the method of a science from
+experimental to deductive, mostly consist in establishing, either by
+deduction or by direct experiment, that the varieties of a particular
+phenomenon uniformly accompany the varieties of some other phenomenon
+better known. Thus the science of sound, which previously stood in the
+lowest rank of merely experimental science, became deductive when it was
+proved by experiment that every variety of sound was consequent on, and
+therefore a mark of, a distinct and definable variety of oscillatory
+motion among the particles of the transmitting medium. When this was
+ascertained, it followed that every relation of succession or
+coexistence which obtained between phenomena of the more known class,
+obtained also between the phenomena which corresponded to them in the
+other class. Every sound, being a mark of a particular oscillatory
+motion, became a mark of everything which, by the laws of dynamics, was
+known to be inferrible from that motion; and everything which by those
+same laws was a mark of any oscillatory motion among the particles of an
+elastic medium, became a mark of the corresponding sound. And thus many
+truths, not before suspected, concerning sound, become deducible from
+the known laws of the propagation of motion through an elastic medium;
+while facts already empirically known respecting sound, become an
+indication of corresponding properties of vibrating bodies, previously
+undiscovered.
+
+But the grand agent for transforming experimental into deductive
+sciences, is the science of number. The properties of numbers, alone
+among all known phenomena, are, in the most rigorous sense, properties
+of all things whatever. All things are not coloured, or ponderable, or
+even extended; but all things are numerable. And if we consider this
+science in its whole extent, from common arithmetic up to the calculus
+of variations, the truths already ascertained seem all but infinite, and
+admit of indefinite extension.
+
+These truths, though affirmable of all things whatever, of course apply
+to them only in respect of their quantity. But if it comes to be
+discovered that variations of quality in any class of phenomena,
+correspond regularly to variations of quantity either in those same or
+in some other phenomena; every formula of mathematics applicable to
+quantities which vary in that particular manner, becomes a mark of a
+corresponding general truth respecting the variations in quality which
+accompany them: and the science of quantity being (as far as any science
+can be) altogether deductive, the theory of that particular kind of
+qualities becomes, to this extent, deductive likewise.
+
+The most striking instance in point which history affords (though not an
+example of an experimental science rendered deductive, but of an
+unparalleled extension given to the deductive process in a science which
+was deductive already), is the revolution in geometry which originated
+with Descartes, and was completed by Clairaut. These great
+mathematicians pointed out the importance of the fact, that to every
+variety of position in points, direction in lines, or form in curves or
+surfaces (all of which are Qualities), there corresponds a peculiar
+relation of quantity between either two or three rectilineal
+co-ordinates; insomuch that if the law were known according to which
+those co-ordinates vary relatively to one another, every other
+geometrical property of the line or surface in question, whether
+relating to quantity or quality, would be capable of being inferred.
+Hence it followed that every geometrical question could be solved, if
+the corresponding algebraical one could; and geometry received an
+accession (actual or potential) of new truths, corresponding to every
+property of numbers which the progress of the calculus had brought, or
+might in future bring, to light. In the same general manner, mechanics,
+astronomy, and in a less degree, every branch of natural philosophy
+commonly so called, have been made algebraical. The varieties of
+physical phenomena with which those sciences are conversant, have been
+found to answer to determinable varieties in the quantity of some
+circumstance or other; or at least to varieties of form or position, for
+which corresponding equations of quantity had already been, or were
+susceptible of being, discovered by geometers.
+
+In these various transformations, the propositions of the science of
+number do but fulfil the function proper to all propositions forming a
+train of reasoning, viz. that of enabling us to arrive in an indirect
+method, by marks of marks, at such of the properties of objects as we
+cannot directly ascertain (or not so conveniently) by experiment. We
+travel from a given visible or tangible fact, through the truths of
+numbers, to the facts sought. The given fact is a mark that a certain
+relation subsists between the quantities of some of the elements
+concerned; while the fact sought presupposes a certain relation between
+the quantities of some other elements: now, if these last quantities are
+dependent in some known manner upon the former, or _vice versâ_, we can
+argue from the numerical relation between the one set of quantities, to
+determine that which subsists between the other set; the theorems of the
+calculus affording the intermediate links. And thus one of the two
+physical facts becomes a mark of the other, by being a mark of a mark of
+a mark of it.
+
+
+
+
+CHAPTER V.
+
+OF DEMONSTRATION, AND NECESSARY TRUTHS.
+
+
+§ 1. If, as laid down in the two preceding chapters, the foundation of
+all sciences, even deductive or demonstrative sciences, is Induction; if
+every step in the ratiocinations even of geometry is an act of
+induction; and if a train of reasoning is but bringing many inductions
+to bear upon the same subject of inquiry, and drawing a case within one
+induction by means of another; wherein lies the peculiar certainty
+always ascribed to the sciences which are entirely, or almost entirely,
+deductive? Why are they called the Exact Sciences? Why are mathematical
+certainty, and the evidence of demonstration, common phrases to express
+the very highest degree of assurance attainable by reason? Why are
+mathematics by almost all philosophers, and (by some) even those
+branches of natural philosophy which, through the medium of mathematics,
+have been converted into deductive sciences, considered to be
+independent of the evidence of experience and observation, and
+characterized as systems of Necessary Truth?
+
+The answer I conceive to be, that this character of necessity, ascribed
+to the truths of mathematics, and even (with some reservations to be
+hereafter made) the peculiar certainty attributed to them, is an
+illusion; in order to sustain which, it is necessary to suppose that
+those truths relate to, and express the properties of, purely imaginary
+objects. It is acknowledged that the conclusions of geometry are
+deduced, partly at least, from the so-called Definitions, and that those
+definitions are assumed to be correct representations, as far as they
+go, of the objects with which geometry is conversant. Now we have
+pointed out that, from a definition as such, no proposition, unless it
+be one concerning the meaning of a word, can ever follow; and that what
+apparently follows from a definition, follows in reality from an
+implied assumption that there exists a real thing conformable thereto.
+This assumption, in the case of the definitions of geometry, is false:
+there exist no real things exactly conformable to the definitions. There
+exist no points without magnitude; no lines without breadth, nor
+perfectly straight; no circles with all their radii exactly equal, nor
+squares with all their angles perfectly right. It will perhaps be said
+that the assumption does not extend to the actual, but only to the
+possible, existence of such things. I answer that, according to any test
+we have of possibility, they are not even possible. Their existence, so
+far as we can form any judgment, would seem to be inconsistent with the
+physical constitution of our planet at least, if not of the universe. To
+get rid of this difficulty, and at the same time to save the credit of
+the supposed system of necessary truth, it is customary to say that the
+points, lines, circles, and squares which are the subject of geometry,
+exist in our conceptions merely, and are part of our minds; which minds,
+by working on their own materials, construct an _à priori_ science, the
+evidence of which is purely mental, and has nothing whatever to do with
+outward experience. By howsoever high authorities this doctrine may have
+been sanctioned, it appears to me psychologically incorrect. The points,
+lines, circles, and squares, which any one has in his mind, are (I
+apprehend) simply copies of the points, lines, circles, and squares
+which he has known in his experience. Our idea of a point, I apprehend
+to be simply our idea of the _minimum visibile_, the smallest portion of
+surface which we can see. A line, as defined by geometers, is wholly
+inconceivable. We can reason about a line as if it had no breadth;
+because we have a power, which is the foundation of all the control we
+can exercise over the operations of our minds; the power, when a
+perception is present to our senses, or a conception to our intellects,
+of _attending_ to a part only of that perception or conception, instead
+of the whole. But we cannot _conceive_ a line without breadth; we can
+form no mental picture of such a line: all the lines which we have in
+our minds are lines possessing breadth. If any one doubts this, we may
+refer him to his own experience. I much question if any one who fancies
+that he can conceive what is called a mathematical line, thinks so from
+the evidence of his consciousness: I suspect it is rather because he
+supposes that unless such a conception were possible, mathematics could
+not exist as a science: a supposition which there will be no difficulty
+in showing to be entirely groundless.
+
+Since, then, neither in nature, nor in the human mind, do there exist
+any objects exactly corresponding to the definitions of geometry, while
+yet that science cannot be supposed to be conversant about non-entities;
+nothing remains but to consider geometry as conversant with such lines,
+angles, and figures, as really exist; and the definitions, as they are
+called, must be regarded as some of our first and most obvious
+generalizations concerning those natural objects. The correctness of
+those generalizations, as generalizations, is without a flaw: the
+equality of all the radii of a circle is true of all circles, so far as
+it is true of any one: but it is not exactly true of any circle; it is
+only nearly true; so nearly that no error of any importance in practice
+will be incurred by feigning it to be exactly true. When we have
+occasion to extend these inductions, or their consequences, to cases in
+which the error would be appreciable--to lines of perceptible breadth or
+thickness, parallels which deviate sensibly from equidistance, and the
+like--we correct our conclusions, by combining with them a fresh set of
+propositions relating to the aberration; just as we also take in
+propositions relating to the physical or chemical properties of the
+material, if those properties happen to introduce any modification into
+the result; which they easily may, even with respect to figure and
+magnitude, as in the case, for instance, of expansion by heat. So long,
+however, as there exists no practical necessity for attending to any of
+the properties of the object except its geometrical properties, or to
+any of the natural irregularities in those, it is convenient to neglect
+the consideration of the other properties and of the irregularities, and
+to reason as if these did not exist: accordingly, we formally announce
+in the definitions, that we intend to proceed on this plan. But it is
+an error to suppose, because we resolve to confine our attention to a
+certain number of the properties of an object, that we therefore
+conceive, or have an idea of, the object, denuded of its other
+properties. We are thinking, all the time, of precisely such objects as
+we have seen and touched, and with all the properties which naturally
+belong to them; but, for scientific convenience, we feign them to be
+divested of all properties, except those which are material to our
+purpose, and in regard to which we design to consider them.
+
+The peculiar accuracy, supposed to be characteristic of the first
+principles of geometry, thus appears to be fictitious. The assertions on
+which the reasonings of the science are founded, do not, any more than
+in other sciences, exactly correspond with the fact; but we suppose that
+they do so, for the sake of tracing the consequences which follow from
+the supposition. The opinion of Dugald Stewart respecting the
+foundations of geometry, is, I conceive, substantially correct; that it
+is built on hypotheses; that it owes to this alone the peculiar
+certainty supposed to distinguish it; and that in any science whatever,
+by reasoning from a set of hypotheses, we may obtain a body of
+conclusions as certain as those of geometry, that is, as strictly in
+accordance with the hypotheses, and as irresistibly compelling assent,
+_on condition_ that those hypotheses are true.
+
+When, therefore, it is affirmed that the conclusions of geometry are
+necessary truths, the necessity consists in reality only in this, that
+they correctly follow from the suppositions from which they are deduced.
+Those suppositions are so far from being necessary, that they are not
+even true; they purposely depart, more or less widely, from the truth.
+The only sense in which necessity can be ascribed to the conclusions of
+any scientific investigation, is that of legitimately following from
+some assumption, which, by the conditions of the inquiry, is not to be
+questioned. In this relation, of course, the derivative truths of every
+deductive science must stand to the inductions, or assumptions, on which
+the science is founded, and which, whether true or untrue, certain or
+doubtful in themselves, are always supposed certain for the purposes of
+the particular science. And therefore the conclusions of all deductive
+sciences were said by the ancients to be necessary propositions. We have
+observed already that to be predicated necessarily was characteristic of
+the predicable Proprium, and that a proprium was any property of a thing
+which could be deduced from its essence, that is, from the properties
+included in its definition.
+
+
+§ 2. The important doctrine of Dugald Stewart, which I have endeavoured
+to enforce, has been contested by Dr. Whewell, both in the dissertation
+appended to his excellent _Mechanical Euclid_, and in his elaborate work
+on the _Philosophy of the Inductive Sciences_; in which last he also
+replies to an article in the Edinburgh Review, (ascribed to a writer of
+great scientific eminence), in which Stewart's opinion was defended
+against his former strictures. The supposed refutation of Stewart
+consists in proving against him (as has also been done in this work)
+that the premises of geometry are not definitions, but assumptions of
+the real existence of things corresponding to those definitions. This,
+however, is doing little for Dr. Whewell's purpose; for it is these very
+assumptions which are asserted to be hypotheses, and which he, if he
+denies that geometry is founded on hypotheses, must show to be absolute
+truths. All he does, however, is to observe, that they at any rate, are
+not _arbitrary_ hypotheses; that we should not be at liberty to
+substitute other hypotheses for them; that not only "a definition, to be
+admissible, must necessarily refer to and agree with some conception
+which we can distinctly frame in our thoughts," but that the straight
+lines, for instance, which we define, must be "those by which angles are
+contained, those by which triangles are bounded, those of which
+parallelism may be predicated, and the like."[19] And this is true; but
+this has never been contradicted. Those who say that the premises of
+geometry are hypotheses, are not bound to maintain them to be hypotheses
+which have no relation whatever to fact. Since an hypothesis framed for
+the purpose of scientific inquiry must relate to something which has
+real existence, (for there can be no science respecting non-entities,)
+it follows that any hypothesis we make respecting an object, to
+facilitate our study of it, must not involve anything which is
+distinctly false, and repugnant to its real nature: we must not ascribe
+to the thing any property which it has not; our liberty extends only to
+slightly exaggerating some of those which it has, (by assuming it to be
+completely what it really is very nearly,) and suppressing others, under
+the indispensable obligation of restoring them whenever, and in as far
+as, their presence or absence would make any material difference in the
+truth of our conclusions. Of this nature, accordingly, are the first
+principles involved in the definitions of geometry. That the hypotheses
+should be of this particular character, is however no further necessary,
+than inasmuch as no others could enable us to deduce conclusions which,
+with due corrections, would be true of real objects: and in fact, when
+our aim is only to illustrate truths, and not to investigate them, we
+are not under any such restriction. We might suppose an imaginary
+animal, and work out by deduction, from the known laws of physiology,
+its natural history; or an imaginary commonwealth, and from the elements
+composing it, might argue what would be its fate. And the conclusions
+which we might thus draw from purely arbitrary hypotheses, might form a
+highly useful intellectual exercise: but as they could only teach us
+what _would_ be the properties of objects which do not really exist,
+they would not constitute any addition to our knowledge of nature: while
+on the contrary, if the hypothesis merely divests a real object of some
+portion of its properties, without clothing it in false ones, the
+conclusions will always express, under known liability to correction,
+actual truth.
+
+
+§ 3. But though Dr. Whewell has not shaken Stewart's doctrine as to the
+hypothetical character of that portion of the first principles of
+geometry which are involved in the so-called definitions, he has, I
+conceive, greatly the advantage of Stewart on another important point in
+the theory of geometrical reasoning; the necessity of admitting, among
+those first principles, axioms as well as definitions. Some of the
+axioms of Euclid might, no doubt, be exhibited in the form of
+definitions, or might be deduced, by reasoning, from propositions
+similar to what are so called. Thus, if instead of the axiom, Magnitudes
+which can be made to coincide are equal, we introduce a definition,
+"Equal magnitudes are those which may be so applied to one another as to
+coincide;" the three axioms which follow (Magnitudes which are equal to
+the same are equal to one another--If equals are added to equals the
+sums are equal--If equals are taken from equals the remainders are
+equal,) may be proved by an imaginary superposition, resembling that by
+which the fourth proposition of the first book of Euclid is
+demonstrated. But though these and several others may be struck out of
+the list of first principles, because, though not requiring
+demonstration, they are susceptible of it; there will be found in the
+list of axioms two or three fundamental truths, not capable of being
+demonstrated: among which must be reckoned the proposition that two
+straight lines cannot inclose a space, (or its equivalent, Straight
+lines which coincide in two points coincide altogether,) and some
+property of parallel lines, other than that which constitutes their
+definition: one of the most suitable for the purpose being that selected
+by Professor Playfair: "Two straight lines which intersect each other
+cannot both of them be parallel to a third straight line."[20]
+
+The axioms, as well those which are indemonstrable as those which admit
+of being demonstrated, differ from that other class of fundamental
+principles which are involved in the definitions, in this, that they
+are true without any mixture of hypothesis. That things which are equal
+to the same thing are equal to one another, is as true of the lines and
+figures in nature, as it would be of the imaginary ones assumed in the
+definitions. In this respect, however, mathematics are only on a par
+with most other sciences. In almost all sciences there are some general
+propositions which are exactly true, while the greater part are only
+more or less distant approximations to the truth. Thus in mechanics, the
+first law of motion (the continuance of a movement once impressed, until
+stopped or slackened by some resisting force) is true without
+qualification or error. The rotation of the earth in twenty-four hours,
+of the same length as in our time, has gone on since the first accurate
+observations, without the increase or diminution of one second in all
+that period. These are inductions which require no fiction to make them
+be received as accurately true: but along with them there are others, as
+for instance the propositions respecting the figure of the earth, which
+are but approximations to the truth; and in order to use them for the
+further advancement of our knowledge, we must feign that they are
+exactly true, though they really want something of being so.
+
+
+§ 4. It remains to inquire, what is the ground of our belief in
+axioms--what is the evidence on which they rest? I answer, they are
+experimental truths; generalizations from observation. The proposition,
+Two straight lines cannot inclose a space--or in other words, Two
+straight lines which have once met, do not meet again, but continue to
+diverge--is an induction from the evidence of our senses.
+
+This opinion runs counter to a scientific prejudice of long standing and
+great strength, and there is probably no proposition enunciated in this
+work for which a more unfavourable reception is to be expected. It is,
+however, no new opinion; and even if it were so, would be entitled to be
+judged, not by its novelty, but by the strength of the arguments by
+which it can be supported. I consider it very fortunate that so eminent
+a champion of the contrary opinion as Dr. Whewell, has found occasion
+for a most elaborate treatment of the whole theory of axioms, in
+attempting to construct the philosophy of the mathematical and physical
+sciences on the basis of the doctrine against which I now contend.
+Whoever is anxious that a discussion should go to the bottom of the
+subject, must rejoice to see the opposite side of the question worthily
+represented. If what is said by Dr. Whewell, in support of an opinion
+which he has made the foundation of a systematic work, can be shown not
+to be conclusive, enough will have been done, without going further in
+quest of stronger arguments and a more powerful adversary.
+
+It is not necessary to show that the truths which we call axioms are
+originally _suggested_ by observation, and that we should never have
+known that two straight lines cannot inclose a space if we had never
+seen a straight line: thus much being admitted by Dr. Whewell, and by
+all, in recent times, who have taken his view of the subject. But they
+contend, that it is not experience which _proves_ the axiom; but that
+its truth is perceived _à priori_, by the constitution of the mind
+itself, from the first moment when the meaning of the proposition is
+apprehended; and without any necessity for verifying it by repeated
+trials, as is requisite in the case of truths really ascertained by
+observation.
+
+They cannot, however, but allow that the truth of the axiom, Two
+straight lines cannot inclose a space, even if evident independently of
+experience, is also evident from experience. Whether the axiom needs
+confirmation or not, it receives confirmation in almost every instant of
+our lives; since we cannot look at any two straight lines which
+intersect one another, without seeing that from that point they continue
+to diverge more and more. Experimental proof crowds in upon us in such
+endless profusion, and without one instance in which there can be even a
+suspicion of an exception to the rule, that we should soon have stronger
+ground for believing the axiom, even as an experimental truth, than we
+have for almost any of the general truths which we confessedly learn
+from the evidence of our senses. Independently of _à priori_ evidence,
+we should certainly believe it with an intensity of conviction far
+greater than we accord to any ordinary physical truth: and this too at a
+time of life much earlier than that from which we date almost any part
+of our acquired knowledge, and much too early to admit of our retaining
+any recollection of the history of our intellectual operations at that
+period. Where then is the necessity for assuming that our recognition of
+these truths has a different origin from the rest of our knowledge, when
+its existence is perfectly accounted for by supposing its origin to be
+the same? when the causes which produce belief in all other instances,
+exist in this instance, and in a degree of strength as much superior to
+what exists in other cases, as the intensity of the belief itself is
+superior? The burden of proof lies on the advocates of the contrary
+opinion: it is for them to point out some fact, inconsistent with the
+supposition that this part of our knowledge of nature is derived from
+the same sources as every other part.[21]
+
+This, for instance, they would be able to do, if they could prove
+chronologically that we had the conviction (at least practically) so
+early in infancy as to be anterior to those impressions on the senses,
+upon which, on the other theory, the conviction is founded. This,
+however, cannot be proved: the point being too far back to be within the
+reach of memory, and too obscure for external observation. The advocates
+of the _à priori_ theory are obliged to have recourse to other
+arguments. These are reducible to two, which I shall endeavour to state
+as clearly and as forcibly as possible.
+
+
+§ 5. In the first place it is said that if our assent to the proposition
+that two straight lines cannot inclose a space, were derived from the
+senses, we could only be convinced of its truth by actual trial, that
+is, by seeing or feeling the straight lines; whereas in fact it is seen
+to be true by merely thinking of them. That a stone thrown into water
+goes to the bottom, may be perceived by our senses, but mere thinking of
+a stone thrown into the water would never have led us to that
+conclusion: not so, however, with the axioms relating to straight lines:
+if I could be made to conceive what a straight line is, without having
+seen one, I should at once recognise that two such lines cannot inclose
+a space. Intuition is "imaginary looking;"[22] but experience must be
+real looking: if we see a property of straight lines to be true by
+merely fancying ourselves to be looking at them, the ground of our
+belief cannot be the senses, or experience; it must be something mental.
+
+To this argument it might be added in the case of this particular axiom,
+(for the assertion would not be true of all axioms,) that the evidence
+of it from actual ocular inspection is not only unnecessary, but
+unattainable. What says the axiom? That two straight lines _cannot_
+inclose a space; that after having once intersected, if they are
+prolonged to infinity they do not meet, but continue to diverge from one
+another. How can this, in any single case, be proved by actual
+observation? We may follow the lines to any distance we please; but we
+cannot follow them to infinity: for aught our senses can testify, they
+may, immediately beyond the farthest point to which we have traced them,
+begin to approach, and at last meet. Unless, therefore, we had some
+other proof of the impossibility than observation affords us, we should
+have no ground for believing the axiom at all.
+
+To these arguments, which I trust I cannot be accused of understating, a
+satisfactory answer will, I conceive, be found, if we advert to one of
+the characteristic properties of geometrical forms--their capacity of
+being painted in the imagination with a distinctness equal to reality:
+in other words, the exact resemblance of our ideas of form to the
+sensations which suggest them. This, in the first place, enables us to
+make (at least with a little practice) mental pictures of all possible
+combinations of lines and angles, which resemble the realities quite as
+well as any which we could make on paper; and in the next place, make
+those pictures just as fit subjects of geometrical experimentation as
+the realities themselves; inasmuch as pictures, if sufficiently
+accurate, exhibit of course all the properties which would be manifested
+by the realities at one given instant, and on simple inspection: and in
+geometry we are concerned only with such properties, and not with that
+which pictures could not exhibit, the mutual action of bodies one upon
+another. The foundations of geometry would therefore be laid in direct
+experience, even if the experiments (which in this case consist merely
+in attentive contemplation) were practised solely upon what we call our
+ideas, that is, upon the diagrams in our minds, and not upon outward
+objects. For in all systems of experimentation we take some objects to
+serve as representatives of all which resemble them; and in the present
+case the conditions which qualify a real object to be the representative
+of its class, are completely fulfilled by an object existing only in our
+fancy. Without denying, therefore, the possibility of satisfying
+ourselves that two straight lines cannot inclose a space, by merely
+thinking of straight lines without actually looking at them; I contend,
+that we do not believe this truth on the ground of the imaginary
+intuition simply, but because we know that the imaginary lines exactly
+resemble real ones, and that we may conclude from them to real ones with
+quite as much certainty as we could conclude from one real line to
+another. The conclusion, therefore, is still an induction from
+observation. And we should not be authorized to substitute observation
+of the image in our mind, for observation of the reality, if we had not
+learnt by long-continued experience that the properties of the reality
+are faithfully represented in the image; just as we should be
+scientifically warranted in describing an animal which we have never
+seen, from a picture made of it with a daguerreotype; but not until we
+had learnt by ample experience, that observation of such a picture is
+precisely equivalent to observation of the original.
+
+These considerations also remove the objection arising from the
+impossibility of ocularly following the lines in their prolongation to
+infinity. For though, in order actually to see that two given lines
+never meet, it would be necessary to follow them to infinity; yet
+without doing so we may know that if they ever do meet, or if, after
+diverging from one another, they begin again to approach, this must take
+place not at an infinite, but at a finite distance. Supposing,
+therefore, such to be the case, we can transport ourselves thither in
+imagination, and can frame a mental image of the appearance which one or
+both of the lines must present at that point, which we may rely on as
+being precisely similar to the reality. Now, whether we fix our
+contemplation upon this imaginary picture, or call to mind the
+generalizations we have had occasion to make from former ocular
+observation, we learn by the evidence of experience, that a line which,
+after diverging from another straight line, begins to approach to it,
+produces the impression on our senses which we describe by the
+expression, "a bent line," not by the expression, "a straight line."[23]
+
+
+§ 6. The first of the two arguments in support of the theory that
+axioms are _à priori_ truths, having, I think, been sufficiently
+answered; I proceed to the second, which is usually the most relied on.
+Axioms (it is asserted) are conceived by us not only as true, but as
+universally and necessarily true. Now, experience cannot possibly give
+to any proposition this character. I may have seen snow a hundred
+times, and may have seen that it was white, but this cannot give me
+entire assurance even that all snow is white; much less that snow _must_
+be white. "However many instances we may have observed of the truth of a
+proposition, there is nothing to assure us that the next case shall not
+be an exception to the rule. If it be strictly true that every ruminant
+animal yet known has cloven hoofs, we still cannot be sure that some
+creature will not hereafter be discovered which has the first of these
+attributes, without having the other.... Experience must always consist
+of a limited number of observations; and, however numerous these may be,
+they can show nothing with regard to the infinite number of cases in
+which the experiment has not been made." Besides, Axioms are not only
+universal, they are also necessary. Now "experience cannot offer the
+smallest ground for the necessity of a proposition. She can observe and
+record what has happened; but she cannot find, in any case, or in any
+accumulation of cases, any reason for what _must_ happen. She may see
+objects side by side; but she cannot see a reason why they must ever be
+side by side. She finds certain events to occur in succession; but the
+succession supplies, in its occurrence, no reason for its recurrence.
+She contemplates external objects; but she cannot detect any internal
+bond, which indissolubly connects the future with the past, the possible
+with the real. To learn a proposition by experience, and to see it to be
+necessarily true, are two altogether different processes of
+thought."[24] And Dr. Whewell adds, "If any one does not clearly
+comprehend this distinction of necessary and contingent truths, he will
+not be able to go along with us in our researches into the foundations
+of human knowledge; nor, indeed, to pursue with success any speculation
+on the subject."[25]
+
+In the following passage, we are told what the distinction is, the
+non-recognition of which incurs this denunciation. "Necessary truths are
+those in which we not only learn that the proposition is true, but see
+that it _must_ be true; in which the negation of the truth is not only
+false, but impossible; in which we cannot, even by an effort of
+imagination, or in a supposition, conceive the reverse of that which is
+asserted. That there are such truths cannot be doubted. We may take, for
+example, all relations of number. Three and Two added together make
+Five. We cannot conceive it to be otherwise. We cannot, by any freak of
+thought, imagine Three and Two to make Seven."[26]
+
+Although Dr. Whewell has naturally and properly employed a variety of
+phrases to bring his meaning more forcibly home, he would, I presume,
+allow that they are all equivalent; and that what he means by a
+necessary truth, would be sufficiently defined, a proposition the
+negation of which is not only false but inconceivable. I am unable to
+find in any of his expressions, turn them what way you will, a meaning
+beyond this, and I do not believe he would contend that they mean
+anything more.
+
+This, therefore, is the principle asserted: that propositions, the
+negation of which is inconceivable, or in other words, which we cannot
+figure to ourselves as being false, must rest on evidence of a higher
+and more cogent description than any which experience can afford.
+
+Now I cannot but wonder that so much stress should be laid on the
+circumstance of inconceivableness, when there is such ample experience
+to show, that our capacity or incapacity of conceiving a thing has very
+little to do with the possibility of the thing in itself; but is in
+truth very much an affair of accident, and depends on the past history
+and habits of our own minds. There is no more generally acknowledged
+fact in human nature, than the extreme difficulty at first felt in
+conceiving anything as possible, which is in contradiction to long
+established and familiar experience; or even to old familiar habits of
+thought. And this difficulty is a necessary result of the fundamental
+laws of the human mind. When we have often seen and thought of two
+things together, and have never in any one instance either seen or
+thought of them separately, there is by the primary law of association
+an increasing difficulty, which may in the end become insuperable, of
+conceiving the two things apart. This is most of all conspicuous in
+uneducated persons, who are in general utterly unable to separate any
+two ideas which have once become firmly associated in their minds; and
+if persons of cultivated intellect have any advantage on the point, it
+is only because, having seen and heard and read more, and being more
+accustomed to exercise their imagination, they have experienced their
+sensations and thoughts in more varied combinations, and have been
+prevented from forming many of these inseparable associations. But this
+advantage has necessarily its limits. The most practised intellect is
+not exempt from the universal laws of our conceptive faculty. If daily
+habit presents to any one for a long period two facts in combination,
+and if he is not led during that period either by accident or by his
+voluntary mental operations to think of them apart, he will probably in
+time become incapable of doing so even by the strongest effort; and the
+supposition that the two facts can be separated in nature, will at last
+present itself to his mind with all the characters of an inconceivable
+phenomenon.[27] There are remarkable instances of this in the history of
+science: instances in which the most instructed men rejected as
+impossible, because inconceivable, things which their posterity, by
+earlier practice and longer perseverance in the attempt, found it quite
+easy to conceive, and which everybody now knows to be true. There was a
+time when men of the most cultivated intellects, and the most
+emancipated from the dominion of early prejudice, could not credit the
+existence of antipodes; were unable to conceive, in opposition to old
+association, the force of gravity acting upwards instead of downwards.
+The Cartesians long rejected the Newtonian doctrine of the
+gravitation of all bodies towards one another, on the faith of
+a general proposition, the reverse of which seemed to them to be
+inconceivable--the proposition that a body cannot act where it is not.
+All the cumbrous machinery of imaginary vortices, assumed without the
+smallest particle of evidence, appeared to these philosophers a more
+rational mode of explaining the heavenly motions, than one which
+involved what seemed to them so great an absurdity.[28] And they no
+doubt found it as impossible to conceive that a body should act upon the
+earth at the distance of the sun or moon, as we find it to conceive an
+end to space or time, or two straight lines inclosing a space. Newton
+himself had not been able to realize the conception, or we should not
+have had his hypothesis of a subtle ether, the occult cause of
+gravitation; and his writings prove, that though he deemed the
+particular nature of the intermediate agency a matter of conjecture, the
+necessity of _some_ such agency appeared to him indubitable. It would
+seem that even now the majority of scientific men have not completely
+got over this very difficulty; for though they have at last learnt to
+conceive the sun _attracting_ the earth without any intervening fluid,
+they cannot yet conceive the sun _illuminating_ the earth without some
+such medium.
+
+If, then, it be so natural to the human mind, even in a high state of
+culture, to be incapable of conceiving, and on that ground to believe
+impossible, what is afterwards not only found to be conceivable but
+proved to be true; what wonder if in cases where the association is
+still older, more confirmed, and more familiar, and in which nothing
+ever occurs to shake our conviction, or even suggest to us any
+conception at variance with the association, the acquired incapacity
+should continue, and be mistaken for a natural incapacity? It is true,
+our experience of the varieties in nature enables us, within certain
+limits, to conceive other varieties analogous to them. We can conceive
+the sun or moon falling; for though we never saw them fall, nor ever
+perhaps imagined them falling, we have seen so many other things fall,
+that we have innumerable familiar analogies to assist the conception;
+which, after all, we should probably have some difficulty in framing,
+were we not well accustomed to see the sun and moon move (or appear to
+move,) so that we are only called upon to conceive a slight change in
+the direction of motion, a circumstance familiar to our experience. But
+when experience affords no model on which to shape the new conception,
+how is it possible for us to form it? How, for example, can we imagine
+an end to space or time? We never saw any object without something
+beyond it, nor experienced any feeling without something following it.
+When, therefore, we attempt to conceive the last point of space, we have
+the idea irresistibly raised of other points beyond it. When we try to
+imagine the last instant of time, we cannot help conceiving another
+instant after it. Nor is there any necessity to assume, as is done by a
+modern school of metaphysicians, a peculiar fundamental law of the mind
+to account for the feeling of infinity inherent in our conceptions of
+space and time; that apparent infinity is sufficiently accounted for by
+simpler and universally acknowledged laws.
+
+Now, in the case of a geometrical axiom, such, for example, as that two
+straight lines cannot inclose a space,--a truth which is testified to us
+by our very earliest impressions of the external world,--how is it
+possible (whether those external impressions be or be not the ground of
+our belief) that the reverse of the proposition _could_ be otherwise
+than inconceivable to us? What analogy have we, what similar order of
+facts in any other branch of our experience, to facilitate to us the
+conception of two straight lines inclosing a space? Nor is even this
+all. I have already called attention to the peculiar property of our
+impressions of form, that the ideas or mental images exactly resemble
+their prototypes, and adequately represent them for the purposes of
+scientific observation. From this, and from the intuitive character of
+the observation, which in this case reduces itself to simple inspection,
+we cannot so much as call up in our imagination two straight lines, in
+order to attempt to conceive them inclosing a space, without by that
+very act repeating the scientific experiment which establishes the
+contrary. Will it really be contended that the inconceivableness of the
+thing, in such circumstances, proves anything against the experimental
+origin of the conviction? Is it not clear that in whichever mode our
+belief in the proposition may have originated, the impossibility of our
+conceiving the negative of it must, on either hypothesis, be the same?
+As, then, Dr. Whewell exhorts those who have any difficulty in
+recognising the distinction held by him between necessary and contingent
+truths, to study geometry,--a condition which I can assure him I have
+conscientiously fulfilled,--I, in return, with equal confidence, exhort
+those who agree with him, to study the general laws of association;
+being convinced that nothing more is requisite than a moderate
+familiarity with those laws, to dispel the illusion which ascribes a
+peculiar necessity to our earliest inductions from experience, and
+measures the possibility of things in themselves, by the human capacity
+of conceiving them.
+
+I hope to be pardoned for adding, that Dr. Whewell himself has both
+confirmed by his testimony the effect of habitual association in giving
+to an experimental truth the appearance of a necessary one, and afforded
+a striking instance of that remarkable law in his own person. In his
+_Philosophy of the Inductive Sciences_ he continually asserts, that
+propositions which not only are not self-evident, but which we know to
+have been discovered gradually, and by great efforts of genius and
+patience, have, when once established, appeared so self-evident that,
+but for historical proof, it would have been impossible to conceive that
+they had not been recognised from the first by all persons in a sound
+state of their faculties. "We now despise those who, in the Copernican
+controversy, could not conceive the apparent motion of the sun on the
+heliocentric hypothesis; or those who, in opposition to Galileo, thought
+that a uniform force might be that which generated a velocity
+proportional to the space; or those who held there was something absurd
+in Newton's doctrine of the different refrangibility of differently
+coloured rays; or those who imagined that when elements combine, their
+sensible qualities must be manifest in the compound; or those who were
+reluctant to give up the distinction of vegetables into herbs, shrubs,
+and trees. We cannot help thinking that men must have been singularly
+dull of comprehension, to find a difficulty in admitting what is to us
+so plain and simple. We have a latent persuasion that we in their place
+should have been wiser and more clear-sighted; that we should have taken
+the right side, and given our assent at once to the truth. Yet in
+reality such a persuasion is a mere delusion. The persons who, in such
+instances as the above, were on the losing side, were very far, in most
+cases, from being persons more prejudiced, or stupid, or narrow-minded,
+than the greater part of mankind now are; and the cause for which they
+fought was far from being a manifestly bad one, till it had been so
+decided by the result of the war.... So complete has been the victory of
+truth in most of these instances, that at present we can hardly imagine
+the struggle to have been necessary. _The very essence of these triumphs
+is, that they lead us to regard the views we reject as not only false
+but inconceivable._"[29]
+
+This last proposition is precisely what I contend for; and I ask no
+more, in order to overthrow the whole theory of its author on the nature
+of the evidence of axioms. For what is that theory? That the truth of
+axioms cannot have been learnt from experience, because their falsity is
+inconceivable. But Dr. Whewell himself says, that we are continually
+led, by the natural progress of thought, to regard as inconceivable what
+our forefathers not only conceived but believed, nay even (he might
+have added) were unable to conceive the reverse of. He cannot intend to
+justify this mode of thought: he cannot mean to say, that we can be
+right in regarding as inconceivable what others have conceived, and as
+self-evident what to others did not appear evident at all. After so
+complete an admission that inconceivableness is an accidental thing, not
+inherent in the phenomenon itself, but dependent on the mental history
+of the person who tries to conceive it, how can he ever call upon us to
+reject a proposition as impossible on no other ground than its
+inconceivableness? Yet he not only does so, but has unintentionally
+afforded some of the most remarkable examples which can be cited of the
+very illusion which he has himself so clearly pointed out. I select as
+specimens, his remarks on the evidence of the three laws of motion, and
+of the atomic theory.
+
+With respect to the laws of motion, Dr. Whewell says: "No one can doubt
+that, in historical fact, these laws were collected from experience.
+That such is the case, is no matter of conjecture. We know the time, the
+persons, the circumstances, belonging to each step of each
+discovery."[30] After this testimony, to adduce evidence of the fact
+would be superfluous. And not only were these laws by no means
+intuitively evident, but some of them were originally paradoxes. The
+first law was especially so. That a body, once in motion, would continue
+for ever to move in the same direction with undiminished velocity unless
+acted upon by some new force, was a proposition which mankind found for
+a long time the greatest difficulty in crediting. It stood opposed to
+apparent experience of the most familiar kind, which taught that it was
+the nature of motion to abate gradually, and at last terminate of
+itself. Yet when once the contrary doctrine was firmly established,
+mathematicians, as Dr. Whewell observes, speedily began to believe that
+laws, thus contradictory to first appearances, and which, even after
+full proof had been obtained, it had required generations to render
+familiar to the minds of the scientific world, were under "a
+demonstrable necessity, compelling them to be such as they are and no
+other;" and he himself, though not venturing "absolutely to pronounce"
+that _all_ these laws "can be rigorously traced to an absolute necessity
+in the nature of things,"[31] does actually so think of the law just
+mentioned; of which he says: "Though the discovery of the first law of
+motion was made, historically speaking, by means of experiment, we have
+now attained a point of view in which we see that it might have been
+certainly known to be true, independently of experience."[32] Can there
+be a more striking exemplification than is here afforded, of the effect
+of association which we have described? Philosophers, for generations,
+have the most extraordinary difficulty in putting certain ideas
+together; they at last succeed in doing so; and after a sufficient
+repetition of the process, they first fancy a natural bond between the
+ideas, then experience a growing difficulty, which at last, by the
+continuation of the same progress, becomes an impossibility, of severing
+them from one another. If such be the progress of an experimental
+conviction of which the date is of yesterday, and which is in opposition
+to first appearances, how must it fare with those which are conformable
+to appearances familiar from the first dawn of intelligence, and of the
+conclusiveness of which, from the earliest records of human thought, no
+sceptic has suggested even a momentary doubt?
+
+The other instance which I shall quote is a truly astonishing one, and
+may be called the _reductio ad absurdum_ of the theory of
+inconceivableness. Speaking of the laws of chemical composition, Dr.
+Whewell says:[33] "That they could never have been clearly understood,
+and therefore never firmly established, without laborious and exact
+experiments, is certain; but yet we may venture to say, that being once
+known, they possess an evidence beyond that of mere experiment. _For how
+in fact can we conceive combinations, otherwise than as definite in kind
+and quality?_ If we were to suppose each element ready to combine with
+any other indifferently, and indifferently in any quantity, we should
+have a world in which all would be confusion and indefiniteness. There
+would be no fixed kinds of bodies. Salts, and stones, and ores, would
+approach to and graduate into each other by insensible degrees. Instead
+of this, we know that the world consists of bodies distinguishable from
+each other by definite differences, capable of being classified and
+named, and of having general propositions asserted concerning them. And
+as _we cannot conceive a world in which this should not be the case_, it
+would appear that we cannot conceive a state of things in which the laws
+of the combination of elements should not be of that definite and
+measured kind which we have above asserted."
+
+That a philosopher of Dr. Whewell's eminence should gravely assert that
+we cannot conceive a world in which the simple elements should combine
+in other than definite proportions; that by dint of meditating on a
+scientific truth, the original discoverer of which was still living, he
+should have rendered the association in his own mind between the idea of
+combination and that of constant proportions so familiar and intimate as
+to be unable to conceive the one fact without the other; is so signal an
+instance of the mental law for which I am contending, that one word more
+in illustration must be superfluous.
+
+In the latest and most complete elaboration of his metaphysical system
+(the _Philosophy of Discovery_), as well as in the earlier discourse on
+the _Fundamental Antithesis of Philosophy_, reprinted as an appendix to
+that work, Dr. Whewell, while very candidly admitting that his language
+was open to misconception, disclaims having intended to say that mankind
+in general can _now_ perceive the law of definite proportions in
+chemical combination to be a necessary truth. All he meant was that
+philosophical chemists in a future generation may possibly see this.
+"Some truths may be seen by intuition, but yet the intuition of them may
+be a rare and a difficult attainment."[34] And he explains that the
+inconceivableness which, according to his theory, is the test of
+axioms, "depends entirely upon the clearness of the Ideas which the
+axioms involve. So long as those Ideas are vague and indistinct, the
+contrary of an Axiom may be assented to, though it cannot be distinctly
+conceived. It may be assented to, not because it is possible, but
+because we do not see clearly what is possible. To a person who is only
+beginning to think geometrically, there may appear nothing absurd in the
+assertion, that two straight lines may inclose a space. And in the same
+manner, to a person who is only beginning to think of mechanical truths,
+it may not appear to be absurd, that in mechanical processes, Reaction
+should be greater or less than Action; and so, again, to a person who
+has not thought steadily about Substance, it may not appear
+inconceivable, that by chemical operations, we should generate new
+matter, or destroy matter which already exists."[35] Necessary truths,
+therefore, are not those of which we cannot conceive, but "those of
+which we cannot _distinctly_ conceive, the contrary."[36] So long as our
+ideas are indistinct altogether, we do not know what is or is not
+capable of being distinctly conceived; but, by the ever increasing
+distinctness with which scientific men apprehend the general conceptions
+of science, they in time come to perceive that there are certain laws of
+nature, which, though historically and as a matter of fact they were
+learnt from experience, we cannot, now that we know them, distinctly
+conceive to be other than they are.
+
+The account which I should give of this progress of the scientific mind
+is somewhat different. After a general law of nature has been
+ascertained, men's minds do not at first acquire a complete facility of
+familiarly representing to themselves the phenomena of nature in the
+character which that law assigns to them. The habit which constitutes
+the scientific cast of mind, that of conceiving facts of all
+descriptions conformably to the laws which regulate them--phenomena of
+all descriptions according to the relations which have been ascertained
+really to exist between them; this habit, in the case of newly
+discovered relations, comes only by degrees. So long as it is not
+thoroughly formed, no necessary character is ascribed to the new truth.
+But in time, the philosopher attains a state of mind in which his mental
+picture of nature spontaneously represents to him all the phenomena with
+which the new theory is concerned, in the exact light in which the
+theory regards them: all images or conceptions derived from any other
+theory, or from the confused view of the facts which is anterior to any
+theory, having entirely disappeared from his mind. The mode of
+representing facts which results from the theory, has now become, to his
+faculties, the only natural mode of conceiving them. It is a known
+truth, that a prolonged habit of arranging phenomena in certain groups,
+and explaining them by means of certain principles, makes any other
+arrangement or explanation of these facts be felt as unnatural: and it
+may at last become as difficult to him to represent the facts to himself
+in any other mode, as it often was, originally, to represent them in
+that mode.
+
+But, further, if the theory is true, as we are supposing it to be, any
+other mode in which he tries, or in which he was formerly accustomed, to
+represent the phenomena, will be seen by him to be inconsistent with the
+facts that suggested the new theory--facts which now form a part of his
+mental picture of nature. And since a contradiction is always
+inconceivable, his imagination rejects these false theories, and
+declares itself incapable of conceiving them. Their inconceivableness to
+him does not, however, result from anything in the theories themselves,
+intrinsically and _à priori_ repugnant to the human faculties; it
+results from the repugnance between them and a portion of the facts;
+which facts as long as he did not know, or did not distinctly realize in
+his mental representations, the false theory did not appear other than
+conceivable; it becomes inconceivable, merely from the fact that
+contradictory elements cannot be combined in the same conception.
+Although, then, his real reason for rejecting theories at variance with
+the true one, is no other than that they clash with his experience, he
+easily falls into the belief, that he rejects them because they are
+inconceivable, and that he adopts the true theory because it is
+self-evident, and does not need the evidence of experience at all.
+
+This I take to be the real and sufficient explanation of the paradoxical
+truth, on which so much stress is laid by Dr. Whewell, that a
+scientifically cultivated mind is actually, in virtue of that
+cultivation, unable to conceive suppositions which a common man
+conceives without the smallest difficulty. For there is nothing
+inconceivable in the suppositions themselves; the impossibility is in
+combining them with facts inconsistent with them, as part of the same
+mental picture; an obstacle of course only felt by those who know the
+facts, and are able to perceive the inconsistency. As far as the
+suppositions themselves are concerned, in the case of many of Dr.
+Whewell's necessary truths the negative of the axiom is, and probably
+will be as long as the human race lasts, as easily conceivable as the
+affirmative. There is no axiom (for example) to which Dr. Whewell
+ascribes a more thorough character of necessity and self-evidence, than
+that of the indestructibility of matter. That this is a true law of
+nature I fully admit; but I imagine there is no human being to whom the
+opposite supposition is inconceivable--who has any difficulty in
+imagining a portion of matter annihilated: inasmuch as its apparent
+annihilation, in no respect distinguishable from real by our unassisted
+senses, takes place every time that water dries up, or fuel is consumed.
+Again, the law that bodies combine chemically in definite proportions is
+undeniably true; but few besides Dr. Whewell have reached the point
+which he seems personally to have arrived at, (though he only dares
+prophesy similar success to the multitude after the lapse of
+generations,) that of being unable to conceive a world in which the
+elements are ready to combine with one another "indifferently in any
+quantity;" nor is it likely that we shall ever rise to this sublime
+height of inability, so long as all the mechanical mixtures in our
+planet, whether solid, liquid, or aëriform, exhibit to our daily
+observation the very phenomenon declared to be inconceivable.
+
+According to Dr. Whewell, these and similar laws of nature cannot be
+drawn from experience, inasmuch as they are, on the contrary, assumed
+in the interpretation of experience. Our inability to "add to or
+diminish the quantity of matter in the world," is a truth which "neither
+is nor can be derived from experience; for the experiments which we make
+to verify it presuppose its truth.... When men began to use the balance
+in chemical analysis, they did not prove by trial, but took for granted,
+as self-evident, that the weight of the whole must be found in the
+aggregate weight of the elements."[37] True, it is assumed; but, I
+apprehend, no otherwise than as all experimental inquiry assumes
+provisionally some theory or hypothesis, which is to be finally held
+true or not, according as the experiments decide. The hypothesis chosen
+for this purpose will naturally be one which groups together some
+considerable number of facts already known. The proposition that the
+material of the world, as estimated by weight, is neither increased nor
+diminished by any of the processes of nature or art, had many
+appearances in its favour to begin with. It expressed truly a great
+number of familiar facts. There were other facts which it had the
+appearance of conflicting with, and which made its truth, as an
+universal law of nature, at first doubtful. Because it was doubtful,
+experiments were devised to verify it. Men assumed its truth
+hypothetically, and proceeded to try whether, on more careful
+examination, the phenomena which apparently pointed to a different
+conclusion, would not be found to be consistent with it. This turned out
+to be the case; and from that time the doctrine took its place as an
+universal truth, but as one proved to be such by experience. That the
+theory itself preceded the proof of its truth--that it had to be
+conceived before it could be proved, and in order that it might be
+proved--does not imply that it was self-evident, and did not need proof.
+Otherwise all the true theories in the sciences are necessary and
+self-evident; for no one knows better than Dr. Whewell that they all
+began by being assumed, for the purpose of connecting them by deductions
+with those facts of experience on which, as evidence, they now
+confessedly rest.[38]
+
+
+
+
+CHAPTER VI.
+
+THE SAME SUBJECT CONTINUED.
+
+
+§ 1. In the examination which formed the subject of the last chapter,
+into the nature of the evidence of those deductive sciences which are
+commonly represented to be systems of necessary truth, we have been led
+to the following conclusions. The results of those sciences are indeed
+necessary, in the sense of necessarily following from certain first
+principles, commonly called axioms and definitions; that is, of being
+certainly true if those axioms and definitions are so; for the word
+necessity, even in this acceptation of it, means no more than certainty.
+But their claim to the character of necessity in any sense beyond this,
+as implying an evidence independent of and superior to observation and
+experience, must depend on the previous establishment of such a claim in
+favour of the definitions and axioms themselves. With regard to axioms,
+we found that, considered as experimental truths, they rest on
+superabundant and obvious evidence. We inquired, whether, since this is
+the case, it be imperative to suppose any other evidence of those truths
+than experimental evidence, any other origin for our belief of them than
+an experimental origin. We decided, that the burden of proof lies with
+those who maintain the affirmative, and we examined, at considerable
+length, such arguments as they have produced. The examination having led
+to the rejection of those arguments, we have thought ourselves warranted
+in concluding that axioms are but a class, the most universal class, of
+inductions from experience; the simplest and easiest cases of
+generalization from the facts furnished to us by our senses or by our
+internal consciousness.
+
+While the axioms of demonstrative sciences thus appeared to be
+experimental truths, the definitions, as they are incorrectly called, in
+those sciences, were found by us to be generalizations from experience
+which are not even, accurately speaking, truths; being propositions in
+which, while we assert of some kind of object, some property or
+properties which observation shows to belong to it, we at the same time
+deny that it possesses any other properties, though in truth other
+properties do in every individual instance accompany, and in almost all
+instances modify, the property thus exclusively predicated. The denial,
+therefore, is a mere fiction, or supposition, made for the purpose of
+excluding the consideration of those modifying circumstances, when their
+influence is of too trifling amount to be worth considering, or
+adjourning it, when important, to a more convenient moment.
+
+From these considerations it would appear that Deductive or
+Demonstrative Sciences are all, without exception, Inductive Sciences;
+that their evidence is that of experience; but that they are also, in
+virtue of the peculiar character of one indispensable portion of the
+general formulæ according to which their inductions are made,
+Hypothetical Sciences. Their conclusions are only true on certain
+suppositions, which are, or ought to be, approximations to the truth,
+but are seldom, if ever, exactly true; and to this hypothetical
+character is to be ascribed the peculiar certainty, which is supposed to
+be inherent in demonstration.
+
+What we have now asserted, however, cannot be received as universally
+true of Deductive or Demonstrative Sciences, until verified by being
+applied to the most remarkable of all those sciences, that of Numbers;
+the theory of the Calculus; Arithmetic and Algebra. It is harder to
+believe of the doctrines of this science than of any other, either that
+they are not truths _à priori_, but experimental truths, or that their
+peculiar certainty is owing to their being not absolute but only
+conditional truths. This, therefore, is a case which merits examination
+apart; and the more so, because on this subject we have a double set of
+doctrines to contend with; that of the _à priori_ philosophers on one
+side; and on the other, a theory the most opposite to theirs, which was
+at one time very generally received, and is still far from being
+altogether exploded, among metaphysicians.
+
+
+§ 2. This theory attempts to solve the difficulty apparently inherent in
+the case, by representing the propositions of the science of numbers as
+merely verbal, and its processes as simple transformations of language,
+substitutions of one expression for another. The proposition, Two and
+one are equal to three, according to these writers, is not a truth, is
+not the assertion of a really existing fact, but a definition of the
+word three; a statement that mankind have agreed to use the name three
+as a sign exactly equivalent to two and one; to call by the former name
+whatever is called by the other more clumsy phrase. According to this
+doctrine, the longest process in algebra is but a succession of changes
+in terminology, by which equivalent expressions are substituted one for
+another; a series of translations of the same fact, from one into
+another language; though how, after such a series of translations, the
+fact itself comes out changed (as when we demonstrate a new geometrical
+theorem by algebra,) they have not explained; and it is a difficulty
+which is fatal to their theory.
+
+It must be acknowledged that there are peculiarities in the processes of
+arithmetic and algebra which render the theory in question very
+plausible, and have not unnaturally made those sciences the stronghold
+of Nominalism. The doctrine that we can discover facts, detect the
+hidden processes of nature, by an artful manipulation of language, is so
+contrary to common sense, that a person must have made some advances in
+philosophy to believe it: men fly to so paradoxical a belief to avoid,
+as they think, some even greater difficulty, which the vulgar do not
+see. What has led many to believe that reasoning is a mere verbal
+process, is, that no other theory seemed reconcileable with the nature
+of the Science of Numbers. For we do not carry any ideas along with us
+when we use the symbols of arithmetic or of algebra. In a geometrical
+demonstration we have a mental diagram, if not one on paper; AB, AC, are
+present to our imagination as lines, intersecting other lines, forming
+an angle with one another, and the like; but not so _a_ and _b_. These
+may represent lines or any other magnitudes, but those magnitudes are
+never thought of; nothing is realized in our imagination but _a_ and
+_b_. The ideas which, on the particular occasion, they happen to
+represent, are banished from the mind during every intermediate part of
+the process, between the beginning, when the premises are translated
+from things into signs, and the end, when the conclusion is translated
+back from signs into things. Nothing, then, being in the reasoner's mind
+but the symbols, what can seem more inadmissible than to contend that
+the reasoning process has to do with anything more? We seem to have come
+to one of Bacon's Prerogative Instances; an _experimentum crucis_ on the
+nature of reasoning itself.
+
+Nevertheless, it will appear on consideration, that this apparently so
+decisive instance is no instance at all; that there is in every step of
+an arithmetical or algebraical calculation a real induction, a real
+inference of facts from facts; and that what disguises the induction is
+simply its comprehensive nature, and the consequent extreme generality
+of the language. All numbers must be numbers of something: there are no
+such things as numbers in the abstract. _Ten_ must mean ten bodies, or
+ten sounds, or ten beatings of the pulse. But though numbers must be
+numbers of something, they may be numbers of anything. Propositions,
+therefore, concerning numbers, have the remarkable peculiarity that they
+are propositions concerning all things whatever; all objects, all
+existences of every kind, known to our experience. All things possess
+quantity; consist of parts which can be numbered; and in that character
+possess all the properties which are called properties of numbers. That
+half of four is two, must be true whatever the word four represents,
+whether four hours, four miles, or four pounds weight. We need only
+conceive a thing divided into four equal parts, (and all things may be
+conceived as so divided,) to be able to predicate of it every property
+of the number four, that is, every arithmetical proposition in which the
+number four stands on one side of the equation. Algebra extends the
+generalization still farther: every number represents that particular
+number of all things without distinction, but every algebraical symbol
+does more, it represents all numbers without distinction. As soon as we
+conceive a thing divided into equal parts, without knowing into what
+number of parts, we may call it _a_ or _x_, and apply to it, without
+danger of error, every algebraical formula in the books. The
+proposition, _2(a + b) = 2a + 2b_, is a truth co-extensive with all
+nature. Since then algebraical truths are true of all things whatever,
+and not, like those of geometry, true of lines only or angles only, it
+is no wonder that the symbols should not excite in our minds ideas of
+any things in particular. When we demonstrate the forty-seventh
+proposition of Euclid, it is not necessary that the words should raise
+in us an image of all right-angled triangles, but only of some one
+right-angled triangle: so in algebra we need not, under the symbol _a_,
+picture to ourselves all things whatever, but only some one thing; why
+not, then, the letter itself? The mere written characters, _a_, _b_,
+_x_, _y_, _z_, serve as well for representatives of Things in general,
+as any more complex and apparently more concrete conception. That we are
+conscious of them however in their character of things, and not of mere
+signs, is evident from the fact that our whole process of reasoning is
+carried on by predicating of them the properties of things. In resolving
+an algebraic equation, by what rules do we proceed? By applying at each
+step to _a_, _b_, and _x_, the proposition that equals added to equals
+make equals; that equals taken from equals leave equals; and other
+propositions founded on these two. These are not properties of language,
+or of signs as such, but of magnitudes, which is as much as to say, of
+all things. The inferences, therefore, which are successively drawn, are
+inferences concerning things, not symbols; though as any Things whatever
+will serve the turn, there is no necessity for keeping the idea of the
+Thing at all distinct, and consequently the process of thought may, in
+this case, be allowed without danger to do what all processes of
+thought, when they have been performed often, will do if permitted,
+namely, to become entirely mechanical. Hence the general language of
+algebra comes to be used familiarly without exciting ideas, as all
+other general language is prone to do from mere habit, though in no
+other case than this can it be done with complete safety. But when we
+look back to see from whence the probative force of the process is
+derived, we find that at every single step, unless we suppose ourselves
+to be thinking and talking of the things, and not the mere symbols, the
+evidence fails.
+
+There is another circumstance, which, still more than that which we have
+now mentioned, gives plausibility to the notion that the propositions of
+arithmetic and algebra are merely verbal. That is, that when considered
+as propositions respecting Things, they all have the appearance of being
+identical propositions. The assertion, Two and one are equal to three,
+considered as an assertion respecting objects, as for instance "Two
+pebbles and one pebble are equal to three pebbles," does not affirm
+equality between two collections of pebbles, but absolute identity. It
+affirms that if we put one pebble to two pebbles, those very pebbles are
+three. The objects, therefore, being the very same, and the mere
+assertion that "objects are themselves" being insignificant, it seems
+but natural to consider the proposition, Two and one are equal to three,
+as asserting mere identity of signification between the two names.
+
+This, however, though it looks so plausible, will not bear examination.
+The expression "two pebbles and one pebble," and the expression, "three
+pebbles," stand indeed for the same aggregation of objects, but they by
+no means stand for the same physical fact. They are names of the same
+objects, but of those objects in two different states: though they
+_de_note the same things, their _con_notation is different. Three
+pebbles in two separate parcels, and three pebbles in one parcel, do not
+make the same impression on our senses; and the assertion that the very
+same pebbles may by an alteration of place and arrangement be made to
+produce either the one set of sensations or the other, though a very
+familiar proposition, is not an identical one. It is a truth known to us
+by early and constant experience: an inductive truth; and such truths
+are the foundation of the science of Number. The fundamental truths of
+that science all rest on the evidence of sense; they are proved by
+showing to our eyes and our fingers that any given number of objects,
+ten balls for example, may by separation and re-arrangement exhibit to
+our senses all the different sets of numbers the sum of which is equal
+to ten. All the improved methods of teaching arithmetic to children
+proceed on a knowledge of this fact. All who wish to carry the child's
+_mind_ along with them in learning arithmetic; all who wish to teach
+numbers, and not mere ciphers--now teach it through the evidence of the
+senses, in the manner we have described.
+
+We may, if we please, call the proposition, "Three is two and one," a
+definition of the number three, and assert that arithmetic, as it has
+been asserted that geometry, is a science founded on definitions. But
+they are definitions in the geometrical sense, not the logical;
+asserting not the meaning of a term only, but along with it an observed
+matter of fact. The proposition, "A circle is a figure bounded by a line
+which has all its points equally distant from a point within it," is
+called the definition of a circle; but the proposition from which so
+many consequences follow, and which is really a first principle in
+geometry, is, that figures answering to this description exist. And thus
+we may call "Three is two and one" a definition of three; but the
+calculations which depend on that proposition do not follow from the
+definition itself, but from an arithmetical theorem presupposed in it,
+namely, that collections of objects exist, which while they impress the
+senses thus,
+
+  o o
+   o,
+
+may be separated into two parts, thus,
+
+  o o     o.
+
+This proposition being granted, we term all such parcels Threes, after
+which the enunciation of the above mentioned physical fact will serve
+also for a definition of the word Three.
+
+The Science of Number is thus no exception to the conclusion we
+previously arrived at, that the processes even of deductive sciences are
+altogether inductive, and that their first principles are
+generalizations from experience. It remains to be examined whether this
+science resembles geometry in the further circumstance, that some of its
+inductions are not exactly true; and that the peculiar certainty
+ascribed to it, on account of which its propositions are called
+Necessary Truths, is fictitious and hypothetical, being true in no other
+sense than that those propositions legitimately follow from the
+hypothesis of the truth of premises which are avowedly mere
+approximations to truth.
+
+
+§ 3. The inductions of arithmetic are of two sorts: first, those which
+we have just expounded, such as One and one are two, Two and one are
+three, &c., which may be called the definitions of the various numbers,
+in the improper or geometrical sense of the word Definition; and
+secondly, the two following axioms: The sums of equals are equal, The
+differences of equals are equal. These two are sufficient; for the
+corresponding propositions respecting unequals may be proved from these,
+by a _reductio ad absurdum_.
+
+These axioms, and likewise the so-called definitions, are, as has
+already been said, results of induction; true of all objects whatever,
+and, as it may seem, exactly true, without the hypothetical assumption
+of unqualified truth where an approximation to it is all that exists.
+The conclusions, therefore, it will naturally be inferred, are exactly
+true, and the science of number is an exception to other demonstrative
+sciences in this, that the categorical certainty which is predicable of
+its demonstrations is independent of all hypothesis.
+
+On more accurate investigation, however, it will be found that, even in
+this case, there is one hypothetical element in the ratiocination. In
+all propositions concerning numbers, a condition is implied, without
+which none of them would be true; and that condition is an assumption
+which maybe false. The condition, is that 1 = 1; that all the numbers
+are numbers of the same or of equal units. Let this be doubtful, and not
+one of the propositions of arithmetic will hold true. How can we know
+that one pound and one pound make two pounds, if one of the pounds may
+be troy, and the other avoirdupois? They may not make two pounds of
+either, or of any weight. How can we know that a forty-horse power is
+always equal to itself, unless we assume that all horses are of equal
+strength? It is certain that 1 is always equal in _number_ to 1; and
+where the mere number of objects, or of the parts of an object, without
+supposing them to be equivalent in any other respect, is all that is
+material, the conclusions of arithmetic, so far as they go to that
+alone, are true without mixture of hypothesis. There are a few such
+cases; as, for instance, an inquiry into the amount of the population of
+any country. It is indifferent to that inquiry whether they are grown
+people or children, strong or weak, tall or short; the only thing we
+want to ascertain is their number. But whenever, from equality or
+inequality of number, equality or inequality in any other respect is to
+be inferred, arithmetic carried into such inquiries becomes as
+hypothetical a science as geometry. All units must be assumed to be
+equal in that other respect; and this is never accurately true, for one
+actual pound weight is not exactly equal to another, nor one measured
+mile's length to another; a nicer balance, or more accurate measuring
+instruments, would always detect some difference.
+
+What is commonly called mathematical certainty, therefore, which
+comprises the twofold conception of unconditional truth and perfect
+accuracy, is not an attribute of all mathematical truths, but of those
+only which relate to pure Number, as distinguished from Quantity in the
+more enlarged sense; and only so long as we abstain from supposing that
+the numbers are a precise index to actual quantities. The certainty
+usually ascribed to the conclusions of geometry, and even to those of
+mechanics, is nothing whatever but certainty of inference. We can have
+full assurance of particular results under particular suppositions, but
+we cannot have the same assurance that these suppositions are accurately
+true, nor that they include all the data which may exercise an influence
+over the result in any given instance.
+
+
+§ 4. It appears, therefore, that the method of all Deductive Sciences is
+hypothetical. They proceed by tracing the consequences of certain
+assumptions; leaving for separate consideration whether the assumptions
+are true or not, and if not exactly true, whether they are a
+sufficiently near approximation to the truth. The reason is obvious.
+Since it is only in questions of pure number that the assumptions are
+exactly true, and even there, only so long as no conclusions except
+purely numerical ones are to be founded on them; it must, in all other
+cases of deductive investigation, form a part of the inquiry, to
+determine how much the assumptions want of being exactly true in the
+case in hand. This is generally a matter of observation, to be repeated
+in every fresh case; or if it has to be settled by argument instead of
+observation, may require in every different case different evidence, and
+present every degree of difficulty from the lowest to the highest. But
+the other part of the process--namely, to determine what else may be
+concluded if we find, and in proportion as we find, the assumptions to
+be true--may be performed once for all, and the results held ready to be
+employed as the occasions turn up for use. We thus do all beforehand
+that can be so done, and leave the least possible work to be performed
+when cases arise and press for a decision. This inquiry into the
+inferences which can be drawn from assumptions, is what properly
+constitutes Demonstrative Science.
+
+It is of course quite as practicable to arrive at new conclusions from
+facts assumed, as from facts observed; from fictitious, as from real,
+inductions. Deduction, as we have seen, consists of a series of
+inferences in this form--_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_,
+therefore _a_ is a mark of _d_, which last may be a truth inaccessible
+to direct observation. In like manner it is allowable to say, _suppose_
+that _a_ were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a
+mark of _d_, which last conclusion was not thought of by those who laid
+down the premises. A system of propositions as complicated as geometry
+might be deduced from assumptions which are false; as was done by
+Ptolemy, Descartes, and others, in their attempts to explain
+synthetically the phenomena of the solar system on the supposition that
+the apparent motions of the heavenly bodies were the real motions, or
+were produced in some way more or less different from the true one.
+Sometimes the same thing is knowingly done, for the purpose of showing
+the falsity of the assumption; which is called a _reductio ad absurdum_.
+In such cases, the reasoning is as follows: _a_ is a mark of _b_, and
+_b_ of _c_; now if _c_ were also a mark of _d_, _a_ would be a mark of
+_d_; but _d_ is known to be a mark of the absence of _a_; consequently
+_a_ would be a mark of its own absence, which is a contradiction;
+therefore _c_ is not a mark of _d_.
+
+
+§ 5. It has even been held by some writers, that all ratiocination rests
+in the last resort on a _reductio ad absurdum_; since the way to enforce
+assent to it, in case of obscurity, would be to show that if the
+conclusion be denied we must deny some one at least of the premises,
+which, as they are all supposed true, would be a contradiction. And in
+accordance with this, many have thought that the peculiar nature of the
+evidence of ratiocination consisted in the impossibility of admitting
+the premises and rejecting the conclusion without a contradiction in
+terms. This theory, however, is inadmissible as an explanation of the
+grounds on which ratiocination itself rests. If any one denies the
+conclusion notwithstanding his admission of the premises, he is not
+involved in any direct and express contradiction until he is compelled
+to deny some premise; and he can only be forced to do this by a
+_reductio ad absurdum_, that is, by another ratiocination: now, if he
+denies the validity of the reasoning process itself, he can no more be
+forced to assent to the second syllogism than to the first. In truth,
+therefore, no one is ever forced to a contradiction in terms: he can
+only be forced to a contradiction (or rather an infringement) of the
+fundamental maxim of ratiocination, namely, that whatever has a mark,
+has what it is a mark of; or, (in the case of universal propositions,)
+that whatever is a mark of anything, is a mark of whatever else that
+thing is a mark of. For in the case of every correct argument, as soon
+as thrown into the syllogistic form, it is evident without the aid of
+any other syllogism, that he who, admitting the premises, fails to draw
+the conclusion, does not conform to the above axiom.
+
+We have now proceeded as far in the theory of Deduction as we can
+advance in the present stage of our inquiry. Any further insight into
+the subject requires that the foundation shall have been laid of the
+philosophic theory of Induction itself; in which theory that of
+deduction, as a mode of induction, which we have now shown it to be,
+will assume spontaneously the place which belongs to it, and will
+receive its share of whatever light may be thrown upon the great
+intellectual operation of which it forms so important a part.
+
+
+
+
+CHAPTER VII.
+
+EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.
+
+
+§ 1. Polemical discussion is foreign to the plan of this work. But an
+opinion which stands in need of much illustration, can often receive it
+most effectually, and least tediously, in the form of a defence against
+objections. And on subjects concerning which speculative minds are still
+divided, a writer does but half his duty by stating his own doctrine, if
+he does not also examine, and to the best of his ability judge, those of
+other thinkers.
+
+In the dissertation which Mr. Herbert Spencer has prefixed to his, in
+many respects, highly philosophical treatise on the Mind,[39] he
+criticises some of the doctrines of the two preceding chapters, and
+propounds a theory of his own on the subject of first principles. Mr.
+Spencer agrees with me in considering axioms to be "simply our earliest
+inductions from experience." But he differs from me "widely as to the
+worth of the test of inconceivableness." He thinks that it is the
+ultimate test of all beliefs. He arrives at this conclusion by two
+steps. First, we never can have any stronger ground for believing
+anything, than that the belief of it "invariably exists." Whenever any
+fact or proposition is invariably believed; that is, if I understand Mr.
+Spencer rightly, believed by all persons, and by oneself at all times;
+it is entitled to be received as one of the primitive truths, or
+original premises of our knowledge. Secondly, the criterion by which we
+decide whether anything is invariably believed to be true, is our
+inability to conceive it as false. "The inconceivability of its negation
+is the test by which we ascertain whether a given belief invariably
+exists or not." "For our primary beliefs, the fact of invariable
+existence, tested by an abortive effort to cause their non-existence, is
+the only reason assignable." He thinks this the sole ground of our
+belief in our own sensations. If I believe that I feel cold, I only
+receive this as true because I cannot conceive that I am not feeling
+cold. "While the proposition remains true, the negation of it remains
+inconceivable." There are numerous other beliefs which Mr. Spencer
+considers to rest on the same basis; being chiefly those, or a part of
+those, which the metaphysicians of the Reid and Stewart school consider
+as truths of immediate intuition. That there exists a material world;
+that this is the very world which we directly and immediately perceive,
+and not merely the hidden cause of our perceptions; that Space, Time,
+Force, Extension, Figure, are not modes of our consciousness, but
+objective realities; are regarded by Mr. Spencer as truths known by the
+inconceivableness of their negatives. We cannot, he says, by any effort,
+conceive these objects of thought as mere states of our mind; as not
+having an existence external to us. Their real existence is, therefore,
+as certain as our sensations themselves. The truths which are the
+subject of direct knowledge, being, according to this doctrine, known to
+be truths only by the inconceivability of their negation; and the truths
+which are not the object of direct knowledge, being known as inferences
+from those which are; and those inferences being believed to follow from
+the premises, only because we cannot conceive them not to follow;
+inconceivability is thus the ultimate ground of all assured beliefs.
+
+Thus far, there is no very wide difference between Mr. Spencer's
+doctrine and the ordinary one of philosophers of the intuitive school,
+from Descartes to Dr. Whewell; but at this point Mr. Spencer diverges
+from them. For he does not, like them, set up the test of
+inconceivability as infallible. On the contrary, he holds that it may be
+fallacious, not from any fault in the test itself, but because "men have
+mistaken for inconceivable things, some things which were not
+inconceivable." And he himself, in this very book, denies not a few
+propositions usually regarded as among the most marked examples of
+truths whose negations are inconceivable. But occasional failure, he
+says, is incident to all tests. If such failure vitiates "the test of
+inconceivableness," it "must similarly vitiate all tests whatever. We
+consider an inference logically drawn from established premises to be
+true. Yet in millions of cases men have been wrong in the inferences
+they have thought thus drawn. Do we therefore argue that it is absurd to
+consider an inference true on no other ground than that it is logically
+drawn from established premises? No: we say that though men may have
+taken for logical inferences, inferences that were not logical, there
+nevertheless _are_ logical inferences, and that we are justified in
+assuming the truth of what seem to us such, until better instructed.
+Similarly, though men may have thought some things inconceivable which
+were not so, there may still be inconceivable things; and the inability
+to conceive the negation of a thing, may still be our best warrant for
+believing it.... Though occasionally it may prove an imperfect test,
+yet, as our most certain beliefs are capable of no better, to doubt any
+one belief because we have no higher guarantee for it, is really to
+doubt all beliefs." Mr. Spencer's doctrine, therefore, does not erect
+the curable, but only the incurable limitations of the human conceptive
+faculty, into laws of the outward universe.
+
+
+§ 2. The doctrine, that "a belief which is proved by the
+inconceivableness of its negation to invariably exist, is true," Mr.
+Spencer enforces by two arguments, one of which may be distinguished as
+positive, and the other as negative.
+
+The positive argument is, that every such belief represents the
+aggregate of all past experience. "Conceding the entire truth of" the
+"position, that during any phase of human progress, the ability or
+inability to form a specific conception wholly depends on the
+experiences men have had; and that, by a widening of their experiences,
+they may, by and by, be enabled to conceive things before inconceivable
+to them; it may still be argued that as, at any time, the best warrant
+men can have for a belief is the perfect agreement of all pre-existing
+experience in support of it, it follows that, at any time, the
+inconceivableness of its negation is the deepest test any belief admits
+of.... Objective facts are ever impressing themselves upon us; our
+experience is a register of these objective facts; and the
+inconceivableness of a thing implies that it is wholly at variance with
+the register. Even were this all, it is not clear how, if every truth is
+primarily inductive, any better test of truth could exist. But it must
+be remembered that whilst many of these facts, impressing themselves
+upon us, are occasional; whilst others again are very general; some are
+universal and unchanging. These universal and unchanging facts are, by
+the hypothesis, certain to establish beliefs of which the negations are
+inconceivable; whilst the others are not certain to do this; and if they
+do, subsequent facts will reverse their action. Hence if, after an
+immense accumulation of experiences, there remain beliefs of which the
+negations are still inconceivable, most, if not all of them, must
+correspond to universal objective facts. If there be ... certain
+absolute uniformities in nature; if these uniformities produce, as they
+must, absolute uniformities in our experience; and if ... these absolute
+uniformities in our experience disable us from conceiving the negations
+of them; then answering to each absolute uniformity in nature which we
+can cognize, there must exist in us a belief of which the negation is
+inconceivable, and which is absolutely true. In this wide range of cases
+subjective inconceivableness must correspond to objective impossibility.
+Further experience will produce correspondence where it may not yet
+exist; and we may expect the correspondence to become ultimately
+complete. In nearly all cases this test of inconceivableness must be
+valid now;" (I wish I could think we were so nearly arrived at
+omniscience) "and where it is not, it still expresses the net result of
+our experience up to the present time; which is the most that any test
+can do."
+
+To this I answer: Even if it were true that inconceivableness represents
+"the net result" of all past experience, why should we stop at the
+representative when we can get at the thing represented? If our
+incapacity to conceive the negation of a given supposition is proof of
+its truth, because proving that our experience has hitherto been
+uniform in its favour, the real evidence for the supposition is not the
+inconceivableness, but the uniformity of experience. Now this, which is
+the substantial and only proof, is directly accessible. We are not
+obliged to presume it from an incidental consequence. If all past
+experience is in favour of a belief, let this be stated, and the belief
+openly rested on that ground: after which the question arises, what that
+fact may be worth as evidence of its truth? For uniformity of experience
+is evidence in very different degrees: in some cases it is strong
+evidence, in others weak, in others it scarcely amounts to evidence at
+all. That all metals sink in water, was an uniform experience, from the
+origin of the human race to the discovery of potassium in the present
+century by Sir Humphry Davy. That all swans are white, was an uniform
+experience down to the discovery of Australia. In the few cases in which
+uniformity of experience does amount to the strongest possible proof, as
+with such propositions as these, Two straight lines cannot inclose a
+space, Every event has a cause, it is not because their negations are
+inconceivable, which is not always the fact; but because the experience,
+which has been thus uniform, pervades all nature. It will be shown in
+the following Book that none of the conclusions either of induction or
+of deduction can be considered certain, except as far as their truth is
+shown to be inseparably bound up with truths of this class.
+
+I maintain then, first, that uniformity of past experience is very far
+from being universally a criterion of truth. But secondly,
+inconceivableness is still farther from being a test even of that test.
+Uniformity of contrary experience is only one of many causes of
+inconceivability. Tradition handed down from a period of more limited
+knowledge, is one of the commonest. The mere familiarity of one mode of
+production of a phenomenon, often suffices to make every other mode
+appear inconceivable. Whatever connects two ideas by a strong
+association may, and continually does, render their separation in
+thought impossible; as Mr. Spencer, in other parts of his speculations,
+frequently recognises. It was not for want of experience that the
+Cartesians were unable to conceive that one body could produce motion
+in another without contact. They had as much experience of other modes
+of producing motion, as they had of that mode. The planets had revolved,
+and heavy bodies had fallen, every hour of their lives. But they fancied
+these phenomena to be produced by a hidden machinery which they did not
+see, because without it they were unable to conceive what they did see.
+The inconceivableness, instead of representing their experience,
+dominated and overrode their experience. It is needless to dwell farther
+on what I have termed the positive argument of Mr. Spencer in support of
+his criterion of truth. I pass to his negative argument, on which he
+lays more stress.
+
+
+§ 3. The negative argument is, that, whether inconceivability be good
+evidence or bad, no stronger evidence is to be obtained. That what is
+inconceivable cannot be true, is postulated in every act of thought. It
+is the foundation of all our original premises. Still more it is assumed
+in all conclusions from those premises. The invariability of belief,
+tested by the inconceivableness of its negation, "is our sole warrant
+for every demonstration. Logic is simply a systematization of the
+process by which we indirectly obtain this warrant for beliefs that do
+not directly possess it. To gain the strongest conviction possible
+respecting any complex fact, we either analytically descend from it by
+successive steps, each of which we unconsciously test by the
+inconceivableness of its negation, until we reach some axiom or truth
+which we have similarly tested; or we synthetically ascend from such
+axiom or truth by such steps. In either case we connect some isolated
+belief, with a belief which invariably exists, by a series of
+intermediate beliefs which invariably exist." The following passage sums
+up the whole theory: "When we perceive that the negation of the belief
+is inconceivable, we have all possible warrant for asserting the
+invariability of its existence: and in asserting this, we express alike
+our logical justification of it, and the inexorable necessity we are
+under of holding it.... We have seen that this is the assumption on
+which every conclusion whatever ultimately rests. We have no other
+guarantee for the reality of consciousness, of sensations, of personal
+existence; we have no other guarantee for any axiom; we have no other
+guarantee for any step in a demonstration. Hence, as being taken for
+granted in every act of the understanding, it must be regarded as the
+Universal Postulate." But as this postulate which we are under an
+"inexorable necessity" of holding true, is sometimes false; as "beliefs
+that once were shown by the inconceivableness of their negations to
+invariably exist, have since been found untrue," and as "beliefs that
+now possess this character may some day share the same fate;" the canon
+of belief laid down by Mr. Spencer is, that "the most certain
+conclusion" is that "which involves the postulate the fewest times."
+Reasoning, therefore, never ought to prevail against one of the
+immediate beliefs (the belief in Matter, in the outward reality of
+Extension, Space, and the like), because each of these involves the
+postulate only once; while an argument, besides involving it in the
+premises, involves it again in every step of the ratiocination, no one
+of the successive acts of inference being recognised as valid except
+because we cannot conceive the conclusion not to follow from the
+premises.
+
+It will be convenient to take the last part of this argument first. In
+every reasoning, according to Mr. Spencer, the assumption of the
+postulate is renewed at every step. At each inference we judge that the
+conclusion follows from the premises, our sole warrant for that judgment
+being that we cannot conceive it not to follow. Consequently if the
+postulate is fallible, the conclusions of reasoning are more vitiated by
+that uncertainty than direct intuitions; and the disproportion is
+greater, the more numerous the steps of the argument.
+
+To test this doctrine, let us first suppose an argument consisting only
+of a single step, which would be represented by one syllogism. This
+argument does rest on an assumption, and we have seen in the preceding
+chapters what the assumption is. It is, that whatever has a mark, has
+what it is a mark of. The evidence of this axiom I shall not consider at
+present;[40] let us suppose it (with Mr. Spencer) to be the
+inconceivableness of its reverse.
+
+Let us now add a second step to the argument: we require, what? Another
+assumption? No: the same assumption a second time; and so on to a third,
+and a fourth. I confess I do not see how, on Mr. Spencer's own
+principles, the repetition of the assumption at all weakens the force of
+the argument. If it were necessary the second time to assume some other
+axiom, the argument would no doubt be weakened, since it would be
+necessary to its validity that both axioms should be true, and it might
+happen that one was true and not the other: making two chances of error
+instead of one. But since it is the _same_ axiom, if it is true once it
+is true every time; and if the argument, being of a hundred links,
+assumed the axiom a hundred times, these hundred assumptions would make
+but one chance of error among them all. It is satisfactory that we are
+not obliged to suppose the deductions of pure mathematics to be among
+the most uncertain of argumentative processes, which on Mr. Spencer's
+theory they could hardly fail to be, since they are the longest. But the
+number of steps in an argument does not subtract from its reliableness,
+if no new _premises_, of an uncertain character, are taken up by the
+way.
+
+To speak next of the premises. Our assurance of their truth, whether
+they be generalities or individual facts, is grounded, in Mr. Spencer's
+opinion, on the inconceivableness of their being false. It is necessary
+to advert to a double meaning of the word inconceivable, which Mr.
+Spencer is aware of, and would sincerely disclaim founding an argument
+upon, but from which his case derives no little advantage
+notwithstanding. By inconceivableness is sometimes meant, inability to
+form or get rid of an _idea_; sometimes, inability to form or get rid of
+a _belief_. The former meaning is the most conformable to the analogy of
+language; for a conception always means an idea, and never a belief.
+The wrong meaning of "inconceivable" is, however, fully as frequent in
+philosophical discussion as the right meaning, and the intuitive school
+of metaphysicians could not well do without either. To illustrate the
+difference, we will take two contrasted examples. The early physical
+speculators considered antipodes incredible, because inconceivable. But
+antipodes were not inconceivable in the primitive sense of the word. An
+idea of them could be formed without difficulty: they could be
+completely pictured to the mental eye. What was difficult, and as it
+then seemed, impossible, was to apprehend them as believable. The idea
+could be put together, of men sticking on by their feet to the under
+side of the earth; but the belief _would_ follow, that they must fall
+off. Antipodes were not unimaginable, but they were unbelievable.
+
+On the other hand, when I endeavour to conceive an end to extension, the
+two ideas refuse to come together. When I attempt to form a conception
+of the last point of space, I cannot help figuring to myself a vast
+space beyond that last point. The combination is, under the conditions
+of our experience, unimaginable. This double meaning of inconceivable it
+is very important to bear in mind, for the argument from
+inconceivableness almost always turns on the alternate substitution of
+each of those meanings for the other.
+
+In which of these two senses does Mr. Spencer employ the term, when he
+makes it a test of the truth of a proposition that its negation is
+inconceivable? Until Mr. Spencer expressly stated the contrary, I
+inferred from the course of his argument, that he meant unbelievable. He
+has, however, in a paper published in the fifth number of the
+_Fortnightly Review_, disclaimed this meaning, and declared that by an
+inconceivable proposition he means, now and always, "one of which the
+terms cannot, by any effort, be brought before consciousness in that
+relation which the proposition asserts between them--a proposition of
+which the subject and predicate offer an insurmountable resistance to
+union in thought." We now, therefore, know positively that Mr. Spencer
+always endeavours to use the word inconceivable in this, its proper,
+sense: but it may yet be questioned whether his endeavour is always
+successful; whether the other, and popular use of the word does not
+sometimes creep in with its associations, and prevent him from
+maintaining a clear separation between the two. When, for example, he
+says, that when I feel cold, I cannot conceive that I am not feeling
+cold, this expression cannot be translated into, "I cannot conceive
+myself not feeling cold," for it is evident that I can: the word
+conceive, therefore, is here used to express the recognition of a matter
+of fact--the perception of truth or falsehood; which I apprehend to be
+exactly the meaning of an act of belief, as distinguished from simple
+conception. Again, Mr. Spencer calls the attempt to conceive something
+which is inconceivable, "an abortive effort to cause the non-existence"
+not of a conception or mental representation, but of a belief. There is
+need, therefore, to revise a considerable part of Mr. Spencer's
+language, if it is to be kept always consistent with his definition of
+inconceivability. But in truth the point is of little importance; since
+inconceivability, in Mr. Spencer's theory, is only a test of truth,
+inasmuch as it is a test of believability. The inconceivableness of a
+supposition is the extreme case of its unbelievability. This is the very
+foundation of Mr. Spencer's doctrine. The invariability of the belief is
+with him the real guarantee. The attempt to conceive the negative, is
+made in order to test the inevitableness of the belief. It should be
+called, an attempt to _believe_ the negative. When Mr. Spencer says that
+while looking at the sun a man cannot conceive that he is looking into
+darkness, he should have said that a man cannot _believe_ that he is
+doing so. For it is surely possible, in broad daylight, to _imagine_
+oneself looking into darkness.[41] As Mr. Spencer himself says, speaking
+of the belief of our own existence: "That he _might_ not exist, he can
+conceive well enough; but that he _does_ not exist, he finds it
+impossible to conceive," _i.e._ to believe. So that the statement
+resolves itself into this: That I exist, and that I have sensations, I
+believe, because I cannot believe otherwise. And in this case every one
+will admit that the necessity is real. Any one's present sensations, or
+other states of subjective consciousness, that one person inevitably
+believes. They are facts known _per se_: it is impossible to ascend
+beyond them. Their negative is really unbelievable, and therefore there
+is never any question about believing it. Mr. Spencer's theory is not
+needed for these truths.
+
+But according to Mr. Spencer there are other beliefs, relating to other
+things than our own subjective feelings, for which we have the same
+guarantee--which are, in a similar manner, invariable and necessary.
+With regard to these other beliefs, they cannot be necessary, since they
+do not always exist. There have been, and are, many persons who do not
+believe the reality of an external world, still less the reality of
+extension and figure as the forms of that external world; who do not
+believe that space and time have an existence independent of the
+mind--nor any other of Mr. Spencer's objective intuitions. The negations
+of these alleged invariable beliefs are not unbelievable, for they are
+believed. It may be maintained, without obvious error, that we cannot
+_imagine_ tangible objects as mere states of our own and other people's
+consciousness; that the perception of them irresistibly suggests to us
+the _idea_ of something external to ourselves: and I am not in a
+condition to say that this is not the fact (though I do not think any
+one is entitled to affirm it of any person besides himself). But many
+thinkers have believed, whether they could conceive it or not, that what
+we represent to ourselves as material objects, are mere modifications of
+consciousness; complex feelings of touch and of muscular action. Mr.
+Spencer may think the inference correct from the unimaginable to the
+unbelievable, because he holds that belief itself is but the persistence
+of an idea, and that what we can succeed in imagining, we cannot at the
+moment help apprehending as believable. But of what consequence is it
+what we apprehend at the moment, if the moment is in contradiction to
+the permanent state of our mind? A person who has been frightened when
+an infant by stories of ghosts, though he disbelieves them in after
+years (and perhaps disbelieved them at first), may be unable all his
+life to be in a dark place, in circumstances stimulating to the
+imagination, without mental discomposure. The idea of ghosts, with all
+its attendant terrors, is irresistibly called up in his mind by the
+outward circumstances. Mr. Spencer may say, that while he is under the
+influence of this terror he does not disbelieve in ghosts, but has a
+temporary and uncontrollable belief in them. Be it so; but allowing it
+to be so, which would it be truest to say of this man on the whole--that
+he believes in ghosts, or that he does not believe in them? Assuredly
+that he does not believe in them. The case is similar with those who
+disbelieve a material world. Though they cannot get rid of the idea;
+though while looking at a solid object they cannot help having the
+conception, and therefore, according to Mr. Spencer's metaphysics, the
+momentary belief, of its externality; even at that moment they would
+sincerely deny holding that belief: and it would be incorrect to call
+them other than disbelievers of the doctrine. The belief therefore is
+not invariable; and the test of inconceivableness fails in the only
+cases to which there could ever be any occasion to apply it.
+
+That a thing may be perfectly believable, and yet may not have become
+conceivable, and that we may habitually believe one side of an
+alternative, and conceive only in the other, is familiarly exemplified
+in the state of mind of educated persons respecting sunrise and sunset.
+All educated persons either know by investigation, or believe on the
+authority of science, that it is the earth and not the sun which moves:
+but there are probably few who habitually _conceive_ the phenomenon
+otherwise than as the ascent or descent of the sun. Assuredly no one can
+do so without a prolonged trial; and it is probably not easier now than
+in the first generation after Copernicus. Mr. Spencer does not say, "In
+looking at sunrise it is impossible not to conceive that it is the sun
+which moves, therefore this is what everybody believes, and we have all
+the evidence for it that we can have for any truth." Yet this would be
+an exact parallel to his doctrine about the belief in matter.
+
+The existence of matter, and other Noumena, as distinguished from the
+phenomenal world, remains a question of argument, as it was before; and
+the very general, but neither necessary nor universal, belief in them,
+stands as a psychological phenomenon to be explained, either on the
+hypothesis of its truth, or on some other. The belief is not a
+conclusive proof of its own truth, unless there are no such things as
+_idola tribûs_; but, being a fact, it calls on antagonists to show, from
+what except the real existence of the thing believed, so general and
+apparently spontaneous a belief can have originated. And its opponents
+have never hesitated to accept this challenge.[42] The amount of their
+success in meeting it will probably determine the ultimate verdict of
+philosophers on the question.
+
+
+§ 4. Sir William Hamilton holds as I do, that inconceivability is no
+criterion of impossibility. "There is no ground for inferring a certain
+fact to be impossible, merely from our inability to conceive its
+possibility." "Things there are which _may_, nay _must_, be true, of
+which the understanding is wholly unable to construe to itself the
+possibility."[43] Sir William Hamilton is however a firm believer in the
+_à priori_ character of many axioms, and of the sciences deduced from
+them; and is so far from considering those axioms to rest on the
+evidence of experience, that he declares certain of them to be true even
+of Noumena--of the Unconditioned--of which it is one of the principal
+aims of his philosophy to prove that the nature of our faculties debars
+us from having any knowledge. The axioms to which he attributes this
+exceptional emancipation from the limits which confine all our other
+possibilities of knowledge; the chinks through which, as he represents,
+one ray of light finds its way to us from behind the curtain which veils
+from us the mysterious world of Things in themselves,--are the two
+principles, which he terms, after the schoolmen, the Principle of
+Contradiction, and the Principle of Excluded Middle: the first, that two
+contradictory propositions cannot both be true; the second, that they
+cannot both be false. Armed with these logical weapons, we may boldly
+face Things in themselves, and tender to them the double alternative,
+sure that they must absolutely elect one or the other side, though we
+may be for ever precluded from discovering which. To take his favourite
+example, we cannot conceive the infinite divisibility of matter, and we
+cannot conceive a minimum, or end to divisibility: yet one or the other
+must be true.
+
+As I have hitherto said nothing of the two axioms in question, those of
+Contradiction and of Excluded Middle, it is not unseasonable to consider
+them here. The former asserts that an affirmative proposition and the
+corresponding negative proposition cannot both be true; which has
+generally been held to be intuitively evident. Sir William Hamilton and
+the Germans consider it to be the statement in words of a form or law of
+our thinking faculty. Other philosophers, not less deserving of
+consideration, deem it to be an identical proposition; an assertion
+involved in the meaning of terms; a mode of defining Negation, and the
+word Not.
+
+I am able to go one step with these last. An affirmative assertion and
+its negative are not two independent assertions, connected with each
+other only as mutually incompatible. That if the negative be true, the
+affirmative must be false, really is a mere identical proposition; for
+the negative proposition asserts nothing but the falsity of the
+affirmative, and has no other sense or meaning whatever. The Principium
+Contradictionis should therefore put off the ambitious phraseology which
+gives it the air of a fundamental antithesis pervading nature, and
+should be enunciated in the simpler form, that the same proposition
+cannot at the same time be false and true. But I can go no farther with
+the Nominalists; for I cannot look upon this last as a merely verbal
+proposition. I consider it to be, like other axioms, one of our first
+and most familiar generalizations from experience. The original
+foundation of it I take to be, that Belief and Disbelief are two
+different mental states, excluding one another. This we know by the
+simplest observation of our own minds. And if we carry our observation
+outwards, we also find that light and darkness, sound and silence,
+motion and quiescence, equality and inequality, preceding and following,
+succession and simultaneousness, any positive phenomenon whatever and
+its negative, are distinct phenomena, pointedly contrasted, and the one
+always absent where the other is present. I consider the maxim in
+question to be a generalization from all these facts.
+
+In like manner as the Principle of Contradiction (that one of two
+contradictories must be false) means that an assertion cannot be _both_
+true and false, so the Principle of Excluded Middle, or that one of two
+contradictories must be true, means that an assertion must be _either_
+true or false: either the affirmative is true, or otherwise the negative
+is true, which means that the affirmative is false. I cannot help
+thinking this principle a surprising specimen of a so-called necessity
+of Thought, since it is not even true, unless with a large
+qualification. A proposition must be either true or false, _provided_
+that the predicate be one which can in any intelligible sense be
+attributed to the subject; (and as this is always assumed to be the case
+in treatises on logic, the axiom is always laid down there as of
+absolute truth). "Abracadabra is a second intention" is neither true nor
+false. Between the true and the false there is a third possibility, the
+Unmeaning: and this alternative is fatal to Sir William Hamilton's
+extension of the maxim to Noumena. That Matter must either have a
+minimum of divisibility or be infinitely divisible, is more than we can
+ever know. For in the first place, Matter, in any other than the
+phenomenal sense of the term, may not exist: and it will scarcely be
+said that a non-entity must be either infinitely or finitely
+divisible.[44] In the second place, though matter, considered as the
+occult cause of our sensations, do really exist, yet what we call
+divisibility may be an attribute only of our sensations of sight and
+touch, and not of their uncognizable cause. Divisibility may not be
+predicable at all, in any intelligible sense, of Things in themselves,
+nor therefore of Matter in itself; and the assumed necessity of being
+either infinitely or finitely divisible, may be an inapplicable
+alternative.
+
+On this question I am happy to have the full concurrence of Mr. Herbert
+Spencer, from whose paper in the _Fortnightly Review_ I extract the
+following passage. The germ of an idea identical with that of Mr.
+Spencer may be found in the present chapter, about a page back, but in
+Mr. Spencer it is not an undeveloped thought, but a philosophical
+theory.
+
+"When remembering a certain thing as in a certain place, the place and
+the thing are mentally represented together; while to think of the
+non-existence of the thing in that place, implies a consciousness in
+which the place is represented, but not the thing. Similarly, if instead
+of thinking of an object as colourless, we think of its having colour,
+the change consists in the addition to the concept of an element that
+was before absent from it--the object cannot be thought of first as red
+and then as not red, without one component of the thought being totally
+expelled from the mind by another. The law of the Excluded Middle, then,
+is simply a generalization of the universal experience that some mental
+states are directly destructive of other states. It formulates a certain
+absolutely constant law, that the appearance of any positive mode of
+consciousness cannot occur without excluding a correlative negative
+mode; and that the negative mode cannot occur without excluding the
+correlative positive mode: the antithesis of positive and negative
+being, indeed, merely an expression of this experience. Hence it follows
+that if consciousness is not in one of the two modes it must be in the
+other."[45]
+
+I must here close this supplementary chapter, and with it the Second
+Book. The theory of Induction, in the most comprehensive sense of the
+term, will form the subject of the Third.
+
+FOOTNOTES:
+
+[1] As Sir William Hamilton has pointed out, "Some A is not B" may also
+be converted in the following form: "No B is _some_ A." Some men are not
+negroes; therefore, No negroes are _some_ men (_e.g._ Europeans).
+
+[2]
+  All A is B } contraries.
+  No  A is B }
+
+  Some A is B     } subcontraries.
+  Some A is not B }
+
+  All  A is B     } contradictories.
+  Some A is not B }
+
+  No   A is B } also contradictories.
+  Some A is B }
+
+  All  A is B } and  No   A is B     } respectively subalternate.
+  Some A is B }      Some A is not B }
+
+[3] His conclusions are, "The first figure is suited to the discovery or
+proof of the properties of a thing; the second to the discovery or proof
+of the distinctions between things; the third to the discovery or proof
+of instances and exceptions; the fourth to the discovery, or exclusion,
+of the different species of a genus." The reference of syllogisms in the
+last three figures to the _dictum de omni et nullo_ is, in Lambert's
+opinion, strained and unnatural: to each of the three belongs, according
+to him, a separate axiom, co-ordinate and of equal authority with that
+_dictum_, and to which he gives the names of _dictum de diverso_ for the
+second figure, _dictum de exemplo_ for the third, and _dictum de
+reciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. §
+229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74)
+takes a similar view of the subject.
+
+[4] Since this chapter was written, two treatises have appeared (or
+rather a treatise and a fragment of a treatise), which aim at a further
+improvement in the theory of the forms of ratiocination: Mr. De Morgan's
+"Formal Logic; or, the Calculus of Inference, Necessary and Probable;"
+and the "New Analytic of Logical Forms," attached as an Appendix to Sir
+William Hamilton's _Discussions on Philosophy_, and at greater length,
+to his posthumous _Lectures on Logic_.
+
+In Mr. De Morgan's volume--abounding, in its more popular parts, with
+valuable observations felicitously expressed--the principal feature of
+originality is an attempt to bring within strict technical rules the
+cases in which a conclusion can be drawn from premises of a form usually
+classed as particular. Mr. De Morgan observes, very justly, that from
+the premises Most Bs are Cs, most Bs are As, it may be concluded with
+certainty that some As are Cs, since two portions of the class B, each
+of them comprising more than half, must necessarily in part consist of
+the same individuals. Following out this line of thought, it is equally
+evident that if we knew exactly what proportion the "most" in each of
+the premises bear to the entire class B, we could increase in a
+corresponding degree the definiteness of the conclusion. Thus if 60 per
+cent of B are included in C, and 70 per cent in A, 30 per cent at least
+must be common to both; in other words, the number of As which are Cs,
+and of Cs which are As, must be at least equal to 30 per cent of the
+class B. Proceeding on this conception of "numerically definite
+propositions," and extending it to such forms as these:--"45 Xs (or
+more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
+them to be found among 70 Ys," and examining what inferences admit of
+being drawn from the various combinations which may be made of premises
+of this description, Mr. De Morgan establishes universal formulæ for
+such inferences; creating for that purpose not only a new technical
+language, but a formidable array of symbols analogous to those of
+algebra.
+
+Since it is undeniable that inferences, in the cases examined by Mr. De
+Morgan, can legitimately be drawn, and that the ordinary theory takes no
+account of them, I will not say that it was not worth while to show in
+detail how these also could be reduced to formulæ as rigorous as those
+of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
+more than once, as a school exercise); but I question if its results are
+worth studying and mastering for any practical purpose. The practical
+use of technical forms of reasoning is to bar out fallacies: but the
+fallacies which require to be guarded against in ratiocination properly
+so called, arise from the incautious use of the common forms of
+language; and the logician must track the fallacy into that territory,
+instead of waiting for it on a territory of his own. While he remains
+among propositions which have acquired the numerical precision of the
+Calculus of Probabilities, the enemy is left in possession of the only
+ground on which he can be formidable. And since the propositions (short
+of universal) on which a thinker has to depend, either for purposes of
+speculation or of practice, do not, except in a few peculiar cases,
+admit of any numerical precision; common reasoning cannot be translated
+into Mr. De Morgan's forms, which therefore cannot serve any purpose as
+a test of it.
+
+Sir William Hamilton's theory of the "quantification of the predicate"
+(concerning the originality of which in his case there can be no doubt,
+however Mr. De Morgan may have also, and independently, originated an
+equivalent doctrine) may be briefly described as follows:--
+
+"Logically" (I quote his own words) "we ought to take into account the
+quantity, always understood in thought, but usually, for manifest
+reasons, elided in its expression, not only of the subject, but also of
+the predicate of a judgment." All A is B, is equivalent to all A is
+_some_ B. No A is B, to No A is _any_ B. Some A is B, is tantamount to
+some A is _some_ B. Some A is not B, to Some A is _not any_ B. As in
+these forms of assertion the predicate is exactly coextensive with the
+subject, they all admit of simple conversion; and by this we obtain two
+additional forms--Some B is _all_ A, and No B is _some_ A. We may also
+make the assertion All A is all B, which will be true if the classes A
+and B are exactly coextensive. The last three forms, though conveying
+real assertions, have no place in the ordinary classification of
+Propositions. All propositions, then, being supposed to be translated
+into this language, and written each in that one of the preceding forms
+which answers to its signification, there emerges a new set of
+syllogistic rules, materially different from the common ones. A general
+view of the points of difference may be given in the words of Sir W.
+Hamilton (_Discussions_, 2nd ed. p. 651):--
+
+"The revocation of the two terms of a Proposition to their true
+relation; a proposition being always an _equation_ of its subject and
+its predicate.
+
+"The consequent reduction of the Conversion of Propositions from three
+species to one--that of Simple Conversion.
+
+"The reduction of all the _General Laws_ of Categorical Syllogisms to a
+single Canon.
+
+"The evolution from that one canon of all the Species and varieties of
+Syllogisms.
+
+"The abrogation of all the _Special Laws_ of Syllogism.
+
+"A demonstration of the exclusive possibility of Three syllogistic
+Figures; and (on new grounds) the scientific and final abolition of the
+Fourth.
+
+"A manifestation that Figure is an unessential variation in syllogistic
+form; and the consequent absurdity of Reducing the syllogisms of the
+other figures to the first.
+
+"An enouncement of _one Organic Principle_ for each Figure.
+
+"A determination of the true number of the Legitimate Moods; with
+
+"Their amplification in number (thirty-six);
+
+"Their numerical equality under all the figures; and
+
+"Their relative equivalence, or virtual identity, throughout every
+schematic difference.
+
+"That, in the second and third figures, the extremes holding both the
+same relation to the middle term, there is not, as in the first, an
+opposition and subordination between a term major and a term minor,
+mutually containing and contained, in the counter wholes of Extension
+and Comprehension.
+
+"Consequently, in the second and third figures, there is no determinate
+major and minor premise, and there are two indifferent conclusions:
+whereas in the first the premises are determinate, and there is a single
+proximate conclusion."
+
+This doctrine, like that of Mr. De Morgan previously noticed, is a real
+addition to the syllogistic theory; and has moreover this advantage over
+Mr. De Morgan's "numerically definite Syllogism," that the forms it
+supplies are really available as a test of the correctness of
+ratiocination; since propositions in the common form may always have
+their predicates quantified, and so be made amenable to Sir W.
+Hamilton's rules. Considered however as a contribution to the _Science_
+of Logic, that is, to the analysis of the mental processes concerned in
+reasoning, the new doctrine appears to me, I confess, not merely
+superfluous, but erroneous; since the form in which it clothes
+propositions does not, like the ordinary form, express what is in the
+mind of the speaker when he enunciates the proposition. I cannot think
+Sir William Hamilton right in maintaining that the quantity of the
+predicate is "always understood in thought." It is implied, but is not
+present to the mind of the person who asserts the proposition. The
+quantification of the predicate, instead of being a means of bringing
+out more clearly the meaning of the proposition, actually leads the mind
+out of the proposition, into another order of ideas. For when we say,
+All men are mortal, we simply mean to affirm the attribute mortality of
+all men; without thinking at all of the _class_ mortal in the concrete,
+or troubling ourselves about whether it contains any other beings or
+not. It is only for some artificial purpose that we ever look at the
+proposition in the aspect in which the predicate also is thought of as a
+class-name, either including the subject only, or the subject and
+something more. (See above, p. 104.)
+
+For a fuller discussion of this subject, see the twenty-second chapter
+of a work already referred to, "An Examination of Sir William Hamilton's
+Philosophy."
+
+[5] Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though
+his theory of the syllogism coincides with all that is essential of
+mine, thinks it a logical fallacy to present the two axioms in the text,
+as the regulating principles of syllogism. He charges me with falling
+into the error pointed out by Archbishop Whately and myself, of
+confounding exact likeness with literal identity; and maintains, that we
+ought not to say that Socrates possesses _the same_ attributes which are
+connoted by the word Man, but only that he possesses attributes _exactly
+like_ them: according to which phraseology, Socrates, and the attribute
+mortality, are not two things coexisting with the same thing, as the
+axiom asserts, but two things coexisting with two different things.
+
+The question between Mr. Spencer and me is merely one of language; for
+neither of us (if I understand Mr. Spencer's opinions rightly) believes
+an attribute to be a real thing, possessed of objective existence; we
+believe it to be a particular mode of naming our sensations, or our
+expectations of sensation, when looked at in their relation to an
+external object which excites them. The question raised by Mr. Spencer
+does not, therefore, concern the properties of any really existing
+thing, but the comparative appropriateness, for philosophical purposes,
+of two different modes of using a name. Considered in this point of
+view, the phraseology I have employed, which is that commonly used by
+philosophers, seems to me to be the best. Mr. Spencer is of opinion that
+because Socrates and Alcibiades are not the same man, the attribute
+which constitutes them men should not be called the same attribute; that
+because the humanity of one man and that of another express themselves
+to our senses not by the same individual sensations but by sensations
+exactly alike, humanity ought to be regarded as a different attribute in
+every different man. But on this showing, the humanity even of any one
+man should be considered as different attributes now and half-an-hour
+hence; for the sensations by which it will then manifest itself to my
+organs will not be a continuation of my present sensations, but a
+repetition of them; fresh sensations, not identical with, but only
+exactly like the present. If every general conception, instead of being
+"the One in the Many," were considered to be as many different
+conceptions as there are things to which it is applicable, there would
+be no such thing as general language. A name would have no general
+meaning if _man_ connoted one thing when predicated of John, and
+another, though closely resembling, thing when predicated of William.
+Accordingly a recent pamphlet asserts the impossibility of general
+knowledge on this precise ground.
+
+The meaning of any general name is some outward or inward phenomenon,
+consisting, in the last resort, of feelings; and these feelings, if
+their continuity is for an instant broken, are no longer the same
+feelings, in the sense of individual identity. What, then, is the common
+something which gives a meaning to the general name? Mr. Spencer can
+only say, it is the similarity of the feelings; and I rejoin, the
+attribute is precisely that similarity. The names of attributes are in
+their ultimate analysis names for the resemblances of our sensations (or
+other feelings). Every general name, whether abstract or concrete,
+denotes or connotes one or more of those resemblances. It will not,
+probably, be denied, that if a hundred sensations are undistinguishably
+alike, their resemblance ought to be spoken of as one resemblance, and
+not a hundred resemblances which merely _resemble_ one another. The
+things compared are many, but the something common to all of them must
+be conceived as one, just as the name is conceived as one, though
+corresponding to numerically different sensations of sound each time it
+is pronounced. The general term _man_ does not connote the sensations
+derived once from one man, which, once gone, can no more occur again
+than the same flash of lightning. It connotes the general type of the
+sensations derived always from all men, and the power (always thought of
+as one) of producing sensations of that type. And the axiom might be
+thus worded: Two _types of sensation_ each of which coexists with a
+third type, coexist with another; or Two _powers_ each of which coexists
+with a third power coexist with one another.
+
+Mr. Spencer has misunderstood me in another particular. He supposes that
+the coexistence spoken of in the axiom, of two things with the same
+third thing, means simultaneousness in time. The coexistence meant is
+that of being jointly attributes of the same subject. The attribute of
+being born without teeth, and the attribute of having thirty-two teeth
+in mature age, are in this sense coexistent, both being attributes of
+man, though _ex vi termini_ never of the same man at the same time.
+
+[6] Supra, p. 128.
+
+[7] _Logic_, p. 239 (9th ed.).
+
+[8] It is hardly necessary to say, that I am not contending for any such
+absurdity as that we _actually_ "ought to have known" and considered the
+case of every individual man, past, present, and future, before
+affirming that all men are mortal: although this interpretation has
+been, strangely enough, put upon the preceding observations. There is no
+difference between me and Archbishop Whately, or any other defender of
+the syllogism, on the practical part of the matter; I am only pointing
+out an inconsistency in the logical theory of it, as conceived by almost
+all writers. I do not say that a person who affirmed, before the Duke of
+Wellington was born, that all men are mortal, _knew_ that the Duke of
+Wellington was mortal; but I do say that he _asserted_ it; and I ask for
+an explanation of the apparent logical fallacy, of adducing in proof of
+the Duke of Wellington's mortality, a general statement which
+presupposes it. Finding no sufficient resolution of this difficulty in
+any of the writers on Logic, I have attempted to supply one.
+
+[9] The language of ratiocination would, I think, be brought into closer
+agreement with the real nature of the process, if the general
+propositions employed in reasoning, instead of being in the form All men
+are mortal, or Every man is mortal, were expressed in the form Any man
+is mortal. This mode of expression, exhibiting as the type of all
+reasoning from experience "The men A, B, C, &c. are so and so, therefore
+_any_ man is so and so," would much better manifest the true idea--that
+inductive reasoning is always, at bottom, inference from particulars to
+particulars, and that the whole function of general propositions in
+reasoning, is to vouch for the legitimacy of such inferences.
+
+[10] Review of Quetelet on Probabilities, _Essays_, p. 367.
+
+[11] _Philosophy of Discovery_, p. 289.
+
+[12] _Theory of Reasoning_, ch. iv. to which I may refer for an able
+statement and enforcement of the grounds of the doctrine.
+
+[13] It is very probable that the doctrine is not new, and that it was,
+as Sir John Herschel thinks, substantially anticipated by Berkeley. But
+I certainly am not aware that it is (as has been affirmed by one of my
+ablest and most candid critics) "among the standing marks of what is
+called the empirical philosophy."
+
+[14] _Logic_, book iv. ch. i. sect. 1.
+
+[15] See the important chapter on Belief, in Professor Bain's great
+treatise, _The Emotions and the Will_, pp. 581-4.
+
+[16] A writer in the "British Quarterly Review" (August 1846), in a
+review of this treatise, endeavours to show that there is no _petitio
+principii_ in the syllogism, by denying that the proposition, All men
+are mortal, asserts or assumes that Socrates is mortal. In support of
+this denial, he argues that we may, and in fact do, admit the general
+proposition that all men are mortal, without having particularly
+examined the case of Socrates, and even without knowing whether the
+individual so named is a man or something else. But this of course was
+never denied. That we can and do draw conclusions concerning cases
+specifically unknown to us, is the datum from which all who discuss this
+subject must set out. The question is, in what terms the evidence, or
+ground, on which we draw these conclusions, may best be
+designated--whether it is most correct to say, that the unknown case is
+proved by known cases, or that it is proved by a general proposition
+including both sets of cases, the unknown and the known? I contend for
+the former mode of expression. I hold it an abuse of language to say,
+that the proof that Socrates is mortal, is that all men are mortal. Turn
+it in what way we will, this seems to me to be asserting that a thing is
+the proof of itself. Whoever pronounces the words, All men are mortal,
+has affirmed that Socrates is mortal, though he may never have heard of
+Socrates; for since Socrates, whether known to be so or not, really is a
+man, he is included in the words, All men, and in every assertion of
+which they are the subject. If the reviewer does not see that there is a
+difficulty here, I can only advise him to reconsider the subject until
+he does: after which he will be a better judge of the success or failure
+of an attempt to remove the difficulty. That he had reflected very
+little on the point when he wrote his remarks, is shown by his oversight
+respecting the _dictum de omni et nullo_. He acknowledges that this
+maxim as commonly expressed,--"Whatever is true of a class, is true of
+everything included in the class," is a mere identical proposition,
+since the class _is_ nothing but the things included in it. But he
+thinks this defect would be cured by wording the maxim thus,--"Whatever
+is true of a class, is true of everything which _can be shown_ to be a
+member of the class:" as if a thing could "be shown" to be a member of
+the class without being one. If a class means the sum of all the things
+included in the class, the things which can "be shown" to be included in
+it are part of the sum, and the _dictum_ is as much an identical
+proposition with respect to them as to the rest. One would almost
+imagine that, in the reviewer's opinion, things are not members of a
+class until they are called up publicly to take their place in it--that
+so long, in fact, as Socrates is not known to be a man, he _is not_ a
+man, and any assertion which can be made concerning men does not at all
+regard him, nor is affected as to its truth or falsity by anything in
+which he is concerned.
+
+The difference between the reviewer's theory and mine may be thus
+stated. Both admit that when we say, All men are mortal, we make an
+assertion reaching beyond the sphere of our knowledge of individual
+cases; and that when a new individual, Socrates, is brought within the
+field of our knowledge by means of the minor premise, we learn that we
+have already made an assertion respecting Socrates without knowing it:
+our own general formula being, to that extent, for the first time
+_interpreted_ to us. But according to the reviewer's theory, the smaller
+assertion is proved by the larger: while I contend, that both assertions
+are proved together, by the same evidence, namely, the grounds of
+experience on which the general assertion was made, and by which it must
+be justified.
+
+The reviewer says, that if the major premise included the conclusion,
+"we should be able to affirm the conclusion without the intervention of
+the minor premise; but every one sees that that is impossible." A
+similar argument is urged by Mr. De Morgan (_Formal Logic_, p. 259):
+"The whole objection tacitly assumes the superfluity of the minor; that
+is, tacitly assumes we know Socrates[46] to be a man as soon as we know
+him to be Socrates." The objection would be well grounded if the
+assertion that the major premise includes the conclusion, meant that it
+individually specifies all it includes. As however the only indication
+it gives is a description by marks, we have still to compare any new
+individual with the marks; and to show that this comparison has been
+made, is the office of the minor. But since, by supposition, the new
+individual has the marks, whether we have ascertained him to have them
+or not; if we have affirmed the major premise, we have asserted him to
+be mortal. Now my position is that this assertion cannot be a necessary
+part of the argument. It cannot be a necessary condition of reasoning
+that we should begin by making an assertion, which is afterwards to be
+employed in proving a part of itself. I can conceive only one way out of
+this difficulty, viz. that what really forms the proof is _the other_
+part of the assertion; the portion of it, the truth of which has been
+ascertained previously: and that the unproved part is bound up in one
+formula with the proved part in mere anticipation, and as a memorandum
+of the nature of the conclusions which we are prepared to prove.
+
+With respect to the minor premise in its formal shape, the minor as it
+stands in the syllogism, predicating of Socrates a definite class name,
+I readily admit that it is no more a necessary part of reasoning than
+the major. When there is a major, doing its work by means of a class
+name, minors are needed to interpret it: but reasoning can be carried on
+without either the one or the other. They are not the conditions of
+reasoning, but a precaution against erroneous reasoning. The only minor
+premise necessary to reasoning in the example under consideration, is,
+Socrates is _like_ A, B, C, and the other individuals who are known to
+have died. And this is the only universal type of that step in the
+reasoning process which is represented by the minor. Experience,
+however, of the uncertainty of this loose mode of inference, teaches the
+expediency of determining beforehand what _kind_ of likeness to the
+cases observed, is necessary to bring an unobserved case within the same
+predicate; and the answer to this question is the major. Thus the
+syllogistic major and the syllogistic minor start into existence
+together, and are called forth by the same exigency. When we conclude
+from personal experience without referring to any record--to any general
+theorems, either written, or traditional, or mentally registered by
+ourselves as conclusions of our own drawing, we do not use, in our
+thoughts, either a major or a minor, such as the syllogism puts into
+words. When, however, we revise this rough inference from particulars to
+particulars, and substitute a careful one, the revision consists in
+selecting two syllogistic premises. But this neither alters nor adds to
+the evidence we had before; it only puts us in a better position for
+judging whether our inference from particulars to particulars is well
+grounded.
+
+[17] Infra, book iii. ch. ii.
+
+[18] Infra, book iii. ch. iv. § 3, and elsewhere.
+
+[19] _Mechanical Euclid_, pp. 149 _et seqq._
+
+[20] We might, it is true, insert this property into the definition of
+parallel lines, framing the definition so as to require, both that when
+produced indefinitely they shall never meet, and also that any straight
+line which intersects one of them shall, if prolonged, meet the other.
+But by doing this we by no means get rid of the assumption; we are still
+obliged to take for granted the geometrical truth, that all straight
+lines in the same plane, which have the former of these properties, have
+also the latter. For if it were possible that they should not, that is,
+if any straight lines other than those which are parallel according to
+the definition, had the property of never meeting although indefinitely
+produced, the demonstrations of the subsequent portions of the theory of
+parallels could not be maintained.
+
+[21] Some persons find themselves prevented from believing that the
+axiom, Two straight lines cannot inclose a space, could ever become
+known to us through experience, by a difficulty which may be stated as
+follows. If the straight lines spoken of are those contemplated in the
+definition--lines absolutely without breadth and absolutely
+straight;--that such are incapable of inclosing a space is not proved by
+experience, for lines such as these do not present themselves in our
+experience. If, on the other hand, the lines meant are such straight
+lines as we do meet with in experience, lines straight enough for
+practical purposes, but in reality slightly zigzag, and with some,
+however trifling, breadth; as applied to these lines the axiom is not
+true, for two of them may, and sometimes do, inclose a small portion of
+space. In neither case, therefore, does experience prove the axiom.
+
+Those who employ this argument to show that geometrical axioms cannot be
+proved by induction, show themselves unfamiliar with a common and
+perfectly valid mode of inductive proof; proof by approximation. Though
+experience furnishes us with no lines so unimpeachably straight that two
+of them are incapable of inclosing the smallest space, it presents us
+with gradations of lines possessing less and less either of breadth or
+of flexure, of which series the straight line of the definition is the
+ideal limit. And observation shows that just as much, and as nearly, as
+the straight lines of experience approximate to having no breadth or
+flexure, so much and so nearly does the space-inclosing power of any two
+of them approach to zero. The inference that if they had no breadth or
+flexure at all, they would inclose no space at all, is a correct
+inductive inference from these facts, conformable to one of the four
+Inductive Methods hereinafter characterized, the Method of Concomitant
+Variations; of which the mathematical Doctrine of Limits presents the
+extreme case.
+
+[22] Whewell's _History of Scientific Ideas_, i. 140.
+
+[23] Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
+unreasonable to contend that we know by experience, that our idea of a
+line exactly resembles a real line. "It does not appear," he says, "how
+we can compare our ideas with the realities, since we know the realities
+only by our ideas." We know the realities (I conceive) by our senses.
+Dr. Whewell surely does not hold the "doctrine of perception by means of
+ideas," which Reid gave himself so much trouble to refute.
+
+If Dr. Whewell doubts whether we compare our ideas with the
+corresponding sensations, and assume that they resemble, let me ask on
+what evidence do we judge that a portrait of a person not present is
+like the original. Surely because it is like our idea, or mental image
+of the person, and because our idea is like the man himself.
+
+Dr. Whewell also says, that it does not appear why this resemblance of
+ideas to the sensations of which they are copies, should be spoken of as
+if it were a peculiarity of one class of ideas, those of space. My reply
+is, that I do not so speak of it. The peculiarity I contend for is only
+one of degree. All our ideas of sensation of course resemble the
+corresponding sensations, but they do so with very different degrees of
+exactness and of reliability. No one, I presume, can recal in
+imagination a colour or an odour with the same distinctness and accuracy
+with which almost every one can mentally reproduce an image of a
+straight line or a triangle. To the extent, however, of their
+capabilities of accuracy, our recollections of colours or of odours may
+serve as subjects of experimentation, as well as those of lines and
+spaces, and may yield conclusions which will be true of their external
+prototypes. A person in whom, either from natural gift or from
+cultivation, the impressions of colour were peculiarly vivid and
+distinct, if asked which of two blue flowers was of the darkest tinge,
+though he might never have compared the two, or even looked at them
+together, might be able to give a confident answer on the faith of his
+distinct recollection of the colours; that is, he might examine his
+mental pictures, and find there a property of the outward objects. But
+in hardly any case except that of simple geometrical forms, could this
+be done by mankind generally, with a degree of assurance equal to that
+which is given by a contemplation of the objects themselves. Persons
+differ most widely in the precision of their recollection, even of
+forms: one person, when he has looked any one in the face for half a
+minute, can draw an accurate likeness of him from memory; another may
+have seen him every day for six months, and hardly know whether his nose
+is long or short. But everybody has a perfectly distinct mental image of
+a straight line, a circle, or a rectangle. And every one concludes
+confidently from these mental images to the corresponding outward
+things. The truth is, that we may, and continually do, study nature in
+our recollections, when the objects themselves are absent; and in the
+case of geometrical forms we can perfectly, but in most other cases only
+imperfectly, trust our recollections.
+
+[24] _History of Scientific Ideas_, i. 65-67.
+
+[25] Ibid. 60.
+
+[26] _History of Scientific Ideas_, i. 58, 59.
+
+[27] "If all mankind had spoken one language, we cannot doubt that there
+would have been a powerful, perhaps a universal, school of philosophers,
+who would have believed in the inherent connexion between names and
+things, who would have taken the sound _man_ to be the mode of agitating
+the air which is essentially communicative of the ideas of reason,
+cookery, bipedality, &c."--De Morgan, _Formal Logic_, p. 246.
+
+[28] It would be difficult to name a man more remarkable at once for the
+greatness and the wide range of his mental accomplishments, than
+Leibnitz. Yet this eminent man gave as a reason for rejecting Newton's
+scheme of the solar system, that God _could not_ make a body revolve
+round a distant centre, unless either by some impelling mechanism, or by
+miracle:--"Tout ce qui n'est pas explicable" says he in a letter to the
+Abbé Conti, "par la nature des créatures, est miraculeux. Il ne suffit
+pas de dire: Dieu a fait une telle loi de nature; donc la chose est
+naturelle. Il faut que la loi soit exécutable par les natures des
+créatures. Si Dieu donnait cette loi, par exemple, à un corps libre, de
+tourner à l'entour d'un certain centre, _il faudrait ou qu'il y joignît
+d'autres corps qui par leur impulsion l'obligeassent de rester toujours
+dans son orbite circulaire, ou qu'il mît un ange à ses trousses, ou
+enfin il faudrait qu'il y concourût extraordinairement_; car
+naturellement il s'écartera par la tangente."--_Works of Leibnitz_, ed.
+Dutens, iii. 446.
+
+[29] _Novum Organum Renovatum_, pp. 32, 33.
+
+[30] _History of Scientific Ideas_, i. 264.
+
+[31] _Hist. Sc. Id._, i. 263.
+
+[32] Ibid. 240.
+
+[33] _Hist. Sc. Id._, ii. 25, 26.
+
+[34] _Phil. of Disc._, p. 339.
+
+[35] _Phil. of Disc._, p. 338.
+
+[36] Ib. p. 463.
+
+[37] _Phil. of Disc._, pp. 472, 473.
+
+[38] The _Quarterly Review_ for June 1841, contained an article of great
+ability on Dr. Whewell's two great works (since acknowledged and
+reprinted in Sir John Herschel's Essays) which maintains, on the subject
+of axioms, the doctrine advanced in the text, that they are
+generalizations from experience, and supports that opinion by a line of
+argument strikingly coinciding with mine. When I state that the whole of
+the present chapter (except the last four pages, added in the fifth
+edition) was written before I had seen the article, (the greater part,
+indeed, before it was published,) it is not my object to occupy the
+reader's attention with a matter so unimportant as the degree of
+originality which may or may not belong to any portion of my own
+speculations, but to obtain for an opinion which is opposed to reigning
+doctrines, the recommendation derived from a striking concurrence of
+sentiment between two inquirers entirely independent of one another. I
+embrace the opportunity of citing from a writer of the extensive
+acquirements in physical and metaphysical knowledge and the capacity of
+systematic thought which the article evinces, passages so remarkably in
+unison with my own views as the following:--
+
+"The truths of geometry are summed up and embodied in its definitions
+and axioms.... Let us turn to the axioms, and what do we find? A string
+of propositions concerning magnitude in the abstract, which are equally
+true of space, time, force, number, and every other magnitude
+susceptible of aggregation and subdivision. Such propositions, where
+they are not mere definitions, as some of them are, carry their
+inductive origin on the face of their enunciation.... Those which
+declare that two straight lines cannot inclose a space, and that two
+straight lines which cut one another cannot both be parallel to a third,
+are in reality the only ones which express characteristic properties of
+space, and these it will be worth while to consider more nearly. Now the
+only clear notion we can form of straightness is uniformity of
+direction, for space in its ultimate analysis is nothing but an
+assemblage of distances and directions. And (not to dwell on the notion
+of continued contemplation, _i.e._, mental experience, as included in
+the very idea of uniformity; nor on that of transfer of the
+contemplating being from point to point, and of experience, during such
+transfer, of the homogeneity of the interval passed over) we cannot even
+propose the proposition in an intelligible form to any one whose
+experience ever since he was born has not assured him of the fact. The
+unity of direction, or that we cannot march from a given point by more
+than one path direct to the same object, is matter of practical
+experience long before it can by possibility become matter of abstract
+thought. _We cannot attempt mentally to exemplify the conditions of the
+assertion in an imaginary case opposed to it, without violating our
+habitual recollection of this experience, and defacing our mental
+picture of space as grounded on it._ What but experience, we may ask,
+can possibly assure us of the homogeneity of the parts of distance,
+time, force, and measurable aggregates in general, on which the truth of
+the other axioms depends? As regards the latter axiom, after what has
+been said it must be clear that the very same course of remarks equally
+applies to its case, and that its truth is quite as much forced on the
+mind as that of the former by daily and hourly experience, ...
+_including always, be it observed, in our notion of experience, that
+which is gained by contemplation of the inward picture which the mind
+forms to itself in any proposed case, or which it arbitrarily selects as
+an example--such picture, in virtue of the extreme simplicity of these
+primary relations, being called up by the imagination with as much
+vividness and clearness as could be done by any external impression,
+which is the only meaning we can attach to the word intuition, as
+applied to such relations_."
+
+And again, of the axioms of mechanics:--"As we admit no such
+propositions, other than as truths inductively collected from
+observation, even in geometry itself, it can hardly be expected that, in
+a science of obviously contingent relations, we should acquiesce in a
+contrary view. Let us take one of these axioms and examine its evidence:
+for instance, that equal forces perpendicularly applied at the opposite
+ends of equal arms of a straight lever will balance each other. What but
+experience, we may ask, in the first place, can possibly inform us that
+a force so applied will have any tendency to turn the lever on its
+centre at all? or that force can be so transmitted along a rigid line
+perpendicular to its direction, as to act elsewhere in space than along
+its own line of action? Surely this is so far from being self-evident
+that it has even a paradoxical appearance, which is only to be removed
+by giving our lever thickness, material composition, and molecular
+powers. Again, we conclude, that the two forces, being equal and applied
+under precisely similar circumstances, must, if they exert any effort at
+all to turn the lever, exert equal and opposite efforts: but what _à
+priori_ reasoning can possibly assure us that they _do_ act under
+precisely similar circumstances? that points which differ in place _are_
+similarly circumstanced as regards the exertion of force? that universal
+space may not have relations to universal force--or, at all events, that
+the organization of the material universe may not be such as to place
+that portion of space occupied by it in such relations to the forces
+exerted in it, as may invalidate the absolute similarity of
+circumstances assumed? Or we may argue, what have we to do with the
+notion of angular movement in the lever at all? The case is one of rest,
+and of quiescent destruction of force by force. Now how is this
+destruction effected? Assuredly by the counter-pressure which supports
+the fulcrum. But would not this destruction equally arise, and by the
+same amount of counter-acting force, if each force simply pressed its
+own half of the lever against the fulcrum? And what can assure us that
+it is not so, except removal of one or other force, and consequent
+tilting of the lever? The other fundamental axiom of statics, that the
+pressure on the point of support is the sum of the weights ... is merely
+a scientific transformation and more refined mode of stating a coarse
+and obvious result of universal experience, viz. that the weight of a
+rigid body is the same, handle it or suspend it in what position or by
+what point we will, and that whatever sustains it sustains its total
+weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever
+made a trial for the purpose of showing that the pressure on the support
+is equal to the sum of the weights.' ... But it is precisely because in
+every action of his life from earliest infancy he has been continually
+making the trial, and seeing it made by every other living being about
+him, that he never dreams of staking its result on one additional
+attempt made with scientific accuracy. This would be as if a man should
+resolve to decide by experiment whether his eyes were useful for the
+purpose of seeing, by hermetically sealing himself up for half an hour
+in a metal case."
+
+On the "paradox of universal propositions obtained by experience," the
+same writer says: "If there be necessary and universal truths
+expressible in propositions of axiomatic simplicity and obviousness, and
+having for their subject-matter the elements of all our experience and
+all our knowledge, surely these are the truths which, if experience
+suggest to us any truths at all, it ought to suggest most readily,
+clearly, and unceasingly. If it were a truth, universal and necessary,
+that a net is spread over the whole surface of every planetary globe, we
+should not travel far on our own without getting entangled in its
+meshes, and making the necessity of some means of extrication an axiom
+of locomotion.... There is, therefore, nothing paradoxical, but the
+reverse, in our being led by observation to a recognition of such
+truths, as _general_ propositions, coextensive at least with all human
+experience. That they pervade all the objects of experience, must ensure
+their continual suggestion _by_ experience; that they are true, must
+ensure that consistency of suggestion, that iteration of uncontradicted
+assertion, which commands implicit assent, and removes all occasion of
+exception; that they are simple, and admit of no misunderstanding, must
+secure their admission by every mind."
+
+"A truth, necessary and universal, relative to any object of our
+knowledge, must verify itself in every instance where that object is
+before our contemplation, and if at the same time it be simple and
+intelligible, its verification must be obvious. _The sentiment of such a
+truth cannot, therefore, but be present to our minds whenever that
+object is contemplated, and must therefore make a part of the mental
+picture or idea of that object which we may on any occasion summon
+before our imagination.... All propositions, therefore, become not only
+untrue but inconceivable_, if ... axioms be violated in their
+enunciation."
+
+Another eminent mathematician had previously sanctioned by his authority
+the doctrine of the origin of geometrical axioms in experience.
+"Geometry is thus founded likewise on observation; but of a kind so
+familiar and obvious, that the primary notions which it furnishes might
+seem intuitive."--_Sir John Leslie_, quoted by Sir William Hamilton,
+_Discourses_, &c. p. 272.
+
+[39] _Principles of Psychology._
+
+[40] Mr. Spencer is mistaken in supposing me to claim any peculiar
+"necessity" for this axiom as compared with others. I have corrected the
+expressions which led him into that misapprehension of my meaning.
+
+[41] Mr. Spencer makes a distinction between conceiving myself looking
+into darkness, and conceiving _that I am_ then and there looking into
+darkness. To me it seems that this change of the expression to the form
+_I am_, just marks the transition from conception to belief, and that
+the phrase "to conceive that _I am_," or "that anything _is_," is not
+consistent with using the word conceive in its rigorous sense.
+
+[42] I have myself accepted the contest, and fought it out on this
+battleground, in the eleventh chapter of _An Examination of Sir William
+Hamilton's Philosophy_.
+
+[43] _Discussions_, &c., 2nd ed. p. 624.
+
+[44] If it be said that the _existence_ of matter is among the things
+proved by the principle of Excluded Middle, that principle must prove
+also the existence of dragons and hippogriffs, because they must be
+either scaly or not scaly, creeping or not creeping, and so forth.
+
+[45] For further considerations respecting the axioms of Contradiction
+and Excluded Middle, see the twenty-first chapter of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[46] Mr. De Morgan says "Plato," but to prevent confusion I have kept to
+my own _exemplum_.
+
+
+
+
+BOOK III.
+
+OF INDUCTION.
+
+
+"According to the doctrine now stated, the highest, or rather the only
+proper object of physics, is to ascertain those established conjunctions
+of successive events, which constitute the order of the universe; to
+record the phenomena which it exhibits to our observations, or which it
+discloses to our experiments; and to refer these phenomena to their
+general laws."--D. STEWART, _Elements of the Philosophy of the Human
+Mind_, vol. ii. chap. iv. sect. 1.
+
+
+
+
+CHAPTER I.
+
+PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.
+
+
+§ 1. The portion of the present inquiry upon which we are now about to
+enter, may be considered as the principal, both from its surpassing in
+intricacy all the other branches, and because it relates to a process
+which has been shown in the preceding Book to be that in which the
+investigation of nature essentially consists. We have found that all
+Inference, consequently all Proof, and all discovery of truths not
+self-evident, consists of inductions, and the interpretation of
+inductions: that all our knowledge, not intuitive, comes to us
+exclusively from that source. What Induction is, therefore, and what
+conditions render it legitimate, cannot but be deemed the main question
+of the science of logic--the question which includes all others. It is,
+however, one which professed writers on logic have almost entirely
+passed over. The generalities of the subject have not been altogether
+neglected by metaphysicians; but, for want of sufficient acquaintance
+with the processes by which science has actually succeeded in
+establishing general truths, their analysis of the inductive operation,
+even when unexceptionable as to correctness, has not been specific
+enough to be made the foundation of practical rules, which might be for
+induction itself what the rules of the syllogism are for the
+interpretation of induction: while those by whom physical science has
+been carried to its present state of improvement--and who, to arrive at
+a complete theory of the process, needed only to generalize, and adapt
+to all varieties of problems, the methods which they themselves employed
+in their habitual pursuits--never until very lately made any serious
+attempt to philosophize on the subject, nor regarded the mode in which
+they arrived at their conclusions as deserving of study, independently
+of the conclusions themselves.
+
+
+§ 2. For the purposes of the present inquiry, Induction may be defined,
+the operation of discovering and proving general propositions. It is
+true that (as already shown) the process of indirectly ascertaining
+individual facts, is as truly inductive as that by which we establish
+general truths. But it is not a different kind of induction; it is a
+form of the very same process: since, on the one hand, generals are but
+collections of particulars, definite in kind but indefinite in number;
+and on the other hand, whenever the evidence which we derive from
+observation of known cases justifies us in drawing an inference
+respecting even one unknown case, we should on the same evidence be
+justified in drawing a similar inference with respect to a whole class
+of cases. The inference either does not hold at all, or it holds in all
+cases of a certain description; in all cases which, in certain definable
+respects, resemble those we have observed.
+
+If these remarks are just; if the principles and rules of inference are
+the same whether we infer general propositions or individual facts; it
+follows that a complete logic of the sciences would be also a complete
+logic of practical business and common life. Since there is no case of
+legitimate inference from experience, in which the conclusion may not
+legitimately be a general proposition; an analysis of the process by
+which general truths are arrived at, is virtually an analysis of all
+induction whatever. Whether we are inquiring into a scientific principle
+or into an individual fact, and whether we proceed by experiment or by
+ratiocination, every step in the train of inferences is essentially
+inductive, and the legitimacy of the induction depends in both cases on
+the same conditions.
+
+True it is that in the case of the practical inquirer, who is
+endeavouring to ascertain facts not for the purposes of science but for
+those of business, such for instance as the advocate or the judge, the
+chief difficulty is one in which the principles of induction will afford
+him no assistance. It lies not in making his inductions, but in the
+selection of them; in choosing from among all general propositions
+ascertained to be true, those which furnish marks by which he may trace
+whether the given subject possesses or not the predicate in question. In
+arguing a doubtful question of fact before a jury, the general
+propositions or principles to which the advocate appeals are mostly, in
+themselves, sufficiently trite, and assented to as soon as stated: his
+skill lies in bringing his case under those propositions or principles;
+in calling to mind such of the known or received maxims of probability
+as admit of application to the case in hand, and selecting from among
+them those best adapted to his object. Success is here dependent on
+natural or acquired sagacity, aided by knowledge of the particular
+subject, and of subjects allied with it. Invention, though it can be
+cultivated, cannot be reduced to rule; there is no science which will
+enable a man to bethink himself of that which will suit his purpose.
+
+But when he _has_ thought of something, science can tell him whether
+that which he has thought of will suit his purpose or not. The inquirer
+or arguer must be guided by his own knowledge and sagacity in the choice
+of the inductions out of which he will construct his argument. But the
+validity of the argument when constructed, depends on principles and
+must be tried by tests which are the same for all descriptions of
+inquiries, whether the result be to give A an estate, or to enrich
+science with a new general truth. In the one case and in the other, the
+senses, or testimony, must decide on the individual facts; the rules of
+the syllogism will determine whether, those facts being supposed
+correct, the case really falls within the formulæ of the different
+inductions under which it has been successively brought; and finally,
+the legitimacy of the inductions themselves must be decided by other
+rules, and these it is now our purpose to investigate. If this third
+part of the operation be, in many of the questions of practical life,
+not the most, but the least arduous portion of it, we have seen that
+this is also the case in some great departments of the field of science;
+in all those which are principally deductive, and most of all in
+mathematics; where the inductions themselves are few in number, and so
+obvious and elementary that they seem to stand in no need of the
+evidence of experience, while to combine them so as to prove a given
+theorem or solve a problem, may call for the utmost powers of invention
+and contrivance with which our species is gifted.
+
+If the identity of the logical processes which prove particular facts
+and those which establish general scientific truths, required any
+additional confirmation, it would be sufficient to consider that in many
+branches of science, single facts have to be proved, as well as
+principles; facts as completely individual as any that are debated in a
+court of justice; but which are proved in the same manner as the other
+truths of the science, and without disturbing in any degree the
+homogeneity of its method. A remarkable example of this is afforded by
+astronomy. The individual facts on which that science grounds its most
+important deductions, such facts as the magnitudes of the bodies of the
+solar system, their distances from one another, the figure of the earth,
+and its rotation, are scarcely any of them accessible to our means of
+direct observation: they are proved indirectly, by the aid of inductions
+founded on other facts which we can more easily reach. For example, the
+distance of the moon from the earth was determined by a very circuitous
+process. The share which direct observation had in the work consisted in
+ascertaining, at one and the same instant, the zenith distances of the
+moon, as seen from two points very remote from one another on the
+earth's surface. The ascertainment of these angular distances
+ascertained their supplements; and since the angle at the earth's centre
+subtended by the distance between the two places of observation was
+deducible by spherical trigonometry from the latitude and longitude of
+those places, the angle at the moon subtended by the same line became
+the fourth angle of a quadrilateral of which the other three angles were
+known. The four angles being thus ascertained, and two sides of the
+quadrilateral being radii of the earth; the two remaining sides and the
+diagonal, or in other words, the moon's distance from the two places of
+observation and from the centre of the earth, could be ascertained, at
+least in terms of the earth's radius, from elementary theorems of
+geometry. At each step in this demonstration we take in a new
+induction, represented, in the aggregate of its results, by a general
+proposition.
+
+Not only is the process by which an individual astronomical fact was
+thus ascertained, exactly similar to those by which the same science
+establishes its general truths, but also (as we have shown to be the
+case in all legitimate reasoning) a general proposition might have been
+concluded instead of a single fact. In strictness, indeed, the result of
+the reasoning _is_ a general proposition; a theorem respecting the
+distance, not of the moon in particular, but of any inaccessible object:
+showing in what relation that distance stands to certain other
+quantities. And although the moon is almost the only heavenly body the
+distance of which from the earth can really be thus ascertained, this is
+merely owing to the accidental circumstances of the other heavenly
+bodies, which render them incapable of affording such data as the
+application of the theorem requires; for the theorem itself is as true
+of them as it is of the moon.[1]
+
+We shall fall into no error, then, if in treating of Induction, we
+limit our attention to the establishment of general propositions. The
+principles and rules of Induction as directed to this end, are the
+principles and rules of all Induction; and the logic of Science is the
+universal Logic, applicable to all inquiries in which man can engage.
+
+
+
+
+CHAPTER II.
+
+OF INDUCTIONS IMPROPERLY SO CALLED.
+
+
+§ 1. Induction, then, is that operation of the mind, by which we infer
+that what we know to be true in a particular case or cases, will be true
+in all cases which resemble the former in certain assignable respects.
+In other words, Induction is the process by which we conclude that what
+is true of certain individuals of a class is true of the whole class, or
+that what is true at certain times will be true in similar circumstances
+at all times.
+
+This definition excludes from the meaning of the term Induction, various
+logical operations, to which it is not unusual to apply that name.
+
+Induction, as above defined, is a process of inference; it proceeds from
+the known to the unknown; and any operation involving no inference, any
+process in which what seems the conclusion is no wider than the premises
+from which it is drawn, does not fall within the meaning of the term.
+Yet in the common books of Logic we find this laid down as the most
+perfect, indeed the only quite perfect, form of induction. In those
+books, every process which sets out from a less general and terminates
+in a more general expression,--which admits of being stated in the form,
+"This and that A are B, therefore every A is B,"--is called an
+induction, whether anything be really concluded or not: and the
+induction is asserted not to be perfect, unless every single individual
+of the class A is included in the antecedent, or premise: that is,
+unless what we affirm of the class has already been ascertained to be
+true of every individual in it, so that the nominal conclusion is not
+really a conclusion, but a mere reassertion of the premises. If we were
+to say, All the planets shine by the sun's light, from observation of
+each separate planet, or All the Apostles were Jews, because this is
+true of Peter, Paul, John, and every other apostle,--these, and such as
+these, would, in the phraseology in question, be called perfect, and the
+only perfect, Inductions. This, however, is a totally different kind of
+induction from ours; it is not an inference from facts known to facts
+unknown, but a mere short-hand registration of facts known. The two
+simulated arguments which we have quoted, are not generalizations; the
+propositions purporting to be conclusions from them, are not really
+general propositions. A general proposition is one in which the
+predicate is affirmed or denied of an unlimited number of individuals;
+namely, all, whether few or many, existing or capable of existing, which
+possess the properties connoted by the subject of the proposition. "All
+men are mortal" does not mean all now living, but all men past, present,
+and to come. When the signification of the term is limited so as to
+render it a name not for any and every individual falling under a
+certain general description, but only for each of a number of
+individuals designated as such, and as it were counted off individually,
+the proposition, though it may be general in its language, is no general
+proposition, but merely that number of singular propositions, written in
+an abridged character. The operation may be very useful, as most forms
+of abridged notation are; but it is no part of the investigation of
+truth, though often bearing an important part in the preparation of the
+materials for that investigation.
+
+As we may sum up a definite number of singular propositions in one
+proposition, which will be apparently, but not really, general, so we
+may sum up a definite number of general propositions in one proposition,
+which will be apparently, but not really, more general. If by a separate
+induction applied to every distinct species of animals, it has been
+established that each possesses a nervous system, and we affirm
+thereupon that all animals have a nervous system; this looks like a
+generalization, though as the conclusion merely affirms of all what has
+already been affirmed of each, it seems to tell us nothing but what we
+knew before. A distinction however must be made. If in concluding that
+all animals have a nervous system, we mean the same thing and no more as
+if we had said "all known animals," the proposition is not general, and
+the process by which it is arrived at is not induction. But if our
+meaning is that the observations made of the various species of animals
+have discovered to us a law of animal nature, and that we are in a
+condition to say that a nervous system will be found even in animals yet
+undiscovered, this indeed is an induction; but in this case the general
+proposition contains more than the sum of the special propositions from
+which it is inferred. The distinction is still more forcibly brought out
+when we consider, that if this real generalization be legitimate at all,
+its legitimacy probably does not require that we should have examined
+without exception every known species. It is the number and nature of
+the instances, and not their being the whole of those which happen to be
+known, that makes them sufficient evidence to prove a general law: while
+the more limited assertion, which stops at all known animals, cannot be
+made unless we have rigorously verified it in every species. In like
+manner (to return to a former example) we might have inferred, not that
+all _the_ planets, but that all _planets_, shine by reflected light: the
+former is no induction; the latter is an induction, and a bad one, being
+disproved by the case of double stars--self-luminous bodies which are
+properly planets, since they revolve round a centre.
+
+
+§ 2. There are several processes used in mathematics which require to be
+distinguished from Induction, being not unfrequently called by that
+name, and being so far similar to Induction properly so called, that the
+propositions they lead to are really general propositions. For example,
+when we have proved with respect to the circle, that a straight line
+cannot meet it in more than two points, and when the same thing has been
+successively proved of the ellipse, the parabola, and the hyperbola, it
+may be laid down as an universal property of the sections of the cone.
+The distinction drawn in the two previous examples can have no place
+here, there being no difference between all _known_ sections of the
+cone and _all_ sections, since a cone demonstrably cannot be intersected
+by a plane except in one of these four lines. It would be difficult,
+therefore, to refuse to the proposition arrived at, the name of a
+generalization, since there is no room for any generalization beyond it.
+But there is no induction, because there is no inference: the conclusion
+is a mere summing up of what was asserted in the various propositions
+from which it is drawn. A case somewhat, though not altogether, similar,
+is the proof of a geometrical theorem by means of a diagram. Whether the
+diagram be on paper or only in the imagination, the demonstration (as
+formerly observed[2]) does not prove directly the general theorem; it
+proves only that the conclusion, which the theorem asserts generally, is
+true of the particular triangle or circle exhibited in the diagram; but
+since we perceive that in the same way in which we have proved it of
+that circle, it might also be proved of any other circle, we gather up
+into one general expression all the singular propositions susceptible of
+being thus proved, and embody them in an universal proposition. Having
+shown that the three angles of the triangle ABC are together equal to
+two right angles, we conclude that this is true of every other triangle,
+not because it is true of ABC, but for the same reason which proved it
+to be true of ABC. If this were to be called Induction, an appropriate
+name for it would be, induction by parity of reasoning. But the term
+cannot properly belong to it; the characteristic quality of Induction is
+wanting, since the truth obtained, though really general, is not
+believed on the evidence of particular instances. We do not conclude
+that all triangles have the property because some triangles have, but
+from the ulterior demonstrative evidence which was the ground of our
+conviction in the particular instances.
+
+There are nevertheless, in mathematics, some examples of so-called
+Induction, in which the conclusion does bear the appearance of a
+generalization grounded on some of the particular cases included in it.
+A mathematician, when he has calculated a sufficient number of the
+terms of an algebraical or arithmetical series to have ascertained what
+is called the _law_ of the series, does not hesitate to fill up any
+number of the succeeding terms without repeating the calculations. But I
+apprehend he only does so when it is apparent from _à priori_
+considerations (which might be exhibited in the form of demonstration)
+that the mode of formation of the subsequent terms, each from that which
+preceded it, must be similar to the formation of the terms which have
+been already calculated. And when the attempt has been hazarded without
+the sanction of such general considerations, there are instances on
+record in which it has led to false results.
+
+It is said that Newton discovered the binomial theorem by induction; by
+raising a binomial successively to a certain number of powers, and
+comparing those powers with one another until he detected the relation
+in which the algebraic formula of each power stands to the exponent of
+that power, and to the two terms of the binomial. The fact is not
+improbable: but a mathematician like Newton, who seemed to arrive _per
+saltum_ at principles and conclusions that ordinary mathematicians only
+reached by a succession of steps, certainly could not have performed the
+comparison in question without being led by it to the _à priori_ ground
+of the law; since any one who understands sufficiently the nature of
+multiplication to venture upon multiplying several lines of symbols at
+one operation, cannot but perceive that in raising a binomial to a
+power, the coefficients must depend on the laws of permutation and
+combination: and as soon as this is recognised, the theorem is
+demonstrated. Indeed, when once it was seen that the law prevailed in a
+few of the lower powers, its identity with the law of permutation would
+at once suggest the considerations which prove it to obtain universally.
+Even, therefore, such cases as these, are but examples of what I have
+called Induction by parity of reasoning, that is, not really Induction,
+because not involving inference of a general proposition from particular
+instances.
+
+
+§ 3. There remains a third improper use of the term Induction, which it
+is of real importance to clear up, because the theory of Induction has
+been, in no ordinary degree, confused by it, and because the confusion
+is exemplified in the most recent and elaborate treatise on the
+inductive philosophy which exists in our language. The error in question
+is that of confounding a mere description, by general terms, of a set of
+observed phenomena, with an induction from them.
+
+Suppose that a phenomenon consists of parts, and that these parts are
+only capable of being observed separately, and as it were piecemeal.
+When the observations have been made, there is a convenience (amounting
+for many purposes to a necessity) in obtaining a representation of the
+phenomenon as a whole, by combining, or as we may say, piecing these
+detached fragments together. A navigator sailing in the midst of the
+ocean discovers land: he cannot at first, or by any one observation,
+determine whether it is a continent or an island; but he coasts along
+it, and after a few days finds himself to have sailed completely round
+it: he then pronounces it an island. Now there was no particular time or
+place of observation at which he could perceive that this land was
+entirely surrounded by water: he ascertained the fact by a succession of
+partial observations, and then selected a general expression which
+summed up in two or three words the whole of what he so observed. But is
+there anything of the nature of an induction in this process? Did he
+infer anything that had not been observed, from something else which
+had? Certainly not. He had observed the whole of what the proposition
+asserts. That the land in question is an island, is not an inference
+from the partial facts which the navigator saw in the course of his
+circumnavigation; it is the facts themselves; it is a summary of those
+facts; the description of a complex fact, to which those simpler ones
+are as the parts of a whole.
+
+Now there is, I conceive, no difference in kind between this simple
+operation, and that by which Kepler ascertained the nature of the
+planetary orbits: and Kepler's operation, all at least that was
+characteristic in it, was not more an inductive act than that of our
+supposed navigator.
+
+The object of Kepler was to determine the real path described by each
+of the planets, or let us say by the planet Mars (since it was of that
+body that he first established the two of his three laws which did not
+require a comparison of planets). To do this there was no other mode
+than that of direct observation: and all which observation could do was
+to ascertain a great number of the successive places of the planet; or
+rather, of its apparent places. That the planet occupied successively
+all these positions, or at all events, positions which produced the same
+impressions on the eye, and that it passed from one of these to another
+insensibly, and without any apparent breach of continuity; thus much the
+senses, with the aid of the proper instruments, could ascertain. What
+Kepler did more than this, was to find what sort of a curve these
+different points would make, supposing them to be all joined together.
+He expressed the whole series of the observed places of Mars by what Dr.
+Whewell calls the general conception of an ellipse. This operation was
+far from being as easy as that of the navigator who expressed the series
+of his observations on successive points of the coast by the general
+conception of an island. But it is the very same sort of operation; and
+if the one is not an induction but a description, this must also be true
+of the other.
+
+The only real induction concerned in the case, consisted in inferring
+that because the observed places of Mars were correctly represented by
+points in an imaginary ellipse, therefore Mars would continue to revolve
+in that same ellipse; and in concluding (before the gap had been filled
+up by further observations) that the positions of the planet during the
+time which intervened between two observations, must have coincided with
+the intermediate points of the curve. For these were facts which had not
+been directly observed. They were inferences from the observations;
+facts inferred, as distinguished from facts seen. But these inferences
+were so far from being a part of Kepler's philosophical operation, that
+they had been drawn long before he was born. Astronomers had long known
+that the planets periodically returned to the same places. When this had
+been ascertained, there was no induction left for Kepler to make, nor
+did he make any further induction. He merely applied his new conception
+to the facts inferred, as he did to the facts observed. Knowing already
+that the planets continued to move in the same paths; when he found that
+an ellipse correctly represented the past path, he knew that it would
+represent the future path. In finding a compendious expression for the
+one set of facts, he found one for the other: but he found the
+expression only, not the inference; nor did he (which is the true test
+of a general truth) add anything to the power of prediction already
+possessed.
+
+
+§ 4. The descriptive operation which enables a number of details to be
+summed up in a single proposition, Dr. Whewell, by an aptly chosen
+expression, has termed the Colligation of Facts. In most of his
+observations concerning that mental process I fully agree, and would
+gladly transfer all that portion of his book into my own pages. I only
+think him mistaken in setting up this kind of operation, which according
+to the old and received meaning of the term, is not induction at all, as
+the type of induction generally; and laying down, throughout his work,
+as principles of induction, the principles of mere colligation.
+
+Dr. Whewell maintains that the general proposition which binds together
+the particular facts, and makes them, as it were, one fact, is not the
+mere sum of those facts, but something more, since there is introduced a
+conception of the mind, which did not exist in the facts themselves.
+"The particular facts," says he,[3] "are not merely brought together,
+but there is a new element added to the combination by the very act of
+thought by which they are combined.... When the Greeks, after long
+observing the motions of the planets, saw that these motions might be
+rightly considered as produced by the motion of one wheel revolving in
+the inside of another wheel, these wheels were creations of their minds,
+added to the facts which they perceived by sense. And even if the
+wheels were no longer supposed to be material, but were reduced to mere
+geometrical spheres or circles, they were not the less products of the
+mind alone,--something additional to the facts observed. The same is the
+case in all other discoveries. The facts are known, but they are
+insulated and unconnected, till the discoverer supplies from his own
+store a principle of connexion. The pearls are there, but they will not
+hang together till some one provides the string."
+
+Let me first remark that Dr. Whewell, in this passage, blends together,
+indiscriminately, examples of both the processes which I am endeavouring
+to distinguish from one another. When the Greeks abandoned the
+supposition that the planetary motions were produced by the revolution
+of material wheels, and fell back upon the idea of "mere geometrical
+spheres or circles," there was more in this change of opinion than the
+mere substitution of an ideal curve for a physical one. There was the
+abandonment of a theory, and the replacement of it by a mere
+description. No one would think of calling the doctrine of material
+wheels a mere description. That doctrine was an attempt to point out the
+force by which the planets were acted upon, and compelled to move in
+their orbits. But when, by a great step in philosophy, the materiality
+of the wheels was discarded, and the geometrical forms alone retained,
+the attempt to account for the motions was given up, and what was left
+of the theory was a mere description of the orbits. The assertion that
+the planets were carried round by wheels revolving in the inside of
+other wheels, gave place to the proposition, that they moved in the same
+lines which would be traced by bodies so carried: which was a mere mode
+of representing the sum of the observed facts; as Kepler's was another
+and a better mode of representing the same observations.
+
+It is true that for these simply descriptive operations, as well as for
+the erroneous inductive one, a conception of the mind was required. The
+conception of an ellipse must have presented itself to Kepler's mind,
+before he could identify the planetary orbits with it. According to Dr.
+Whewell, the conception was something added to the facts. He expresses
+himself as if Kepler had put something into the facts by his mode of
+conceiving them. But Kepler did no such thing. The ellipse was in the
+facts before Kepler recognised it; just as the island was an island
+before it had been sailed round. Kepler did not _put_ what he had
+conceived into the facts, but _saw_ it in them. A conception implies,
+and corresponds to, something conceived: and though the conception
+itself is not in the facts, but in our mind, yet if it is to convey any
+knowledge relating to them, it must be a conception _of_ something which
+really is in the facts, some property which they actually possess, and
+which they would manifest to our senses, if our senses were able to take
+cognizance of it. If, for instance, the planet left behind it in space a
+visible track, and if the observer were in a fixed position at such a
+distance from the plane of the orbit as would enable him to see the
+whole of it at once, he would see it to be an ellipse; and if gifted
+with appropriate instruments and powers of locomotion, he could prove it
+to be such by measuring its different dimensions. Nay, further: if the
+track were visible, and he were so placed that he could see all parts of
+it in succession, but not all of them at once, he might be able, by
+piecing together his successive observations, to discover both that it
+was an ellipse and that the planet moved in it. The case would then
+exactly resemble that of the navigator who discovers the land to be an
+island by sailing round it. If the path was visible, no one I think
+would dispute that to identify it with an ellipse is to describe it: and
+I cannot see why any difference should be made by its not being directly
+an object of sense, when every point in it is as exactly ascertained as
+if it were so.
+
+Subject to the indispensable condition which has just been stated, I
+cannot conceive that the part which conceptions have in the operation of
+studying facts, has ever been overlooked or undervalued. No one ever
+disputed that in order to reason about anything we must have a
+conception of it; or that when we include a multitude of things under a
+general expression, there is implied in the expression a conception of
+something common to those things. But it by no means follows that the
+conception is necessarily pre-existent, or constructed by the mind out
+of its own materials. If the facts are rightly classed under the
+conception, it is because there is in the facts themselves something of
+which the conception is itself a copy; and which if we cannot directly
+perceive, it is because of the limited power of our organs, and not
+because the thing itself is not there. The conception itself is often
+obtained by abstraction from the very facts which, in Dr. Whewell's
+language, it is afterwards called in to connect. This he himself admits,
+when he observes, (which he does on several occasions,) how great a
+service would be rendered to the science of physiology by the
+philosopher "who should establish a precise, tenable, and consistent
+conception of life."[4] Such a conception can only be abstracted from
+the phenomena of life itself; from the very facts which it is put in
+requisition to connect. In other cases, no doubt, instead of collecting
+the conception from the very phenomena which we are attempting to
+colligate, we select it from among those which have been previously
+collected by abstraction from other facts. In the instance of Kepler's
+laws, the latter was the case. The facts being out of the reach of being
+observed, in any such manner as would have enabled the senses to
+identify directly the path of the planet, the conception requisite for
+framing a general description of that path could not be collected by
+abstraction from the observations themselves; the mind had to supply
+hypothetically, from among the conceptions it had obtained from other
+portions of its experience, some one which would correctly represent the
+series of the observed facts. It had to frame a supposition respecting
+the general course of the phenomenon, and ask itself, If this be the
+general description, what will the details be? and then compare these
+with the details actually observed. If they agreed, the hypothesis would
+serve for a description of the phenomenon: if not, it was necessarily
+abandoned, and another tried. It is such a case as this which gives rise
+to the doctrine that the mind, in framing the descriptions, adds
+something of its own which it does not find in the facts.
+
+Yet it is a fact surely, that the planet does describe an ellipse; and a
+fact which we could see, if we had adequate visual organs and a suitable
+position. Not having these advantages, but possessing the conception of
+an ellipse, or (to express the meaning in less technical language)
+knowing what an ellipse was, Kepler tried whether the observed places of
+the planet were consistent with such a path. He found they were so; and
+he, consequently, asserted as a fact that the planet moved in an
+ellipse. But this fact, which Kepler did not add to, but found in, the
+motions of the planet, namely, that it occupied in succession the
+various points in the circumference of a given ellipse, was the very
+fact, the separate parts of which had been separately observed; it was
+the sum of the different observations.
+
+Having stated this fundamental difference between my opinion and that of
+Dr. Whewell, I must add, that his account of the manner in which a
+conception is selected, suitable to express the facts, appears to me
+perfectly just. The experience of all thinkers will, I believe, testify
+that the process is tentative; that it consists of a succession of
+guesses; many being rejected, until one at last occurs fit to be chosen.
+We know from Kepler himself that before hitting upon the "conception" of
+an ellipse, he tried nineteen other imaginary paths, which, finding them
+inconsistent with the observations, he was obliged to reject. But as Dr.
+Whewell truly says, the successful hypothesis, though a guess, ought
+generally to be called, not a lucky, but a skilful guess. The guesses
+which serve to give mental unity and wholeness to a chaos of scattered
+particulars, are accidents which rarely occur to any minds but those
+abounding in knowledge and disciplined in intellectual combinations.
+
+How far this tentative method, so indispensable as a means to the
+colligation of facts for purposes of description, admits of application
+to Induction itself, and what functions belong to it in that department,
+will be considered in the chapter of the present Book which relates to
+Hypotheses. On the present occasion we have chiefly to distinguish this
+process of Colligation from Induction properly so called; and that the
+distinction may be made clearer, it is well to advert to a curious and
+interesting remark, which is as strikingly true of the former operation,
+as it appears to me unequivocally false of the latter.
+
+In different stages of the progress of knowledge, philosophers have
+employed, for the colligation of the same order of facts, different
+conceptions. The early rude observations of the heavenly bodies, in
+which minute precision was neither attained nor sought, presented
+nothing inconsistent with the representation of the path of a planet as
+an exact circle, having the earth for its centre. As observations
+increased in accuracy, and facts were disclosed which were not
+reconcileable with this simple supposition; for the colligation of those
+additional facts, the supposition was varied; and varied again and again
+as facts became more numerous and precise. The earth was removed from
+the centre to some other point within the circle; the planet was
+supposed to revolve in a smaller circle called an epicycle, round an
+imaginary point which revolved in a circle round the earth: in
+proportion as observation elicited fresh facts contradictory to these
+representations, other epicycles and other excentrics were added,
+producing additional complication; until at last Kepler swept all these
+circles away, and substituted the conception of an exact ellipse. Even
+this is found not to represent with complete correctness the accurate
+observations of the present day, which disclose many slight deviations
+from an orbit exactly elliptical. Now Dr. Whewell has remarked that
+these successive general expressions, though apparently so conflicting,
+were all correct: they all answered the purpose of colligation; they all
+enabled the mind to represent to itself with facility, and by a
+simultaneous glance, the whole body of facts at the time ascertained:
+each in its turn served as a correct description of the phenomena, so
+far as the senses had up to that time taken cognizance of them. If a
+necessity afterwards arose for discarding one of these general
+descriptions of the planet's orbit, and framing a different imaginary
+line, by which to express the series of observed positions, it was
+because a number of new facts had now been added, which it was necessary
+to combine with the old facts into one general description. But this did
+not affect the correctness of the former expression, considered as a
+general statement of the only facts which it was intended to represent.
+And so true is this, that, as is well remarked by M. Comte, these
+ancient generalizations, even the rudest and most imperfect of them,
+that of uniform movement in a circle, are so far from being entirely
+false, that they are even now habitually employed by astronomers when
+only a rough approximation to correctness is required. "L'astronomie
+moderne, en détruisant sans retour les hypothèses primitives, envisagées
+comme lois réelles du monde, a soigneusement maintenu leur valeur
+positive et permanente, la propriété de représenter commodément les
+phénomènes quand il s'agit d'une première ébauche. Nos ressources à cet
+égard sont même bien plus étendues, précisément à cause que nous ne nous
+faisons aucune illusion sur la réalité des hypothèses; ce qui nous
+permet d'employer sans scrupule, en chaque cas, celle que nous jugeons
+la plus avantageuse."[5]
+
+Dr. Whewell's remark, therefore, is philosophically correct. Successive
+expressions for the colligation of observed facts, or in other words,
+successive descriptions of a phenomenon as a whole, which has been
+observed only in parts, may, though conflicting, be all correct as far
+as they go. But it would surely be absurd to assert this of conflicting
+inductions.
+
+The scientific study of facts may be undertaken for three different
+purposes: the simple description of the facts; their explanation; or
+their prediction: meaning by prediction, the determination of the
+conditions under which similar facts may be expected again to occur. To
+the first of these three operations the name of Induction does not
+properly belong: to the other two it does. Now, Dr. Whewell's
+observation is true of the first alone. Considered as a mere
+description, the circular theory of the heavenly motions represents
+perfectly well their general features: and by adding epicycles without
+limit, those motions, even as now known to us, might be expressed with
+any degree of accuracy that might be required. The elliptical theory, as
+a mere description, would have a great advantage in point of simplicity,
+and in the consequent facility of conceiving it and reasoning about it;
+but it would not really be more true than the other. Different
+descriptions, therefore, may be all true: but not, surely, different
+explanations. The doctrine that the heavenly bodies moved by a virtue
+inherent in their celestial nature; the doctrine that they were moved by
+impact, (which led to the hypothesis of vortices as the only impelling
+force capable of whirling bodies in circles,) and the Newtonian
+doctrine, that they are moved by the composition of a centripetal with
+an original projectile force; all these are explanations, collected by
+real induction from supposed parallel cases; and they were all
+successively received by philosophers, as scientific truths on the
+subject of the heavenly bodies. Can it be said of these, as was said of
+the different descriptions, that they are all true as far as they go? Is
+it not clear that only one can be true in any degree, and the other two
+must be altogether false? So much for explanations: let us now compare
+different predictions: the first, that eclipses will occur when one
+planet or satellite is so situated as to cast its shadow upon another;
+the second, that they will occur when some great calamity is impending
+over mankind. Do these two doctrines only differ in the degree of their
+truth, as expressing real facts with unequal degrees of accuracy?
+Assuredly the one is true, and the other absolutely false.[6]
+
+In every way, therefore, it is evident that to explain induction as the
+colligation of facts by means of appropriate conceptions, that is,
+conceptions which will really express them, is to confound mere
+description of the observed facts with inference from those facts, and
+ascribe to the latter what is a characteristic property of the former.
+
+There is, however, between Colligation and Induction, a real
+correlation, which it is important to conceive correctly. Colligation is
+not always induction; but induction is always colligation. The assertion
+that the planets move in ellipses, was but a mode of representing
+observed facts; it was but a colligation; while the assertion that they
+are drawn, or tend, towards the sun, was the statement of a new fact,
+inferred by induction. But the induction, once made, accomplishes the
+purposes of colligation likewise. It brings the same facts, which Kepler
+had connected by his conception of an ellipse, under the additional
+conception of bodies acted upon by a central force, and serves therefore
+as a new bond of connexion for those facts; a new principle for their
+classification.
+
+Further, the descriptions which are improperly confounded with
+induction, are nevertheless a necessary preparation for induction; no
+less necessary than correct observation of the facts themselves. Without
+the previous colligation of detached observations by means of one
+general conception, we could never have obtained any basis for an
+induction, except in the case of phenomena of very limited compass. We
+should not be able to affirm any predicates at all, of a subject
+incapable of being observed otherwise than piecemeal: much less could we
+extend those predicates by induction to other similar subjects.
+Induction, therefore, always presupposes, not only that the necessary
+observations are made with the necessary accuracy, but also that the
+results of these observations are, so far as practicable, connected
+together by general descriptions, enabling the mind to represent to
+itself as wholes whatever phenomena are capable of being so represented.
+
+
+§ 5. Dr. Whewell has replied at some length to the preceding
+observations, re-stating his opinions, but without (as far as I can
+perceive) adding anything material to his former arguments. Since,
+however, mine have not had the good fortune to make any impression upon
+him, I will subjoin a few remarks, tending to show more clearly in what
+our difference of opinion consists, as well as, in some measure, to
+account for it.
+
+Nearly all the definitions of induction, by writers of authority, make
+it consist in drawing inferences from known cases to unknown; affirming
+of a class, a predicate which has been found true of some cases
+belonging to the class; concluding, because some things have a certain
+property, that other things which resemble them have the same
+property--or because a thing has manifested a property at a certain
+time, that it has and will have that property at other times.
+
+It will scarcely be contended that Kepler's operation was an Induction
+in this sense of the term. The statement, that Mars moves in an
+elliptical orbit, was no generalization from individual cases to a class
+of cases. Neither was it an extension to all time, of what had been
+found true at some particular time. The whole amount of generalization
+which the case admitted of, was already completed, or might have been
+so. Long before the elliptic theory was thought of, it had been
+ascertained that the planets returned periodically to the same apparent
+places; the series of these places was, or might have been, completely
+determined, and the apparent course of each planet marked out on the
+celestial globe in an uninterrupted line. Kepler did not extend an
+observed truth to other cases than those in which it had been observed:
+he did not widen the _subject_ of the proposition which expressed the
+observed facts. The alteration he made was in the predicate. Instead of
+saying, the successive places of Mars are so and so, he summed them up
+in the statement, that the successive places of Mars are points in an
+ellipse. It is true, this statement, as Dr. Whewell says, was not the
+sum of the observations _merely_; it was the sum of the observations
+_seen under a new point of view_.[7] But it was not the sum of _more_
+than the observations, as a real induction is. It took in no cases but
+those which had been actually observed, or which could have been
+inferred from the observations before the new point of view presented
+itself. There was not that transition from known cases to unknown,
+which constitutes Induction in the original and acknowledged meaning of
+the term.
+
+Old definitions, it is true, cannot prevail against new knowledge: and
+if the Keplerian operation, as a logical process, be really identical
+with what takes place in acknowledged induction, the definition of
+induction ought to be so widened as to take it in; since scientific
+language ought to adapt itself to the true relations which subsist
+between the things it is employed to designate. Here then it is that I
+am at issue with Dr. Whewell. He does think the operations identical. He
+allows of no logical process in any case of induction, other than what
+there was in Kepler's case, namely, guessing until a guess is found
+which tallies with the facts; and accordingly, as we shall see
+hereafter, he rejects all canons of induction, because it is not by
+means of them that we guess. Dr. Whewell's theory of the logic of
+science would be very perfect if it did not pass over altogether the
+question of Proof. But in my apprehension there is such a thing as
+proof, and inductions differ altogether from descriptions in their
+relation to that element. Induction is proof; it is inferring something
+unobserved from something observed: it requires, therefore, an
+appropriate test of proof; and to provide that test, is the special
+purpose of inductive logic. When, on the contrary, we merely collate
+known observations, and, in Dr. Whewell's phraseology, connect them by
+means of a new conception; if the conception does serve to connect the
+observations, we have all we want. As the proposition in which it is
+embodied pretends to no other truth than what it may share with many
+other modes of representing the same facts, to be consistent with the
+facts is all it requires: it neither needs nor admits of proof; though
+it may serve to prove other things, inasmuch as, by placing the facts in
+mental connexion with other facts, not previously seen to resemble them,
+it assimilates the case to another class of phenomena, concerning which
+real Inductions have already been made. Thus Kepler's so-called law
+brought the orbit of Mars into the class ellipse, and by doing so,
+proved all the properties of an ellipse to be true of the orbit: but in
+this proof Kepler's law supplied the minor premise, and not (as is the
+case with real Inductions) the major.
+
+Dr. Whewell calls nothing Induction where there is not a new mental
+conception introduced, and everything induction where there is. But this
+is to confound two very different things, Invention and Proof. The
+introduction of a new conception belongs to Invention: and invention may
+be required in any operation, but is the essence of none. A new
+conception may be introduced for descriptive purposes, and so it may for
+inductive purposes. But it is so far from constituting induction, that
+induction does not necessarily stand in need of it. Most inductions
+require no conception but what was present in every one of the
+particular instances on which the induction is grounded. That all men
+are mortal is surely an inductive conclusion; yet no new conception is
+introduced by it. Whoever knows that any man has died, has all the
+conceptions involved in the inductive generalization. But Dr. Whewell
+considers the process of invention which consists in framing a new
+conception consistent with the facts, to be not merely a necessary part
+of all induction, but the whole of it.
+
+The mental operation which extracts from a number of detached
+observations certain general characters in which the observed phenomena
+resemble one another, or resemble other known facts, is what Bacon,
+Locke, and most subsequent metaphysicians, have understood by the word
+Abstraction. A general expression obtained by abstraction, connecting
+known facts by means of common characters, but without concluding from
+them to unknown, may, I think, with strict logical correctness, be
+termed a Description; nor do I know in what other way things can ever be
+described. My position, however, does not depend on the employment of
+that particular word; I am quite content to use Dr. Whewell's term
+Colligation, or the more general phrases, "mode of representing, or of
+expressing, phenomena:" provided it be clearly seen that the process is
+not Induction, but something radically different.
+
+What more may usefully be said on the subject of Colligation, or of the
+correlative expression invented by Dr. Whewell, the Explication of
+Conceptions, and generally on the subject of ideas and mental
+representations as connected with the study of facts, will find a more
+appropriate place in the Fourth Book, on the Operations Subsidiary to
+Induction: to which I must refer the reader for the removal of any
+difficulty which the present discussion may have left.
+
+
+
+
+CHAPTER III.
+
+OF THE GROUND OF INDUCTION.
+
+
+§ 1. Induction properly so called, as distinguished from those mental
+operations, sometimes though improperly designated by the name, which I
+have attempted in the preceding chapter to characterize, may, then, be
+summarily defined as Generalization from Experience. It consists in
+inferring from some individual instances in which a phenomenon is
+observed to occur, that it occurs in all instances of a certain class;
+namely, in all which _resemble_ the former, in what are regarded as the
+material circumstances.
+
+In what way the material circumstances are to be distinguished from
+those which are immaterial, or why some of the circumstances are
+material and others not so, we are not yet ready to point out. We must
+first observe, that there is a principle implied in the very statement
+of what Induction is; an assumption with regard to the course of nature
+and the order of the universe; namely, that there are such things in
+nature as parallel cases; that what happens once, will, under a
+sufficient degree of similarity of circumstances, happen again, and not
+only again, but as often as the same circumstances recur. This, I say,
+is an assumption, involved in every case of induction. And, if we
+consult the actual course of nature, we find that the assumption is
+warranted. The universe, so far as known to us, is so constituted, that
+whatever is true in any one case, is true in all cases of a certain
+description; the only difficulty is, to find what description.
+
+This universal fact, which is our warrant for all inferences from
+experience, has been described by different philosophers in different
+forms of language: that the course of nature is uniform; that the
+universe is governed by general laws; and the like. One of the most
+usual of these modes of expression, but also one of the most inadequate,
+is that which has been brought into familiar use by the metaphysicians
+of the school of Reid and Stewart. The disposition of the human mind to
+generalize from experience,--a propensity considered by these
+philosophers as an instinct of our nature,--they usually describe under
+some such name as "our intuitive conviction that the future will
+resemble the past." Now it has been well pointed out by Mr. Bailey,[8]
+that (whether the tendency be or not an original and ultimate element of
+our nature), Time, in its modifications of past, present, and future,
+has no concern either with the belief itself, or with the grounds of it.
+We believe that fire will burn to-morrow, because it burned to-day and
+yesterday; but we believe, on precisely the same grounds, that it burned
+before we were born, and that it burns this very day in Cochin-China. It
+is not from the past to the future, as past and future, that we infer,
+but from the known to the unknown; from facts observed to facts
+unobserved; from what we have perceived, or been directly conscious of,
+to what has not come within our experience. In this last predicament is
+the whole region of the future; but also the vastly greater portion of
+the present and of the past.
+
+Whatever be the most proper mode of expressing it, the proposition that
+the course of nature is uniform, is the fundamental principle, or
+general axiom, of Induction. It would yet be a great error to offer this
+large generalization as any explanation of the inductive process. On the
+contrary, I hold it to be itself an instance of induction, and induction
+by no means of the most obvious kind. Far from being the first induction
+we make, it is one of the last, or at all events one of those which are
+latest in attaining strict philosophical accuracy. As a general maxim,
+indeed, it has scarcely entered into the minds of any but philosophers;
+nor even by them, as we shall have many opportunities of remarking, have
+its extent and limits been always very justly conceived. The truth is,
+that this great generalization is itself founded on prior
+generalizations. The obscurer laws of nature were discovered by means
+of it, but the more obvious ones must have been understood and assented
+to as general truths before it was ever heard of. We should never have
+thought of affirming that all phenomena take place according to general
+laws, if we had not first arrived, in the case of a great multitude of
+phenomena, at some knowledge of the laws themselves; which could be done
+no otherwise than by induction. In what sense, then, can a principle,
+which is so far from being our earliest induction, be regarded as our
+warrant for all the others? In the only sense, in which (as we have
+already seen) the general propositions which we place at the head of our
+reasonings when we throw them into syllogisms, ever really contribute to
+their validity. As Archbishop Whately remarks, every induction is a
+syllogism with the major premise suppressed; or (as I prefer expressing
+it) every induction may be thrown into the form of a syllogism, by
+supplying a major premise. If this be actually done, the principle which
+we are now considering, that of the uniformity of the course of nature,
+will appear as the ultimate major premise of all inductions, and will,
+therefore, stand to all inductions in the relation in which, as has been
+shown at so much length, the major proposition of a syllogism always
+stands to the conclusion; not contributing at all to prove it, but being
+a necessary condition of its being proved; since no conclusion is
+proved, for which there cannot be found a true major premise.[9]
+
+The statement, that the uniformity of the course of nature is the
+ultimate major premise in all cases of induction, may be thought to
+require some explanation. The immediate major premise in every inductive
+argument, it certainly is not. Of that, Archbishop Whately's must be
+held to be the correct account. The induction, "John, Peter, &c. are
+mortal, therefore all mankind are mortal," may, as he justly says, be
+thrown into a syllogism by prefixing as a major premise (what is at any
+rate a necessary condition of the validity of the argument) namely, that
+what is true of John, Peter, &c. is true of all mankind. But how came we
+by this major premise? It is not self-evident; nay, in all cases of
+unwarranted generalization, it is not true. How, then, is it arrived at?
+Necessarily either by induction or ratiocination; and if by induction,
+the process, like all other inductive arguments, may be thrown into the
+form of a syllogism. This previous syllogism it is, therefore, necessary
+to construct. There is, in the long run, only one possible construction.
+The real proof that what is true of John, Peter, &c. is true of all
+mankind, can only be, that a different supposition would be inconsistent
+with the uniformity which we know to exist in the course of nature.
+Whether there would be this inconsistency or not, may be a matter of
+long and delicate inquiry; but unless there would, we have no sufficient
+ground for the major of the inductive syllogism. It hence appears, that
+if we throw the whole course of any inductive argument into a series of
+syllogisms, we shall arrive by more or fewer steps at an ultimate
+syllogism, which will have for its major premise the principle, or
+axiom, of the uniformity of the course of nature.[10]
+
+It was not to be expected that in the case of this axiom, any more than
+of other axioms, there should be unanimity among thinkers with respect
+to the grounds on which it is to be received as true. I have already
+stated that I regard it as itself a generalization from experience.
+Others hold it to be a principle which, antecedently to any verification
+by experience, we are compelled by the constitution of our thinking
+faculty to assume as true. Having so recently, and at so much length,
+combated a similar doctrine as applied to the axioms of mathematics, by
+arguments which are in a great measure applicable to the present case, I
+shall defer the more particular discussion of this controverted point in
+regard to the fundamental axiom of induction, until a more advanced
+period of our inquiry.[11] At present it is of more importance to
+understand thoroughly the import of the axiom itself. For the
+proposition, that the course of nature is uniform, possesses rather the
+brevity suitable to popular, than the precision requisite in
+philosophical language: its terms require to be explained, and a
+stricter than their ordinary signification given to them, before the
+truth of the assertion can be admitted.
+
+
+§ 2. Every person's consciousness assures him that he does not always
+expect uniformity in the course of events; he does not always believe
+that the unknown will be similar to the known, that the future will
+resemble the past. Nobody believes that the succession of rain and fine
+weather will be the same in every future year as in the present. Nobody
+expects to have the same dreams repeated every night. On the contrary,
+everybody mentions it as something extraordinary, if the course of
+nature is constant, and resembles itself, in these particulars. To look
+for constancy where constancy is not to be expected, as for instance
+that a day which has once brought good fortune will always be a
+fortunate day, is justly accounted superstition.
+
+The course of nature, in truth, is not only uniform, it is also
+infinitely various. Some phenomena are always seen to recur in the very
+same combinations in which we met with them at first; others seem
+altogether capricious; while some, which we had been accustomed to
+regard as bound down exclusively to a particular set of combinations, we
+unexpectedly find detached from some of the elements with which we had
+hitherto found them conjoined, and united to others of quite a contrary
+description. To an inhabitant of Central Africa, fifty years ago, no
+fact probably appeared to rest on more uniform experience than this,
+that all human beings are black. To Europeans, not many years ago, the
+proposition, All swans are white, appeared an equally unequivocal
+instance of uniformity in the course of nature. Further experience has
+proved to both that they were mistaken; but they had to wait fifty
+centuries for this experience. During that long time, mankind believed
+in an uniformity of the course of nature where no such uniformity really
+existed.
+
+According to the notion which the ancients entertained of induction, the
+foregoing were cases of as legitimate inference as any inductions
+whatever. In these two instances, in which, the conclusion being false,
+the ground of inference must have been insufficient, there was,
+nevertheless, as much ground for it as this conception of induction
+admitted of. The induction of the ancients has been well described by
+Bacon, under the name of "Inductio per enumerationem simplicem, ubi non
+reperitur instantia contradictoria." It consists in ascribing the
+character of general truths to all propositions which are true in every
+instance that we happen to know of. This is the kind of induction which
+is natural to the mind when unaccustomed to scientific methods. The
+tendency, which some call an instinct, and which others account for by
+association, to infer the future from the past, the known from the
+unknown, is simply a habit of expecting that what has been found true
+once or several times, and never yet found false, will be found true
+again. Whether the instances are few or many, conclusive or
+inconclusive, does not much affect the matter: these are considerations
+which occur only on reflection; the unprompted tendency of the mind is
+to generalize its experience, provided this points all in one direction;
+provided no other experience of a conflicting character comes unsought.
+The notion of seeking it, of experimenting for it, of _interrogating_
+nature (to use Bacon's expression) is of much later growth. The
+observation of nature, by uncultivated intellects, is purely passive:
+they accept the facts which present themselves, without taking the
+trouble of searching for more: it is a superior mind only which asks
+itself what facts are needed to enable it to come to a safe conclusion,
+and then looks out for these.
+
+But though we have always a propensity to generalize from unvarying
+experience, we are not always warranted in doing so. Before we can be at
+liberty to conclude that something is universally true because we have
+never known an instance to the contrary, we must have reason to believe
+that if there were in nature any instances to the contrary, we should
+have known of them. This assurance, in the great majority of cases, we
+cannot have, or can have only in a very moderate degree. The possibility
+of having it, is the foundation on which we shall see hereafter that
+induction by simple enumeration may in some remarkable cases amount
+practically to proof.[12] No such assurance, however, can be had, on any
+of the ordinary subjects of scientific inquiry. Popular notions are
+usually founded on induction by simple enumeration; in science it
+carries us but a little way. We are forced to begin with it; we must
+often rely on it provisionally, in the absence of means of more
+searching investigation. But, for the accurate study of nature, we
+require a surer and a more potent instrument.
+
+It was, above all, by pointing out the insufficiency of this rude and
+loose conception of Induction, that Bacon merited the title so generally
+awarded to him, of Founder of the Inductive Philosophy. The value of his
+own contributions to a more philosophical theory of the subject has
+certainly been exaggerated. Although (along with some fundamental
+errors) his writings contain, more or less fully developed, several of
+the most important principles of the Inductive Method, physical
+investigation has now far outgrown the Baconian conception of Induction.
+Moral and political inquiry, indeed, are as yet far behind that
+conception. The current and approved modes of reasoning on these
+subjects are still of the same vicious description against which Bacon
+protested; the method almost exclusively employed by those professing to
+treat such matters inductively, is the very _inductio per enumerationem
+simplicem_ which he condemns; and the experience which we hear so
+confidently appealed to by all sects, parties, and interests, is still,
+in his own emphatic words, _mera palpatio_.
+
+
+§ 3. In order to a better understanding of the problem which the
+logician must solve if he would establish a scientific theory of
+Induction, let us compare a few cases of incorrect inductions with
+others which are acknowledged to be legitimate. Some, we know, which
+were believed for centuries to be correct, were nevertheless incorrect.
+That all swans are white, cannot have been a good induction, since the
+conclusion has turned out erroneous. The experience, however, on which
+the conclusion rested, was genuine. From the earliest records, the
+testimony of the inhabitants of the known world was unanimous on the
+point. The uniform experience, therefore, of the inhabitants of the
+known world, agreeing in a common result, without one known instance of
+deviation from that result, is not always sufficient to establish a
+general conclusion.
+
+But let us now turn to an instance apparently not very dissimilar to
+this. Mankind were wrong, it seems, in concluding that all swans were
+white: are we also wrong, when we conclude that all men's heads grow
+above their shoulders, and never below, in spite of the conflicting
+testimony of the naturalist Pliny? As there were black swans, though
+civilized people had existed for three thousand years on the earth
+without meeting with them, may there not also be "men whose heads do
+grow beneath their shoulders," notwithstanding a rather less perfect
+unanimity of negative testimony from observers? Most persons would
+answer No; it was more credible that a bird should vary in its colour,
+than that men should vary in the relative position of their principal
+organs. And there is no doubt that in so saying they would be right: but
+to say why they are right, would be impossible, without entering more
+deeply than is usually done, into the true theory of Induction.
+
+Again, there are cases in which we reckon with the most unfailing
+confidence upon uniformity, and other cases in which we do not count
+upon it at all. In some we feel complete assurance that the future will
+resemble the past, the unknown be precisely similar to the known. In
+others, however invariable may be the result obtained from the instances
+which have been observed, we draw from them no more than a very feeble
+presumption that the like result will hold in all other cases. That a
+straight line is the shortest distance between two points, we do not
+doubt to be true even in the region of the fixed stars. When a chemist
+announces the existence and properties of a newly-discovered substance,
+if we confide in his accuracy, we feel assured that the conclusions he
+has arrived at will hold universally, though the induction be founded
+but on a single instance. We do not withhold our assent, waiting for a
+repetition of the experiment; or if we do, it is from a doubt whether
+the one experiment was properly made, not whether if properly made it
+would be conclusive. Here, then, is a general law of nature, inferred
+without hesitation from a single instance; an universal proposition from
+a singular one. Now mark another case, and contrast it with this. Not
+all the instances which have been observed since the beginning of the
+world, in support of the general proposition that all crows are black,
+would be deemed a sufficient presumption of the truth of the
+proposition, to outweigh the testimony of one unexceptionable witness
+who should affirm that in some region of the earth not fully explored,
+he had caught and examined a crow, and had found it to be grey.
+
+Why is a single instance, in some cases, sufficient for a complete
+induction, while in others, myriads of concurring instances, without a
+single exception known or presumed, go such a very little way towards
+establishing an universal proposition? Whoever can answer this question
+knows more of the philosophy of logic than the wisest of the ancients,
+and has solved the problem of induction.
+
+
+
+
+CHAPTER IV.
+
+OF LAWS OF NATURE.
+
+
+§ 1. In the contemplation of that uniformity in the course of nature,
+which is assumed in every inference from experience, one of the first
+observations that present themselves is, that the uniformity in question
+is not properly uniformity, but uniformities. The general regularity
+results from the coexistence of partial regularities. The course of
+nature in general is constant, because the course of each of the various
+phenomena that compose it is so. A certain fact invariably occurs
+whenever certain circumstances are present, and does not occur when they
+are absent; the like is true of another fact; and so on. From these
+separate threads of connexion between parts of the great whole which we
+term nature, a general tissue of connexion unavoidably weaves itself, by
+which the whole is held together. If A is always accompanied by D, B by
+E, and C by F, it follows that A B is accompanied by D E, A C by D F, B
+C by E F, and finally A B C by D E F; and thus the general character of
+regularity is produced, which, along with and in the midst of infinite
+diversity, pervades all nature.
+
+The first point, therefore, to be noted in regard to what is called the
+uniformity of the course of nature, is, that it is itself a complex
+fact, compounded of all the separate uniformities which exist in respect
+to single phenomena. These various uniformities, when ascertained by
+what is regarded as a sufficient induction, we call in common parlance,
+Laws of Nature. Scientifically speaking, that title is employed in a
+more restricted sense, to designate the uniformities when reduced to
+their most simple expression. Thus in the illustration already employed,
+there were seven uniformities; all of which, if considered sufficiently
+certain, would in the more lax application of the term, be called laws
+of nature. But of the seven, three alone are properly distinct and
+independent: these being presupposed, the others follow of course. The
+three first, therefore, according to the stricter acceptation, are
+called laws of nature; the remainder not; because they are in truth mere
+_cases_ of the three first; virtually included in them; said, therefore,
+to _result_ from them: whoever affirms those three has already affirmed
+all the rest.
+
+To substitute real examples for symbolical ones, the following are three
+uniformities, or call them laws of nature: the law that air has weight,
+the law that pressure on a fluid is propagated equally in all
+directions, and the law that pressure in one direction, not opposed by
+equal pressure in the contrary direction, produces motion, which does
+not cease until equilibrium is restored. From these three uniformities
+we should be able to predict another uniformity, namely, the rise of the
+mercury in the Torricellian tube. This, in the stricter use of the
+phrase, is not a law of nature. It is the result of laws of nature. It
+is a _case_ of each and every one of the three laws: and is the only
+occurrence by which they could all be fulfilled. If the mercury were not
+sustained in the barometer, and sustained at such a height that the
+column of mercury were equal in weight to a column of the atmosphere of
+the same diameter; here would be a case, either of the air not pressing
+upon the surface of the mercury with the force which is called its
+weight, or of the downward pressure on the mercury not being propagated
+equally in an upward direction, or of a body pressed in one direction
+and not in the direction opposite, either not moving in the direction in
+which it is pressed, or stopping before it had attained equilibrium. If
+we knew, therefore, the three simple laws, but had never tried the
+Torricellian experiment, we might _deduce_ its result from those laws.
+The known weight of the air, combined with the position of the
+apparatus, would bring the mercury within the first of the three
+inductions; the first induction would bring it within the second, and
+the second within the third, in the manner which we characterized in
+treating of Ratiocination. We should thus come to know the more complex
+uniformity, independently of specific experience, through our knowledge
+of the simpler ones from which it results; though, for reasons which
+will appear hereafter, _verification_ by specific experience would still
+be desirable, and might possibly be indispensable.
+
+Complex uniformities which, like this, are mere cases of simpler ones,
+and have, therefore, been virtually affirmed in affirming those, may
+with propriety be called _laws_, but can scarcely, in the strictness of
+scientific speech, be termed Laws of Nature. It is the custom in
+science, wherever regularity of any kind can be traced, to call the
+general proposition which expresses the nature of that regularity, a
+law; as when, in mathematics, we speak of the law of decrease of the
+successive terms of a converging series. But the expression _law of
+nature_ has generally been employed with a sort of tacit reference to
+the original sense of the word law, namely, the expression of the will
+of a superior. When, therefore, it appeared that any of the uniformities
+which were observed in nature, would result spontaneously from certain
+other uniformities, no separate act of creative will being supposed
+necessary for the production of the derivative uniformities, these have
+not usually been spoken of as laws of nature. According to one mode of
+expression, the question, What are the laws of nature? may be stated
+thus:--What are the fewest and simplest assumptions, which being
+granted, the whole existing order of nature would result? Another mode
+of stating it would be thus: What are the fewest general propositions
+from which all the uniformities which exist in the universe might be
+deductively inferred?
+
+Every great advance which marks an epoch in the progress of science, has
+consisted in a step made towards the solution of this problem. Even a
+simple colligation of inductions already made, without any fresh
+extension of the inductive inference, is already an advance in that
+direction. When Kepler expressed the regularity which exists in the
+observed motions of the heavenly bodies, by the three general
+propositions called his laws, he, in so doing, pointed out three simple
+suppositions which, instead of a much greater number, would suffice to
+construct the whole scheme of the heavenly motions, so far as it was
+known up to that time. A similar and still greater step was made when
+these laws, which at first did not seem to be included in any more
+general truths, were discovered to be cases of the three laws of motion,
+as obtaining among bodies which mutually tend towards one another with a
+certain force, and have had a certain instantaneous impulse originally
+impressed upon them. After this great discovery, Kepler's three
+propositions, though still called laws, would hardly, by any person
+accustomed to use language with precision, be termed laws of nature:
+that phrase would be reserved for the simpler and more general laws into
+which Newton is said to have resolved them.
+
+According to this language, every well-grounded inductive generalization
+is either a law of nature, or a result of laws of nature, capable, if
+those laws are known, of being predicted from them. And the problem of
+Inductive Logic may be summed up in two questions: how to ascertain the
+laws of nature; and how, after having ascertained them, to follow them
+into their results. On the other hand, we must not suffer ourselves to
+imagine that this mode of statement amounts to a real analysis, or to
+anything but a mere verbal transformation of the problem; for the
+expression, Laws of Nature, _means_ nothing but the uniformities which
+exist among natural phenomena (or, in other words, the results of
+induction), when reduced to their simplest expression. It is, however,
+something to have advanced so far, as to see that the study of nature is
+the study of laws, not _a_ law; of uniformities, in the plural number:
+that the different natural phenomena have their separate rules or modes
+of taking place, which, though much intermixed and entangled with one
+another, may, to a certain extent, be studied apart: that (to resume our
+former metaphor) the regularity which exists in nature is a web composed
+of distinct threads, and only to be understood by tracing each of the
+threads separately; for which purpose it is often necessary to unravel
+some portion of the web, and exhibit the fibres apart. The rules of
+experimental inquiry are the contrivances for unravelling the web.
+
+
+§ 2. In thus attempting to ascertain the general order of nature by
+ascertaining the particular order of the occurrence of each one of the
+phenomena of nature, the most scientific proceeding can be no more than
+an improved form of that which was primitively pursued by the human
+understanding, while undirected by science. When mankind first formed
+the idea of studying phenomena according to a stricter and surer method
+than that which they had in the first instance spontaneously adopted,
+they did not, conformably to the well-meant but impracticable precept of
+Descartes, set out from the supposition that nothing had been already
+ascertained. Many of the uniformities existing among phenomena are so
+constant, and so open to observation, as to force themselves upon
+involuntary recognition. Some facts are so perpetually and familiarly
+accompanied by certain others, that mankind learnt, as children learn,
+to expect the one where they found the other, long before they knew how
+to put their expectation into words by asserting, in a proposition, the
+existence of a connexion between those phenomena. No science was needed
+to teach that food nourishes, that water drowns, or quenches thirst,
+that the sun gives light and heat, that bodies fall to the ground. The
+first scientific inquirers assumed these and the like as known truths,
+and set out from them to discover others which were unknown: nor were
+they wrong in so doing, subject, however, as they afterwards began to
+see, to an ulterior revision of these spontaneous generalizations
+themselves, when the progress of knowledge pointed out limits to them,
+or showed their truth to be contingent on some circumstance not
+originally attended to. It will appear, I think, from the subsequent
+part of our inquiry, that there is no logical fallacy in this mode of
+proceeding; but we may see already that any other mode is rigorously
+impracticable: since it is impossible to frame any scientific method of
+induction, or test of the correctness of inductions, unless on the
+hypothesis that some inductions deserving of reliance have been already
+made.
+
+Let us revert, for instance, to one of our former illustrations, and
+consider why it is that, with exactly the same amount of evidence, both
+negative and positive, we did not reject the assertion that there are
+black swans, while we should refuse credence to any testimony which
+asserted that there were men wearing their heads underneath their
+shoulders. The first assertion was more credible than the latter. But
+why more credible? So long as neither phenomenon had been actually
+witnessed, what reason was there for finding the one harder to be
+believed than the other? Apparently because there is less constancy in
+the colours of animals, than in the general structure of their anatomy.
+But how do we know this? Doubtless, from experience. It appears, then,
+that we need experience to inform us, in what degree, and in what cases,
+or sort of cases, experience is to be relied on. Experience must be
+consulted in order to learn from it under what circumstances arguments
+from it will be valid. We have no ulterior test to which we subject
+experience in general; but we make experience its own test. Experience
+testifies, that among the uniformities which it exhibits or seems to
+exhibit, some are more to be relied on than others; and uniformity,
+therefore, may be presumed, from any given number of instances, with a
+greater degree of assurance, in proportion as the case belongs to a
+class in which the uniformities have hitherto been found more uniform.
+
+This mode of correcting one generalization by means of another, a
+narrower generalization by a wider, which common sense suggests and
+adopts in practice, is the real type of scientific Induction. All that
+art can do is but to give accuracy and precision to this process, and
+adapt it to all varieties of cases, without any essential alteration in
+its principle.
+
+There are of course no means of applying such a test as that above
+described, unless we already possess a general knowledge of the
+prevalent character of the uniformities existing throughout nature. The
+indispensable foundation, therefore, of a scientific formula of
+induction, must be a survey of the inductions to which mankind have been
+conducted in unscientific practice; with the special purpose of
+ascertaining what kinds of uniformities have been found perfectly
+invariable, pervading all nature, and what are those which have been
+found to vary with difference of time, place, or other changeable
+circumstances.
+
+
+§ 3. The necessity of such a survey is confirmed by the consideration,
+that the stronger inductions are the touchstone to which we always
+endeavour to bring the weaker. If we find any means of deducing one of
+the less strong inductions from stronger ones, it acquires, at once, all
+the strength of those from which it is deduced; and even adds to that
+strength; since the independent experience on which the weaker induction
+previously rested, becomes additional evidence of the truth of the
+better established law in which it is now found to be included. We may
+have inferred, from historical evidence, that the uncontrolled power of
+a monarch, of an aristocracy, or of the majority, will often be abused:
+but we are entitled to rely on this generalization with much greater
+assurance when it is shown to be a corollary from still better
+established facts; the very low degree of elevation of character ever
+yet attained by the average of mankind, and the little efficacy, for the
+most part, of the modes of education hitherto practised, in maintaining
+the predominance of reason and conscience over the selfish propensities.
+It is at the same time obvious that even these more general facts derive
+an accession of evidence from the testimony which history bears to the
+effects of despotism. The strong induction becomes still stronger when a
+weaker one has been bound up with it.
+
+On the other hand, if an induction conflicts with stronger inductions,
+or with conclusions capable of being correctly deduced from them, then,
+unless on reconsideration it should appear that some of the stronger
+inductions have been expressed with greater universality than their
+evidence warrants, the weaker one must give way. The opinion so long
+prevalent that a comet, or any other unusual appearance in the heavenly
+regions, was the precursor of calamities to mankind, or to those at
+least who witnessed it; the belief in the veracity of the oracles
+of Delphi or Dodona; the reliance on astrology, or on the
+weather-prophecies in almanacs, were doubtless inductions supposed to be
+grounded on experience:[13] and faith in such delusions seems quite
+capable of holding out against a great multitude of failures, provided
+it be nourished by a reasonable number of casual coincidences between
+the prediction and the event. What has really put an end to these
+insufficient inductions, is their inconsistency with the stronger
+inductions subsequently obtained by scientific inquiry, respecting the
+causes on which terrestrial events really depend; and where those
+scientific truths have not yet penetrated, the same or similar delusions
+still prevail.
+
+It may be affirmed as a general principle, that all inductions, whether
+strong or weak, which can be connected by ratiocination, are
+confirmatory of one another; while any which lead deductively to
+consequences that are incompatible, become mutually each other's test,
+showing that one or other must be given up, or at least more guardedly
+expressed. In the case of inductions which confirm each other, the one
+which becomes a conclusion from ratiocination rises to at least the
+level of certainty of the weakest of those from which it is deduced;
+while in general all are more or less increased in certainty. Thus the
+Torricellian experiment, though a mere case of three more general laws,
+not only strengthened greatly the evidence on which those laws rested,
+but converted one of them (the weight of the atmosphere) from a doubtful
+generalization into a completely established doctrine.
+
+If, then, a survey of the uniformities which have been ascertained to
+exist in nature, should point out some which, as far as any human
+purpose requires certainty, may be considered quite certain and quite
+universal; then by means of these uniformities we may be able to raise
+multitudes of other inductions to the same point in the scale. For if we
+can show, with respect to any inductive inference, that either it must
+be true, or one of these certain and universal inductions must admit of
+an exception; the former generalization will attain the same certainty,
+and indefeasibleness within the bounds assigned to it, which are the
+attributes of the latter. It will be proved to be a law; and if not a
+result of other and simpler laws, it will be a law of nature.
+
+There are such certain and universal inductions; and it is because there
+are such, that a Logic of Induction is possible.
+
+
+
+
+CHAPTER V.
+
+OF THE LAW OF UNIVERSAL CAUSATION.
+
+
+§ 1. The phenomena of nature exist in two distinct relations to one
+another; that of simultaneity, and that of succession. Every phenomenon
+is related, in an uniform manner, to some phenomena that coexist with
+it, and to some that have preceded and will follow it.
+
+Of the uniformities which exist among synchronous phenomena, the most
+important, on every account, are the laws of number; and next to them
+those of space, or, in other words, of extension and figure. The laws of
+number are common to synchronous and successive phenomena. That two and
+two make four, is equally true whether the second two follow the first
+two or accompany them. It is as true of days and years as of feet and
+inches. The laws of extension and figure (in other words, the theorems
+of geometry, from its lowest to its highest branches) are, on the
+contrary, laws of simultaneous phenomena only. The various parts of
+space, and of the objects which are said to fill space, coexist; and the
+unvarying laws which are the subject of the science of geometry, are an
+expression of the mode of their coexistence.
+
+This is a class of laws, or in other words, of uniformities, for the
+comprehension and proof of which it is not necessary to suppose any
+lapse of time, any variety of facts or events succeeding one another. If
+all the objects in the universe were unchangeably fixed, and had
+remained in that condition from eternity, the propositions of geometry
+would still be true of those objects. All things which possess
+extension, or, in other words, which fill space, are subject to
+geometrical laws. Possessing extension, they possess figure; possessing
+figure, they must possess some figure in particular, and have all the
+properties which geometry assigns to that figure. If one body be a
+sphere and another a cylinder, of equal height and diameter, the one
+will be exactly two-thirds of the other, let the nature and quality of
+the material be what it will. Again, each body, and each point of a
+body, must occupy some place or position among other bodies; and the
+position of two bodies relatively to each other, of whatever nature the
+bodies be, may be unerringly inferred from the position of each of them
+relatively to any third body.
+
+In the laws of number, then, and in those of space, we recognise in the
+most unqualified manner, the rigorous universality of which we are in
+quest. Those laws have been in all ages the type of certainty, the
+standard of comparison for all inferior degrees of evidence. Their
+invariability is so perfect, that it renders us unable even to conceive
+any exception to them; and philosophers have been led, though (as I have
+endeavoured to show) erroneously, to consider their evidence as lying
+not in experience, but in the original constitution of the intellect. If
+therefore, from the laws of space and number, we were able to deduce
+uniformities of any other description, this would be conclusive evidence
+to us that those other uniformities possessed the same rigorous
+certainty. But this we cannot do. From laws of space and number alone,
+nothing can be deduced but laws of space and number.
+
+Of all truths relating to phenomena, the most valuable to us are those
+which relate to the order of their succession. On a knowledge of these
+is founded every reasonable anticipation of future facts, and whatever
+power we possess of influencing those facts to our advantage. Even the
+laws of geometry are chiefly of practical importance to us as being a
+portion of the premises from which the order of the succession of
+phenomena may be inferred. Inasmuch as the motion of bodies, the action
+of forces, and the propagation of influences of all sorts, take place in
+certain lines and over definite spaces, the properties of those lines
+and spaces are an important part of the laws to which those phenomena
+are themselves subject. Again, motions, forces or other influences, and
+times, are numerable quantities; and the properties of number are
+applicable to them as to all other things. But though the laws of number
+and space are important elements in the ascertainment of uniformities
+of succession, they can do nothing towards it when taken by themselves.
+They can only be made instrumental to that purpose when we combine with
+them additional premises, expressive of uniformities of succession
+already known. By taking, for instance, as premises these propositions,
+that bodies acted upon by an instantaneous force move with uniform
+velocity in straight lines; that bodies acted upon by a continuous force
+move with accelerated velocity in straight lines; and that bodies acted
+upon by two forces in different directions move in the diagonal of a
+parallelogram, whose sides represent the direction and quantity of those
+forces; we may by combining these truths with propositions relating to
+the properties of straight lines and of parallelograms, (as that a
+triangle is half a parallelogram of the same base and altitude,) deduce
+another important uniformity of succession, viz., that a body moving
+round a centre of force describes areas proportional to the times. But
+unless there had been laws of succession in our premises, there could
+have been no truths of succession in our conclusions. A similar remark
+might be extended to every other class of phenomena really peculiar;
+and, had it been attended to, would have prevented many chimerical
+attempts at demonstrations of the indemonstrable, and explanations which
+do not explain.
+
+It is not, therefore, enough for us that the laws of space, which are
+only laws of simultaneous phenomena, and the laws of number, which
+though true of successive phenomena do not relate to their succession,
+possess the rigorous certainty and universality of which we are in
+search. We must endeavour to find some law of succession which has those
+same attributes, and is therefore fit to be made the foundation of
+processes for discovering, and of a test for verifying, all other
+uniformities of succession. This fundamental law must resemble the
+truths of geometry in their most remarkable peculiarity, that of never
+being, in any instance whatever, defeated or suspended by any change of
+circumstances.
+
+Now among all those uniformities in the succession of phenomena, which
+common observation is sufficient to bring to light, there are very few
+which have any, even apparent, pretension to this rigorous
+indefeasibility: and of those few, one only has been found capable of
+completely sustaining it. In that one, however, we recognise a law which
+is universal also in another sense; it is coextensive with the entire
+field of successive phenomena, all instances whatever of succession
+being examples of it. This law is the Law of Causation. The truth that
+every fact which has a beginning has a cause, is coextensive with human
+experience.
+
+This generalization may appear to some minds not to amount to much,
+since after all it asserts only this: "it is a law; that every event
+depends on some law:" "it is a law, that there is a law for everything."
+We must not, however, conclude that the generality of the principle is
+merely verbal; it will be found on inspection to be no vague or
+unmeaning assertion, but a most important and really fundamental truth.
+
+
+§ 2. The notion of Cause being the root of the whole theory of
+Induction, it is indispensable that this idea should, at the very outset
+of our inquiry, be, with the utmost practicable degree of precision,
+fixed and determined. If, indeed, it were necessary for the purpose of
+inductive logic that the strife should be quelled, which has so long
+raged among the different schools of metaphysicians, respecting the
+origin and analysis of our idea of causation; the promulgation, or at
+least the general reception, of a true theory of induction, might be
+considered desperate for a long time to come. But the science of the
+Investigation of Truth by means of Evidence, is happily independent of
+many of the controversies which perplex the science of the ultimate
+constitution of the human mind, and is under no necessity of pushing the
+analysis of mental phenomena to that extreme limit which alone ought to
+satisfy a metaphysician.
+
+I premise, then, that when in the course of this inquiry I speak of the
+cause of any phenomenon, I do not mean a cause which is not itself a
+phenomenon; I make no research into the ultimate or ontological cause of
+anything. To adopt a distinction familiar in the writings of the Scotch
+metaphysicians, and especially of Reid, the causes with which I concern
+myself are not _efficient_, but _physical_ causes. They are causes in
+that sense alone, in which one physical fact is said to be the cause of
+another. Of the efficient causes of phenomena, or whether any such
+causes exist at all, I am not called upon to give an opinion. The notion
+of causation is deemed, by the schools of metaphysics most in vogue at
+the present moment, to imply a mysterious and most powerful tie, such as
+cannot, or at least does not, exist between any physical fact and that
+other physical fact on which it is invariably consequent, and which is
+popularly termed its cause: and thence is deduced the supposed necessity
+of ascending higher, into the essences and inherent constitution of
+things, to find the true cause, the cause which is not only followed by,
+but actually produces, the effect. No such necessity exists for the
+purposes of the present inquiry, nor will any such doctrine be found in
+the following pages. The only notion of a cause, which the theory of
+induction requires, is such a notion as can be gained from experience.
+The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it; independently of all
+consideration respecting the ultimate mode of production of phenomena,
+and of every other question regarding the nature of "Things in
+themselves."
+
+Between the phenomena, then, which exist at any instant, and the
+phenomena which exist at the succeeding instant, there is an invariable
+order of succession; and, as we said in speaking of the general
+uniformity of the course of nature, this web is composed of separate
+fibres; this collective order is made up of particular sequences,
+obtaining invariably among the separate parts. To certain facts, certain
+facts always do, and, as we believe, will continue to, succeed. The
+invariable antecedent is termed the cause; the invariable consequent,
+the effect. And the universality of the law of causation consists in
+this, that every consequent is connected in this manner with some
+particular antecedent, or set of antecedents. Let the fact be what it
+may, if it has begun to exist, it was preceded by some fact or facts,
+with which it is invariably connected. For every event there exists some
+combination of objects or events, some given concurrence of
+circumstances, positive and negative, the occurrence of which is always
+followed by that phenomenon. We may not have found out what this
+concurrence of circumstances may be; but we never doubt that there is
+such a one, and that it never occurs without having the phenomenon in
+question as its effect or consequence. On the universality of this truth
+depends the possibility of reducing the inductive process to rules. The
+undoubted assurance we have that there is a law to be found if we only
+knew how to find it, will be seen presently to be the source from which
+the canons of the Inductive Logic derive their validity.
+
+
+§ 3. It is seldom, if ever, between a consequent and a single
+antecedent, that this invariable sequence subsists. It is usually
+between a consequent and the sum of several antecedents; the concurrence
+of all of them being requisite to produce, that is, to be certain of
+being followed by, the consequent. In such cases it is very common to
+single out one only of the antecedents under the denomination of Cause,
+calling the others merely Conditions. Thus, if a person eats of a
+particular dish, and dies in consequence, that is, would not have died
+if he had not eaten of it, people would be apt to say that eating of
+that dish was the cause of his death. There needs not, however, be any
+invariable connexion between eating of the dish and death; but there
+certainly is, among the circumstances which took place, some combination
+or other on which death is invariably consequent: as, for instance, the
+act of eating of the dish, combined with a particular bodily
+constitution, a particular state of present health, and perhaps even a
+certain state of the atmosphere; the whole of which circumstances
+perhaps constituted in this particular case the _conditions_ of the
+phenomenon, or, in other words, the set of antecedents which determined
+it, and but for which it would not have happened. The real Cause, is the
+whole of these antecedents; and we have, philosophically speaking, no
+right to give the name of cause to one of them, exclusively of the
+others. What, in the case we have supposed, disguises the incorrectness
+of the expression, is this: that the various conditions, except the
+single one of eating the food, were not _events_ (that is, instantaneous
+changes, or successions of instantaneous changes) but _states_,
+possessing more or less of permanency; and might therefore have preceded
+the effect by an indefinite length of duration, for want of the event
+which was requisite to complete the required concurrence of conditions:
+while as soon as that event, eating the food, occurs, no other cause is
+waited for, but the effect begins immediately to take place: and hence
+the appearance is presented of a more immediate and close connexion
+between the effect and that one antecedent, than between the effect and
+the remaining conditions. But though we may think proper to give the
+name of cause to that one condition, the fulfilment of which completes
+the tale, and brings about the effect without further delay; this
+condition has really no closer relation to the effect than any of the
+other conditions has. The production of the consequent required that
+they should all _exist_ immediately previous, though not that they
+should all _begin_ to exist immediately previous. The statement of the
+cause is incomplete, unless in some shape or other we introduce all the
+conditions. A man takes mercury, goes out of doors, and catches cold. We
+say, perhaps, that the cause of his taking cold was exposure to the air.
+It is clear, however, that his having taken mercury may have been a
+necessary condition of catching cold; and though it might consist with
+usage to say that the cause of his attack was exposure to the air, to be
+accurate we ought to say that the cause was exposure to the air while
+under the effect of mercury.
+
+If we do not, when aiming at accuracy, enumerate all the conditions, it
+is only because some of them will in most cases be understood without
+being expressed, or because for the purpose in view they may without
+detriment be overlooked. For example, when we say, the cause of a man's
+death was that his foot slipped in climbing a ladder, we omit as a
+thing unnecessary to be stated the circumstance of his weight, though
+quite as indispensable a condition of the effect which took place. When
+we say that the assent of the crown to a bill makes it law, we mean that
+the assent, being never given until all the other conditions are
+fulfilled, makes up the sum of the conditions, though no one now regards
+it as the principal one. When the decision of a legislative assembly has
+been determined by the casting vote of the chairman, we sometimes say
+that this one person was the cause of all the effects which resulted
+from the enactment. Yet we do not really suppose that his single vote
+contributed more to the result than that of any other person who voted
+in the affirmative; but, for the purpose we have in view, which is to
+insist on his individual responsibility, the part which any other person
+had in the transaction is not material.
+
+In all these instances the fact which was dignified with the name of
+cause, was the one condition which came last into existence. But it must
+not be supposed that in the employment of the term this or any other
+rule is always adhered to. Nothing can better show the absence of any
+scientific ground for the distinction between the cause of a phenomenon
+and its conditions, than the capricious manner in which we select from
+among the conditions that which we choose to denominate the cause.
+However numerous the conditions may be, there is hardly any of them
+which may not, according to the purpose of our immediate discourse,
+obtain that nominal pre-eminence. This will be seen by analysing the
+conditions of some one familiar phenomenon. For example, a stone thrown
+into water falls to the bottom. What are the conditions of this event?
+In the first place there must be a stone, and water, and the stone must
+be thrown into the water; but these suppositions forming part of the
+enunciation of the phenomenon itself, to include them also among the
+conditions would be a vicious tautology; and this class of conditions,
+therefore, have never received the name of cause from any but the
+Aristotelians, by whom they were called the _material_ cause, _causa
+materialis_. The next condition is, there must be an earth: and
+accordingly it is often said, that the fall of a stone is caused by the
+earth; or by a power or property of the earth, or a force exerted by the
+earth, all of which are merely roundabout ways of saying that it is
+caused by the earth; or, lastly, the earth's attraction; which also is
+only a technical mode of saying that the earth causes the motion, with
+the additional particularity that the motion is towards the earth, which
+is not a character of the cause, but of the effect. Let us now pass to
+another condition. It is not enough that the earth should exist; the
+body must be within that distance from it, in which the earth's
+attraction preponderates over that of any other body. Accordingly we may
+say, and the expression would be confessedly correct, that the cause of
+the stone's falling is its being _within the sphere_ of the earth's
+attraction. We proceed to a further condition. The stone is immersed in
+water: it is therefore a condition of its reaching the ground, that its
+specific gravity exceed that of the surrounding fluid, or in other words
+that it surpass in weight an equal volume of water. Accordingly any one
+would be acknowledged to speak correctly who said, that the cause of the
+stone's going to the bottom is its exceeding in specific gravity the
+fluid in which it is immersed.
+
+Thus we see that each and every condition of the phenomenon may be taken
+in its turn, and, with equal propriety in common parlance, but with
+equal impropriety in scientific discourse, may be spoken of as if it
+were the entire cause. And in practice, that particular condition is
+usually styled the cause, whose share in the matter is superficially the
+most conspicuous, or whose requisiteness to the production of the effect
+we happen to be insisting on at the moment. So great is the force of
+this last consideration, that it sometimes induces us to give the name
+of cause even to one of the negative conditions. We say, for example,
+The army was surprised because the sentinel was off his post. But since
+the sentinel's absence was not what created the enemy, or put the
+soldiers asleep, how did it cause them to be surprised? All that is
+really meant is, that the event would not have happened if he had been
+at his duty. His being off his post was no producing cause, but the mere
+absence of a preventing cause: it was simply equivalent to his
+non-existence. From nothing, from a mere negation, no consequences can
+proceed. All effects are connected, by the law of causation, with some
+set of _positive_ conditions; negative ones, it is true, being almost
+always required in addition. In other words, every fact or phenomenon
+which has a beginning, invariably arises when some certain combination
+of positive facts exists, provided certain other positive facts do not
+exist.
+
+There is, no doubt, a tendency (which our first example, that of death
+from taking a particular food, sufficiently illustrates) to associate
+the idea of causation with the proximate antecedent _event_, rather than
+with any of the antecedent _states_, or permanent facts, which may
+happen also to be conditions of the phenomenon; the reason being that
+the event not only exists, but begins to exist immediately previous;
+while the other conditions may have pre-existed for an indefinite time.
+And this tendency shows itself very visibly in the different logical
+fictions which are resorted to, even by men of science, to avoid the
+necessity of giving the name of cause to anything which had existed for
+an indeterminate length of time before the effect. Thus, rather than say
+that the earth causes the fall of bodies, they ascribe it to a _force_
+exerted by the earth, or an _attraction_ by the earth, abstractions
+which they can represent to themselves as exhausted by each effort, and
+therefore constituting at each successive instant a fresh fact,
+simultaneous with, or only immediately preceding, the effect. Inasmuch
+as the coming of the circumstance which completes the assemblage of
+conditions, is a change or event, it thence happens that an event is
+always the antecedent in closest apparent proximity to the consequent:
+and this may account for the illusion which disposes us to look upon the
+proximate event as standing more peculiarly in the position of a cause
+than any of the antecedent states. But even this peculiarity, of being
+in closer proximity to the effect than any other of its conditions, is,
+as we have already seen, far from being necessary to the common notion
+of a cause; with which notion, on the contrary, any one of the
+conditions, either positive or negative, is found, on occasion,
+completely to accord.[14]
+
+The cause, then, philosophically speaking, is the sum total of the
+conditions, positive and negative taken together; the whole of the
+contingencies of every description, which being realized, the consequent
+invariably follows. The negative conditions, however, of any
+phenomenon, a special enumeration of which would generally be very
+prolix, may be all summed up under one head, namely, the absence of
+preventing or counteracting causes. The convenience of this mode of
+expression is mainly grounded on the fact, that the effects of any cause
+in counteracting another cause may in most cases be, with strict
+scientific exactness, regarded as a mere extension of its own proper and
+separate effects. If gravity retards the upward motion of a projectile,
+and deflects it into a parabolic trajectory, it produces, in so doing,
+the very same kind of effect, and even (as mathematicians know) the
+same quantity of effect, as it does in its ordinary operation of causing
+the fall of bodies when simply deprived of their support. If an alkaline
+solution mixed with an acid destroys its sourness, and prevents it from
+reddening vegetable blues, it is because the specific effect of the
+alkali is to combine with the acid, and form a compound with totally
+different qualities. This property, which causes of all descriptions
+possess, of preventing the effects of other causes by virtue (for the
+most part) of the same laws according to which they produce their
+own,[15] enables us, by establishing the general axiom that all causes
+are liable to be counteracted in their effects by one another, to
+dispense with the consideration of negative conditions entirely, and
+limit the notion of cause to the assemblage of the positive conditions
+of the phenomenon: one negative condition invariably understood, and the
+same in all instances (namely, the absence of counteracting causes)
+being sufficient, along with the sum of the positive conditions, to make
+up the whole set of circumstances on which the phenomenon is dependent.
+
+
+§ 4. Among the positive conditions, as we have seen that there are some
+to which, in common parlance, the term cause is more readily and
+frequently awarded, so there are others to which it is, in ordinary
+circumstances, refused. In most cases of causation a distinction is
+commonly drawn between something which acts, and some other thing which
+is acted upon; between an _agent_ and a _patient_. Both of these, it
+would be universally allowed, are conditions of the phenomenon; but it
+would be thought absurd to call the latter the cause, that title being
+reserved for the former. The distinction, however, vanishes on
+examination, or rather is found to be only verbal; arising from an
+incident of mere expression, namely, that the object said to be acted
+upon, and which is considered as the scene in which the effect takes
+place, is commonly included in the phrase by which the effect is spoken
+of, so that if it were also reckoned as part of the cause, the seeming
+incongruity would arise of its being supposed to cause itself. In the
+instance which we have already had, of falling bodies, the question was
+thus put: What is the cause which makes a stone fall? and if the answer
+had been "the stone itself," the expression would have been in apparent
+contradiction to the meaning of the word cause. The stone, therefore, is
+conceived as the patient, and the earth (or, according to the common and
+most unphilosophical practice, some occult quality of the earth) is
+represented as the agent or cause. But that there is nothing fundamental
+in the distinction may be seen from this, that it is quite possible to
+conceive the stone as causing its own fall, provided the language
+employed be such as to save the mere verbal incongruity. We might say
+that the stone moves towards the earth by the properties of the matter
+composing it; and according to this mode of presenting the phenomenon,
+the stone itself might without impropriety be called the agent; though,
+to save the established doctrine of the inactivity of matter, men
+usually prefer here also to ascribe the effect to an occult quality, and
+say that the cause is not the stone itself, but the _weight_ or
+_gravitation_ of the stone.
+
+Those who have contended for a radical distinction between agent and
+patient, have generally conceived the agent as that which causes some
+state of, or some change in the state of, another object which is called
+the patient. But a little reflection will show that the licence we
+assume of speaking of phenomena as _states_ of the various objects which
+take part in them, (an artifice of which so much use has been made by
+some philosophers, Brown in particular, for the apparent explanation of
+phenomena,) is simply a sort of logical fiction, useful sometimes as one
+among several modes of expression, but which should never be supposed to
+be the enunciation of a scientific truth. Even those attributes of an
+object which might seem with greatest propriety to be called states of
+the object itself, its sensible qualities, its colour, hardness, shape,
+and the like, are in reality (as no one has pointed out more clearly
+than Brown himself) phenomena of causation, in which the substance is
+distinctly the agent, or producing cause, the patient being our own
+organs, and those of other sentient beings. What we call states of
+objects, are always sequences into which the objects enter, generally as
+antecedents or causes; and things are never more active than in the
+production of those phenomena in which they are said to be acted upon.
+Thus, in the example of a stone falling to the earth, according to the
+theory of gravitation the stone is as much an agent as the earth, which
+not only attracts, but is itself attracted by, the stone. In the case of
+a sensation produced in our organs, the laws of our organization, and
+even those of our minds, are as directly operative in determining the
+effect produced, as the laws of the outward object. Though we call
+prussic acid the agent of a person's death, the whole of the vital and
+organic properties of the patient are as actively instrumental as the
+poison, in the chain of effects which so rapidly terminates his sentient
+existence. In the process of education, we may call the teacher the
+agent, and the scholar only the material acted upon; yet in truth all
+the facts which pre-existed in the scholar's mind exert either
+co-operating or counteracting agencies in relation to the teacher's
+efforts. It is not light alone which is the agent in vision, but light
+coupled with the active properties of the eye and brain, and with those
+of the visible object. The distinction between agent and patient is
+merely verbal: patients are always agents; in a great proportion,
+indeed, of all natural phenomena, they are so to such a degree as to
+react forcibly on the causes which acted upon them: and even when this
+is not the case, they contribute, in the same manner as any of the other
+conditions, to the production of the effect of which they are vulgarly
+treated as the mere theatre. All the positive conditions of a phenomenon
+are alike agents, alike active; and in any expression of the cause which
+professes to be complete, none of them can with reason be excluded,
+except such as have already been implied in the words used for
+describing the effect; nor by including even these would there be
+incurred any but a merely verbal impropriety.
+
+
+§ 5. It now remains to advert to a distinction which is of first-rate
+importance both for clearing up the notion of cause, and for obviating a
+very specious objection often made against the view which we have taken
+of the subject.
+
+When we define the cause of anything (in the only sense in which the
+present inquiry has any concern with causes) to be "the antecedent which
+it invariably follows," we do not use this phrase as exactly synonymous
+with "the antecedent which it invariably _has_ followed in our past
+experience." Such a mode of conceiving causation would be liable to the
+objection very plausibly urged by Dr. Reid, namely, that according to
+this doctrine night must be the cause of day, and day the cause of
+night; since these phenomena have invariably succeeded one another from
+the beginning of the world. But it is necessary to our using the word
+cause, that we should believe not only that the antecedent always _has_
+been followed by the consequent, but that, as long as the present
+constitution of things[16] endures, it always _will_ be so. And this
+would not be true of day and night. We do not believe that night will be
+followed by day under all imaginable circumstances, but only that it
+will be so _provided_ the sun rises above the horizon. If the sun ceased
+to rise, which, for aught we know, may be perfectly compatible with the
+general laws of matter, night would be, or might be, eternal. On the
+other hand, if the sun is above the horizon, his light not extinct, and
+no opaque body between us and him, we believe firmly that unless a
+change takes place in the properties of matter, this combination of
+antecedents will be followed by the consequent, day; that if the
+combination of antecedents could be indefinitely prolonged, it would be
+always day; and that if the same combination had always existed, it
+would always have been day, quite independently of night as a previous
+condition. Therefore is it that we do not call night the cause, nor even
+a condition, of day. The existence of the sun (or some such luminous
+body), and there being no opaque medium in a straight line[17] between
+that body and the part of the earth where we are situated, are the sole
+conditions; and the union of these, without the addition of any
+superfluous circumstance, constitutes the cause. This is what writers
+mean when they say that the notion of cause involves the idea of
+necessity. If there be any meaning which confessedly belongs to the term
+necessity, it is _unconditionalness_. That which is necessary, that
+which _must_ be, means that which will be, whatever supposition we may
+make in regard to all other things. The succession of day and night
+evidently is not necessary in this sense. It is conditional on the
+occurrence of other antecedents. That which will be followed by a given
+consequent when, and only when, some third circumstance also exists, is
+not the cause, even though no case should ever have occurred in which
+the phenomenon took place without it.
+
+Invariable sequence, therefore, is not synonymous with causation, unless
+the sequence, besides being invariable, is unconditional. There are
+sequences, as uniform in past experience as any others whatever, which
+yet we do not regard as cases of causation, but as conjunctions in some
+sort accidental. Such, to an accurate thinker, is that of day and night.
+The one might have existed for any length of time, and the other not
+have followed the sooner for its existence; it follows only if certain
+other antecedents exist; and where those antecedents existed, it would
+follow in any case. No one, probably, ever called night the cause of
+day; mankind must so soon have arrived at the very obvious
+generalization, that the state of general illumination which we call day
+would follow from the presence of a sufficiently luminous body, whether
+darkness had preceded or not.
+
+We may define, therefore, the cause of a phenomenon, to be the
+antecedent, or the concurrence of antecedents, on which it is invariably
+and _unconditionally_ consequent. Or if we adopt the convenient
+modification of the meaning of the word cause, which confines it to the
+assemblage of positive conditions without the negative, then instead of
+"unconditionally," we must say, "subject to no other than negative
+conditions."
+
+To some it may appear, that the sequence between night and day being
+invariable in our experience, we have as much ground in this case as
+experience can give in any case, for recognising the two phenomena as
+cause and effect; and that to say that more is necessary--to require a
+belief that the succession is unconditional, or in other words that it
+would be invariable under all changes of circumstances, is to
+acknowledge in causation an element of belief not derived from
+experience. The answer to this is, that it is experience itself which
+teaches us that one uniformity of sequence is conditional and another
+unconditional. When we judge that the succession of night and day is a
+derivative sequence, depending on something else, we proceed on grounds
+of experience. It is the evidence of experience which convinces us that
+day could equally exist without being followed by night, and that night
+could equally exist without being followed by day. To say that these
+beliefs are "not generated by our mere observation of sequence,"[18] is
+to forget that twice in every twenty-four hours, when the sky is clear,
+we have an _experimentum crucis_ that the cause of day is the sun. We
+have an experimental knowledge of the sun which justifies us on
+experimental grounds in concluding, that if the sun were always above
+the horizon there would be day, though there had been no night, and that
+if the sun were always below the horizon there would be night, though
+there had been no day. We thus know from experience that the succession
+of night and day is not unconditional. Let me add, that the antecedent
+which is only conditionally invariable, is not the invariable
+antecedent. Though a fact may, in experience, have always been followed
+by another fact, yet if the remainder of our experience teaches us that
+it might not always be so followed, or if the experience itself is such
+as leaves room for a possibility that the known cases may not correctly
+represent all possible cases, the hitherto invariable antecedent is not
+accounted the cause; but why? Because we are not sure that it _is_ the
+invariable antecedent.
+
+Such cases of sequence as that of day and night not only do not
+contradict the doctrine which resolves causation into invariable
+sequence, but are necessarily implied in that doctrine. It is evident,
+that from a limited number of unconditional sequences, there will
+result a much greater number of conditional ones. Certain causes being
+given, that is, certain antecedents which are unconditionally followed
+by certain consequents; the mere coexistence of these causes will give
+rise to an unlimited number of additional uniformities. If two causes
+exist together, the effects of both will exist together; and if many
+causes coexist, these causes (by what we shall term hereafter the
+intermixture of their laws) will give rise to new effects, accompanying
+or succeeding one another in some particular order, which order will be
+invariable while the causes continue to coexist, but no longer. The
+motion of the earth in a given orbit round the sun, is a series of
+changes which follow one another as antecedents and consequents, and
+will continue to do so while the sun's attraction, and the force with
+which the earth tends to advance in a direct line through space,
+continue to coexist in the same quantities as at present. But vary
+either of these causes, and this particular succession of motions would
+cease to take place. The series of the earth's motions, therefore,
+though a case of sequence invariable within the limits of human
+experience, is not a case of causation. It is not unconditional.
+
+This distinction between the relations of succession which so far as we
+know are unconditional, and those relations, whether of succession or of
+coexistence, which, like the earth's motions, or the succession of day
+and night, depend on the existence or on the coexistence of other
+antecedent facts--corresponds to the great division which Dr. Whewell
+and other writers have made of the field of science, into the
+investigation of what they term the Laws of Phenomena, and the
+investigation of causes; a phraseology, as I conceive, not
+philosophically sustainable, inasmuch as the ascertainment of causes,
+such causes as the human faculties can ascertain, namely, causes which
+are themselves phenomena, is, therefore, merely the ascertainment of
+other and more universal Laws of Phenomena. And let me here observe,
+that Dr. Whewell, and in some degree even Sir John Herschel, seem to
+have misunderstood the meaning of those writers who, like M. Comte,
+limit the sphere of scientific investigation to Laws of Phenomena, and
+speak of the inquiry into causes as vain and futile. The causes which M.
+Comte designates as inaccessible, are efficient causes. The
+investigation of physical, as opposed to efficient, causes (including
+the study of all the active forces in Nature, considered as facts of
+observation) is as important a part of M. Comte's conception of science
+as of Dr. Whewell's. His objection to the _word_ cause is a mere matter
+of nomenclature, in which, as a matter of nomenclature, I consider him
+to be entirely wrong. "Those," it is justly remarked by Mr. Bailey,[19]
+"who, like M. Comte, object to designate _events_ as causes, are
+objecting without any real ground to a mere but extremely convenient
+generalization, to a very useful common name, the employment of which
+involves, or needs involve, no particular theory." To which it may be
+added, that by rejecting this form of expression, M. Comte leaves
+himself without any term for marking a distinction which, however
+incorrectly expressed, is not only real, but is one of the fundamental
+distinctions in science; indeed it is on this alone, as we shall
+hereafter find, that the possibility rests of framing a rigorous Canon
+of Induction. And as things left without a name are apt to be forgotten,
+a Canon of that description is not one of the many benefits which the
+philosophy of Induction has received from M. Comte's great powers.
+
+
+§ 6. Does a cause always stand with its effect in the relation of
+antecedent and consequent? Do we not often say of two simultaneous facts
+that they are cause and effect--as when we say that fire is the cause of
+warmth, the sun and moisture the cause of vegetation, and the like?
+Since a cause does not necessarily perish because its effect has been
+produced, the two things do very generally coexist; and there are some
+appearances, and some common expressions, seeming to imply not only that
+causes may, but that they must, be contemporaneous with their effects.
+_Cessante causâ cessat et effectus_, has been a dogma of the schools:
+the necessity for the continued existence of the cause in order to the
+continuance of the effect, seems to have been once a generally received
+doctrine. Kepler's numerous attempts to account for the motions of the
+heavenly bodies on mechanical principles, were rendered abortive by his
+always supposing that the agency which set those bodies in motion must
+continue to operate in order to keep up the motion which it at first
+produced. Yet there were at all times many familiar instances of the
+continuance of effects, long after their causes had ceased. A _coup de
+soleil_ gives a person a brain fever: will the fever go off as soon as
+he is moved out of the sunshine? A sword is run through his body: must
+the sword remain in his body in order that he may continue dead? A
+ploughshare once made, remains a ploughshare, without any continuance of
+heating and hammering, and even after the man who heated and hammered it
+has been gathered to his fathers. On the other hand, the pressure which
+forces up the mercury in an exhausted tube must be continued in order to
+sustain it in the tube. This (it may be replied) is because another
+force is acting without intermission, the force of gravity, which would
+restore it to its level, unless counterpoised by a force equally
+constant. But again; a tight bandage causes pain, which pain will
+sometimes go off as soon as the bandage is removed. The illumination
+which the sun diffuses over the earth ceases when the sun goes down.
+
+There is, therefore, a distinction to be drawn. The conditions which are
+necessary for the first production of a phenomenon, are occasionally
+also necessary for its continuance; though more commonly its continuance
+requires no condition except negative ones. Most things, once produced,
+continue as they are, until something changes or destroys them; but some
+require the permanent presence of the agencies which produced them at
+first. These may, if we please, be considered as instantaneous
+phenomena, requiring to be renewed at each instant by the cause by which
+they were at first generated. Accordingly, the illumination of any given
+point of space has always been looked upon as an instantaneous fact,
+which perishes and is perpetually renewed as long as the necessary
+conditions subsist. If we adopt this language we avoid the necessity of
+admitting that the continuance of the cause is ever required to maintain
+the effect. We may say, it is not required to maintain, but to
+reproduce, the effect, or else to counteract some force tending to
+destroy it. And this may be a convenient phraseology. But it is only a
+phraseology. The fact remains, that in some cases (though these are a
+minority) the continuance of the conditions which produced an effect is
+necessary to the continuance of the effect.
+
+As to the ulterior question, whether it is strictly necessary that the
+cause, or assemblage of conditions, should precede, by ever so short an
+instant, the production of the effect, (a question raised and argued
+with much ingenuity by Sir John Herschel in an Essay already
+quoted,[20]) the inquiry is of no consequence for our present purpose.
+There certainly are cases in which the effect follows without any
+interval perceptible by our faculties: and when there is an interval, we
+cannot tell by how many intermediate links imperceptible to us that
+interval may really be filled up. But even granting that an effect may
+commence simultaneously with its cause, the view I have taken of
+causation is in no way practically affected. Whether the cause and its
+effect be necessarily successive or not, the beginning of a phenomenon
+is what implies a cause, and causation is the law of the succession of
+phenomena. If these axioms be granted, we can afford, though I see no
+necessity for doing so, to drop the words antecedent and consequent as
+applied to cause and effect. I have no objection to define a cause, the
+assemblage of phenomena, which occurring, some other phenomenon
+invariably commences, or has its origin. Whether the effect coincides in
+point of time with, or immediately follows, the hindmost of its
+conditions, is immaterial. At all events it does not precede it; and
+when we are in doubt, between two coexistent phenomena, which is cause
+and which effect, we rightly deem the question solved if we can
+ascertain which of them preceded the other.
+
+
+§ 7. It continually happens that several different phenomena, which are
+not in the slightest degree dependent or conditional on one another, are
+found all to depend, as the phrase is, on one and the same agent; in
+other words, one and the same phenomenon is seen to be followed by
+several sorts of effects quite heterogeneous, but which go on
+simultaneously one with another; provided, of course, that all other
+conditions requisite for each of them also exist. Thus, the sun produces
+the celestial motions, it produces daylight, and it produces heat. The
+earth causes the fall of heavy bodies, and it also, in its capacity of a
+great magnet, causes the phenomena of the magnetic needle. A crystal of
+galena causes the sensations of hardness, of weight, of cubical form, of
+grey colour, and many others between which we can trace no
+interdependence. The purpose to which the phraseology of Properties and
+Powers is specially adapted, is the expression of this sort of cases.
+When the same phenomenon is followed (either subject or not to the
+presence of other conditions) by effects of different and dissimilar
+orders, it is usual to say that each different sort of effect is
+produced by a different property of the cause. Thus we distinguish the
+attractive or gravitative property of the earth, and its magnetic
+property: the gravitative, luminiferous, and calorific properties of the
+sun: the colour, shape, weight, and hardness of a crystal. These are
+mere phrases, which explain nothing, and add nothing to our knowledge of
+the subject; but, considered as abstract names denoting the connexion
+between the different effects produced and the object which produces
+them, they are a very powerful instrument of abridgment, and of that
+acceleration of the process of thought which abridgment accomplishes.
+
+This class of considerations leads to a conception which we shall find
+to be of great importance, that of a Permanent Cause, or original
+natural agent. There exist in nature a number of permanent causes, which
+have subsisted ever since the human race has been in existence, and for
+an indefinite and probably an enormous length of time previous. The sun,
+the earth, and planets, with their various constituents, air, water, and
+other distinguishable substances, whether simple or compound, of which
+nature is made up, are such Permanent Causes. These have existed, and
+the effects or consequences which they were fitted to produce have taken
+place (as often as the other conditions of the production met,) from the
+very beginning of our experience. But we can give no account of the
+origin of the Permanent Causes themselves. Why these particular natural
+agents existed originally and no others, or why they are commingled in
+such and such proportions, and distributed in such and such a manner
+throughout space, is a question we cannot answer. More than this: we can
+discover nothing regular in the distribution itself; we can reduce it to
+no uniformity, to no law. There are no means by which, from the
+distribution of these causes or agents in one part of space, we could
+conjecture whether a similar distribution prevails in another. The
+coexistence, therefore, of Primeval Causes, ranks, to us, among merely
+casual concurrences: and all those sequences or coexistences among the
+effects of several such causes, which, though invariable while those
+causes coexist, would, if the coexistence terminated, terminate along
+with it, we do not class as cases of causation, or laws of nature: we
+can only calculate on finding these sequences or coexistences where we
+know by direct evidence, that the natural agents on the properties of
+which they ultimately depend, are distributed in the requisite manner.
+These Permanent Causes are not always objects; they are sometimes
+events, that is to say, periodical cycles of events, that being the only
+mode in which events can possess the property of permanence. Not only,
+for instance, is the earth itself a permanent cause, or primitive
+natural agent, but the earth's rotation is so too: it is a cause which
+has produced, from the earliest period, (by the aid of other necessary
+conditions,) the succession of day and night, the ebb and flow of the
+sea, and many other effects, while, as we can assign no cause (except
+conjecturally) for the rotation itself, it is entitled to be ranked as a
+primeval cause. It is, however, only the _origin_ of the rotation which
+is mysterious to us: once begun, its continuance is accounted for by the
+first law of motion (that of the permanence of rectilinear motion once
+impressed) combined with the gravitation of the parts of the earth
+towards one another.
+
+All phenomena without exception which begin to exist, that is, all
+except the primeval causes, are effects either immediate or remote of
+those primitive facts, or of some combination of them. There is no Thing
+produced, no event happening, in the known universe, which is not
+connected by an uniformity, or invariable sequence, with some one or
+more of the phenomena which preceded it; insomuch that it will happen
+again as often as those phenomena occur again, and as no other
+phenomenon having the character of a counteracting cause shall coexist.
+These antecedent phenomena, again, were connected in a similar manner
+with some that preceded them; and so on, until we reach, as the ultimate
+step attainable by us, either the properties of some one primeval cause,
+or the conjunction of several. The whole of the phenomena of nature were
+therefore the necessary, or in other words, the unconditional,
+consequences of some former collocation of the Permanent Causes.
+
+The state of the whole universe at any instant, we believe to be the
+consequence of its state at the previous instant; insomuch that one who
+knew all the agents which exist at the present moment, their collocation
+in space, and all their properties, in other words, the laws of their
+agency, could predict the whole subsequent history of the universe, at
+least unless some new volition of a power capable of controlling the
+universe should supervene.[21] And if any particular state of the
+entire universe could ever recur a second time, all subsequent states
+would return too, and history would, like a circulating decimal of many
+figures, periodically repeat itself:--
+
+    Jam redit et virgo, redeunt Saturnia regna....
+    Alter erit tum Tiphys, et altera quæ vehat Argo
+    Delectos heroas; erunt quoque altera bella,
+    Atque iterum ad Trojam magnus mittetur Achilles.
+
+And though things do not really revolve in this eternal round, the whole
+series of events in the history of the universe, past and future, is not
+the less capable, in its own nature, of being constructed _à priori_ by
+any one whom we can suppose acquainted with the original distribution of
+all natural agents, and with the whole of their properties, that is, the
+laws of succession existing between them and their effects: saving the
+far more than human powers of combination and calculation which would be
+required, even in one possessing the data, for the actual performance of
+the task.
+
+
+§ 8. Since everything which occurs is determined by laws of causation
+and collocations of the original causes, it follows that the
+coexistences which are observable among effects cannot be themselves the
+subject of any similar set of laws, distinct from laws of causation.
+Uniformities there are, as well of coexistence as of succession, among
+effects; but these must in all cases be a mere result either of the
+identity or of the coexistence of their causes: if the causes did not
+coexist, neither could the effects. And these causes being also effects
+of prior causes, and these of others, until we reach the primeval
+causes, it follows that (except in the case of effects which can be
+traced immediately or remotely to one and the same cause) the
+coexistences of phenomena can in no case be universal, unless the
+coexistences of the primeval causes to which the effects are ultimately
+traceable, can be reduced to an universal law: but we have seen that
+they cannot. There are, accordingly, no original and independent, in
+other words no unconditional, uniformities of coexistence, between
+effects of different causes; if they coexist, it is only because the
+causes have casually coexisted. The only independent and unconditional
+coexistences which are sufficiently invariable to have any claim to the
+character of laws, are between different and mutually independent
+effects of the same cause; in other words, between different properties
+of the same natural agent. This portion of the Laws of Nature will be
+treated of in the latter part of the present Book, under the name of the
+Specific Properties of Kinds.
+
+
+§ 9. It is proper in this place to advert to a rather ancient doctrine
+respecting causation, which has been revived during the last few years
+in many quarters, and at present gives more signs of life than any other
+theory of causation at variance with that set forth in the preceding
+pages.
+
+According to the theory in question, Mind, or, to speak more precisely,
+Will, is the only cause of phenomena. The type of Causation, as well as
+the exclusive source from which we derive the idea, is our own voluntary
+agency. Here, and here only (it is said) we have direct evidence of
+causation. We know that we can move our bodies. Respecting the phenomena
+of inanimate nature, we have no other direct knowledge than that of
+antecedence and sequence. But in the case of our voluntary actions, it
+is affirmed that we are conscious of power, before we have experience of
+results. An act of volition, whether followed by an effect or not, is
+accompanied by a consciousness of effort, "of force exerted, of power in
+action, which is necessarily causal, or causative." This feeling of
+energy or force, inherent in an act of will, is knowledge _à priori_;
+assurance, prior to experience, that we have the power of causing
+effects. Volition, therefore, it is asserted, is something more than an
+unconditional antecedent; it is a cause, in a different sense from that
+in which physical phenomena are said to cause one another: it is an
+Efficient Cause. From this the transition is easy to the further
+doctrine, that Volition is the _sole_ Efficient Cause of all phenomena.
+"It is inconceivable that dead force could continue unsupported for a
+moment beyond its creation. We cannot even conceive of change or
+phenomena without the energy of a mind." "The word _action_" itself,
+says another writer of the same school, "has no real significance except
+when applied to the doings of an intelligent agent. Let any one
+conceive, if he can, of any power, energy, or force, inherent in a lump
+of matter." Phenomena may have the semblance of being produced by
+physical causes, but they are in reality produced, say these writers, by
+the immediate agency of mind. All things which do not proceed from a
+human (or, I suppose, an animal) will, proceed, they say, directly from
+divine will. The earth is not moved by the combination of a centripetal
+and a projectile force; this is but a mode of speaking, which serves to
+facilitate our conceptions. It is moved by the direct volition of an
+omnipotent Being, in a path coinciding with that which we deduce from
+the hypothesis of these two forces.
+
+As I have so often observed, the general question of the existence of
+Efficient Causes does not fall within the limits of our subject: but a
+theory which represents them as capable of being subjects of human
+knowledge, and which passes off as efficient causes what are only
+physical or phenomenal causes, belongs as much to Logic as to
+Metaphysics, and is a fit subject for discussion here.
+
+To my apprehension, a volition is not an efficient, but simply a
+physical, cause. Our will causes our bodily actions in the same sense,
+and in no other, in which cold causes ice, or a spark causes an
+explosion of gunpowder. The volition, a state of our mind, is the
+antecedent; the motion of our limbs in conformity to the volition, is
+the consequent. This sequence I conceive to be not a subject of direct
+consciousness, in the sense intended by the theory. The antecedent,
+indeed, and the consequent, are subjects of consciousness. But the
+connexion between them is a subject of experience. I cannot admit that
+our consciousness of the volition contains in itself any _à priori_
+knowledge that the muscular motion will follow. If our nerves of motion
+were paralysed, or our muscles stiff and inflexible, and had been so all
+our lives, I do not see the slightest ground for supposing that we
+should ever (unless by information from other people) have known
+anything of volition as a physical power, or been conscious of any
+tendency in feelings of our mind to produce motions of our body, or of
+other bodies. I will not undertake to say whether we should in that case
+have had the physical feeling which I suppose is meant when these
+writers speak of "consciousness of effort:" I see no reason why we
+should not; since that physical feeling is probably a state of nervous
+sensation beginning and ending in the brain, without involving the
+motory apparatus: but we certainly should not have designated it by any
+term equivalent to effort, since effort implies consciously aiming at an
+end, which we should not only in that case have had no reason to do, but
+could not even have had the idea of doing. If conscious at all of this
+peculiar sensation, we should have been conscious of it, I conceive,
+only as a kind of uneasiness, accompanying our feelings of desire.
+
+It is well argued by Sir William Hamilton against the theory in
+question, that it "is refuted by the consideration, that between the
+overt fact of corporeal movement of which we are cognisant, and the
+internal act of mental determination of which we are also cognisant,
+there intervenes a numerous series of intermediate agencies of which we
+have no knowledge; and, consequently, that we can have no consciousness
+of any causal connexion between the extreme links of this chain, the
+volition to move and the limb moving, as this hypothesis asserts. No one
+is immediately conscious, for example, of moving his arm through his
+volition. Previously to this ultimate movement, muscles, nerves, a
+multitude of solid and fluid parts, must be set in motion by the will,
+but of this motion we know, from consciousness, absolutely nothing. A
+person struck with paralysis is conscious of no inability in his limb to
+fulfil the determinations of his will; and it is only after having
+willed, and finding that his limbs do not obey his volition, that he
+learns by this experience, that the external movement does not follow
+the internal act. But as the paralytic learns after the volition that
+his limbs do not obey his mind; so it is only after volition that the
+man in health learns, that his limbs do obey the mandates of his
+will."[22]
+
+Those against whom I am contending have never produced, and do not
+pretend to produce, any positive evidence[23] that the power of our will
+to move our bodies would be known to us independently of experience.
+What they have to say on the subject is, that the production of physical
+events by a will seems to carry its own explanation with it, while the
+action of matter upon matter seems to require something else to explain
+it; and is even, according to them, "inconceivable" on any other
+supposition than that some will intervenes between the apparent cause
+and its apparent effect. They thus rest their case on an appeal to the
+inherent laws of our conceptive faculty; mistaking, as I apprehend, for
+the laws of that faculty its acquired habits, grounded on the
+spontaneous tendencies of its uncultured state. The succession between
+the will to move a limb and the actual motion, is one of the most direct
+and instantaneous of all sequences which come under our observation, and
+is familiar to every moment's experience from our earliest infancy; more
+familiar than any succession of events exterior to our bodies, and
+especially more so than any other case of the apparent origination (as
+distinguished from the mere communication) of motion. Now, it is the
+natural tendency of the mind to be always attempting to facilitate its
+conception of unfamiliar facts by assimilating them to others which are
+familiar. Accordingly, our voluntary acts, being the most familiar to us
+of all cases of causation, are, in the infancy and early youth of the
+human race, spontaneously taken as the type of causation in general, and
+all phenomena are supposed to be directly produced by the will of some
+sentient being. This original Fetichism I shall not characterize in the
+words of Hume, or of any follower of Hume, but in those of a religious
+metaphysician, Dr. Reid, in order more effectually to show the unanimity
+which exists on the subject among all competent thinkers.
+
+"When we turn our attention to external objects, and begin to exercise
+our rational faculties about them, we find that there are some motions
+and changes in them which we have power to produce, and that there are
+many which must have some other cause. Either the objects must have life
+and active power, as we have, or they must be moved or changed by
+something that has life and active power, as external objects are moved
+by us.
+
+"Our first thoughts seem to be, that the objects in which we perceive
+such motion have understanding and active power as we have. 'Savages,'
+says the Abbé Raynal, 'wherever they see motion which they cannot
+account for, there they suppose a soul.' All men may be considered as
+savages in this respect, until they are capable of instruction, and of
+using their faculties in a more perfect manner than savages do.
+
+"The Abbé Raynal's observation is sufficiently confirmed, both from
+fact, and from the structure of all languages.
+
+"Rude nations do really believe sun, moon, and stars, earth, sea, and
+air, fountains, and lakes, to have understanding and active power. To
+pay homage to them, and implore their favour, is a kind of idolatry
+natural to savages.
+
+"All languages carry in their structure the marks of their being formed
+when this belief prevailed. The distinction of verbs and participles
+into active and passive, which is found in all languages, must have been
+originally intended to distinguish what is really active from what is
+merely passive; and in all languages, we find active verbs applied to
+those objects, in which, according to the Abbé Raynal's observation,
+savages suppose a soul.
+
+"Thus we say the sun rises and sets, and comes to the meridian, the moon
+changes, the sea ebbs and flows, the winds blow. Languages were formed
+by men who believed these objects to have life and active power in
+themselves. It was therefore proper and natural to express their motions
+and changes by active verbs.
+
+"There is no surer way of tracing the sentiments of nations before they
+have records, than by the structure of their language, which,
+notwithstanding the changes produced in it by time, will always retain
+some signatures of the thoughts of those by whom it was invented. When
+we find the same sentiments indicated in the structure of all languages,
+those sentiments must have been common to the human species when
+languages were invented.
+
+"When a few, of superior intellectual abilities, find leisure for
+speculation, they begin to philosophize, and soon discover, that many of
+those objects which at first they believed to be intelligent and active
+are really lifeless and passive. This is a very important discovery. It
+elevates the mind, emancipates from many vulgar superstitions, and
+invites to further discoveries of the same kind.
+
+"As philosophy advances, life and activity in natural objects retires,
+and leaves them dead and inactive. Instead of moving voluntarily, we
+find them to be moved necessarily; instead of acting, we find them to be
+acted upon; and Nature appears as one great machine, where one wheel is
+turned by another, that by a third; and how far this necessary
+succession may reach, the philosopher does not know."[24]
+
+There is, then, a spontaneous tendency of the intellect to account to
+itself for all cases of causation by assimilating them to the
+intentional acts of voluntary agents like itself. This is the
+instinctive philosophy of the human mind in its earliest stage, before
+it has become familiar with any other invariable sequences than those
+between its own volitions or those of other human beings and their
+voluntary acts. As the notion of fixed laws of succession among external
+phenomena gradually establishes itself, the propensity to refer all
+phenomena to voluntary agency slowly gives way before it. The
+suggestions, however, of daily life continuing to be more powerful than
+those of scientific thought, the original instinctive philosophy
+maintains its ground in the mind, underneath the growths obtained by
+cultivation, and keeps up a constant resistance to their throwing their
+roots deep into the soil. The theory against which I am contending
+derives its nourishment from that substratum. Its strength does not lie
+in argument, but in its affinity to an obstinate tendency of the infancy
+of the human mind.
+
+That this tendency, however, is not the result of an inherent mental
+law, is proved by superabundant evidence. The history of science, from
+its earliest dawn, shows that mankind have not been unanimous in
+thinking either that the action of matter upon matter was not
+conceivable, or that the action of mind upon matter was. To some
+thinkers, and some schools of thinkers, both in ancient and in modern
+times, this last has appeared much more inconceivable than the former.
+Sequences entirely physical and material, as soon as they had become
+sufficiently familiar to the human mind, came to be thought perfectly
+natural, and were regarded not only as needing no explanation
+themselves, but as being capable of affording it to others, and even of
+serving as the ultimate explanation of things in general.
+
+One of the ablest recent supporters of the Volitional theory has
+furnished an explanation, at once historically true and philosophically
+acute, of the failure of the Greek philosophers in physical inquiry, in
+which, as I conceive, he unconsciously depicts his own state of mind.
+"Their stumbling-block was one as to the nature of the evidence they had
+to expect for their conviction.... They had not seized the idea that
+they must not expect to understand the processes of outward causes, but
+only their results: and consequently, the whole physical philosophy of
+the Greeks was an attempt to identify mentally the effect with its
+cause, to feel after some not only necessary but natural connexion,
+where they meant by natural that which would _per se_ carry some
+presumption to their own mind.... They wanted to see some _reason_ why
+the physical antecedent should produce this particular consequent, and
+their only attempts were in directions where they could find such
+reasons."[25] In other words, they were not content merely to know that
+one phenomenon was always followed by another; they thought that they
+had not attained the true aim of science, unless they could perceive
+something in the nature of the one phenomenon from which it might have
+been known or presumed _previous to trial_ that it would be followed by
+the other: just what the writer, who has so clearly pointed out their
+error, thinks that he perceives in the nature of the phenomenon
+Volition. And to complete the statement of the case, he should have
+added that these early speculators not only made this their aim, but
+were quite satisfied with their success in it; not only sought for
+causes which should carry in their mere statement evidence of their
+efficiency, but fully believed that they had found such causes. The
+reviewer can see plainly that this was an error, because _he_ does not
+believe that there exist any relations between material phenomena which
+can account for their producing one another: but the very fact of the
+persistency of the Greeks in this error, shows that their minds were in
+a very different state: they were able to derive from the assimilation
+of physical facts to other physical facts, the kind of mental
+satisfaction which we connect with the word explanation, and which the
+reviewer would have us think can only be found in referring phenomena to
+a will. When Thales and Hippo held that moisture was the universal
+cause, and external element, of which all other things were but the
+infinitely various sensible manifestations; when Anaximenes predicated
+the same thing of air, Pythagoras of numbers, and the like, they all
+thought that they had found a real explanation; and were content to rest
+in this explanation as ultimate. The ordinary sequences of the external
+universe appeared to them, no less than to their critic, to be
+inconceivable without the supposition of some universal agency to
+connect the antecedents with the consequents; but they did not think
+that Volition, exerted by minds, was the only agency which fulfilled
+this requirement. Moisture, or air, or numbers, carried to their minds a
+precisely similar impression of making intelligible what was otherwise
+inconceivable, and gave the same full satisfaction to the demands of
+their conceptive faculty.
+
+It was not the Greeks alone, who "wanted to see some reason why the
+physical antecedent should produce this particular consequent," some
+connexion "which would _per se_ carry some presumption to their own
+mind." Among modern philosophers, Leibnitz laid it down as a
+self-evident principle that all physical causes without exception must
+contain in their own nature something which makes it intelligible that
+they should be able to produce the effects which they do produce. Far
+from admitting Volition as the only kind of cause which carried internal
+evidence of its own power, and as the real bond of connexion between
+physical antecedents and their consequents, he demanded some naturally
+and _per se_ efficient physical antecedent as the bond of connexion
+between Volition itself and its effects. He distinctly refused to admit
+the will of God as a sufficient explanation of anything except miracles;
+and insisted upon finding something that would account _better_ for the
+phenomena of nature than a mere reference to divine volition.[26]
+
+Again, and conversely, the action of mind upon matter (which, we are now
+told, not only needs no explanation itself, but is the explanation of
+all other effects), has appeared to some thinkers to be itself the grand
+inconceivability. It was to get over this very difficulty that the
+Cartesians invented the system of Occasional Causes. They could not
+conceive that thoughts in a mind could produce movements in a body, or
+that bodily movements could produce thoughts. They could see no
+necessary connexion, no relation _à priori_, between a motion and a
+thought. And as the Cartesians, more than any other school of
+philosophical speculation before or since, made their own minds the
+measure of all things, and refused, on principle, to believe that Nature
+had done what they were unable to see any reason why she must do, they
+affirmed it to be impossible that a material and a mental fact could be
+causes one of another. They regarded them as mere Occasions on which the
+real agent, God, thought fit to exert his power as a Cause. When a man
+wills to move his foot, it is not his will that moves it, but God (they
+said) moves it on the occasion of his will. God, according to this
+system, is the only efficient cause, not _quâ_ mind, or _quâ_ endowed
+with volition, but _quâ_ omnipotent. This hypothesis was, as I said,
+originally suggested by the supposed inconceivability of any real mutual
+action between Mind and Matter: but it was afterwards extended to the
+action of Matter upon Matter, for on a nicer examination they found this
+inconceivable too, and therefore, according to their logic, impossible.
+The _deus ex machinâ_ was ultimately called in to produce a spark on the
+occasion of a flint and steel coming together, or to break an egg on the
+occasion of its falling on the ground.
+
+All this, undoubtedly, shows that it is the disposition of mankind in
+general, not to be satisfied with knowing that one fact is invariably
+antecedent and another consequent, but to look out for something which
+may seem to explain their being so. But we also see that this demand may
+be completely satisfied by an agency purely physical, provided it be
+much more familiar than that which it is invoked to explain. To Thales
+and Anaximenes, it appeared inconceivable that the antecedents which we
+see in nature, should produce the consequents; but perfectly natural
+that water, or air, should produce them. The writers whom I oppose
+declare this inconceivable, but can conceive that mind, or volition, is
+_per se_ an efficient cause: while the Cartesians could not conceive
+even that, but peremptorily declared that no mode of production of any
+fact whatever was conceivable, except the direct agency of an omnipotent
+being. Thus giving additional proof of what finds new confirmation in
+every stage of the history of science: that both what persons can, and
+what they cannot, conceive, is very much an affair of accident, and
+depends altogether on their experience, and their habits of thought;
+that by cultivating the requisite associations of ideas, people may make
+themselves unable to conceive any given thing; and may make themselves
+able to conceive most things, however inconceivable these may at first
+appear: and the same facts in each person's mental history which
+determine what is or is not conceivable to him, determine also which
+among the various sequences in nature will appear to him so natural and
+plausible, as to need no other proof of their existence; to be evident
+by their own light, independent equally of experience and of
+explanation.
+
+By what rule is any one to decide between one theory of this description
+and another? The theorists do not direct us to any external evidence;
+they appeal each to his own subjective feelings. One says, the
+succession C, B, appears to me more natural, conceivable, and credible
+_per se_, than the succession A, B; you are therefore mistaken in
+thinking that B depends upon A; I am certain, though I can give no other
+evidence of it, that C comes in between A and B, and is the real and
+only cause of B. The other answers--the successions C, B, and A, B,
+appear to me equally natural and conceivable, or the latter more so than
+the former: A is quite capable of producing B without any other
+intervention. A third agrees with the first in being unable to conceive
+that A can produce B, but finds the sequence D, B, still more natural
+than C, B, or of nearer kin to the subject matter, and prefers his D
+theory to the C theory. It is plain that there is no universal law
+operating here, except the law that each person's conceptions are
+governed and limited by his individual experience and habits of thought.
+We are warranted in saying of all three, what each of them already
+believes of the other two, namely, that they exalt into an original law
+of the human intellect and of outward nature, one particular sequence of
+phenomena, which appears to them more natural and more conceivable than
+other sequences, only because it is more familiar. And from this
+judgment I am unable to except the theory, that Volition is an Efficient
+Cause.
+
+I am unwilling to leave the subject without adverting to the additional
+fallacy contained in the corollary from this theory; in the inference
+that because Volition is an efficient cause, therefore it is the only
+cause, and the direct agent in producing even what is apparently
+produced by something else. Volitions are not known to produce anything
+directly except nervous action, for the will influences even the muscles
+only through the nerves. Though it were granted, then, that every
+phenomenon has an efficient, and not merely a phenomenal cause, and that
+volition, in the case of the peculiar phenomena which are known to be
+produced by it, is that efficient cause; are we therefore to say, with
+these writers, that since we know of no other efficient cause, and ought
+not to assume one without evidence, there _is_ no other, and volition is
+the direct cause of all phenomena? A more outrageous stretch of
+inference could hardly be made. Because among the infinite variety of
+the phenomena of nature there is one, namely, a particular mode of
+action of certain nerves, which has for its cause, and as we are now
+supposing for its efficient cause, a state of our mind; and because this
+is the only efficient cause of which we are conscious, being the only
+one of which in the nature of the case we _can_ be conscious, since it
+is the only one which exists within ourselves; does this justify us in
+concluding that all other phenomena must have the same kind of efficient
+cause with that one eminently special, narrow, and peculiarly human or
+animal, phenomenon? The nearest parallel to this specimen of
+generalization is suggested by the recently revived controversy on the
+old subject of Plurality of Worlds, in which the contending parties have
+been so conspicuously successful in overthrowing one another. Here also
+we have experience only of a single case, that of the world in which we
+live, but that this is inhabited we know absolutely, and without
+possibility of doubt. Now if on this evidence any one were to infer that
+every heavenly body without exception, sun, planet, satellite, comet,
+fixed star or nebula, is inhabited, and must be so from the inherent
+constitution of things, his inference would exactly resemble that of the
+writers who conclude that because volition is the efficient cause of our
+own bodily motions, it must be the efficient cause of everything else in
+the universe. It is true there are cases in which, with acknowledged
+propriety, we generalize from a single instance to a multitude of
+instances. But they must be instances which resemble the one known
+instance, and not such as have no circumstance in common with it except
+that of being instances. I have, for example, no direct evidence that
+any creature is alive except myself: yet I attribute, with full
+assurance, life and sensation to other human beings and animals. But I
+do not conclude that all other things are alive merely because I am. I
+ascribe to certain other creatures a life like my own, because they
+manifest it by the same sort of indications by which mine is manifested.
+I find that their phenomena and mine conform to the same laws, and it is
+for this reason that I believe both to arise from a similar cause.
+Accordingly I do not extend the conclusion beyond the grounds for it.
+Earth, fire, mountains, trees, are remarkable agencies, but their
+phenomena do not conform to the same laws as my actions do, and I
+therefore do not believe earth or fire, mountains or trees, to possess
+animal life. But the supporters of the Volition Theory ask us to infer
+that volition causes everything, for no reason except that it causes one
+particular thing; although that one phenomenon, far from being a type of
+all natural phenomena, is eminently peculiar; its laws bearing scarcely
+any resemblance to those of any other phenomenon, whether of inorganic
+or of organic nature.
+
+
+NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
+
+     The author of the Second Burnett Prize Essay (Dr. Tulloch), who
+     has employed a considerable number of pages in controverting
+     the doctrines of the preceding chapter, has somewhat surprised
+     me by denying a fact, which I imagined too well known to
+     require proof--that there have been philosophers who found in
+     physical explanations of phenomena the same complete mental
+     satisfaction which we are told is only given by volitional
+     explanation, and others who denied the Volitional Theory on the
+     same ground of inconceivability on which it is defended. The
+     assertion of the Essayist is countersigned still more
+     positively by an able reviewer of the Essay:[27] "Two
+     illustrations," says the reviewer, "are advanced by Mr. Mill:
+     the case of Thales and Anaximenes, stated by him to have
+     maintained, the one Moisture and the other Air to be the origin
+     of all things; and that of Descartes and Leibnitz, whom he
+     asserts to have found the action of Mind upon Matter the grand
+     inconceivability. In counterstatement as to the first of these
+     cases the author shows--what we believe now hardly admits of
+     doubt--that the Greek philosophers distinctly recognised as
+     beyond and above their primal material source, the _νοῦς_, or
+     Divine Intelligence, as the efficient and originating Source of
+     all: and as to the second, by proof that it was the _mode_, not
+     the _fact_, of that action on matter, which was represented as
+     inconceivable."
+
+     A greater quantity of historical error has seldom been
+     comprised in a single sentence. With regard to Thales, the
+     assertion that he considered water as a mere material in the
+     hands of _νοῦς_ rests on a passage of Cicero _de Naturâ
+     Deorum_: and whoever will refer to any of the accurate
+     historians of philosophy, will find that they treat this as a
+     mere fancy of Cicero, resting on no authority, opposed to all
+     the evidence; and make surmises as to the manner in which
+     Cicero may have been led into the error. (See Ritter, vol. i.
+     p. 211, 2nd ed.; Brandis, vol. i. pp. 118-9, 1st ed.; Preller,
+     _Historia Philosophiæ Græco-Romanæ_, p. 10. "Schiefe Ansicht,
+     durchaus zu verwerfen;" "augenscheinlich folgernd statt zu
+     berichten;" "quibus vera sententia Thaletis plane detorquetur;"
+     are the expressions of these writers.) As for Anaximenes, he,
+     even according to Cicero, maintained, not that air was the
+     material out of which God made the world, but that the air was
+     a god: "Anaximenes aëra deum statuit:" or according to St.
+     Augustine, that it was the material out of which the gods were
+     made; "non tamen ab ipsis [Diis] aërem factum, sed ipsos ex
+     aëre ortos credidit." Those who are not familiar with the
+     metaphysical terminology of antiquity, must not be misled by
+     finding it stated that Anaximenes attributed _ψυχὴ_ (translated
+     _soul_, or _life_) to his universal element, the air. The Greek
+     philosophers acknowledged several kinds of _ψυχὴ_, the
+     nutritive, the sensitive, and the intellective.[28] Even the
+     moderns with admitted correctness attribute life to plants. As
+     far as we can make out the meaning of Anaximenes, he made
+     choice of Air as the universal agent, on the ground that it is
+     perpetually in motion, without any apparent cause external to
+     itself: so that he conceived it as exercising spontaneous
+     force, and as the principle of life and activity in all
+     things, men and gods inclusive. If this be not representing it
+     as the Efficient Cause, the dispute altogether has no meaning.
+
+     If either Anaximenes, or Thales, or any of their cotemporaries,
+     had held the doctrine that _νοῦς_ was the Efficient Cause, that
+     doctrine could not have been reputed, as it was throughout
+     antiquity, to have originated with Anaxagoras. The testimony of
+     Aristotle, in the first book of his Metaphysics, is perfectly
+     decisive with respect to these early speculations. After
+     enumerating four kinds of causes, or rather four different
+     meanings of the word Cause, viz. the Essence of a thing, the
+     Matter of it, the Origin of Motion (Efficient Cause), and the
+     End or Final Cause, he proceeds to say, that most of the early
+     philosophers recognised only the second kind of Cause, the
+     Matter of a thing, _τὰς ἐν ὕλης εἴδει μόνας ᾠήθησαν ἀρχὰς εἶναι
+     πάντων_. As his first example he specifies Thales, whom he
+     describes as taking the lead in this view of the subject, _ὁ
+     τῆς τοιαύτης ἀρχηγὸς φιλοσοφίας_, and goes on to Hippon,
+     Anaximenes, Diogenes (of Apollonia), Hippasus of Metapontum,
+     Heraclitus, and Empedocles. Anaxagoras, however, (he proceeds
+     to say,) taught a different doctrine, as we know, and it is
+     _alleged_ that Hermotimus of Clazomenæ taught it before him.
+     Anaxagoras represented, that even if these various theories of
+     the universal material were true, there would be need of some
+     other cause to account for the transformations of the material,
+     since the material cannot originate its own changes: _οὐ γὰρ δὴ
+     τό γε ὑποκείμενον αὐτὸ ποιεῖ μεταβάλλειν ἑαῦτο; λέγω δ' οἶον
+     οὔτε τὸ ξύλον οὔτε ὅ χαλκὸς αἴτιος τοῦ μεταβάλλειν έκάτερον
+     αὐτῶν, οὐδὲ ποιεῖ τὸ μἑν ξύλον κλίνην ὅ δέ χαλκὸς ἀνδριάντα,
+     ἀλλ' ἑτερον τι τῆς μεταβολῆς αἴτιον_, viz., the other kind of
+     cause, _ὅθεν ἡ ἀρχὴ τῆς κινήσεως_--an Efficient Cause.
+     Aristotle expresses great approbation of this doctrine (which
+     he says made its author appear the only sober man among persons
+     raving, _οἶον νήφων ἐφάνη παρ' εἰκῆ λέγοντας τοῦς πρότερον_);
+     but while describing the influence which it exercised over
+     subsequent speculation, he remarks that the philosophers
+     against whom this, as he thinks, insuperable difficulty was
+     urged, had not felt it to be any difficulty: _οὐδὲν ἐδυσχεράναν
+     ἐν ἑαυτοῖς_. It is surely unnecessary to say more in proof of
+     the matter of fact which Dr. Tulloch and his reviewer deny.
+
+     Having pointed out what he thinks the error of these early
+     speculators in not recognising the need of an efficient cause,
+     Aristotle goes on to mention two other efficient causes to
+     which they might have had recourse, instead of intelligence:
+     _τύχη_, chance, and _τὸ αὐτομάτον_, spontaneity. He indeed puts
+     these aside as not sufficiently worthy causes for the order in
+     the universe, _οὐδ' αὖ τῷ αὐτομάτῳ καὶ τῇ τύχῃ τοσοῦτον
+     ἐπιτρέψαι πρᾶγμα καλῶς εἶχεν_: but he does not reject them as
+     incapable of producing any effect, but only as incapable of
+     producing _that_ effect. He himself recognises _τύχη_ and _τὸ
+     αὐτομάτον_ as co-ordinate agents with Mind in producing the
+     phenomena of the universe; the department allotted to them
+     being composed of all the classes of phenomena which are not
+     supposed to follow any uniform law. By thus including Chance
+     among efficient causes, Aristotle fell into an error which
+     philosophy has now outgrown, but which is by no means so alien
+     to the spirit even of modern speculation as it may at first
+     sight appear. Up to quite a recent period philosophers went on
+     ascribing, and many of them have not yet ceased to ascribe, a
+     real existence to the results of abstraction. Chance could
+     make out as good a title to that dignity as many other of the
+     mind's abstract creations: it had had a name given to it, and
+     why should it not be a reality? As for _τὸ αὐτομάτον_, it is
+     recognised even yet as one of the modes of origination of
+     phenomena, by all those thinkers who maintain what is called
+     the Freedom of the Will. The same self-determining power which
+     that doctrine attributes to volitions, was supposed by the
+     ancients to be possessed also by some other natural phenomena:
+     a circumstance which throws considerable light on more than one
+     of the supposed invincible necessities of belief. I have
+     introduced it here, because this belief of Aristotle, or rather
+     of the Greek philosophers generally, is as fatal as the
+     doctrines of Thales and the Ionic school, to the theory that
+     the human mind is compelled by its constitution to conceive
+     volition as the origin of all force, and the efficient cause of
+     all phenomena.[29]
+
+     With regard to the modern philosophers (Leibnitz and the
+     Cartesians) whom I had cited as having maintained that the
+     action of mind upon matter, so far from being the only
+     conceivable origin of material phenomena, is itself
+     inconceivable; the attempt to rebut this argument by asserting
+     that the mode, not the fact, of the action of mind on matter
+     was represented as inconceivable, is an abuse of the privilege
+     of writing confidently about authors without reading them: for
+     any knowledge whatever of Leibnitz would have taught those who
+     thus speak of him, that the inconceivability of the mode, and
+     the impossibility of the thing, were in his mind convertible
+     expressions. What was his famous Principle of the Sufficient
+     Reason, the very corner stone of his philosophy, from which the
+     Preestablished Harmony, the doctrine of Monads, and all the
+     opinions most characteristic of Leibnitz, were corollaries? It
+     was, that nothing exists, the existence of which is not capable
+     of being proved and explained _à priori_; the proof and
+     explanation in the case of contingent facts being derived from
+     the nature of their causes; which could not be the causes
+     unless there was something in their nature showing them to be
+     capable of producing those particular effects. And this
+     "something" which accounts for the production of physical
+     effects, he was able to find in many physical causes, but could
+     not find it in any finite minds, which therefore he
+     unhesitatingly asserted to be incapable of producing any
+     physical effects whatever. "On ne saurait concevoir," he says,
+     "une action réciproque de la matière et de l'intelligence l'une
+     sur l'autre," and there is therefore (he contends) no choice
+     but between the Occasional Causes of the Cartesians, and his
+     own Preestablished Harmony, according to which there is no more
+     connexion between our volitions and our muscular actions than
+     there is between two clocks which are wound up to strike at the
+     same instant. But he felt no similar difficulty as to physical
+     causes: and throughout his speculations, as in the passage I
+     have already cited respecting gravitation, he distinctly
+     refuses to consider as part of the order of nature any fact
+     which is not explicable from the nature of its physical cause.
+
+     With regard to the Cartesians (not Descartes; I did not make
+     that mistake, though the reviewer of Dr. Tulloch's Essay
+     attributes it to me) I take a passage almost at random from
+     Malebranche, who is the best known of the Cartesians, and,
+     though not the inventor of the system of Occasional Causes, is
+     its principal expositor. In Part 2, chap. 3, of his Sixth Book,
+     having first said that matter cannot have the power of moving
+     itself, he proceeds to argue that neither can mind have the
+     power of moving it. "Quand on examine l'idée que l'on a de tous
+     les esprits finis, on ne voit point de liaison nécessaire entre
+     leur volonté et le mouvement de quelque corps que ce soit, on
+     voit au contraire qu'il n'y en a point, et qu'il n'y en peut
+     avoir;" (there is nothing in the idea of finite mind which can
+     account for its causing the motion of a body;) "on doit aussi
+     conclure, si on veut raisonner selon ses lumières, qu'il n'y a
+     aucun esprit créé qui puisse remuer quelque corps que ce soit
+     comme cause véritable ou principale, de même que l'on a dit
+     qu'aucun corps ne se pouvait remuer soi-même:" thus the idea of
+     Mind is according to him as incompatible as the idea of Matter
+     with the exercise of active force. But when, he continues, we
+     consider not a created but a Divine Mind, the case is altered;
+     for the idea of a Divine Mind includes omnipotence; and the
+     idea of omnipotence does contain the idea of being able to move
+     bodies. Thus it is the nature of omnipotence which renders the
+     motion of bodies even by the divine mind credible or
+     conceivable, while, so far as depended on the mere nature of
+     mind, it would have been inconceivable and incredible. If
+     Malebranche had not believed in an omnipotent being, he would
+     have held all action of mind on body to be a demonstrated
+     impossibility.[30]
+
+     A doctrine more precisely the reverse of the Volitional theory
+     of causation cannot well be imagined. The volitional theory is,
+     that we know by intuition or by direct experience the action of
+     our own mental volitions on matter; that we may hence infer all
+     other action upon matter to be that of volition, and might thus
+     know, without any other evidence, that matter is under the
+     government of a divine mind. Leibnitz and the Cartesians, on
+     the contrary, maintain that our volitions do not and cannot act
+     upon matter, and that it is only the existence of an
+     all-governing Being, and that Being omnipotent, which can
+     account for the sequence between our volitions and our bodily
+     actions. When we consider that each of these two theories,
+     which, as theories of causation, stand at the opposite extremes
+     of possible divergence from one another, invokes not only as
+     its evidence, but as its sole evidence, the absolute
+     inconceivability of any theory but itself, we are enabled to
+     measure the worth of this kind of evidence; and when we find
+     the Volitional theory entirely built upon the assertion that by
+     our mental constitution we are compelled to recognise our
+     volitions as efficient causes, and then find other thinkers
+     maintaining that we know that they are not, and cannot be such
+     causes, and cannot conceive them to be so, I think we have a
+     right to say, that this supposed law of our mental constitution
+     does not exist.
+
+     Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this,
+     that Leibnitz and the Cartesians were Theists, and believed the
+     will of God to be an efficient cause. Doubtless they did, and
+     the Cartesians even believed, though Leibnitz did not, that it
+     is the only such cause. Dr. Tulloch mistakes the nature of the
+     question. I was not writing on Theism, as Dr. Tulloch is, but
+     against a particular theory of causation, which if it be
+     unfounded, can give no effective support to Theism or to
+     anything else. I found it asserted that volition is the only
+     efficient cause, on the ground that no other efficient cause is
+     conceivable. To this assertion I oppose the instances of
+     Leibnitz and of the Cartesians, who affirmed with equal
+     positiveness that volition as an efficient cause is itself not
+     conceivable, and that omnipotence, which renders all things
+     conceivable, can alone take away the impossibility. This I
+     thought, and think, a conclusive answer to the argument on
+     which this theory of causation avowedly depends. But I
+     certainly did not imagine that Theism was bound up with that
+     theory; nor expected to be charged with denying Leibnitz and
+     the Cartesians to be Theists because I denied that they held
+     the theory.
+
+
+
+
+CHAPTER VI.
+
+ON THE COMPOSITION OF CAUSES.
+
+
+§ 1. To complete the general notion of causation on which the rules of
+experimental inquiry into the laws of nature must be founded, one
+distinction still remains to be pointed out: a distinction so radical,
+and of so much importance, as to require a chapter to itself.
+
+The preceding discussions have rendered us familiar with the case in
+which several agents, or causes, concur as conditions to the production
+of an effect: a case, in truth, almost universal, there being very few
+effects to the production of which no more than one agent contributes.
+Suppose, then, that two different agents, operating jointly, are
+followed, under a certain set of collateral conditions, by a given
+effect. If either of these agents, instead of being joined with the
+other, had operated alone, under the same set of conditions in all other
+respects, some effect would probably have followed; which would have
+been different from the joint effect of the two, and more or less
+dissimilar to it. Now, if we happen to know what would be the effect of
+each cause when acting separately from the other, we are often able to
+arrive deductively, or _à priori_, at a correct prediction of what will
+arise from their conjunct agency. To enable us to do this, it is only
+necessary that the same law which expresses the effect of each cause
+acting by itself, shall also correctly express the part due to that
+cause, of the effect which follows from the two together. This condition
+is realized in the extensive and important class of phenomena commonly
+called mechanical, namely the phenomena of the communication of motion
+(or of pressure, which is tendency to motion) from one body to another.
+In this important class of cases of causation, one cause never, properly
+speaking, defeats or frustrates another; both have their full effect.
+If a body is propelled in two directions by two forces, one tending to
+drive it to the north and the other to the east, it is caused to move in
+a given time exactly as far in both directions as the two forces would
+separately have carried it; and is left precisely where it would have
+arrived if it had been acted upon first by one of the two forces, and
+afterwards by the other. This law of nature is called, in dynamics, the
+principle of the Composition of Forces: and in imitation of that
+well-chosen expression, I shall give the name of the Composition of
+Causes to the principle which is exemplified in all cases in which the
+joint effect of several causes is identical with the sum of their
+separate effects.
+
+This principle, however, by no means prevails in all departments of the
+field of nature. The chemical combination of two substances produces, as
+is well known, a third substance with properties entirely different from
+those of either of the two substances separately, or both of them taken
+together. Not a trace of the properties of hydrogen or of oxygen is
+observable in those of their compound, water. The taste of sugar of lead
+is not the sum of the tastes of its component elements, acetic acid and
+lead or its oxide; nor is the colour of blue vitriol a mixture of the
+colours of sulphuric acid and copper. This explains why mechanics is a
+deductive or demonstrative science, and chemistry not. In the one, we
+can compute the effects of all combinations of causes, whether real or
+hypothetical, from the laws which we know to govern those causes when
+acting separately; because they continue to observe the same laws when
+in combination which they observed when separate: whatever would have
+happened in consequence of each cause taken by itself, happens when they
+are together, and we have only to cast up the results. Not so in the
+phenomena which are the peculiar subject of the science of chemistry.
+There, most of the uniformities to which the causes conformed when
+separate, cease altogether when they are conjoined; and we are not, at
+least in the present state of our knowledge, able to foresee what result
+will follow from any new combination, until we have tried the specific
+experiment.
+
+If this be true of chemical combinations, it is still more true of those
+far more complex combinations of elements which constitute organized
+bodies; and in which those extraordinary new uniformities arise, which
+are called the laws of life. All organized bodies are composed of parts
+similar to those composing inorganic nature, and which have even
+themselves existed in an inorganic state; but the phenomena of life,
+which result from the juxtaposition of those parts in a certain manner,
+bear no analogy to any of the effects which would be produced by the
+action of the component substances considered as mere physical agents.
+To whatever degree we might imagine our knowledge of the properties of
+the several ingredients of a living body to be extended and perfected,
+it is certain that no mere summing up of the separate actions of those
+elements will ever amount to the action of the living body itself. The
+tongue, for instance, is, like all other parts of the animal frame,
+composed of gelatine, fibrin, and other products of the chemistry of
+digestion, but from no knowledge of the properties of those substances
+could we ever predict that it could taste, unless gelatine or fibrin
+could themselves taste; for no elementary fact can be in the conclusion,
+which was not in the premises.
+
+There are thus two different modes of the conjunct action of causes;
+from which arise two modes of conflict, or mutual interference, between
+laws of nature. Suppose, at a given point of time and space, two or more
+causes, which, if they acted separately, would produce effects contrary,
+or at least conflicting with each other; one of them tending to undo,
+wholly or partially, what the other tends to do. Thus, the expansive
+force of the gases generated by the ignition of gunpowder tends to
+project a bullet towards the sky, while its gravity tends to make it
+fall to the ground. A stream running into a reservoir at one end tends
+to fill it higher and higher, while a drain at the other extremity tends
+to empty it. Now, in such cases as these, even if the two causes which
+are in joint action exactly annul one another, still the laws of both
+are fulfilled; the effect is the same as if the drain had been open for
+half an hour first,[31] and the stream had flowed in for as long
+afterwards. Each agent produced the same amount of effect as if it had
+acted separately, though the contrary effect which was taking place
+during the same time obliterated it as fast as it was produced. Here
+then are two causes, producing by their joint operation an effect which
+at first seems quite dissimilar to those which they produce separately,
+but which on examination proves to be really the sum of those separate
+effects. It will be noticed that we here enlarge the idea of the sum of
+two effects, so as to include what is commonly called their difference,
+but which is in reality the result of the addition of opposites; a
+conception to which mankind are indebted for that admirable extension of
+the algebraical calculus, which has so vastly increased its powers as an
+instrument of discovery, by introducing into its reasonings (with the
+sign of subtraction prefixed, and under the name of Negative Quantities)
+every description whatever of positive phenomena, provided they are of
+such a quality in reference to those previously introduced, that to add
+the one is equivalent to subtracting an equal quantity of the other.
+
+There is, then, one mode of the mutual interference of laws of nature,
+in which, even when the concurrent causes annihilate each other's
+effects, each exerts its full efficacy according to its own law, its law
+as a separate agent. But in the other description of cases, the agencies
+which are brought together cease entirely, and a totally different set
+of phenomena arise: as in the experiment of two liquids which, when
+mixed in certain proportions, instantly become, not a larger amount of
+liquid, but a solid mass.
+
+
+§ 2. This difference between the case in which the joint effect of
+causes is the sum of their separate effects, and the case in which it
+is heterogeneous to them; between laws which work together without
+alteration, and laws which, when called upon to work together, cease and
+give place to others; is one of the fundamental distinctions in nature.
+The former case, that of the Composition of Causes, is the general one;
+the other is always special and exceptional. There are no objects which
+do not, as to some of their phenomena, obey the principle of the
+Composition of Causes; none that have not some laws which are rigidly
+fulfilled in every combination into which the objects enter. The weight
+of a body, for instance, is a property which it retains in all the
+combinations in which it is placed. The weight of a chemical compound,
+or of an organized body, is equal to the sum of the weights of the
+elements which compose it. The weight either of the elements or of the
+compound will vary, if they be carried farther from their centre of
+attraction, or brought nearer to it; but whatever affects the one
+affects the other. They always remain precisely equal. So again, the
+component parts of a vegetable or animal substance do not lose their
+mechanical and chemical properties as separate agents, when, by a
+peculiar mode of juxtaposition, they, as an aggregate whole, acquire
+physiological or vital properties in addition. Those bodies continue, as
+before, to obey mechanical and chemical laws, in so far as the operation
+of those laws is not counteracted by the new laws which govern them as
+organized beings. When, in short, a concurrence of causes takes place
+which calls into action new laws bearing no analogy to any that we can
+trace in the separate operation of the causes, the new laws, while they
+supersede one portion of the previous laws, may coexist with another
+portion, and may even compound the effect of those previous laws with
+their own.
+
+Again, laws which were themselves generated in the second mode, may
+generate others in the first. Though there are laws which, like those of
+chemistry and physiology, owe their existence to a breach of the
+principle of Composition of Causes, it does not follow that these
+peculiar, or as they might be termed, _heteropathic_ laws, are not
+capable of composition with one another. The causes which by one
+combination have had their laws altered, may carry their new laws with
+them unaltered into their ulterior combinations. And hence there is no
+reason to despair of ultimately raising chemistry and physiology to the
+condition of deductive sciences; for though it is impossible to deduce
+all chemical and physiological truths from the laws or properties of
+simple substances or elementary agents, they may possibly be deducible
+from laws which commence when these elementary agents are brought
+together into some moderate number of not very complex combinations. The
+Laws of Life will never be deducible from the mere laws of the
+ingredients, but the prodigiously complex Facts of Life may all be
+deducible from comparatively simple laws of life; which laws (depending
+indeed on combinations, but on comparatively simple combinations, of
+antecedents) may, in more complex circumstances, be strictly compounded
+with one another, and with the physical and chemical laws of the
+ingredients. The details of the vital phenomena, even now, afford
+innumerable exemplifications of the Composition of Causes; and in
+proportion as these phenomena are more accurately studied, there appears
+more reason to believe that the same laws which operate in the simpler
+combinations of circumstances do, in fact, continue to be observed in
+the more complex. This will be found equally true in the phenomena of
+mind; and even in social and political phenomena, the results of the
+laws of mind. It is in the case of chemical phenomena that the least
+progress has yet been made in bringing the special laws under general
+ones from which they may be deduced; but there are even in chemistry
+many circumstances to encourage the hope that such general laws will
+hereafter be discovered. The different actions of a chemical compound
+will never, undoubtedly, be found to be the sums of the actions of its
+separate elements; but there may exist, between the properties of the
+compound and those of its elements, some constant relation, which, if
+discoverable by a sufficient induction, would enable us to foresee the
+sort of compound which will result from a new combination before we have
+actually tried it, and to judge of what sort of elements some new
+substance is compounded before we have analysed it. The law of definite
+proportions, first discovered in its full generality by Dalton, is a
+complete solution of this problem in one, though but a secondary aspect,
+that of quantity: and in respect to quality, we have already some
+partial generalizations sufficient to indicate the possibility of
+ultimately proceeding farther. We can predicate some common properties
+of the kind of compounds which result from the combination, in each of
+the small number of possible proportions, of any acid whatever with any
+base. We have also the curious law, discovered by Berthollet, that two
+soluble salts mutually decompose one another whenever the new
+combinations which result produce an insoluble compound, or one less
+soluble than the two former. Another uniformity is that called the law
+of isomorphism; the identity of the crystalline forms of substances
+which possess in common certain peculiarities of chemical composition.
+Thus it appears that even heteropathic laws, such laws of combined
+agency as are not compounded of the laws of the separate agencies, are
+yet, at least in some cases, derived from them according to a fixed
+principle. There may, therefore, be laws of the generation of laws from
+others dissimilar to them; and in chemistry, these undiscovered laws of
+the dependence of the properties of the compound on the properties of
+its elements, may, together with the laws of the elements themselves,
+furnish the premises by which the science is perhaps destined one day to
+be rendered deductive.
+
+It would seem, therefore, that there is no class of phenomena in which
+the Composition of Causes does not obtain: that as a general rule,
+causes in combination produce exactly the same effects as when acting
+singly: but that this rule, though general, is not universal: that in
+some instances, at some particular points in the transition from
+separate to united action, the laws change, and an entirely new set of
+effects are either added to, or take the place of, those which arise
+from the separate agency of the same causes: the laws of these new
+effects being again susceptible of composition, to an indefinite extent,
+like the laws which they superseded.
+
+
+§ 3. That effects are proportional to their causes is laid down by some
+writers as an axiom in the theory of causation; and great use is
+sometimes made of this principle in reasonings respecting the laws of
+nature, though it is incumbered with many difficulties and apparent
+exceptions, which much ingenuity has been expended in showing not to be
+real ones. This proposition, in so far as it is true, enters as a
+particular case into the general principle of the Composition of Causes;
+the causes compounded being, in this instance, homogeneous; in which
+case, if in any, their joint effect might be expected to be identical
+with the sum of their separate effects. If a force equal to one hundred
+weight will raise a certain body along an inclined plane, a force equal
+to two hundred weight will raise two bodies exactly similar, and thus
+the effect is proportional to the cause. But does not a force equal to
+two hundred weight actually contain in itself two forces each equal to
+one hundred weight, which, if employed apart, would separately raise the
+two bodies in question? The fact, therefore, that when exerted jointly
+they raise both bodies at once, results from the Composition of Causes,
+and is a mere instance of the general fact that mechanical forces are
+subject to the law of Composition. And so in every other case which can
+be supposed. For the doctrine of the proportionality of effects to their
+causes cannot of course be applicable to cases in which the augmentation
+of the cause alters the _kind_ of effect; that is, in which the surplus
+quantity superadded to the cause does not become compounded with it, but
+the two together generate an altogether new phenomenon. Suppose that the
+application of a certain quantity of heat to a body merely increases its
+bulk, that a double quantity melts it, and a triple quantity decomposes
+it: these three effects being heterogeneous, no ratio, whether
+corresponding or not to that of the quantities of heat applied, can be
+established between them. Thus the supposed axiom of the proportionality
+of effects to their causes fails at the precise point where the
+principle of the Composition of Causes also fails; viz., where the
+concurrence of causes is such as to determine a change in the properties
+of the body generally, and render it subject to new laws, more or less
+dissimilar to those to which it conformed in its previous state. The
+recognition, therefore, of any such law of proportionality, is
+superseded by the more comprehensive principle, in which as much of it
+as is true is implicitly asserted.
+
+The general remarks on causation, which seemed necessary as an
+introduction to the theory of the inductive process, may here terminate.
+That process is essentially an inquiry into cases of causation. All the
+uniformities which exist in the succession of phenomena, and most of the
+uniformities in their coexistence, are either, as we have seen,
+themselves laws of causation, or consequences resulting from, and
+corollaries capable of being deduced from, such laws. If we could
+determine what causes are correctly assigned to what effects, and what
+effects to what causes, we should be virtually acquainted with the whole
+course of nature. All those uniformities which are mere results of
+causation, might then be explained and accounted for; and every
+individual fact or event might be predicted, provided we had the
+requisite data, that is, the requisite knowledge of the circumstances
+which, in the particular instance, preceded it.
+
+To ascertain, therefore, what are the laws of causation which exist in
+nature; to determine the effect of every cause, and the causes of all
+effects,--is the main business of Induction; and to point out how this
+is done is the chief object of Inductive Logic.
+
+
+
+
+CHAPTER VII.
+
+OF OBSERVATION AND EXPERIMENT.
+
+
+§ 1. It results from the preceding exposition, that the process of
+ascertaining what consequents, in nature, are invariably connected with
+what antecedents, or in other words what phenomena are related to each
+other as causes and effects, is in some sort a process of analysis. That
+every fact which begins to exist has a cause, and that this cause must
+be found somewhere among the facts which immediately preceded the
+occurrence, may be taken for certain. The whole of the present facts are
+the infallible result of all past facts, and more immediately of all the
+facts which existed at the moment previous. Here, then, is a great
+sequence, which we know to be uniform. If the whole prior state of the
+entire universe could again recur, it would again be followed by the
+present state. The question is, how to resolve this complex uniformity
+into the simpler uniformities which compose it, and assign to each
+portion of the vast antecedent the portion of the consequent which is
+attendant on it.
+
+This operation, which we have called analytical, inasmuch as it is the
+resolution of a complex whole into the component elements, is more than
+a merely mental analysis. No mere contemplation of the phenomena, and
+partition of them by the intellect alone, will of itself accomplish the
+end we have now in view. Nevertheless, such a mental partition is an
+indispensable first step. The order of nature, as perceived at a first
+glance, presents at every instant a chaos followed by another chaos. We
+must decompose each chaos into single facts. We must learn to see in the
+chaotic antecedent a multitude of distinct antecedents, in the chaotic
+consequent a multitude of distinct consequents. This, supposing it done,
+will not of itself tell us on which of the antecedents each consequent
+is invariably attendant. To determine that point, we must endeavour to
+effect a separation of the facts from one another, not in our minds
+only, but in nature. The mental analysis, however, must take place
+first. And every one knows that in the mode of performing it, one
+intellect differs immensely from another. It is the essence of the act
+of observing; for the observer is not he who merely sees the thing which
+is before his eyes, but he who sees what parts that thing is composed
+of. To do this well is a rare talent. One person, from inattention, or
+attending only in the wrong place, overlooks half of what he sees:
+another sets down much more than he sees, confounding it with what he
+imagines, or with what he infers; another takes note of the _kind_ of
+all the circumstances, but being inexpert in estimating their degree,
+leaves the quantity of each vague and uncertain; another sees indeed the
+whole, but makes such an awkward division of it into parts, throwing
+things into one mass which require to be separated, and separating
+others which might more conveniently be considered as one, that the
+result is much the same, sometimes even worse, than if no analysis had
+been attempted at all. It would be possible to point out what qualities
+of mind, and modes of mental culture, fit a person for being a good
+observer: that, however, is a question not of Logic, but of the Theory
+of Education, in the most enlarged sense of the term. There is not
+properly an Art of Observing. There may be rules for observing. But
+these, like rules for inventing, are properly instructions for the
+preparation of one's own mind; for putting it into the state in which it
+will be most fitted to observe, or most likely to invent. They are,
+therefore, essentially rules of self-education, which is a different
+thing from Logic. They do not teach how to do the thing, but how to make
+ourselves capable of doing it. They are an art of strengthening the
+limbs, not an art of using them.
+
+The extent and minuteness of observation which may be requisite, and the
+degree of decomposition to which it may be necessary to carry the mental
+analysis, depend on the particular purpose in view. To ascertain the
+state of the whole universe at any particular moment is impossible, but
+would also be useless. In making chemical experiments, we do not think
+it necessary to note the position of the planets; because experience has
+shown, as a very superficial experience is sufficient to show, that in
+such cases that circumstance is not material to the result: and,
+accordingly, in the ages when men believed in the occult influences of
+the heavenly bodies, it might have been unphilosophical to omit
+ascertaining the precise condition of those bodies at the moment of the
+experiment. As to the degree of minuteness of the mental subdivision; if
+we were obliged to break down what we observe into its very simplest
+elements, that is, literally into single facts, it would be difficult to
+say where we should find them: we can hardly ever affirm that our
+divisions of any kind have reached the ultimate unit. But this too is
+fortunately unnecessary. The only object of the mental separation is to
+suggest the requisite physical separation, so that we may either
+accomplish it ourselves, or seek for it in nature; and we have done
+enough when we have carried the subdivision as far as the point at which
+we are able to see what observations or experiments we require. It is
+only essential, at whatever point our mental decomposition of facts may
+for the present have stopped, that we should hold ourselves ready and
+able to carry it farther as occasion requires, and should not allow the
+freedom of our discriminating faculty to be imprisoned by the swathes
+and bands of ordinary classification; as was the case with all early
+speculative inquirers, not excepting the Greeks, to whom it seldom
+occurred that what was called by one abstract name might, in reality, be
+several phenomena, or that there was a possibility of decomposing the
+facts of the universe into any elements but those which ordinary
+language already recognised.
+
+
+§ 2. The different antecedents and consequents, being, then, supposed to
+be, so far as the case requires, ascertained and discriminated from one
+another; we are to inquire which is connected with which. In every
+instance which comes under our observation, there are many antecedents
+and many consequents. If those antecedents could not be severed from
+one another except in thought, or if those consequents never were found
+apart, it would be impossible for us to distinguish (_à posteriori_ at
+least) the real laws, or to assign to any cause its effect, or to any
+effect its cause. To do so, we must be able to meet with some of the
+antecedents apart from the rest, and observe what follows from them; or
+some of the consequents, and observe by what they are preceded. We must,
+in short, follow the Baconian rule of _varying the circumstances_. This
+is, indeed, only the first rule of physical inquiry, and not, as some
+have thought, the sole rule; but it is the foundation of all the rest.
+
+For the purpose of varying the circumstances, we may have recourse
+(according to a distinction commonly made) either to observation or to
+experiment; we may either _find_ an instance in nature, suited to our
+purposes, or, by an artificial arrangement of circumstances, _make_ one.
+The value of the instance depends on what it is in itself, not on the
+mode in which it is obtained: its employment for the purposes of
+induction depends on the same principles in the one case and in the
+other; as the uses of money are the same whether it is inherited or
+acquired. There is, in short, no difference in kind, no real logical
+distinction, between the two processes of investigation. There are,
+however, practical distinctions to which it is of considerable
+importance to advert.
+
+
+§ 3. The first and most obvious distinction between Observation and
+Experiment is, that the latter is an immense extension of the former. It
+not only enables us to produce a much greater number of variations in
+the circumstances than nature spontaneously offers, but also, in
+thousands of cases, to produce the precise _sort_ of variation which we
+are in want of for discovering the law of the phenomenon; a service
+which nature, being constructed on a quite different scheme from that of
+facilitating our studies, is seldom so friendly as to bestow upon us.
+For example, in order to ascertain what principle in the atmosphere
+enables it to sustain life, the variation we require is that a living
+animal should be immersed in each component element of the atmosphere
+separately. But nature does not supply either oxygen or azote in a
+separate state. We are indebted to artificial experiment for our
+knowledge that it is the former, and not the latter, which supports
+respiration; and for our knowledge of the very existence of the two
+ingredients.
+
+Thus far the advantage of experimentation over simple observation is
+universally recognised: all are aware that it enables us to obtain
+innumerable combinations of circumstances which are not to be found in
+nature, and so add to nature's experiments a multitude of experiments of
+our own. But there is another superiority (or, as Bacon would have
+expressed it, another prerogative) of instances artificially obtained
+over spontaneous instances,--of our own experiments over even the same
+experiments when made by nature,--which is not of less importance, and
+which is far from being felt and acknowledged in the same degree.
+
+When we can produce a phenomenon artificially, we can take it, as it
+were, home with us, and observe it in the midst of circumstances with
+which in all other respects we are accurately acquainted. If we desire
+to know what are the effects of the cause A, and are able to produce A
+by means at our disposal, we can generally determine at our own
+discretion, so far as is compatible with the nature of the phenomenon A,
+the whole of the circumstances which shall be present along with it: and
+thus, knowing exactly the simultaneous state of everything else which is
+within the reach of A's influence, we have only to observe what
+alteration is made in that state by the presence of A.
+
+For example, by the electric machine we can produce in the midst of
+known circumstances, the phenomena which nature exhibits on a grander
+scale in the form of lightning and thunder. Now let any one consider
+what amount of knowledge of the effects and laws of electric agency
+mankind could have obtained from the mere observation of thunder-storms,
+and compare it with that which they have gained, and may expect to gain,
+from electrical and galvanic experiments. This example is the more
+striking, now that we have reason to believe that electric action is of
+all natural phenomena (except heat) the most pervading and universal,
+which, therefore, it might antecedently have been supposed could stand
+least in need of artificial means of production to enable it to be
+studied; while the fact is so much the contrary, that without the
+electric machine, the Leyden jar, and the voltaic battery, we probably
+should never have suspected the existence of electricity as one of the
+great agents in nature; the few electric phenomena we should have known
+of would have continued to be regarded either as supernatural, or as a
+sort of anomalies and eccentricities in the order of the universe.
+
+When we have succeeded in insulating the phenomenon which is the subject
+of inquiry, by placing it among known circumstances, we may produce
+further variations of circumstances to any extent, and of such kinds as
+we think best calculated to bring the laws of the phenomenon into a
+clear light. By introducing one well-defined circumstance after another
+into the experiment, we obtain assurance of the manner in which the
+phenomenon behaves under an indefinite variety of possible
+circumstances. Thus, chemists, after having obtained some
+newly-discovered substance in a pure state, (that is, having made sure
+that there is nothing present which can interfere with and modify its
+agency,) introduce various other substances, one by one, to ascertain
+whether it will combine with them, or decompose them, and with what
+result; and also apply heat, or electricity, or pressure, to discover
+what will happen to the substance under each of these circumstances.
+
+But if, on the other hand, it is out of our power to produce the
+phenomenon, and we have to seek for instances in which nature produces
+it, the task before us is very different. Instead of being able to
+choose what the concomitant circumstances shall be, we now have to
+discover what they are; which, when we go beyond the simplest and most
+accessible cases, it is next to impossible to do, with any precision and
+completeness. Let us take, as an exemplification of a phenomenon which
+we have no means of fabricating artificially, a human mind. Nature
+produces many; but the consequence of our not being able to produce
+them by art is, that in every instance in which we see a human mind
+developing itself, or acting upon other things, we see it surrounded and
+obscured by an indefinite multitude of unascertainable circumstances,
+rendering the use of the common experimental methods almost delusive. We
+may conceive to what extent this is true, if we consider, among other
+things, that whenever nature produces a human mind, she produces, in
+close connexion with it, a body; that is, a vast complication of
+physical facts, in no two cases perhaps exactly similar, and most of
+which (except the mere structure, which we can examine in a sort of
+coarse way after it has ceased to act), are radically out of the reach
+of our means of exploration. If, instead of a human mind, we suppose the
+subject of investigation to be a human society or State, all the same
+difficulties recur in a greatly augmented degree.
+
+We have thus already come within sight of a conclusion, which the
+progress of the inquiry will, I think, bring before us with the clearest
+evidence: namely, that in the sciences which deal with phenomena in
+which artificial experiments are impossible (as in the case of
+astronomy), or in which they have a very limited range (as in mental
+philosophy, social science, and even physiology), induction from direct
+experience is practised at a disadvantage in most cases equivalent to
+impracticability: from which it follows that the methods of those
+sciences, in order to accomplish anything worthy of attainment, must be
+to a great extent, if not principally, deductive. This is already known
+to be the case with the first of the sciences we have mentioned,
+astronomy; that it is not generally recognised as true of the others, is
+probably one of the reasons why they are not in a more advanced state.
+
+
+§ 4. If what is called pure observation is at so great a disadvantage,
+compared with artificial experimentation, in one department of the
+direct exploration of phenomena, there is another branch in which the
+advantage is all on the side of the former.
+
+Inductive inquiry having for its object to ascertain what causes are
+connected with what effects, we may begin this search at either end of
+the road which leads from the one point to the other: we may either
+inquire into the effects of a given cause, or into the causes of a given
+effect. The fact that light blackens chloride of silver might have been
+discovered either by experiments on light, trying what effect it would
+produce on various substances, or by observing that portions of the
+chloride had repeatedly become black, and inquiring into the
+circumstances. The effect of the urali poison might have become known
+either by administering it to animals, or by examining how it happened
+that the wounds which the Indians of Guiana inflict with their arrows
+prove so uniformly mortal. Now it is manifest from the mere statement of
+the examples, without any theoretical discussion, that artificial
+experimentation is applicable only to the former of these modes of
+investigation. We can take a cause, and try what it will produce: but we
+cannot take an effect, and try what it will be produced by. We can only
+watch till we see it produced, or are enabled to produce it by accident.
+
+This would be of little importance, if it always depended on our choice
+from which of the two ends of the sequence we would undertake our
+inquiries. But we have seldom any option. As we can only travel from the
+known to the unknown, we are obliged to commence at whichever end we are
+best acquainted with. If the agent is more familiar to us than its
+effects, we watch for, or contrive, instances of the agent, under such
+varieties of circumstances as are open to us, and observe the result.
+If, on the contrary, the conditions on which a phenomenon depends are
+obscure, but the phenomenon itself familiar, we must commence our
+inquiry from the effect. If we are struck with the fact that chloride of
+silver has been blackened, and have no suspicion of the cause, we have
+no resource but to compare instances in which the fact has chanced to
+occur, until by that comparison we discover that in all those instances
+the substances had been exposed to light. If we knew nothing of the
+Indian arrows but their fatal effect, accident alone could turn our
+attention to experiments on the urali; in the regular course of
+investigation, we could only inquire, or try to observe, what had been
+done to the arrows in particular instances.
+
+Wherever, having nothing to guide us to the cause, we are obliged to set
+out from the effect, and to apply the rule of varying the circumstances
+to the consequents, not the antecedents, we are necessarily destitute of
+the resource of artificial experimentation. We cannot, at our choice,
+obtain consequents, as we can antecedents, under any set of
+circumstances compatible with their nature. There are no means of
+producing effects but through their causes, and by the supposition the
+causes of the effect in question are not known to us. We have therefore
+no expedient but to study it where it offers itself spontaneously. If
+nature happens to present us with instances sufficiently varied in their
+circumstances, and if we are able to discover, either among the
+proximate antecedents or among some other order of antecedents,
+something which is always found when the effect is found, however
+various the circumstances, and never found when it is not; we may
+discover, by mere observation without experiment, a real uniformity in
+nature.
+
+But though this is certainly the most favourable case for sciences of
+pure observation, as contrasted with those in which artificial
+experiments are possible, there is in reality no case which more
+strikingly illustrates the inherent imperfection of direct induction
+when not founded on experimentation. Suppose that, by a comparison of
+cases of the effect, we have found an antecedent which appears to be,
+and perhaps is, invariably connected with it: we have not yet proved
+that antecedent to be the cause, until we have reversed the process, and
+produced the effect by means of that antecedent. If we can produce the
+antecedent artificially, and if, when we do so, the effect follows, the
+induction is complete; that antecedent is the cause of that
+consequent.[32] But we have then added the evidence of experiment to
+that of simple observation. Until we had done so, we had only proved
+_invariable_ antecedence within the limits of experience, but not
+_unconditional_ antecedence, or causation. Until it had been shown by
+the actual production of the antecedent under known circumstances, and
+the occurrence thereupon of the consequent, that the antecedent was
+really the condition on which it depended; the uniformity of succession
+which was proved to exist between them might, for aught we knew, be
+(like the succession of day and night) not a case of causation at all;
+both antecedent and consequent might be successive stages of the effect
+of an ulterior cause. Observation, in short, without experiment
+(supposing no aid from deduction) can ascertain sequences and
+coexistences, but cannot prove causation.
+
+In order to see these remarks verified by the actual state of the
+sciences, we have only to think of the condition of natural history. In
+zoology, for example, there is an immense number of uniformities
+ascertained, some of coexistence, others of succession, to many of
+which, notwithstanding considerable variations of the attendant
+circumstances, we know not any exception: but the antecedents, for the
+most part, are such as we cannot artificially produce; or if we can, it
+is only by setting in motion the exact process by which nature produces
+them; and this being to us a mysterious process, of which the main
+circumstances are not only unknown but unobservable, we do not succeed
+in obtaining the antecedents under known circumstances. What is the
+result? That on this vast subject, which affords so much and such varied
+scope for observation, we have made most scanty progress in ascertaining
+any laws of causation. We know not with certainty, in the case of most
+of the phenomena that we find conjoined, which is the condition of the
+other; which is cause, and which effect, or whether either of them is
+so, or they are not rather conjunct effects of causes yet to be
+discovered, complex results of laws hitherto unknown.
+
+Although some of the foregoing observations may be, in technical
+strictness of arrangement, premature in this place, it seemed that a few
+general remarks on the difference between sciences of mere observation
+and sciences of experimentation, and the extreme disadvantage under
+which directly inductive inquiry is necessarily carried on in the
+former, were the best preparation for discussing the methods of direct
+induction; a preparation rendering superfluous much that must otherwise
+have been introduced, with some inconvenience, into the heart of that
+discussion. To the consideration of these methods we now proceed.
+
+
+
+
+CHAPTER VIII.
+
+OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.
+
+
+§ 1. The simplest and most obvious modes of singling out from among the
+circumstances which precede or follow a phenomenon, those with which it
+is really connected by an invariable law, are two in number. One is, by
+comparing together different instances in which the phenomenon occurs.
+The other is, by comparing instances in which the phenomenon does occur,
+with instances in other respects similar in which it does not. These two
+methods may be respectively denominated, the Method of Agreement, and
+the Method of Difference.
+
+In illustrating these methods, it will be necessary to bear in mind the
+twofold character of inquiries into the laws of phenomena; which may be
+either inquiries into the cause of a given effect, or into the effects
+or properties of a given cause. We shall consider the methods in their
+application to either order of investigation, and shall draw our
+examples equally from both.
+
+We shall denote antecedents by the large letters of the alphabet, and
+the consequents corresponding to them by the small. Let A, then, be an
+agent or cause, and let the object of our inquiry be to ascertain what
+are the effects of this cause. If we can either find, or produce, the
+agent A in such varieties of circumstances, that the different cases
+have no circumstance in common except A; then whatever effect we find to
+be produced in all our trials, is indicated as the effect of A. Suppose,
+for example, that A is tried along with B and C, and that the effect is
+_a b c_; and suppose that A is next tried with D and E, but without B
+and C, and that the effect is _a d e_. Then we may reason thus: _b_ and
+_c_ are not effects of A, for they were not produced by it in the second
+experiment; nor are _d_ and _e_, for they were not produced in the
+first. Whatever is really the effect of A must have been produced in
+both instances; now this condition is fulfilled by no circumstance
+except _a_. The phenomenon _a_ cannot have been the effect of B or C,
+since it was produced where they were not; nor of D or E, since it was
+produced where they were not. Therefore it is the effect of A.
+
+For example, let the antecedent A be the contact of an alkaline
+substance and an oil. This combination being tried under several
+varieties of circumstances, resembling each other in nothing else, the
+results agree in the production of a greasy and detersive or saponaceous
+substance: it is therefore concluded that the combination of an oil and
+an alkali causes the production of a soap. It is thus we inquire, by the
+Method of Agreement, into the effect of a given cause.
+
+In a similar manner we may inquire into the cause of a given effect. Let
+_a_ be the effect. Here, as shown in the last chapter, we have only the
+resource of observation without experiment: we cannot take a phenomenon
+of which we know not the origin, and try to find its mode of production
+by producing it: if we succeeded in such a random trial it could only be
+by accident. But if we can observe _a_ in two different combinations, _a
+b c_, and _a d e_; and if we know, or can discover, that the antecedent
+circumstances in these cases respectively were A B C and A D E; we may
+conclude by a reasoning similar to that in the preceding example, that A
+is the antecedent connected with the consequent _a_ by a law of
+causation. B and C, we may say, cannot be causes of _a_, since on its
+second occurrence they were not present; nor are D and E, for they were
+not present on its first occurrence. A, alone of the five circumstances,
+was found among the antecedents of _a_ in both instances.
+
+For example, let the effect _a_ be crystallization. We compare instances
+in which bodies are known to assume crystalline structure, but which
+have no other point of agreement; and we find them to have one, and as
+far as we can observe, only one, antecedent in common: the deposition of
+a solid matter from a liquid state, either a state of fusion or of
+solution. We conclude, therefore, that the solidification of a
+substance from a liquid state is an invariable antecedent of its
+crystallization.
+
+In this example we may go farther, and say, it is not only the
+invariable antecedent but the cause; or at least the proximate event
+which completes the cause. For in this case we are able, after detecting
+the antecedent A, to produce it artificially, and by finding that _a_
+follows it, verify the result of our induction. The importance of thus
+reversing the proof was strikingly manifested when by keeping a phial of
+water charged with siliceous particles undisturbed for years, a chemist
+(I believe Dr. Wollaston) succeeded in obtaining crystals of quartz: and
+in the equally interesting experiment in which Sir James Hall produced
+artificial marble, by the cooling of its materials from fusion under
+immense pressure: two admirable examples of the light which may be
+thrown upon the most secret processes of nature by well-contrived
+interrogation of her.
+
+But if we cannot artificially produce the phenomenon A, the conclusion
+that it is the cause of _a_ remains subject to very considerable doubt.
+Though an invariable, it may not be the unconditional antecedent of _a_,
+but may precede it as day precedes night or night day. This uncertainty
+arises from the impossibility of assuring ourselves that A is the _only_
+immediate antecedent common to both the instances. If we could be
+certain of having ascertained all the invariable antecedents, we might
+be sure that the unconditional invariable antecedent, or cause, must be
+found somewhere among them. Unfortunately it is hardly ever possible to
+ascertain all the antecedents, unless the phenomenon is one which we can
+produce artificially. Even then, the difficulty is merely lightened, not
+removed: men knew how to raise water in pumps long before they adverted
+to what was really the operating circumstance in the means they
+employed, namely, the pressure of the atmosphere on the open surface of
+the water. It is, however, much easier to analyse completely a set of
+arrangements made by ourselves, than the whole complex mass of the
+agencies which nature happens to be exerting at the moment of the
+production of a given phenomenon. We may overlook some of the material
+circumstances in an experiment with an electrical machine; but we shall,
+at the worst, be better acquainted with them than with those of a
+thunder-storm.
+
+The mode of discovering and proving laws of nature, which we have now
+examined, proceeds on the following axiom: Whatever circumstances can be
+excluded, without prejudice to the phenomenon, or can be absent
+notwithstanding its presence, is not connected with it in the way of
+causation. The casual circumstances being thus eliminated, if only one
+remains, that one is the cause which we are in search of: if more than
+one, they either are, or contain among them, the cause; and so, _mutatis
+mutandis_, of the effect. As this method proceeds by comparing different
+instances to ascertain in what they agree, I have termed it the Method
+of Agreement: and we may adopt as its regulating principle the following
+canon:--
+
+FIRST CANON.
+
+_If two or more instances of the phenomenon under investigation have
+only one circumstance in common, the circumstance in which alone all the
+instances agree, is the cause (or effect) of the given phenomenon._
+
+Quitting for the present the Method of Agreement, to which we shall
+almost immediately return, we proceed to a still more potent instrument
+of the investigation of nature, the Method of Difference.
+
+
+§ 2. In the Method of Agreement, we endeavoured to obtain instances
+which agreed in the given circumstance but differed in every other: in
+the present method we require, on the contrary, two instances resembling
+one another in every other respect, but differing in the presence or
+absence of the phenomenon we wish to study. If our object be to discover
+the effects of an agent A, we must procure A in some set of ascertained
+circumstances, as A B C, and having noted the effects produced, compare
+them with the effect of the remaining circumstances B C, when A is
+absent. If the effect of A B C is _a b c_, and the effect of B C, _b c_,
+it is evident that the effect of A is _a_. So again, if we begin at the
+other end, and desire to investigate the cause of an effect _a_, we must
+select an instance, as _a b c_, in which the effect occurs, and in which
+the antecedents were A B C, and we must look out for another instance in
+which the remaining circumstances, _b c_, occur without _a_. If the
+antecedents, in that instance, are B C, we know that the cause of _a_
+must be A: either A alone, or A in conjunction with some of the other
+circumstances present.
+
+It is scarcely necessary to give examples of a logical process to which
+we owe almost all the inductive conclusions we draw in daily life. When
+a man is shot through the heart, it is by this method we know that it
+was the gun-shot which killed him: for he was in the fulness of life
+immediately before, all circumstances being the same, except the wound.
+
+The axioms implied in this method are evidently the following. Whatever
+antecedent cannot be excluded without preventing the phenomenon, is the
+cause, or a condition, of that phenomenon: Whatever consequent can be
+excluded, with no other difference in the antecedents than the absence
+of a particular one, is the effect of that one. Instead of comparing
+different instances of a phenomenon, to discover in what they agree,
+this method compares an instance of its occurrence with an instance of
+its non-occurrence, to discover in what they differ. The canon which is
+the regulating principle of the Method of Difference may be expressed as
+follows:
+
+SECOND CANON.
+
+_If an instance in which the phenomenon under investigation occurs, and
+an instance in which it does not occur, have every circumstance in
+common save one, that one occurring only in the former; the circumstance
+in which alone the two instances differ, is the effect, or the cause, or
+an indispensable part of the cause, of the phenomenon._
+
+
+§ 3. The two methods which we have now stated have many features of
+resemblance, but there are also many distinctions between them. Both
+are methods of _elimination_. This term (employed in the theory of
+equations to denote the process by which one after another of the
+elements of a question is excluded, and the solution made to depend on
+the relation between the remaining elements only) is well suited to
+express the operation, analogous to this, which has been understood
+since the time of Bacon to be the foundation of experimental inquiry:
+namely, the successive exclusion of the various circumstances which are
+found to accompany a phenomenon in a given instance, in order to
+ascertain what are those among them which can be absent consistently
+with the existence of the phenomenon. The Method of Agreement stands on
+the ground that whatever can be eliminated, is not connected with the
+phenomenon by any law. The Method of Difference has for its foundation,
+that whatever cannot be eliminated, is connected with the phenomenon by
+a law.
+
+Of these methods, that of Difference is more particularly a method of
+artificial experiment; while that of Agreement is more especially the
+resource employed where experimentation is impossible. A few reflections
+will prove the fact, and point out the reason of it.
+
+It is inherent in the peculiar character of the Method of Difference,
+that the nature of the combinations which it requires is much more
+strictly defined than in the Method of Agreement. The two instances
+which are to be compared with one another must be exactly similar, in
+all circumstances except the one which we are attempting to investigate:
+they must be in the relation of A B C and B C, or of _a b c_ and _b c_.
+It is true that this similarity of circumstances needs not extend to
+such as are already known to be immaterial to the result. And in the
+case of most phenomena we learn at once, from the commonest experience,
+that most of the coexistent phenomena of the universe may be either
+present or absent without affecting the given phenomenon; or, if
+present, are present indifferently when the phenomenon does not happen
+and when it does. Still, even limiting the identity which is required
+between the two instances, A B C and B C, to such circumstances as are
+not already known to be indifferent; it is very seldom that nature
+affords two instances, of which we can be assured that they stand in
+this precise relation to one another. In the spontaneous operations of
+nature there is generally such complication and such obscurity, they are
+mostly either on so overwhelmingly large or on so inaccessibly minute a
+scale, we are so ignorant of a great part of the facts which really take
+place, and even those of which we are not ignorant are so multitudinous,
+and therefore so seldom exactly alike in any two cases, that a
+spontaneous experiment, of the kind required by the Method of
+Difference, is commonly not to be found. When, on the contrary, we
+obtain a phenomenon by an artificial experiment, a pair of instances
+such as the method requires is obtained almost as a matter of course,
+provided the process does not last a long time. A certain state of
+surrounding circumstances existed before we commenced the experiment;
+this is B C. We then introduce A; say, for instance, by merely bringing
+an object from another part of the room, before there has been time for
+any change in the other elements. It is, in short (as M. Comte
+observes), the very nature of an experiment, to introduce into the
+pre-existing state of circumstances a change perfectly definite. We
+choose a previous state of things with which we are well acquainted, so
+that no unforeseen alteration in that state is likely to pass
+unobserved; and into this we introduce, as rapidly as possible, the
+phenomenon which we wish to study; so that in general we are entitled to
+feel complete assurance that the pre-existing state, and the state which
+we have produced, differ in nothing except the presence or absence of
+that phenomenon. If a bird is taken from a cage, and instantly plunged
+into carbonic acid gas, the experimentalist may be fully assured (at all
+events after one or two repetitions) that no circumstance capable of
+causing suffocation had supervened in the interim, except the change
+from immersion in the atmosphere to immersion in carbonic acid gas.
+There is one doubt, indeed, which may remain in some cases of this
+description; the effect may have been produced not by the change, but by
+the means employed to produce the change. The possibility, however, of
+this last supposition generally admits of being conclusively tested by
+other experiments. It thus appears that in the study of the various
+kinds of phenomena which we can, by our voluntary agency, modify or
+control, we can in general satisfy the requisitions of the Method of
+Difference; but that by the spontaneous operations of nature those
+requisitions are seldom fulfilled.
+
+The reverse of this is the case with the Method of Agreement. We do not
+here require instances of so special and determinate a kind. Any
+instances whatever, in which nature presents us with a phenomenon, may
+be examined for the purposes of this method; and if all such instances
+agree in anything, a conclusion of considerable value is already
+attained. We can seldom, indeed, be sure that the one point of agreement
+is the only one; but this ignorance does not, as in the Method of
+Difference, vitiate the conclusion; the certainty of the result, as far
+as it goes, is not affected. We have ascertained one invariable
+antecedent or consequent, however many other invariable antecedents or
+consequents may still remain unascertained. If A B C, A D E, A F G, are
+all equally followed by _a_, then _a_ is an invariable consequent of A.
+If _a b c_, _a d e_, _a f g_, all number A among their antecedents, then
+A is connected as an antecedent, by some invariable law, with _a_. But
+to determine whether this invariable antecedent is a cause, or this
+invariable consequent an effect, we must be able, in addition, to
+produce the one by means of the other; or, at least, to obtain that
+which alone constitutes our assurance of having produced anything,
+namely, an instance in which the effect, _a_, has come into existence,
+with no other change in the pre-existing circumstances than the addition
+of A. And this, if we can do it, is an application of the Method of
+Difference, not of the Method of Agreement.
+
+It thus appears to be by the Method of Difference alone that we can
+ever, in the way of direct experience, arrive with certainty at causes.
+The Method of Agreement leads only to laws of phenomena (as some writers
+call them, but improperly, since laws of causation are also laws of
+phenomena): that is, to uniformities, which either are not laws of
+causation, or in which the question of causation must for the present
+remain undecided. The Method of Agreement is chiefly to be resorted to,
+as a means of suggesting applications of the Method of Difference (as in
+the last example the comparison of A B C, A D E, A F G, suggested that A
+was the antecedent on which to try the experiment whether it could
+produce _a_); or as an inferior resource, in case the Method of
+Difference is impracticable; which, as we before showed, generally
+arises from the impossibility of artificially producing the phenomena.
+And hence it is that the Method of Agreement, though applicable in
+principle to either case, is more emphatically the method of
+investigation on those subjects where artificial experimentation is
+impossible: because on those it is, generally, our only resource of a
+directly inductive nature; while, in the phenomena which we can produce
+at pleasure, the Method of Difference generally affords a more
+efficacious process, which will ascertain causes as well as mere laws.
+
+
+§ 4. There are, however, many cases in which, though our power of
+producing the phenomenon is complete, the Method of Difference either
+cannot be made available at all, or not without a previous employment of
+the Method of Agreement. This occurs when the agency by which we can
+produce the phenomenon is not that of one single antecedent, but a
+combination of antecedents, which we have no power of separating from
+each other, and exhibiting apart. For instance, suppose the subject of
+inquiry to be the cause of the double refraction of light. We can
+produce this phenomenon at pleasure, by employing any one of the many
+substances which are known to refract light in that peculiar manner. But
+if, taking one of those substances, as Iceland spar for example, we wish
+to determine on which of the properties of Iceland spar this remarkable
+phenomenon depends, we can make no use, for that purpose, of the Method
+of Difference; for we cannot find another substance precisely resembling
+Iceland spar except in some one property. The only mode, therefore, of
+prosecuting this inquiry is that afforded by the Method of Agreement; by
+which, in fact, through a comparison of all the known substances which
+have the property of doubly refracting light, it was ascertained that
+they agree in the circumstance of being crystalline substances; and
+though the converse does not hold, though all crystalline substances
+have not the property of double refraction, it was concluded, with
+reason, that there is a real connexion between these two properties;
+that either crystalline structure, or the cause which gives rise to that
+structure, is one of the conditions of double refraction.
+
+Out of this employment of the Method of Agreement arises a peculiar
+modification of that method, which is sometimes of great avail in the
+investigation of nature. In cases similar to the above, in which it is
+not possible to obtain the precise pair of instances which our second
+canon requires--instances agreeing in every antecedent except A, or in
+every consequent except _a_; we may yet be able, by a double employment
+of the Method of Agreement, to discover in what the instances which
+contain A or _a_, differ from those which do not.
+
+If we compare various instances in which _a_ occurs, and find that they
+all have in common the circumstance A, and (as far as can be observed)
+no other circumstance, the Method of Agreement, so far, bears testimony
+to a connexion between A and _a_. In order to convert this evidence of
+connexion into proof of causation by the direct Method of Difference, we
+ought to be able, in some one of these instances, as for example A B C,
+to leave out A, and observe whether by doing so, _a_ is prevented. Now
+supposing (what is often the case) that we are not able to try this
+decisive experiment; yet, provided we can by any means discover what
+would be its result if we could try it, the advantage will be the same.
+Suppose, then, that as we previously examined a variety of instances in
+which _a_ occurred, and found them to agree in containing A, so we now
+observe a variety of instances in which _a_ does not occur, and find
+them agree in not containing A; which establishes, by the Method of
+Agreement, the same connexion between the absence of A and the absence
+of _a_, which was before established between their presence. As, then,
+it had been shown that whenever A is present _a_ is present, so it being
+now shown that when A is taken away _a_ is removed along with it, we
+have by the one proposition A B C, _a b c_, by the other B C, _b c_,
+the positive and negative instances which the Method of Difference
+requires.
+
+This method may be called the Indirect Method of Difference, or the
+Joint Method of Agreement and Difference; and consists in a double
+employment of the Method of Agreement, each proof being independent of
+the other, and corroborating it. But it is not equivalent to a proof by
+the direct Method of Difference. For the requisitions of the Method of
+Difference are not satisfied, unless we can be quite sure either that
+the instances affirmative of _a_ agree in no antecedent whatever but A,
+or that the instances negative of _a_ agree in nothing but the negation
+of A. Now if it were possible, which it never is, to have this
+assurance, we should not need the joint method; for either of the two
+sets of instances separately would then be sufficient to prove
+causation. This indirect method, therefore, can only be regarded as a
+great extension and improvement of the Method of Agreement, but not as
+participating in the more cogent nature of the Method of Difference. The
+following may be stated as its canon:--
+
+THIRD CANON.
+
+_If two or more instances in which the phenomenon occurs have only one
+circumstance in common, while two or more instances in which it does not
+occur have nothing in common save the absence of that circumstance; the
+circumstance in which alone the two sets of instances differ, is the
+effect, or the cause, or an indispensable part of the cause, of the
+phenomenon._
+
+We shall presently see that the Joint Method of Agreement and Difference
+constitutes, in another respect not yet adverted to, an improvement upon
+the common Method of Agreement, namely, in being unaffected by a
+characteristic imperfection of that method, the nature of which still
+remains to be pointed out. But as we cannot enter into this exposition
+without introducing a new element of complexity into this long and
+intricate discussion, I shall postpone it to a subsequent chapter, and
+shall at once proceed to a statement of two other methods, which will
+complete the enumeration of the means which mankind possess for
+exploring the laws of nature by specific observation and experience.
+
+
+§ 5. The first of these has been aptly denominated the Method of
+Residues. Its principle is very simple. Subducting from any given
+phenomenon all the portions which, by virtue of preceding inductions,
+can be assigned to known causes, the remainder will be the effect of the
+antecedents which had been overlooked, or of which the effect was as yet
+an unknown quantity.
+
+Suppose, as before, that we have the antecedents A B C, followed by the
+consequents _a b c_, and that by previous inductions (founded, we will
+suppose, on the Method of Difference) we have ascertained the causes of
+some of these effects, or the effects of some of these causes; and are
+thence apprised that the effect of A is _a_, and that the effect of B is
+_b_. Subtracting the sum of these effects from the total phenomenon,
+there remains _c_, which now, without any fresh experiments, we may know
+to be the effect of C. This Method of Residues is in truth a peculiar
+modification of the Method of Difference. If the instance A B C, _a b
+c_, could have been compared with a single instance A B, _a b_, we
+should have proved C to be the cause of _c_, by the common process of
+the Method of Difference. In the present case, however, instead of a
+single instance A B, we have had to study separately the causes A and B,
+and to infer from the effects which they produce separately, what effect
+they must produce in the case A B C where they act together. Of the two
+instances, therefore, which the Method of Difference requires,--the one
+positive, the other negative,--the negative one, or that in which the
+given phenomenon is absent, is not the direct result of observation and
+experiment, but has been arrived at by deduction. As one of the forms of
+the Method of Difference, the Method of Residues partakes of its
+rigorous certainty, provided the previous inductions, those which gave
+the effects of A and B, were obtained by the same infallible method, and
+provided we are certain that C is the _only_ antecedent to which the
+residual phenomenon _c_ can be referred; the only agent of which we had
+not already calculated and subducted the effect. But as we can never be
+quite certain of this, the evidence derived from the Method of Residues
+is not complete unless we can obtain C artificially and try it
+separately, or unless its agency, when once suggested, can be accounted
+for, and proved deductively from known laws.
+
+Even with these reservations, the Method of Residues is one of the most
+important among our instruments of discovery. Of all the methods of
+investigating laws of nature, this is the most fertile in unexpected
+results; often informing us of sequences in which neither the cause nor
+the effect were sufficiently conspicuous to attract of themselves the
+attention of observers. The agent C may be an obscure circumstance, not
+likely to have been perceived unless sought for, nor likely to have been
+sought for until attention had been awakened by the insufficiency of the
+obvious causes to account for the whole of the effect. And _c_ may be so
+disguised by its intermixture with _a_ and _b_, that it would scarcely
+have presented itself spontaneously as a subject of separate study. Of
+these uses of the method, we shall presently cite some remarkable
+examples. The canon of the Method of Residues is as follows:--
+
+FOURTH CANON.
+
+_Subduct from any phenomenon such part as is known by previous
+inductions to be the effect of certain antecedents, and the residue of
+the phenomenon is the effect of the remaining antecedents._
+
+
+§ 6. There remains a class of laws which it is impracticable to
+ascertain by any of the three methods which I have attempted to
+characterize; namely, the laws of those Permanent Causes, or
+indestructible natural agents, which it is impossible either to exclude
+or to isolate; which we can neither hinder from being present, nor
+contrive that they shall be present alone. It would appear at first
+sight that we could by no means separate the effects of these agents
+from the effects of those other phenomena with which they cannot be
+prevented from coexisting. In respect, indeed, to most of the permanent
+causes, no such difficulty exists; since though we cannot eliminate
+them as coexisting facts, we can eliminate them as influencing agents,
+by simply trying our experiment in a local situation beyond the limits
+of their influence. The pendulum, for example, has its oscillations
+disturbed by the vicinity of a mountain: we remove the pendulum to a
+sufficient distance from the mountain, and the disturbance ceases: from
+these data we can determine by the Method of Difference, the amount of
+effect due to the mountain; and beyond a certain distance everything
+goes on precisely as it would do if the mountain exercised no influence
+whatever, which, accordingly, we, with sufficient reason, conclude to be
+the fact.
+
+The difficulty, therefore, in applying the methods already treated of to
+determine the effects of Permanent Causes, is confined to the cases in
+which it is impossible for us to get out of the local limits of their
+influence. The pendulum can be removed from the influence of the
+mountain, but it cannot be removed from the influence of the earth: we
+cannot take away the earth from the pendulum, nor the pendulum from the
+earth, to ascertain whether it would continue to vibrate if the action
+which the earth exerts upon it were withdrawn. On what evidence, then,
+do we ascribe its vibrations to the earth's influence? Not on any
+sanctioned by the Method of Difference; for one of the two instances,
+the negative instance, is wanting. Nor by the Method of Agreement; for
+though all pendulums agree in this, that during their oscillations the
+earth is always present, why may we not as well ascribe the phenomenon
+to the sun, which is equally a coexistent fact in all the experiments?
+It is evident that to establish even so simple a fact of causation as
+this, there was required some method over and above those which we have
+yet examined.
+
+As another example, let us take the phenomenon Heat. Independently of
+all hypothesis as to the real nature of the agency so called, this fact
+is certain, that we are unable to exhaust any body of the whole of its
+heat. It is equally certain, that no one ever perceived heat not
+emanating from a body. Being unable, then, to separate Body and Heat, we
+cannot effect such a variation of circumstances as the foregoing three
+methods require; we cannot ascertain, by those methods, what portion of
+the phenomena exhibited by any body is due to the heat contained in it.
+If we could observe a body with its heat, and the same body entirely
+divested of heat, the Method of Difference would show the effect due to
+the heat, apart from that due to the body. If we could observe heat
+under circumstances agreeing in nothing but heat, and therefore not
+characterized also by the presence of a body, we could ascertain the
+effects of heat, from an instance of heat with a body and an instance of
+heat without a body, by the Method of Agreement; or we could determine
+by the Method of Difference what effect was due to the body, when the
+remainder which was due to the heat would be given by the Method of
+Residues. But we can do none of these things; and without them the
+application of any of the three methods to the solution of this problem
+would be illusory. It would be idle, for instance, to attempt to
+ascertain the effect of heat by subtracting from the phenomena exhibited
+by a body, all that is due to its other properties; for as we have never
+been able to observe any bodies without a portion of heat in them,
+effects due to that heat might form a part of the very results, which we
+were affecting to subtract in order that the effect of heat might be
+shown by the residue.
+
+If, therefore, there were no other methods of experimental investigation
+than these three, we should be unable to determine the effects due to
+heat as a cause. But we have still a resource. Though we cannot exclude
+an antecedent altogether, we may be able to produce, or nature may
+produce for us, some modification in it. By a modification is here
+meant, a change in it, not amounting to its total removal. If some
+modification in the antecedent A is always followed by a change in the
+consequent _a_, the other consequents _b_ and _c_ remaining the same; or
+_vice versâ_, if every change in _a_ is found to have been preceded by
+some modification in A, none being observable in any of the other
+antecedents; we may safely conclude that _a_ is, wholly or in part, an
+effect traceable to A, or at least in some way connected with it through
+causation. For example, in the case of heat, though we cannot expel it
+altogether from any body, we can modify it in quantity, we can increase
+or diminish it; and doing so, we find by the various methods of
+experimentation or observation already treated of, that such increase or
+diminution of heat is followed by expansion or contraction of the body.
+In this manner we arrive at the conclusion, otherwise unattainable by
+us, that one of the effects of heat is to enlarge the dimensions of
+bodies; or what is the same thing in other words, to widen the distances
+between their particles.
+
+A change in a thing, not amounting to its total removal, that is, a
+change which leaves it still the same thing it was, must be a change
+either in its quantity, or in some of its variable relations to other
+things, of which variable relations the principal is its position in
+space. In the previous example, the modification which was produced in
+the antecedent was an alteration in its quantity. Let us now suppose the
+question to be, what influence the moon exerts on the surface of the
+earth. We cannot try an experiment in the absence of the moon, so as to
+observe what terrestrial phenomena her annihilation would put an end to;
+but when we find that all the variations in the _position_ of the moon
+are followed by corresponding variations in the time and place of high
+water, the place being always either the part of the earth which is
+nearest to, or that which is most remote from, the moon, we have ample
+evidence that the moon is, wholly or partially, the cause which
+determines the tides. It very commonly happens, as it does in this
+instance, that the variations of an effect are correspondent, or
+analogous, to those of its cause; as the moon moves farther towards the
+east, the high water point does the same: but this is not an
+indispensable condition; as may be seen in the same example, for along
+with that high water point there is at the same instant another high
+water point diametrically opposite to it, and which, therefore, of
+necessity, moves towards the west, as the moon, followed by the nearer
+of the tide waves, advances towards the east: and yet both these motions
+are equally effects of the moon's motion.
+
+That the oscillations of the pendulum are caused by the earth, is proved
+by similar evidence. Those oscillations take place between equidistant
+points on the two sides of a line, which, being perpendicular to the
+earth, varies with every variation in the earth's position, either in
+space or relatively to the object. Speaking accurately, we only know by
+the method now characterized, that all terrestrial bodies tend to the
+earth, and not to some unknown fixed point lying in the same direction.
+In every twenty-four hours, by the earth's rotation, the line drawn from
+the body at right angles to the earth coincides successively with all
+the radii of a circle, and in the course of six months the place of that
+circle varies by nearly two hundred millions of miles; yet in all these
+changes of the earth's position, the line in which bodies tend to fall
+continues to be directed towards it: which proves that terrestrial
+gravity is directed to the earth, and not, as was once fancied by some,
+to a fixed point of space.
+
+The method by which these results were obtained, may be termed the
+Method of Concomitant Variations: it is regulated by the following
+canon:--
+
+FIFTH CANON.
+
+_Whatever phenomenon varies in any manner whenever another phenomenon
+varies in some particular manner, is either a cause or an effect of that
+phenomenon, or is connected with it through some fact of causation._
+
+The last clause is subjoined, because it by no means follows when two
+phenomena accompany each other in their variations, that the one is
+cause and the other effect. The same thing may, and indeed must happen,
+supposing them to be two different effects of a common cause: and by
+this method alone it would never be possible to ascertain which of the
+suppositions is the true one. The only way to solve the doubt would be
+that which we have so often adverted to, viz. by endeavouring to
+ascertain whether we can produce the one set of variations by means of
+the other. In the case of heat, for example, by increasing the
+temperature of a body we increase its bulk, but by increasing its bulk
+we do not increase its temperature; on the contrary, (as in the
+rarefaction of air under the receiver of an air-pump,) we generally
+diminish it: therefore heat is not an effect, but a cause, of increase
+of bulk. If we cannot ourselves produce the variations, we must
+endeavour, though it is an attempt which is seldom successful, to find
+them produced by nature in some case in which the pre-existing
+circumstances are perfectly known to us.
+
+It is scarcely necessary to say, that in order to ascertain the uniform
+concomitance of variations in the effect with variations in the cause,
+the same precautions must be used as in any other case of the
+determination of an invariable sequence. We must endeavour to retain all
+the other antecedents unchanged, while that particular one is subjected
+to the requisite series of variations; or in other words, that we may be
+warranted in inferring causation from concomitance of variations, the
+concomitance itself must be proved by the Method of Difference.
+
+It might at first appear that the Method of Concomitant Variations
+assumes a new axiom, or law of causation in general, namely, that every
+modification of the cause is followed by a change in the effect. And it
+does usually happen that when a phenomenon A causes a phenomenon _a_,
+any variation in the quantity or in the various relations of A, is
+uniformly followed by a variation in the quantity or relations of _a_.
+To take a familiar instance, that of gravitation. The sun causes a
+certain tendency to motion in the earth; here we have cause and effect;
+but that tendency is _towards_ the sun, and therefore varies in
+direction as the sun varies in the relation of position; and moreover
+the tendency varies in intensity, in a certain numerical correspondence
+to the sun's distance from the earth, that is, according to another
+relation of the sun. Thus we see that there is not only an invariable
+connexion between the sun and the earth's gravitation, but that two of
+the relations of the sun, its position with respect to the earth and its
+distance from the earth, are invariably connected as antecedents with
+the quantity and direction of the earth's gravitation. The cause of the
+earth's gravitating at all, is simply the sun; but the cause of its
+gravitating with a given intensity and in a given direction, is the
+existence of the sun in a given direction and at a given distance. It is
+not strange that a modified cause, which is in truth a different cause,
+should produce a different effect.
+
+Although it is for the most part true that a modification of the cause
+is followed by a modification of the effect, the Method of Concomitant
+Variations does not, however, presuppose this as an axiom. It only
+requires the converse proposition; that anything on whose modifications,
+modifications of an effect are invariably consequent, must be the cause
+(or connected with the cause) of that effect; a proposition, the truth
+of which is evident; for if the thing itself had no influence on the
+effect, neither could the modifications of the thing have any influence.
+If the stars have no power over the fortunes of mankind, it is implied
+in the very terms, that the conjunctions or oppositions of different
+stars can have no such power.
+
+Although the most striking applications of the Method of Concomitant
+Variations take place in the cases in which the Method of Difference,
+strictly so called, is impossible, its use is not confined to those
+cases; it may often usefully follow after the Method of Difference, to
+give additional precision to a solution which that has found. When by
+the Method of Difference it has first been ascertained that a certain
+object produces a certain effect, the Method of Concomitant Variations
+may be usefully called in, to determine according to what law the
+quantity or the different relations of the effect follow those of the
+cause.
+
+
+§ 7. The case in which this method admits of the most extensive
+employment, is that in which the variations of the cause are variations
+of quantity. Of such variations we may in general affirm with safety,
+that they will be attended not only with variations, but with similar
+variations, of the effect: the proposition, that more of the cause is
+followed by more of the effect, being a corollary from the principle of
+the Composition of Causes, which, as we have seen, is the general rule
+of causation; cases of the opposite description, in which causes change
+their properties on being conjoined with one another, being, on the
+contrary, special and exceptional. Suppose, then, that when A changes
+in quantity, _a_ also changes in quantity, and in such a manner that we
+can trace the numerical relation which the changes of the one bear to
+such changes of the other as take place within our limits of
+observation. We may then, with certain precautions, safely conclude that
+the same numerical relation will hold beyond those limits. If, for
+instance, we find that when A is double, _a_ is double; that when A is
+treble or quadruple, _a_ is treble or quadruple; we may conclude that if
+A were a half or a third, _a_ would be a half or a third, and finally,
+that if A were annihilated, _a_ would be annihilated, and that _a_ is
+wholly the effect of A, or wholly the effect of the same cause with A.
+And so with any other numerical relation according to which A and _a_
+would vanish simultaneously; as for instance, if _a_ were proportional
+to the square of A. If, on the other hand, _a_ is not wholly the effect
+of A, but yet varies when A varies, it is probably a mathematical
+function not of A alone, but of A and something else: its changes, for
+example, may be such as would occur if part of it remained constant, or
+varied on some other principle, and the remainder varied in some
+numerical relation to the variations of A. In that case, when A
+diminishes, _a_ will be seen to approach not towards zero, but towards
+some other limit: and when the series of variations is such as to
+indicate what that limit is, if constant, or the law of its variation if
+variable, the limit will exactly measure how much of _a_ is the effect
+of some other and independent cause, and the remainder will be the
+effect of A (or of the cause of A).
+
+These conclusions, however, must not be drawn without certain
+precautions. In the first place, the possibility of drawing them at all,
+manifestly supposes that we are acquainted not only with the variations,
+but with the absolute quantities both of A and _a_. If we do not know
+the total quantities, we cannot, of course, determine the real numerical
+relation according to which those quantities vary. It is therefore an
+error to conclude, as some have concluded, that because increase of heat
+expands bodies, that is, increases the distance between their particles,
+therefore the distance is wholly the effect of heat, and that if we
+could entirely exhaust the body of its heat, the particles would be in
+complete contact. This is no more than a guess, and of the most
+hazardous sort, not a legitimate induction: for since we neither know
+how much heat there is in any body, nor what is the real distance
+between any two of its particles, we cannot judge whether the
+contraction of the distance does or does not follow the diminution of
+the quantity of heat according to such a numerical relation that the two
+quantities would vanish simultaneously.
+
+In contrast with this, let us consider a case in which the absolute
+quantities are known; the case contemplated in the first law of motion;
+viz. that all bodies in motion continue to move in a straight line with
+uniform velocity until acted upon by some new force. This assertion is
+in open opposition to first appearances; all terrestrial objects, when
+in motion, gradually abate their velocity and at last stop; which
+accordingly the ancients, with their _inductio per enumerationem
+simplicem_, imagined to be the law. Every moving body, however,
+encounters various obstacles, as friction, the resistance of the
+atmosphere, &c., which we know by daily experience to be causes capable
+of destroying motion. It was suggested that the whole of the retardation
+might be owing to these causes. How was this inquired into? If the
+obstacles could have been entirely removed, the case would have been
+amenable to the Method of Difference. They could not be removed, they
+could only be diminished, and the case, therefore, admitted only of the
+Method of Concomitant Variations. This accordingly being employed, it
+was found that every diminution of the obstacles diminished the
+retardation of the motion: and inasmuch as in this case (unlike the case
+of heat) the total quantities both of the antecedent and of the
+consequent were known; it was practicable to estimate, with an approach
+to accuracy, both the amount of the retardation and the amount of the
+retarding causes, or resistances, and to judge how near they both were
+to being exhausted; and it appeared that the effect dwindled as rapidly,
+and at each step was as far on the road towards annihilation, as the
+cause was. The simple oscillation of a weight suspended from a fixed
+point, and moved a little out of the perpendicular, which in ordinary
+circumstances lasts but a few minutes, was prolonged in Borda's
+experiments to more than thirty hours, by diminishing as much as
+possible the friction at the point of suspension, and by making the body
+oscillate in a space exhausted as nearly as possible of its air. There
+could therefore be no hesitation in assigning the whole of the
+retardation of motion to the influence of the obstacles; and since,
+after subducting this retardation from the total phenomenon, the
+remainder was an uniform velocity, the result was the proposition known
+as the first law of motion.
+
+There is also another characteristic uncertainty affecting the inference
+that the law of variation which the quantities observe within our limits
+of observation, will hold beyond those limits. There is of course, in
+the first instance, the possibility that beyond the limits, and in
+circumstances therefore of which we have no direct experience, some
+counteracting cause might develop itself; either a new agent, or a new
+property of the agents concerned, which lies dormant in the
+circumstances we are able to observe. This is an element of uncertainty
+which enters largely into all our predictions of effects; but it is not
+peculiarly applicable to the Method of Concomitant Variations. The
+uncertainty, however, of which I am about to speak, is characteristic of
+that method; especially in the cases in which the extreme limits of our
+observation are very narrow, in comparison with the possible variations
+in the quantities of the phenomena. Any one who has the slightest
+acquaintance with mathematics, is aware that very different laws of
+variation may produce numerical results which differ but slightly from
+one another within narrow limits; and it is often only when the absolute
+amounts of variation are considerable, that the difference between the
+results given by one law and by another becomes appreciable. When,
+therefore, such variations in the quantity of the antecedents as we have
+the means of observing, are small in comparison with the total
+quantities, there is much danger lest we should mistake the numerical
+law, and be led to miscalculate the variations which would take place
+beyond the limits; a miscalculation which would vitiate any conclusion
+respecting the dependence of the effect upon the cause, that could be
+founded on those variations. Examples are not wanting of such mistakes.
+"The formulæ," says Sir John Herschel,[33] "which have been empirically
+deduced for the elasticity of steam, (till very recently,) and those for
+the resistance of fluids, and other similar subjects," when relied on
+beyond the limits of the observations from which they were deduced,
+"have almost invariably failed to support the theoretical structures
+which have been erected on them."
+
+In this uncertainty, the conclusion we may draw from the concomitant
+variations of _a_ and A, to the existence of an invariable and exclusive
+connexion between them, or to the permanency of the same numerical
+relation between their variations when the quantities are much greater
+or smaller than those which we have had the means of observing, cannot
+be considered to rest on a complete induction. All that in such a case
+can be regarded as proved on the subject of causation is, that there is
+some connexion between the two phenomena; that A, or something which can
+influence A, must be _one_ of the causes which collectively determine
+_a_. We may, however, feel assured that the relation which we have
+observed to exist between the variations of A and _a_, will hold true in
+all cases which fall between the same extreme limits; that is, wherever
+the utmost increase or diminution in which the result has been found by
+observation to coincide with the law, is not exceeded.
+
+The four methods which it has now been attempted to describe, are the
+only possible modes of experimental inquiry--of direct induction _à
+posteriori_, as distinguished from deduction: at least, I know not, nor
+am able to imagine, any others. And even of these, the Method of
+Residues, as we have seen, is not independent of deduction; though, as
+it also requires specific experience, it may, without impropriety, be
+included among methods of direct observation and experiment.
+
+These, then, with such assistance as can be obtained from Deduction,
+compose the available resources of the human mind for ascertaining the
+laws of the succession of phenomena. Before proceeding to point out
+certain circumstances, by which the employment of these methods is
+subjected to an immense increase of complication and of difficulty, it
+is expedient to illustrate the use of the methods, by suitable examples
+drawn from actual physical investigations. These, accordingly, will form
+the subject of the succeeding chapter.
+
+
+
+
+CHAPTER IX.
+
+MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.
+
+
+§ 1. I shall select, as a first example, an interesting speculation of
+one of the most eminent of theoretical chemists, Baron Liebig. The
+object in view, is to ascertain the immediate cause of the death
+produced by metallic poisons.
+
+Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
+introduced into the animal organism, except in the smallest doses,
+destroy life. These facts have long been known, as insulated truths of
+the lowest order of generalization; but it was reserved for Liebig, by
+an apt employment of the first two of our methods of experimental
+inquiry, to connect these truths together by a higher induction,
+pointing out what property, common to all these deleterious substances,
+is the really operating cause of their fatal effect.
+
+When solutions of these substances are placed in sufficiently close
+contact with many animal products, albumen, milk, muscular fibre, and
+animal membranes, the acid or salt leaves the water in which it was
+dissolved, and enters into combination with the animal substance: which
+substance, after being thus acted upon, is found to have lost its
+tendency to spontaneous decomposition, or putrefaction.
+
+Observation also shows, in cases where death has been produced by these
+poisons, that the parts of the body with which the poisonous substances
+have been brought into contact, do not afterwards putrefy.
+
+And, finally, when the poison has been supplied in too small a quantity
+to destroy life, eschars are produced, that is, certain superficial
+portions of the tissues are destroyed, which are afterwards thrown off
+by the reparative process taking place in the healthy parts.
+
+These three sets of instances admit of being treated according to the
+Method of Agreement. In all of them the metallic compounds are brought
+into contact with the substances which compose the human or animal body;
+and the instances do not seem to agree in any other circumstance. The
+remaining antecedents are as different, and even opposite, as they could
+possibly be made; for in some the animal substances exposed to the
+action of the poisons are in a state of life, in others only in a state
+of organization, in others not even in that. And what is the result
+which follows in all the cases? The conversion of the animal substance
+(by combination with the poison) into a chemical compound, held together
+by so powerful a force as to resist the subsequent action of the
+ordinary causes of decomposition. Now, organic life (the necessary
+condition of sensitive life) consisting in a continual state of
+decomposition and recomposition of the different organs and tissues;
+whatever incapacitates them for this decomposition destroys life. And
+thus the proximate cause of the death produced by this description of
+poisons, is ascertained, as far as the Method of Agreement can ascertain
+it.
+
+Let us now bring our conclusion to the test of the Method of Difference.
+Setting out from the cases already mentioned, in which the antecedent is
+the presence of substances forming with the tissues a compound incapable
+of putrefaction, (and _à fortiori_ incapable of the chemical actions
+which constitute life,) and the consequent is death, either of the whole
+organism, or of some portion of it; let us compare with these cases
+other cases, as much resembling them as possible, but in which that
+effect is not produced. And, first, "many insoluble basic salts of
+arsenious acid are known not to be poisonous. The substance called
+alkargen, discovered by Bunsen, which contains a very large quantity of
+arsenic, and approaches very closely in composition to the organic
+arsenious compounds found in the body, has not the slightest injurious
+action upon the organism." Now when these substances are brought into
+contact with the tissues in any way, they do not combine with them; they
+do not arrest their progress to decomposition. As far, therefore, as
+these instances go, it appears that when the effect is absent, it is by
+reason of the absence of that antecedent which we had already good
+ground for considering as the proximate cause.
+
+But the rigorous conditions of the Method of Difference are not yet
+satisfied; for we cannot be sure that these unpoisonous bodies agree
+with the poisonous substances in every property, except the particular
+one, of entering into a difficultly decomposable compound with the
+animal tissues. To render the method strictly applicable, we need an
+instance, not of a different substance, but of one of the very same
+substances, in circumstances which would prevent it from forming, with
+the tissues, the sort of compound in question; and then, if death does
+not follow, our case is made out. Now such instances are afforded by the
+antidotes to these poisons. For example, in case of poisoning by
+arsenious acid, if hydrated peroxide of iron is administered, the
+destructive agency is instantly checked. Now this peroxide is known to
+combine with the acid, and form a compound, which, being insoluble,
+cannot act at all on animal tissues. So, again, sugar is a well-known
+antidote to poisoning by salts of copper; and sugar reduces those salts
+either into metallic copper, or into the red suboxide, neither of which
+enters into combination with animal matter. The disease called painter's
+colic, so common in manufactories of white lead, is unknown where the
+workmen are accustomed to take, as a preservative, sulphuric acid
+lemonade (a solution of sugar rendered acid by sulphuric acid). Now
+diluted sulphuric acid has the property of decomposing all compounds of
+lead with organic matter, or of preventing them from being formed.
+
+There is another class of instances, of the nature required by the
+Method of Difference, which seem at first sight to conflict with the
+theory. Soluble salts of silver, such for instance as the nitrate, have
+the same stiffening antiseptic effect on decomposing animal substances
+as corrosive sublimate and the most deadly metallic poisons; and when
+applied to the external parts of the body, the nitrate is a powerful
+caustic; depriving those parts of all active vitality, and causing them
+to be thrown off by the neighbouring living structures, in the form of
+an eschar. The nitrate and the other salts of silver ought, then, it
+would seem, if the theory be correct, to be poisonous; yet they may be
+administered internally with perfect impunity. From this apparent
+exception arises the strongest confirmation which the theory has yet
+received. Nitrate of silver, in spite of its chemical properties, does
+not poison when introduced into the stomach; but in the stomach, as in
+all animal liquids, there is common salt; and in the stomach there is
+also free muriatic acid. These substances operate as natural antidotes,
+combining with the nitrate, and if its quantity is not too great,
+immediately converting it into chloride of silver; a substance very
+slightly soluble, and therefore incapable of combining with the tissues,
+although to the extent of its solubility it has a medicinal influence,
+though an entirely different class of organic actions.
+
+The preceding instances have afforded an induction of a high order of
+conclusiveness, illustrative of the two simplest of our four methods;
+though not rising to the maximum of certainty which the Method of
+Difference, in its most perfect exemplification, is capable of
+affording. For (let us not forget) the positive instance and the
+negative one which the rigour of that method requires, ought to differ
+only in the presence or absence of one single circumstance. Now, in the
+preceding argument, they differ in the presence or absence not of a
+single _circumstance_, but of a single _substance_: and as every
+substance has innumerable properties, there is no knowing what number of
+real differences are involved in what is nominally and apparently only
+one difference. It is conceivable that the antidote, the peroxide of
+iron for example, may counteract the poison through some other of its
+properties than that of forming an insoluble compound with it; and if
+so, the theory would fall to the ground, so far as it is supported by
+that instance. This source of uncertainty, which is a serious hindrance
+to all extensive generalizations in chemistry, is however reduced in the
+present case to almost the lowest degree possible, when we find that
+not only one substance, but many substances, possess the capacity of
+acting as antidotes to metallic poisons, and that all these agree in the
+property of forming insoluble compounds with the poisons, while they
+cannot be ascertained to agree in any other property whatsoever. We have
+thus, in favour of the theory, all the evidence which can be obtained by
+what we termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference; the evidence of which, though it never can
+amount to that of the Method of Difference properly so called, may
+approach indefinitely near to it.
+
+
+§ 2. Let the object be[34] to ascertain the law of what is termed
+_induced_ electricity; to find under what conditions any electrified
+body, whether positively or negatively electrified, gives rise to a
+contrary electric state in some other body adjacent to it.
+
+The most familiar exemplification of the phenomenon to be investigated
+is the following. Around the prime conductors of an electrical machine,
+the atmosphere to some distance, or any conducting surface suspended in
+that atmosphere, is found to be in an electric condition opposite to
+that of the prime conductor itself. Near and around the positive prime
+conductor there is negative electricity, and near and around the
+negative prime conductor there is positive electricity. When pith balls
+are brought near to either of the conductors, they become electrified
+with the opposite electricity to it; either receiving a share from the
+already electrified atmosphere by conduction, or acted upon by the
+direct inductive influence of the conductor itself: they are then
+attracted by the conductor to which they are in opposition; or, if
+withdrawn in their electrified state, they will be attracted by any
+other oppositely charged body. In like manner the hand, if brought near
+enough to the conductor, receives or gives an electric discharge; now we
+have no evidence that a charged conductor can be suddenly discharged
+unless by the approach of a body oppositely electrified. In the case,
+therefore, of the electric machine, it appears that the accumulation of
+electricity in an insulated conductor is always accompanied by the
+excitement of the contrary electricity in the surrounding atmosphere,
+and in every conductor placed near the former conductor. It does not
+seem possible, in this case, to produce one electricity by itself.
+
+Let us now examine all the other instances which we can obtain,
+resembling this instance in the given consequent, namely, the evolution
+of an opposite electricity in the neighbourhood of an electrified body.
+As one remarkable instance we have the Leyden jar; and after the
+splendid experiments of Faraday in complete and final establishment of
+the substantial identity of magnetism and electricity, we may cite the
+magnet, both the natural and the electro-magnet, in neither of which it
+is possible to produce one kind of electricity by itself, or to charge
+one pole without charging an opposite pole with the contrary electricity
+at the same time. We cannot have a magnet with one pole: if we break a
+natural loadstone into a thousand pieces, each piece will have its two
+oppositely electrified poles complete within itself. In the voltaic
+circuit, again, we cannot have one current without its opposite. In the
+ordinary electric machine, the glass cylinder or plate, and the rubber,
+acquire opposite electricities.
+
+From all these instances, treated by the Method of Agreement, a general
+law appears to result. The instances embrace all the known modes in
+which a body can become charged with electricity; and in all of them
+there is found, as a concomitant or consequent, the excitement of the
+opposite electric state in some other body or bodies. It seems to follow
+that the two facts are invariably connected, and that the excitement of
+electricity in any body has for one of its necessary conditions the
+possibility of a simultaneous excitement of the opposite electricity in
+some neighbouring body.
+
+As the two contrary electricities can only be produced together, so
+they can only cease together. This may be shown by an application of the
+Method of Difference to the example of the Leyden jar. It needs scarcely
+be here remarked that in the Leyden jar, electricity can be accumulated
+and retained in considerable quantity, by the contrivance of having two
+conducting surfaces of equal extent, and parallel to each other through
+the whole of that extent, with a non-conducting substance such as glass
+between them. When one side of the jar is charged positively, the other
+is charged negatively, and it was by virtue of this fact that the Leyden
+jar served just now as an instance in our employment of the Method of
+Agreement. Now it is impossible to discharge one of the coatings unless
+the other can be discharged at the same time. A conductor held to the
+positive side cannot convey away any electricity unless an equal
+quantity be allowed to pass from the negative side: if one coating be
+perfectly insulated, the charge is safe. The dissipation of one must
+proceed _pari passu_ with that of the other.
+
+The law thus strongly indicated admits of corroboration by the Method of
+Concomitant Variations. The Leyden jar is capable of receiving a much
+higher charge than can ordinarily be given to the conductor of an
+electrical machine. Now in the case of the Leyden jar, the metallic
+surface which receives the induced electricity is a conductor exactly
+similar to that which receives the primary charge, and is therefore as
+susceptible of receiving and retaining the one electricity, as the
+opposite surface of receiving and retaining the other; but in the
+machine, the neighbouring body which is to be oppositely electrified is
+the surrounding atmosphere, or any body casually brought near to the
+conductor; and as these are generally much inferior in their capacity of
+becoming electrified, to the conductor itself, their limited power
+imposes a corresponding limit to the capacity of the conductor for being
+charged. As the capacity of the neighbouring body for supporting the
+opposition increases, a higher charge becomes possible: and to this
+appears to be owing the great superiority of the Leyden jar.
+
+A further and most decisive confirmation by the Method of Difference,
+is to be found in one of Faraday's experiments in the course of his
+researches on the subject of induced electricity.
+
+Since common or machine electricity, and voltaic electricity, may be
+considered for the present purpose to be identical, Faraday wished to
+know whether, as the prime conductor develops opposite electricity upon
+a conductor in its vicinity, so a voltaic current running along a wire
+would induce an opposite current upon another wire laid parallel to it
+at a short distance. Now this case is similar to the cases previously
+examined, in every circumstance except the one to which we have ascribed
+the effect. We found in the former instances that whenever electricity
+of one kind was excited in one body, electricity of the opposite kind
+must be excited in a neighbouring body. But in Faraday's experiment this
+indispensable opposition exists within the wire itself. From the nature
+of a voltaic charge, the two opposite currents necessary to the
+existence of each other are both accommodated in one wire; and there is
+no need of another wire placed beside it to contain one of them, in the
+same way as the Leyden jar must have a positive and a negative surface.
+The exciting cause can and does produce all the effect which its laws
+require, independently of any electric excitement of a neighbouring
+body. Now the result of the experiment with the second wire was, that no
+opposite current was produced. There was an instantaneous effect at the
+closing and breaking of the voltaic circuit; electric inductions
+appeared when the two wires were moved to and from one another; but
+these are phenomena of a different class. There was no induced
+electricity in the sense in which this is predicated of the Leyden jar;
+there was no sustained current running up the one wire while an opposite
+current ran down the neighbouring wire; and this alone would have been a
+true parallel case to the other.
+
+It thus appears by the combined evidence of the Method of Agreement, the
+Method of Concomitant Variations, and the most rigorous form of the
+Method of Difference, that neither of the two kinds of electricity can
+be excited without an equal excitement of the other and opposite kind:
+that both are effects of the same cause; that the possibility of the one
+is a condition of the possibility of the other, and the quantity of the
+one an impassable limit to the quantity of the other. A scientific
+result of considerable interest in itself, and illustrating those three
+methods in a manner both characteristic and easily intelligible.[35]
+
+
+§ 3. Our third example shall be extracted from Sir John Herschel's
+_Discourse on the Study of Natural Philosophy_, a work replete with
+happily-selected exemplifications of inductive processes from almost
+every department of physical science, and in which alone, of all books
+which I have met with, the four methods of induction are distinctly
+recognised, though not so clearly characterized and defined, nor their
+correlation so fully shown, as has appeared to me desirable. The present
+example is described by Sir John Herschel as "one of the most beautiful
+specimens" which can be cited "of inductive experimental inquiry lying
+within a moderate compass;" the theory of dew, first promulgated by the
+late Dr. Wells, and now universally adopted by scientific authorities.
+The passages in inverted commas are extracted verbatim from the
+Discourse.[36]
+
+"Suppose _dew_ were the phenomenon proposed, whose cause we would know.
+In the first place" we must determine precisely what we mean by dew:
+what the fact really is, whose cause we desire to investigate. "We must
+separate dew from rain, and the moisture of fogs, and limit the
+application of the term to what is really meant, which is the
+spontaneous appearance of moisture on substances exposed in the open air
+when no rain or _visible_ wet is falling." This answers to a preliminary
+operation which will be characterized in the ensuing book, treating of
+operations subsidiary to induction.[37]
+
+"Now, here we have analogous phenomena in the moisture which bedews a
+cold metal or stone when we breathe upon it; that which appears on a
+glass of water fresh from the well in hot weather; that which appears on
+the inside of windows when sudden rain or hail chills the external air;
+that which runs down our walls when, after a long frost, a warm moist
+thaw comes on." Comparing these cases, we find that they all contain the
+phenomenon which was proposed as the subject of investigation. Now "all
+these instances agree in one point, the coldness of the object dewed, in
+comparison with the air in contact with it." But there still remains the
+most important case of all, that of nocturnal dew: does the same
+circumstance exist in this case? "Is it a fact that the object dewed is
+colder than the air? Certainly not, one would at first be inclined to
+say; for what is to _make_ it so? But ... the experiment is easy: we
+have only to lay a thermometer in contact with the dewed substance, and
+hang one at a little distance above it, out of reach of its influence.
+The experiment has been therefore made, the question has been asked, and
+the answer has been invariably in the affirmative. Whenever an object
+contracts dew, it _is_ colder than the air."
+
+Here then is a complete application of the Method of Agreement,
+establishing the fact of an invariable connexion between the deposition
+of dew on a surface, and the coldness of that surface compared with the
+external air. But which of these is cause, and which effect? or are they
+both effects of something else? On this subject the Method of Agreement
+can afford us no light: we must call in a more potent method. "We must
+collect more facts, or, which comes to the same thing, vary the
+circumstances; since every instance in which the circumstances differ is
+a fresh fact: and especially, we must note the contrary or negative
+cases, _i.e._ where no dew is produced:" a comparison between instances
+of dew and instances of no dew, being the condition necessary to bring
+the Method of Difference into play.
+
+"Now, first, no dew is produced on the surface of polished metals, but
+it _is_ very copiously on glass, both exposed with their faces upwards,
+and in some cases the under side of a horizontal plate of glass is also
+dewed." Here is an instance in which the effect is produced, and another
+instance in which it is not produced; but we cannot yet pronounce, as
+the canon of the Method of Difference requires, that the latter instance
+agrees with the former in all its circumstances except one; for the
+differences between glass and polished metals are manifold, and the only
+thing we can as yet be sure of is, that the cause of dew will be found
+among the circumstances by which the former substance is distinguished
+from the latter. But if we could be sure that glass, and the various
+other substances on which dew is deposited, have only one quality in
+common, and that polished metals and the other substances on which dew
+is not deposited have also nothing in common but the one circumstance,
+of not having the one quality which the others have; the requisitions of
+the Method of Difference would be completely satisfied, and we should
+recognise, in that quality of the substances, the cause of dew. This,
+accordingly, is the path of inquiry which is next to be pursued.
+
+"In the cases of polished metal and polished glass, the contrast shows
+evidently that the _substance_ has much to do with the phenomenon;
+therefore let the substance _alone_ be diversified as much as possible,
+by exposing polished surfaces of various kinds. This done, a _scale of
+intensity_ becomes obvious. Those polished substances are found to be
+most strongly dewed which conduct heat worst; while those which conduct
+well, resist dew most effectually." The complication increases; here is
+the Method of Concomitant Variations called to our assistance; and no
+other method was practicable on this occasion; for the quality of
+conducting heat could not be excluded, since all substances conduct heat
+in some degree. The conclusion obtained is, that _cæteris paribus_ the
+deposition of dew is in some proportion to the power which the body
+possesses of resisting the passage of heat; and that this, therefore,
+(or something connected with this,) must be at least one of the causes
+which assist in producing the deposition of dew on the surface.
+
+"But if we expose rough surfaces instead of polished, we sometimes find
+this law interfered with. Thus, roughened iron, especially if painted
+over or blackened, becomes dewed sooner than varnished paper; the kind
+of _surface_, therefore, has a great influence. Expose, then, the _same_
+material in very diversified states as to surface," (that is, employ the
+Method of Difference to ascertain concomitance of variations,) "and
+another scale of intensity becomes at once apparent; those _surfaces_
+which _part with their heat_ most readily by radiation, are found to
+contract dew most copiously." Here, therefore, are the requisites for a
+second employment of the Method of Concomitant Variations; which in this
+case also is the only method available, since all substances radiate
+heat in some degree or other. The conclusion obtained by this new
+application of the method is, that _cæteris paribus_ the deposition of
+dew is also in some proportion to the power of radiating heat; and that
+the quality of doing this abundantly (or some cause on which that
+quality depends) is another of the causes which promote the deposition
+of dew on the substance.
+
+"Again, the influence ascertained to exist of _substance_ and _surface_
+leads us to consider that of _texture_: and here, again, we are
+presented on trial with remarkable differences, and with a third scale
+of intensity, pointing out substances of a close firm texture, such as
+stones, metals, &c., as unfavourable, but those of a loose one, as
+cloth, velvet, wool, eider-down, cotton, &c., as eminently favourable to
+the contraction of dew." The Method of Concomitant Variations is here,
+for the third time, had recourse to; and, as before, from necessity,
+since the texture of no substance is absolutely firm or absolutely
+loose. Looseness of texture, therefore, or something which is the cause
+of that quality, is another circumstance which promotes the deposition
+of dew; but this third cause resolves itself into the first, viz. the
+quality of resisting the passage of heat: for substances of loose
+texture "are precisely those which are best adapted for clothing, or for
+impeding the free passage of heat from the skin into the air, so as to
+allow their outer surfaces to be very cold, while they remain warm
+within;" and this last is, therefore, an induction (from fresh
+instances) simply _corroborative_ of a former induction.
+
+It thus appears that the instances in which much dew is deposited, which
+are very various, agree in this, and, so far as we are able to observe,
+in this only, that they either radiate heat rapidly or conduct it
+slowly: qualities between which there is no other circumstance of
+agreement, than that by virtue of either, the body tends to lose heat
+from the surface more rapidly than it can be restored from within. The
+instances, on the contrary, in which no dew, or but a small quantity of
+it, is formed, and which are also extremely various, agree (as far as we
+can observe) in nothing except in _not_ having this same property. We
+seem, therefore, to have detected the characteristic difference between
+the substances on which dew is produced, and those on which it is not
+produced. And thus have been realized the requisitions of what we have
+termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference. The example afforded of this indirect method,
+and of the manner in which the data are prepared for it by the Methods
+of Agreement and of Concomitant Variations, is the most important of all
+the illustrations of induction afforded by this interesting speculation.
+
+We might now consider the question, on what the deposition of dew
+depends, to be completely solved, if we could be quite sure that the
+substances on which dew is produced differ from those on which it is
+not, in _nothing_ but in the property of losing heat from the surface
+faster than the loss can be repaired from within. And though we never
+can have that complete certainty, this is not of so much importance as
+might at first be supposed; for we have, at all events, ascertained
+that even if there be any other quality hitherto unobserved which is
+present in all the substances which contract dew, and absent in those
+which do not, this other property must be one which, in all that great
+number of substances, is present or absent exactly where the property of
+being a better radiator than conductor is present or absent; an extent
+of coincidence which affords a strong presumption of a community of
+cause, and a consequent invariable coexistence between the two
+properties; so that the property of being a better radiator than
+conductor, if not itself the cause, almost certainly always accompanies
+the cause, and, for purposes of prediction, no error is likely to be
+committed by treating it as if it were really such.
+
+Reverting now to an earlier stage of the inquiry, let us remember that
+we had ascertained that, in every instance where dew is formed, there is
+actual coldness of the surface below the temperature of the surrounding
+air; but we were not sure whether this coldness was the cause of dew, or
+its effect. This doubt we are now able to resolve. We have found that,
+in every such instance, the substance is one which, by its own
+properties or laws, would, if exposed in the night, become colder than
+the surrounding air. The coldness therefore being accounted for
+independently of the dew, while it is proved that there is a connexion
+between the two, it must be the dew which depends on the coldness; or in
+other words, the coldness is the cause of the dew.
+
+This law of causation, already so amply established, admits, however, of
+efficient additional corroboration in no less than three ways. First, by
+deduction from the known laws of aqueous vapour when diffused through
+air or any other gas; and though we have not yet come to the Deductive
+Method, we will not omit what is necessary to render this speculation
+complete. It is known by direct experiment that only a limited quantity
+of water can remain suspended in the state of vapour at each degree of
+temperature, and that this maximum grows less and less as the
+temperature diminishes. From this it follows, deductively, that if there
+is already as much vapour suspended as the air will contain at its
+existing temperature, any lowering of that temperature will cause a
+portion of the vapour to be condensed, and become water. But, again, we
+know deductively, from the laws of heat, that the contact of the air
+with a body colder than itself, will necessarily lower the temperature
+of the stratum of air immediately applied to its surface; and will
+therefore cause it to part with a portion of its water, which
+accordingly will, by the ordinary laws of gravitation or cohesion,
+attach itself to the surface of the body, thereby constituting dew. This
+deductive proof, it will have been seen, has the advantage of at once
+proving causation as well as coexistence; and it has the additional
+advantage that it also accounts for the exceptions to the occurrence of
+the phenomenon, the cases in which, although the body is colder than the
+air, yet no dew is deposited; by showing that this will necessarily be
+the case when the air is so under-supplied with aqueous vapour,
+comparatively to its temperature, that even when somewhat cooled by the
+contact of the colder body, it can still continue to hold in suspension
+all the vapour which was previously suspended in it: thus in a very dry
+summer there are no dews, in a very dry winter no hoar frost. Here,
+therefore, is an additional condition of the production of dew, which
+the methods we previously made use of failed to detect, and which might
+have remained still undetected, if recourse had not been had to the plan
+of deducing the effect from the ascertained properties of the agents
+known to be present.
+
+The second corroboration of the theory is by direct experiment,
+according to the canon of the Method of Difference. We can, by cooling
+the surface of any body, find in all cases some temperature, (more or
+less inferior to that of the surrounding air, according to its
+hygrometric condition,) at which dew will begin to be deposited. Here,
+too, therefore, the causation is directly proved. We can, it is true,
+accomplish this only on a small scale; but we have ample reason to
+conclude that the same operation, if conducted in Nature's great
+laboratory, would equally produce the effect.
+
+And, finally, even on that great scale we are able to verify the result.
+The case is one of those rare cases, as we have shown them to be, in
+which nature works the experiment for us in the same manner in which we
+ourselves perform it; introducing into the previous state of things a
+single and perfectly definite new circumstance, and manifesting the
+effect so rapidly that there is not time for any other material change
+in the pre-existing circumstances. "It is observed that dew is never
+copiously deposited in situations much screened from the open sky, and
+not at all in a cloudy night; but _if the clouds withdraw even for a few
+minutes, and leave a clear opening, a deposition of dew presently
+begins_, and goes on increasing.... Dew formed in clear intervals will
+often even evaporate again when the sky becomes thickly overcast." The
+proof, therefore, is complete, that the presence or absence of an
+uninterrupted communication with the sky causes the deposition or
+non-deposition of dew. Now, since a clear sky is nothing but the absence
+of clouds, and it is a known property of clouds, as of all other bodies
+between which and any given object nothing intervenes but an elastic
+fluid, that they tend to raise or keep up the superficial temperature of
+the object by radiating heat to it, we see at once that the
+disappearance of clouds will cause the surface to cool; so that Nature,
+in this case, produces a change in the antecedent by definite and known
+means, and the consequent follows accordingly: a natural experiment
+which satisfies the requisitions of the Method of Difference.[38]
+
+The accumulated proof of which the Theory of Dew has been found
+susceptible, is a striking instance of the fulness of assurance which
+the inductive evidence of laws of causation may attain, in cases in
+which the invariable sequence is by no means obvious to a superficial
+view.
+
+
+§ 4. The admirable physiological investigations of Dr. Brown-Séquard
+afford brilliant examples of the application of the Inductive Methods to
+a class of inquiries in which, for reasons which will presently be
+given, direct induction takes place under peculiar difficulties and
+disadvantages. As one of the most apt instances I select his speculation
+(in the Proceedings of the Royal Society for May 16, 1861) on the
+relations between muscular irritability, cadaveric rigidity, and
+putrefaction.
+
+The law which Dr. Brown-Séquard's investigation tends to establish, is
+the following:--"The greater the degree of muscular irritability at the
+time of death, the later the cadaveric rigidity sets in, and the longer
+it lasts, and the later also putrefaction appears, and the slower it
+progresses." One would say at first sight that the method here required
+must be that of Concomitant Variations. But this is a delusive
+appearance, arising from the circumstance that the conclusion to be
+tested is itself a fact of concomitant variation. For the establishment
+of that fact any of the Methods may be put in requisition, and it will
+be found that the fourth Method, though really employed, has only a
+subordinate place in this particular investigation.
+
+The evidences by which Dr. Brown-Séquard establishes the law may be
+enumerated as follows:--
+
+1st. Paralysed muscles have greater irritability than healthy muscles.
+Now, paralysed muscles are later in assuming the cadaveric rigidity than
+healthy muscles, the rigidity lasts longer, and putrefaction sets in
+later and proceeds more slowly.
+
+Both these propositions had to be proved by experiment; and for the
+experiments which prove them, science is also indebted to Dr.
+Brown-Séquard. The former of the two--that paralysed muscles have
+greater irritability than healthy muscles--he ascertained in various
+ways, but most decisively by "comparing the duration of irritability in
+a paralysed muscle and in the corresponding healthy one of the opposite
+side, while they are both submitted to the same excitation." He "often
+found in experimenting in that way, that the paralysed muscle remained
+irritable twice, three times, or even four times as long as the healthy
+one." This is a case of induction by the Method of Difference. The two
+limbs, being those of the same animal, were presumed to differ in no
+circumstance material to the case except the paralysis, to the presence
+and absence of which, therefore, the difference in the muscular
+irritability was to be attributed. This assumption of complete
+resemblance in all material circumstances save one, evidently could not
+be safely made in any one pair of experiments, because the two legs of
+any given animal might be accidentally in very different pathological
+conditions; but if, besides taking pains to avoid any such difference,
+the experiment was repeated sufficiently often in different animals to
+exclude the supposition that any abnormal circumstance could be present
+in them all, the conditions of the Method of Difference were adequately
+secured.
+
+In the same manner in which Dr. Brown-Séquard proved that paralysed
+muscles have greater irritability, he also proved the correlative
+proposition respecting cadaveric rigidity and putrefaction. Having, by
+section of the roots of the sciatic nerve, and again of a lateral half
+of the spinal cord, produced paralysis in one hind leg of an animal
+while the other remained healthy, he found that not only did muscular
+irritability last much longer in the paralysed limb, but rigidity set in
+later and ended later, and putrefaction began later and was less rapid
+than on the healthy side. This is a common case of the Method of
+Difference, requiring no comment. A further and very important
+corroboration was obtained by the same method. When the animal was
+killed, not shortly after the section of the nerve, but a month later,
+the effect was reversed; rigidity set in sooner, and lasted a shorter
+time, than in the healthy muscles. But after this lapse of time, the
+paralysed muscles, having been kept by the paralysis in a state of rest,
+had lost a great part of their irritability, and instead of more, had
+become less irritable than those on the healthy side. This gives the A B
+C, a b c, and B C, b c, of the Method of Difference. One antecedent,
+increased irritability, being changed, and the other circumstances being
+the same, the consequence did not follow; and moreover, when a new
+antecedent, contrary to the first, was supplied, it was followed by a
+contrary consequent. This instance is attended with the special
+advantage, of proving that the retardation and prolongation of the
+rigidity do not depend directly on the paralysis, since that was the
+same in both the instances; but specifically on one effect of the
+paralysis, namely, the increased irritability; since they ceased when it
+ceased, and were reversed when it was reversed.
+
+2ndly. Diminution of the temperature of muscles before death increases
+their irritability. But diminution of their temperature also retards
+cadaveric rigidity and putrefaction.
+
+Both these truths were first made known by Dr. Brown-Séquard himself,
+through experiments which conclude according to the Method of
+Difference. There is nothing in the nature of the process requiring
+specific analysis.
+
+3rdly. Muscular exercise, prolonged to exhaustion, diminishes the
+muscular irritability. This is a well-known truth, dependent on the most
+general laws of muscular action, and proved by experiments under the
+Method of Difference, constantly repeated. Now it has been shown by
+observation that overdriven cattle, if killed before recovery from their
+fatigue, become rigid and putrefy in a surprisingly short time. A
+similar fact has been observed in the case of animals hunted to death;
+cocks killed during or shortly after a fight; and soldiers slain in the
+field of battle. These various cases agree in no circumstance, directly
+connected with the muscles, except that these have just been subjected
+to exhausting exercise. Under the canon, therefore, of the Method of
+Agreement, it may be inferred that there is a connexion between the two
+facts. The Method of Agreement, indeed, as has been shown, is not
+competent to prove causation. The present case, however, is already
+known to be a case of causation, it being certain that the state of the
+body after death must somehow depend upon its state at the time of
+death. We are therefore warranted in concluding that the single
+circumstance in which all the instances agree, is the part of the
+antecedent which is the cause of that particular consequent.
+
+4thly. In proportion as the nutrition of muscles is in a good state,
+their irritability is high. This fact also rests on the general evidence
+of the laws of physiology, grounded on many familiar applications of the
+Method of Difference. Now, in the case of those who die from accident or
+violence, with their muscles in a good state of nutrition, the muscular
+irritability continues long after death, rigidity sets in late, and
+persists long without the putrefactive change. On the contrary, in cases
+of disease in which nutrition has been diminished for a long time before
+death, all these effects are reversed. These are the conditions of the
+Joint Method of Agreement and Difference. The cases of retarded and long
+continued rigidity here in question, agree only in being preceded by a
+high state of nutrition of the muscles; the cases of rapid and brief
+rigidity agree only in being preceded by a low state of muscular
+nutrition; a connexion is therefore inductively proved between the
+degree of the nutrition, and the slowness and prolongation of the
+rigidity.
+
+5thly. Convulsions, like exhausting exercise, but in a still greater
+degree, diminish the muscular irritability. Now, when death follows
+violent and prolonged convulsions, as in tetanus, hydrophobia, some
+cases of cholera, and certain poisons, rigidity sets in very rapidly,
+and after a very brief duration, gives place to putrefaction. This is
+another example of the Method of Agreement, of the same character with
+No. 3.
+
+6thly. The series of instances which we shall take last, is of a more
+complex character, and requires a more minute analysis.
+
+It has long been observed that in some cases of death by lightning,
+cadaveric rigidity either does not take place at all, or is of such
+extremely brief duration as to escape notice, and that in these cases
+putrefaction is very rapid. In other cases, however, the usual cadaveric
+rigidity appears. There must be some difference in the cause, to account
+for this difference in the effect. Now "death by lightning may be the
+result of, 1st, a syncope by fright, or in consequence of a direct or
+reflex influence of lightning on the par vagum; 2ndly, hemorrhage in or
+around the brain, or in the lungs, the pericardium, &c.; 3rdly,
+concussion, or some other alteration in the brain;" none of which
+phenomena have any known property capable of accounting for the
+suppression, or almost suppression, of the cadaveric rigidity. But the
+cause of death may also be that the lightning produces "a violent
+convulsion of every muscle in the body," of which, if of sufficient
+intensity, the known effect would be that "muscular irritability ceases
+almost at once." If Dr. Brown-Séquard's generalization is a true law,
+these will be the very cases in which rigidity is so much abridged as to
+escape notice; and the cases in which, on the contrary, rigidity takes
+place as usual, will be those in which the stroke of lightning operates
+in some of the other modes which have been enumerated. How, then, is
+this brought to the test? By experiments not on lightning, which cannot
+be commanded at pleasure, but on the same natural agency in a manageable
+form, that of artificial galvanism. Dr. Brown-Séquard galvanized the
+entire bodies of animals immediately after death. Galvanism cannot
+operate in any of the modes in which the stroke of lightning may have
+operated, except the single one of producing muscular convulsions. If,
+therefore, after the bodies have been galvanized, the duration of
+rigidity is much shortened and putrefaction much accelerated, it is
+reasonable to ascribe the same effects when produced by lightning, to
+the property which galvanism shares with lightning, and not to those
+which it does not. Now this Dr. Brown-Séquard found to be the fact. The
+galvanic experiment was tried with charges of very various degrees of
+strength; and the more powerful the charge, the shorter was found to be
+the duration of rigidity, and the more speedy and rapid the
+putrefaction. In the experiment in which the charge was strongest, and
+the muscular irritability most promptly destroyed, the rigidity only
+lasted fifteen minutes. On the principle, therefore, of the Method of
+Concomitant Variations, it maybe inferred that the duration of the
+rigidity depends on the degree of the irritability; and that if the
+charge had been as much stronger than Dr. Brown-Séquard's strongest, as
+a stroke of lightning must be stronger than any electric shock which we
+can produce artificially, the rigidity would have been shortened in a
+corresponding ratio, and might have disappeared altogether. This
+conclusion having been arrived at, the case of an electric shock,
+whether natural or artificial, becomes an instance in addition to all
+those already ascertained, of correspondence between the irritability of
+the muscle and the duration of rigidity.
+
+All these instances are summed up in the following statement:--"That
+when the degree of muscular irritability at the time of death is
+considerable, either in consequence of a good state of nutrition, as in
+persons who die in full health from an accidental cause, or in
+consequence of rest, as in cases of paralysis, or on account of the
+influence of cold, cadaveric rigidity in all these cases sets in late
+and lasts long, and putrefaction appears late, and progresses slowly:"
+but "that when the degree of muscular irritability at the time of death
+is slight, either in consequence of a bad state of nutrition, or of
+exhaustion from over-exertion, or from convulsions caused by disease or
+poison, cadaveric rigidity sets in and ceases soon, and putrefaction
+appears and progresses quickly." These facts present, in all their
+completeness, the conditions of the Joint Method of Agreement and
+Difference. Early and brief rigidity takes place in cases which agree
+only in the circumstance of a low state of muscular irritability.
+Rigidity begins late and lasts long in cases which agree only in the
+contrary circumstance, of a muscular irritability high and unusually
+prolonged. It follows that there is a connexion through causation
+between the degree of muscular irritability after death, and the
+tardiness and prolongation of the cadaveric rigidity. This
+investigation places in a strong light the value and efficacy of the
+Joint Method. For, as we have already seen, the defect of that Method
+is, that like the Method of Agreement, of which it is only an improved
+form, it cannot prove causation. But in the present case (as in one of
+the steps in the argument which led up to it) causation is already
+proved; since there could never be any doubt that the rigidity
+altogether, and the putrefaction which follows it, are caused by the
+fact of death: the observations and experiments on which this rests are
+too familiar to need analysis, and fall under the Method of Difference.
+It being, therefore, beyond doubt that the aggregate antecedent, the
+death, is the actual cause of the whole train of consequents, whatever
+of the circumstances attending the death can be shown to be followed in
+all its variations by variations in the effect under investigation, must
+be the particular feature of the fact of death on which that effect
+depends. The degree of muscular irritability at the time of death
+fulfils this condition. The only point that could be brought into
+question, would be whether the effect depended on the irritability
+itself, or on something which always accompanied the irritability: and
+this doubt is set at rest by establishing, as the instances do, that by
+whatever cause the high or low irritability is produced, the effect
+equally follows; and cannot, therefore, depend upon the causes of
+irritability, nor upon the other effects of those causes, which are as
+various as the causes themselves; but upon the irritability, solely.
+
+
+§ 5. The last two examples will have conveyed to any one by whom they
+have been duly followed, so clear a conception of the use and practical
+management of three of the four methods of experimental inquiry, as to
+supersede the necessity of any further exemplification of them. The
+remaining method, that of Residues, not having found a place in any of
+the preceding investigations, I shall quote from Sir John Herschel some
+examples of that method, with the remarks by which they are introduced.
+
+"It is by this process, in fact, that science, in its present advanced
+state, is chiefly promoted. Most of the phenomena which Nature presents
+are very complicated; and when the effects of all known causes are
+estimated with exactness, and subducted, the residual facts are
+constantly appearing in the form of phenomena altogether new, and
+leading to the most important conclusions.
+
+"For example: the return of the comet predicted by Professor Encke, a
+great many times in succession, and the general good agreement of its
+calculated with its observed place during any one of its periods of
+visibility, would lead us to say that its gravitation towards the sun
+and planets is the sole and sufficient cause of all the phenomena of its
+orbitual motion; but when the effect of this cause is strictly
+calculated and subducted from the observed motion, there is found to
+remain behind a _residual phenomenon_, which would never have been
+otherwise ascertained to exist, which is a small anticipation of the
+time of its reappearance, or a diminution of its periodic time, which
+cannot be accounted for by gravity, and whose cause is therefore to be
+inquired into. Such an anticipation would be caused by the resistance of
+a medium disseminated through the celestial regions; and as there are
+other good reasons for believing this to be a _vera causa_," (an
+actually existing antecedent,) "it has therefore been ascribed to such a
+resistance.[39]
+
+"M. Arago, having suspended a magnetic needle by a silk thread, and set
+it in vibration, observed, that it came much sooner to a state of rest
+when suspended over a plate of copper, than when no such plate was
+beneath it. Now, in both cases there were two _veræ causæ_" (antecedents
+known to exist) "why it _should_ come at length to rest, viz. the
+resistance of the air, which opposes, and at length destroys, all
+motions performed in it; and the want of perfect mobility in the silk
+thread. But the effect of these causes being exactly known by the
+observation made in the absence of the copper, and being thus allowed
+for and subducted, a residual phenomenon appeared, in the fact that a
+retarding influence was exerted by the copper itself; and this fact,
+once ascertained, speedily led to the knowledge of an entirely new and
+unexpected class of relations." This example belongs, however, not to
+the Method of Residues but to the Method of Difference, the law being
+ascertained by a direct comparison of the results of two experiments,
+which differed in nothing but the presence or absence of the plate of
+copper. To have made it exemplify the Method of Residues, the effect of
+the resistance of the air and that of the rigidity of the silk should
+have been calculated _à priori_, from the laws obtained by separate and
+foregone experiments.
+
+"Unexpected and peculiarly striking confirmations of inductive laws
+frequently occur in the form of residual phenomena, in the course of
+investigations of a widely different nature from those which gave rise
+to the inductions themselves. A very elegant example may be cited in the
+unexpected confirmation of the law of the development of heat in elastic
+fluids by compression, which is afforded by the phenomena of sound. The
+inquiry into the cause of sound had led to conclusions respecting its
+mode of propagation, from which its velocity in the air could be
+precisely calculated. The calculations were performed; but, when
+compared with fact, though the agreement was quite sufficient to show
+the general correctness of the cause and mode of propagation assigned,
+yet the _whole_ velocity could not be shown to arise from this theory.
+There was still a residual velocity to be accounted for, which placed
+dynamical philosophers for a long time in great dilemma. At length
+Laplace struck on the happy idea, that this might arise from the _heat_
+developed in the act of that condensation which necessarily takes place
+at every vibration by which sound is conveyed. The matter was subjected
+to exact calculation, and the result was at once the complete
+explanation of the residual phenomenon, and a striking confirmation of
+the general law of the development of heat by compression, under
+circumstances beyond artificial imitation."
+
+"Many of the new elements of chemistry have been detected in the
+investigation of residual phenomena. Thus Arfwedson discovered lithia by
+perceiving an excess of weight in the sulphate produced from a small
+portion of what he considered as magnesia present in a mineral he had
+analysed. It is on this principle, too, that the small concentrated
+residues of great operations in the arts are almost sure to be the
+lurking places of new chemical ingredients: witness iodine, brome,
+selenium, and the new metals accompanying platina in the experiments of
+Wollaston and Tennant. It was a happy thought of Glauber to examine what
+everybody else threw away."[40]
+
+"Almost all the greatest discoveries in Astronomy," says the same
+author,[41] "have resulted from the consideration of residual phenomena
+of a quantitative or numerical kind.... It was thus that the grand
+discovery of the precession of the equinoxes resulted as a residual
+phenomenon, from the imperfect explanation of the return of the seasons
+by the return of the sun to the same apparent place among the fixed
+stars. Thus, also, aberration and nutation resulted as residual
+phenomena from that portion of the changes of the apparent places of the
+fixed stars which was left unaccounted for by precession. And thus again
+the apparent proper motions of the stars are the observed residues of
+their apparent movements outstanding and unaccounted for by strict
+calculation of the effects of precession, nutation, and aberration. The
+nearest approach which human theories can make to perfection is to
+diminish this residue, this _caput mortuum_ of observation, as it may be
+considered, as much as practicable, and, if possible, to reduce it to
+nothing, either by showing that something has been neglected in our
+estimation of known causes, or by reasoning upon it as a new fact, and
+on the principle of the inductive philosophy ascending from the effect
+to its cause or causes."
+
+The disturbing effects mutually produced by the earth and planets upon
+each other's motions were first brought to light as residual phenomena,
+by the difference which appeared between the observed places of those
+bodies, and the places calculated on a consideration solely of their
+gravitation towards the sun. It was this which determined astronomers
+to consider the law of gravitation as obtaining between all bodies
+whatever, and therefore between all particles of matter; their first
+tendency having been to regard it as a force acting only between each
+planet or satellite and the central body to whose system it belonged.
+Again, the catastrophists, in geology, be their opinion right or wrong,
+support it on the plea, that after the effect of all causes now in
+operation has been allowed for, there remains in the existing
+constitution of the earth a large residue of facts, proving the
+existence at former periods either of other forces, or of the same
+forces in a much greater degree of intensity. To add one more example:
+those who assert, what no one has shown any real ground for believing,
+that there is in one human individual, one sex, or one race of mankind
+over another, an inherent and inexplicable superiority in mental
+faculties, could only substantiate their proposition by subtracting from
+the differences of intellect which we in fact see, all that can be
+traced by known laws either to the ascertained differences of physical
+organization, or to the differences which have existed in the outward
+circumstances in which the subjects of the comparison have hitherto been
+placed. What these causes might fail to account for, would constitute a
+residual phenomenon, which and which alone would be evidence of an
+ulterior original distinction, and the measure of its amount. But the
+assertors of such supposed differences have not provided themselves with
+these necessary logical conditions of the establishment of their
+doctrine.
+
+The spirit of the Method of Residues being, it is hoped, sufficiently
+intelligible from these examples, and the other three methods having
+already been so fully exemplified, we may here close our exposition of
+the four methods, considered as employed in the investigation of the
+simpler and more elementary order of the combinations of phenomena.
+
+
+§ 6. Dr. Whewell has expressed a very unfavourable opinion of the
+utility of the Four Methods, as well as of the aptness of the examples
+by which I have attempted to illustrate them. His words are these:--[42]
+
+"Upon these methods, the obvious thing to remark is, that they take for
+granted the very thing which is most difficult to discover, the
+reduction of the phenomena to formulæ such as are here presented to us.
+When we have any set of complex facts offered to us; for instance, those
+which were offered in the cases of discovery which I have
+mentioned,--the facts of the planetary paths, of falling bodies, of
+refracted rays, of cosmical motions, of chemical analysis; and when, in
+any of these cases, we would discover the law of nature which governs
+them, or, if any one chooses so to term it, the feature in which all the
+cases agree, where are we to look for our A, B, C, and _a_, _b_, _c_?
+Nature does not present to us the cases in this form; and how are we to
+reduce them to this form? You say, _when_ we find the combination of A B
+C with _a b c_ and A B D with _a b d_, then we may draw our inference.
+Granted; but when and where are we to find such combinations? Even now
+that the discoveries are made, who will point out to us what are the A,
+B, C, and _a_, _b_, _c_ elements of the cases which have just been
+enumerated? Who will tell us which of the methods of inquiry those
+historically real and successful inquiries exemplify? Who will carry
+these formulæ through the history of the sciences, as they have really
+grown up; and show us that these four methods have been operative in
+their formation; or that any light is thrown upon the steps of their
+progress by reference to these formulæ?"
+
+He adds that, in this work, the methods have not been applied "to a
+large body of conspicuous and undoubted examples of discovery, extending
+along the whole history of science;" which ought to have been done in
+order that the methods might be shown to possess the "advantage" (which
+he claims as belonging to his own) of being those "by which all great
+discoveries in science have really been made."--(p. 277.)
+
+There is a striking similarity between the objections here made against
+Canons of Induction, and what was alleged, in the last century, by as
+able men as Dr. Whewell, against the acknowledged Canon of
+Ratiocination. Those who protested against the Aristotelian Logic said
+of the Syllogism, what Dr. Whewell says of the Inductive Methods, that
+it "takes for granted the very thing which is most difficult to
+discover, the reduction of the argument to formulæ such as are here
+presented to us." The grand difficulty, they said, is to obtain your
+syllogism, not to judge of its correctness when obtained. On the matter
+of fact, both they and Dr. Whewell are right. The greatest difficulty in
+both cases is first that of obtaining the evidence, and next, of
+reducing it to the form which tests its conclusiveness. But if we try to
+reduce it without knowing _to what_, we are not likely to make much
+progress. It is a more difficult thing to solve a geometrical problem,
+than to judge whether a proposed solution is correct: but if people were
+not able to judge of the solution when found, they would have little
+chance of finding it. And it cannot be pretended that to judge of an
+induction when found, is perfectly easy, is a thing for which aids and
+instruments are superfluous; for erroneous inductions, false inferences
+from experience, are quite as common, on some subjects much commoner,
+than true ones. The business of Inductive Logic is to provide rules and
+models (such as the Syllogism and its rules are for ratiocination) to
+which if inductive arguments conform, those arguments are conclusive,
+and not otherwise. This is what the Four Methods profess to be, and what
+I believe they are universally considered to be by experimental
+philosophers, who had practised all of them long before any one sought
+to reduce the practice to theory.
+
+The assailants of the Syllogism had also anticipated Dr. Whewell in the
+other branch of his argument. They said that no discoveries were ever
+made by syllogism; and Dr. Whewell says, or seems to say, that none were
+ever made by the four Methods of Induction. To the former objectors,
+Archbishop Whately very pertinently answered, that their argument, if
+good at all, was good against the reasoning process altogether; for
+whatever cannot be reduced to syllogism, is not reasoning. And Dr.
+Whewell's argument, if good at all, is good against all inferences from
+experience. In saying that no discoveries were ever made by the four
+Methods, he affirms that none were ever made by observation and
+experiment; for assuredly if any were, it was by processes reducible to
+one or other of those methods.
+
+This difference between us accounts for the dissatisfaction which my
+examples give him; for I did not select them with a view to satisfy any
+one who required to be convinced that observation and experiment are
+modes of acquiring knowledge: I confess that in the choice of them I
+thought only of illustration, and of facilitating the _conception_ of
+the Methods by concrete instances. If it had been my object to justify
+the processes themselves as means of investigation, there would have
+been no need to look far off, or make use of recondite or complicated
+instances. As a specimen of a truth ascertained by the Method of
+Agreement, I might have chosen the proposition "Dogs bark." This dog,
+and that dog, and the other dog, answer to A B C, A D E, A F G. The
+circumstance of being a dog, answers to A. Barking answers to _a_. As a
+truth made known by the Method of Difference, "Fire burns" might have
+sufficed. Before I touch the fire I am not burnt; this is B C; I touch
+it, and am burnt; this is A B C, _a_ B C.
+
+Such familiar experimental processes are not regarded as inductions by
+Dr. Whewell; but they are perfectly homogeneous with those by which,
+even on his own showing, the pyramid of science is supplied with its
+base. In vain he attempts to escape from this conclusion by laying the
+most arbitrary restrictions on the choice of examples admissible as
+instances of Induction: they must neither be such as are still matter of
+discussion (p. 265), nor must any of them be drawn from mental and
+social subjects (p. 269), nor from ordinary observation and practical
+life (pp. 241-247). They must be taken exclusively from the
+generalizations by which scientific thinkers have ascended to great and
+comprehensive laws of natural phenomena. Now it is seldom possible, in
+these complicated inquiries, to go much beyond the initial steps,
+without calling in the instrument of Deduction, and the temporary aid of
+hypotheses; as I myself, in common with Dr. Whewell, have maintained
+against the purely empirical school. Since therefore such cases could
+not conveniently be selected to illustrate the principles of mere
+observation and experiment, Dr. Whewell is misled by their absence into
+representing the Experimental Methods as serving no purpose in
+scientific investigation; forgetting that if those methods had not
+supplied the first generalizations, there would have been no materials
+for his own conception of Induction to work upon.
+
+His challenge, however, to point out which of the four methods are
+exemplified in certain important cases of scientific inquiry, is easily
+answered. "The planetary paths," as far as they are a case of induction
+at all,[43] fall under the Method of Agreement. The law of "falling
+bodies," namely that they describe spaces proportional to the squares of
+the times, was historically a deduction from the first law of motion;
+but the experiments by which it was verified, and by which it might have
+been discovered, were examples of the Method of Agreement; and the
+apparent variation from the true law, caused by the resistance of the
+air, was cleared up by experiments _in vacuo_, constituting an
+application of the Method of Difference. The law of "refracted rays"
+(the constancy of the ratio between the sines of incidence and of
+refraction for each refracting substance) was ascertained by direct
+measurement, and therefore by the Method of Agreement. The "cosmical
+motions" were determined by highly complex processes of thought, in
+which Deduction was predominant, but the Methods of Agreement and of
+Concomitant Variations had a large part in establishing the empirical
+laws. Every case without exception of "chemical analysis" constitutes a
+well-marked example of the Method of Difference. To any one acquainted
+with the subjects--to Dr. Whewell himself, there would not be the
+smallest difficulty in setting out "the A B C and _a b c_ elements" of
+these cases.
+
+If discoveries are ever made by observation and experiment without
+Deduction, the four methods are methods of discovery: but even if they
+were not methods of discovery, it would not be the less true that they
+are the sole methods of Proof; and in that character, even the results
+of deduction are amenable to them. The great generalizations which begin
+as Hypotheses, must end by being proved, and are in reality (as will be
+shown hereafter) proved, by the Four Methods. Now it is with Proof, as
+such, that Logic is principally concerned. This distinction has indeed
+no chance of finding favour with Dr. Whewell; for it is the peculiarity
+of his system, not to recognise, in cases of Induction, any necessity
+for proof. If, after assuming an hypothesis and carefully collating it
+with facts, nothing is brought to light inconsistent with it, that is,
+if experience does not _disprove_ it, he is content: at least until a
+simpler hypothesis, equally consistent with experience, presents itself.
+If this be Induction, doubtless there is no necessity for the four
+methods. But to suppose that it is so, appears to me a radical
+misconception of the nature of the evidence of physical truths.
+
+So real and practical is the need of a test for induction, similar to
+the syllogistic test of ratiocination, that inferences which bid
+defiance to the most elementary notions of inductive logic are put forth
+without misgiving by persons eminent in physical science, as soon as
+they are off the ground on which they are conversant with the facts, and
+not reduced to judge only by the arguments; and as for educated persons
+in general, it may be doubted if they are better judges of a good or a
+bad induction than they were before Bacon wrote. The improvement in the
+results of thinking has seldom extended to the processes; or has
+reached, if any process, that of investigation only, not that of proof.
+A knowledge of many laws of nature has doubtless been arrived at, by
+framing hypotheses and finding that the facts corresponded to them; and
+many errors have been got rid of by coming to a knowledge of facts which
+were inconsistent with them, but not by discovering that the mode of
+thought which led to the errors was itself faulty, and might have been
+known to be such independently of the facts which disproved the
+specific conclusion. Hence it is, that while the thoughts of mankind
+have on many subjects worked themselves practically right, the thinking
+power remains as weak as ever: and on all subjects on which the facts
+which would check the result are not accessible, as in what relates to
+the invisible world, and even, as has been seen lately, to the visible
+world of the planetary regions, men of the greatest scientific
+acquirements argue as pitiably as the merest ignoramus. For though they
+have made many sound inductions, they have not learnt from them (and Dr.
+Whewell thinks there is no necessity that they should learn) the
+principles of inductive _evidence_.
+
+
+
+
+CHAPTER X.
+
+OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS.
+
+
+§ 1. In the preceding exposition of the four methods of observation and
+experiment, by which we contrive to distinguish among a mass of
+coexistent phenomena the particular effect due to a given cause, or the
+particular cause which gave birth to a given effect; it has been
+necessary to suppose, in the first instance, for the sake of
+simplification, that this analytical operation is encumbered by no other
+difficulties than what are essentially inherent in its nature; and to
+represent to ourselves, therefore, every effect, on the one hand as
+connected exclusively with a single cause, and on the other hand as
+incapable of being mixed and confounded with any other coexistent
+effect. We have regarded _a b c d e_, the aggregate of the phenomena
+existing at any moment, as consisting of dissimilar facts, _a_, _b_,
+_c_, _d_, and _e_, for each of which one, and only one, cause needs be
+sought; the difficulty being only that of singling out this one cause
+from the multitude of antecedent circumstances, A, B, C, D, and E. The
+cause indeed may not be simple; it may consist of an assemblage of
+conditions; but we have supposed that there was only one possible
+assemblage of conditions, from which the given effect could result.
+
+If such were the fact, it would be comparatively an easy task to
+investigate the laws of nature. But the supposition does not hold, in
+either of its parts. In the first place, it is not true that the same
+phenomenon is always produced by the same cause: the effect _a_ may
+sometimes arise from A, sometimes from B. And, secondly, the effects of
+different causes are often not dissimilar, but homogeneous, and marked
+out by no assignable boundaries from one another: A and B may produce
+not _a_ and _b_, but different portions of an effect _a_. The obscurity
+and difficulty of the investigation of the laws of phenomena is
+singularly increased by the necessity of adverting to these two
+circumstances; Intermixture of Effects, and Plurality of Causes. To the
+latter, being the simpler of the two considerations, we shall first
+direct our attention.
+
+It is not true, then, that one effect must be connected with only one
+cause, or assemblage of conditions; that each phenomenon can be produced
+only in one way. There are often several independent modes in which the
+same phenomenon could have originated. One fact may be the consequent in
+several invariable sequences; it may follow, with equal uniformity, any
+one of several antecedents, or collections of antecedents. Many causes
+may produce motion: many causes may produce some kinds of sensation:
+many causes may produce death. A given effect may really be produced by
+a certain cause, and yet be perfectly capable of being produced without
+it.
+
+
+§ 2. One of the principal consequences of this fact of Plurality of
+Causes is, to render the first of the inductive methods, that of
+Agreement, uncertain. To illustrate that method, we supposed two
+instances, A B C followed by _a b c_, and A D E followed by _a d e_.
+From these instances it might apparently be concluded that A is an
+invariable antecedent of _a_, and even that it is the unconditional
+invariable antecedent, or cause, if we could be sure that there is no
+other antecedent common to the two cases. That this difficulty may not
+stand in the way, let us suppose the two cases positively ascertained to
+have no antecedent in common except A. The moment, however, that we let
+in the possibility of a plurality of causes, the conclusion fails. For
+it involves a tacit supposition, that _a_ must have been produced in
+both instances by the same cause. If there can possibly have been two
+causes, those two may, for example, be C and E: the one may have been
+the cause of _a_ in the former of the instances, the other in the
+latter, A having no influence in either case.
+
+Suppose, for example, that two great artists, or great philosophers,
+that two extremely selfish, or extremely generous characters, were
+compared together as to the circumstances of their education and
+history, and the two cases were found to agree only in one circumstance:
+would it follow that this one circumstance was the cause of the quality
+which characterized both those individuals? Not at all; for the causes
+which may produce any type of character are innumerable; and the two
+persons might equally have agreed in their character, though there had
+been no manner of resemblance in their previous history.
+
+This, therefore, is a characteristic imperfection of the Method of
+Agreement; from which imperfection the Method of Difference is free. For
+if we have two instances, A B C and B C, of which B C gives _b c_, and A
+being added converts it into _a b c_, it is certain that in this
+instance at least, A was either the cause of _a_, or an indispensable
+portion of its cause, even though the cause which produces it in other
+instances may be altogether different. Plurality of Causes, therefore,
+not only does not diminish the reliance due to the Method of Difference,
+but does not even render a greater number of observations or experiments
+necessary: two instances, the one positive and the other negative, are
+still sufficient for the most complete and rigorous induction. Not so,
+however, with the Method of Agreement. The conclusions which that
+yields, when the number of instances compared is small, are of no real
+value, except as, in the character of suggestions, they may lead either
+to experiments bringing them to the test of the Method of Difference, or
+to reasonings which may explain and verify them deductively.
+
+It is only when the instances, being indefinitely multiplied and varied,
+continue to suggest the same result, that this result acquires any high
+degree of independent value. If there are but two instances, A B C and A
+D E, though these instances have no antecedent in common except A, yet
+as the effect may possibly have been produced in the two cases by
+different causes, the result is at most only a slight probability in
+favour of A; there may be causation, but it is almost equally probable
+that there was only a coincidence. But the oftener we repeat the
+observation, varying the circumstances, the more we advance towards a
+solution of this doubt. For if we try A F G, A H K, &c., all unlike one
+another except in containing the circumstance A, and if we find the
+effect _a_ entering into the result in all these cases, we must suppose
+one of two things, either that it is caused by A, or that it has as many
+different causes as there are instances. With each addition, therefore,
+to the number of instances, the presumption is strengthened in favour of
+A. The inquirer, of course, will not neglect, if an opportunity present
+itself, to exclude A from some one of these combinations, from A H K for
+instance, and by trying H K separately, appeal to the Method of
+Difference in aid of the Method of Agreement. By the Method of
+Difference alone can it be ascertained that A is the cause of _a_; but
+that it is either the cause, or another effect of the same cause, may be
+placed beyond any reasonable doubt by the Method of Agreement, provided
+the instances are very numerous, as well as sufficiently various.
+
+After how great a multiplication, then, of varied instances, all
+agreeing in no other antecedent except A, is the supposition of a
+plurality of causes sufficiently rebutted, and the conclusion that _a_
+is connected with A divested of the characteristic imperfection, and
+reduced to a virtual certainty? This is a question which we cannot be
+exempted from answering: but the consideration of it belongs to what is
+called the Theory of Probability, which will form the subject of a
+chapter hereafter. It is seen, however, at once, that the conclusion
+does amount to a practical certainty after a sufficient number of
+instances, and that the method, therefore, is not radically vitiated by
+the characteristic imperfection. The result of these considerations is
+only, in the first place, to point out a new source of inferiority in
+the Method of Agreement as compared with other modes of investigation,
+and new reasons for never resting contented with the results obtained by
+it, without attempting to confirm them either by the Method of
+Difference, or by connecting them deductively with some law or laws
+already ascertained by that superior method. And, in the second place,
+we learn from this the true theory of the value of mere _number_ of
+instances in inductive inquiry. The Plurality of Causes is the only
+reason why mere number is of any importance. The tendency of
+unscientific inquirers is to rely too much on number, without analysing
+the instances; without looking closely enough into their nature, to
+ascertain what circumstances are or are not eliminated by means of them.
+Most people hold their conclusions with a degree of assurance
+proportioned to the mere _mass_ of the experience on which they appear
+to rest; not considering that by the addition of instances to instances,
+all of the same kind, that is, differing from one another only in points
+already recognised as immaterial, nothing whatever is added to the
+evidence of the conclusion. A single instance eliminating some
+antecedent which existed in all the other cases, is of more value than
+the greatest multitude of instances which are reckoned by their number
+alone. It is necessary, no doubt, to assure ourselves, by repetition of
+the observation or experiment, that no error has been committed
+concerning the individual facts observed; and until we have assured
+ourselves of this, instead of varying the circumstances, we cannot too
+scrupulously repeat the same experiment or observation without any
+change. But when once this assurance has been obtained, the
+multiplication of instances which do not exclude any more circumstances
+is entirely useless, provided there have been already enough to exclude
+the supposition of Plurality of Causes.
+
+It is of importance to remark, that the peculiar modification of the
+Method of Agreement, which, as partaking in some degree of the nature of
+the Method of Difference, I have called the Joint Method of Agreement
+and Difference, is not affected by the characteristic imperfection now
+pointed out. For, in the joint method, it is supposed not only that the
+instances in which _a_ is, agree only in containing A, but also that the
+instances in which _a_ is not, agree only in not containing A. Now, if
+this be so, A must be not only the cause of _a_, but the only possible
+cause: for if there were another, as for example B, then in the
+instances in which _a_ is not, B must have been absent as well as A, and
+it would not be true that these instances agree _only_ in not containing
+A. This, therefore, constitutes an immense advantage of the joint
+method over the simple Method of Agreement. It may seem, indeed, that
+the advantage does not belong so much to the joint method, as to one of
+its two premises, (if they may be so called,) the negative premise. The
+Method of Agreement, when applied to negative instances, or those in
+which a phenomenon does _not_ take place, is certainly free from the
+characteristic imperfection which affects it in the affirmative case.
+The negative premise, it might therefore be supposed, could be worked as
+a simple case of the Method of Agreement, without requiring an
+affirmative premise to be joined with it. But though this is true in
+principle, it is generally altogether impossible to work the Method of
+Agreement by negative instances without positive ones: it is so much
+more difficult to exhaust the field of negation than that of
+affirmation. For instance, let the question be, what is the cause of the
+transparency of bodies; with what prospect of success could we set
+ourselves to inquire directly in what the multifarious substances which
+are _not_ transparent, agree? But we might hope much sooner to seize
+some point of resemblance among the comparatively few and definite
+species of objects which _are_ transparent; and this being attained, we
+should quite naturally be put upon examining whether the _absence_ of
+this one circumstance be not precisely the point in which all opaque
+substances will be found to resemble.
+
+The Joint Method of Agreement and Difference, therefore, or, as I have
+otherwise called it, the Indirect Method of Difference (because, like
+the Method of Difference properly so called, it proceeds by ascertaining
+how and in what the cases where the phenomenon is present, differ from
+those in which it is absent) is, after the Direct Method of Difference,
+the most powerful of the remaining instruments of inductive
+investigation; and in the sciences which depend on pure observation,
+with little or no aid from experiment, this method, so well exemplified
+in the speculation on the cause of dew, is the primary resource, so far
+as direct appeals to experience are concerned.
+
+
+§ 3. We have thus far treated Plurality of Causes only as a possible
+supposition, which, until removed, renders our inductions uncertain; and
+have only considered by what means, where the plurality does not really
+exist, we may be enabled to disprove it. But we must also consider it as
+a case actually occurring in nature, and which, as often as it does
+occur, our methods of induction ought to be capable of ascertaining and
+establishing. For this, however, there is required no peculiar method.
+When an effect is really producible by two or more causes, the process
+for detecting them is in no way different from that by which we discover
+single causes. They may (first) be discovered as separate sequences, by
+separate sets of instances. One set of observations or experiments shows
+that the sun is a cause of heat, another that friction is a source of
+it, another that percussion, another that electricity, another that
+chemical action is such a source. Or (secondly) the plurality may come
+to light in the course of collating a number of instances, when we
+attempt to find some circumstance in which they all agree, and fail in
+doing so. We find it impossible to trace, in all the cases in which the
+effect is met with, any common circumstance. We find that we can
+eliminate _all_ the antecedents; that no one of them is present in all
+the instances, no one of them indispensable to the effect. On closer
+scrutiny, however, it appears that though no one is always present, one
+or other of several always is. If, on further analysis, we can detect in
+these any common element, we may be able to ascend from them to some one
+cause which is the really operative circumstance in them all. Thus it is
+now thought that in the production of heat by friction, percussion,
+chemical action, &c., the ultimate source is one and the same. But if
+(as continually happens) we cannot take this ulterior step, the
+different antecedents must be set down provisionally as distinct causes,
+each sufficient of itself to produce the effect.
+
+We here close our remarks on the Plurality of Causes, and proceed to the
+still more peculiar and more complex case of the Intermixture of
+Effects, and the interference of causes with one another: a case
+constituting the principal part of the complication and difficulty of
+the study of nature; and with which the four only possible methods of
+directly inductive investigation by observation and experiment, are for
+the most part, as will appear presently, quite unequal to cope. The
+instrument of Deduction alone is adequate to unravel the complexities
+proceeding from this source; and the four methods have little more in
+their power than to supply premises for, and a verification of, our
+deductions.
+
+
+§ 4. A concurrence of two or more causes, not separately producing each
+its own effect, but interfering with or modifying the effects of one
+another, takes place, as has already been explained, in two different
+ways. In the one, which is exemplified by the joint operation of
+different forces in mechanics, the separate effects of all the causes
+continue to be produced, but are compounded with one another, and
+disappear in one total. In the other, illustrated by the case of
+chemical action, the separate effects cease entirely, and are succeeded
+by phenomena altogether different, and governed by different laws.
+
+Of these cases the former is by far the more frequent, and this case it
+is which, for the most part, eludes the grasp of our experimental
+methods. The other and exceptional case is essentially amenable to them.
+When the laws of the original agents cease entirely, and a phenomenon
+makes its appearance, which, with reference to those laws, is quite
+heterogeneous; when, for example, two gaseous substances, hydrogen and
+oxygen, on being brought together, throw off their peculiar properties,
+and produce the substance called water; in such cases the new fact may
+be subjected to experimental inquiry, like any other phenomenon; and the
+elements which are said to compose it may be considered as the mere
+agents of its production; the conditions on which it depends, the facts
+which make up its cause.
+
+The _effects_ of the new phenomenon, the _properties_ of water, for
+instance, are as easily found by experiment as the effects of any other
+cause. But to discover the _cause_ of it, that is, the particular
+conjunction of agents from which it results, is often difficult enough.
+In the first place, the origin and actual production of the phenomenon
+are most frequently inaccessible to our observation. If we could not
+have learned the composition of water until we found instances in which
+it was actually produced from oxygen and hydrogen, we should have been
+forced to wait until the casual thought struck some one of passing an
+electric spark through a mixture of the two gases, or inserting a
+lighted taper into it, merely to try what would happen. Besides, many
+substances, though they can be analysed, cannot by any known artificial
+means be recompounded. Further, even if we could have ascertained, by
+the Method of Agreement, that oxygen and hydrogen were both present when
+water is produced, no experimentation on oxygen and hydrogen separately,
+no knowledge of their laws, could have enabled us deductively to infer
+that they would produce water. We require a specific experiment on the
+two combined.
+
+Under these difficulties, we should generally have been indebted for our
+knowledge of the causes of this class of effects, not to any inquiry
+directed specifically towards that end, but either to accident, or to
+the gradual progress of experimentation on the different combinations of
+which the producing agents are susceptible; if it were not for a
+peculiarity belonging to effects of this description, that they often,
+under some particular combination of circumstances, reproduce their
+causes. If water results from the juxtaposition of hydrogen and oxygen
+whenever this can be made sufficiently close and intimate, so, on the
+other hand, if water itself be placed in certain situations, hydrogen
+and oxygen are reproduced from it: an abrupt termination is put to the
+new laws, and the agents reappear separately with their own properties
+as at first. What is called chemical analysis is the process of
+searching for the causes of a phenomenon among its effects, or rather
+among the effects produced by the action of some other causes upon it.
+
+Lavoisier, by heating mercury to a high temperature in a close vessel
+containing air, found that the mercury increased in weight, and became
+what was then called red precipitate, while the air, on being examined
+after the experiment, proved to have lost weight, and to have become
+incapable of supporting life or combustion. When red precipitate was
+exposed to a still greater heat, it became mercury again, and gave off a
+gas which did support life and flame. Thus the agents which by their
+combination produced red precipitate, namely the mercury and the gas,
+reappear as effects resulting from that precipitate when acted upon by
+heat. So, if we decompose water by means of iron filings, we produce two
+effects, rust and hydrogen: now rust is already known by experiments
+upon the component substances, to be an effect of the union of iron and
+oxygen: the iron we ourselves supplied, but the oxygen must have been
+produced from the water. The result therefore is that water has
+disappeared, and hydrogen and oxygen have appeared in its stead: or in
+other words, the original laws of these gaseous agents, which had been
+suspended by the superinduction of the new laws called the properties of
+water, have again started into existence, and the causes of water are
+found among its effects.
+
+Where two phenomena, between the laws or properties of which considered
+in themselves no connexion can be traced, are thus reciprocally cause
+and effect, each capable in its turn of being produced from the other,
+and each, when it produces the other, ceasing itself to exist (as water
+is produced from oxygen and hydrogen, and oxygen and hydrogen are
+reproduced from water); this causation of the two phenomena by one
+another, each being generated by the other's destruction, is properly
+transformation. The idea of chemical composition is an idea of
+transformation, but of a transformation which is incomplete; since we
+consider the oxygen and hydrogen to be present in the water _as_ oxygen
+and hydrogen, and capable of being discovered in it if our senses were
+sufficiently keen: a supposition (for it is no more) grounded solely on
+the fact, that the weight of the water is the sum of the separate
+weights of the two ingredients. If there had not been this exception to
+the entire disappearance, in the compound, of the laws of the separate
+ingredients; if the combined agents had not, in this one particular of
+weight, preserved their own laws, and produced a joint result equal to
+the sum of their separate results; we should never, probably, have had
+the notion now implied by the words chemical composition: and, in the
+facts of water produced from hydrogen and oxygen, and hydrogen and
+oxygen produced from water, as the transformation would have been
+complete, we should have seen only a transformation.
+
+The very promising generalization now commonly known as the Conservation
+or Persistence of Force, bears a close resemblance to what the
+conception of chemical composition would become, if divested of the one
+circumstance which now distinguishes it from simple transformation. It
+has long been known that heat is capable of producing electricity, and
+electricity heat; that mechanical motion in numerous cases produces and
+is produced by them both; and so of all other physical forces. It has of
+late become the general belief of scientific inquirers that mechanical
+force, electricity, magnetism, heat, light, and chemical action (to
+which has subsequently been added vital action) are not so much causes
+of one another as convertible into one another; and they are now
+generally spoken of as forms of one and the same force, varying only in
+its manifestations. This doctrine may be admitted, without by any means
+implying that Force is a real entity, a Thing in itself, distinct from
+all its phenomenal manifestations to our organs. Supposing the doctrine
+true, the several kinds of phenomena which it identifies in respect of
+their origin would nevertheless remain different facts; facts which
+would be causes of one another--reciprocally causes and effects, which
+is the first element in the form of causation properly called
+transformation. What the doctrine contains more than this, is, that in
+each of these cases of reciprocal causation, the causes are reproduced
+without alteration in quantity. This is what takes place in the
+transformations of matter: when water has been converted into hydrogen
+and oxygen, these can be reconverted into precisely the same quantity of
+water from which they were produced. To establish a corresponding law in
+regard to Force, it has to be proved that heat is capable of being
+converted into electricity, electricity into chemical action, chemical
+action into mechanical force, and mechanical force back again into the
+exact quantity of heat which was originally expended; and so through
+all the interchanges. Were this proved, it would establish what
+constitutes transformation, as distinguished from the simple fact of
+reciprocal causation. The fact in issue is simply the quantitative
+equivalence of all these natural agencies; whereby a given quantity of
+any one is convertible into, and interchangeable with, a given, and
+always the same, quantity of any other: this, no less, but also no more.
+It cannot yet be said that the law has been fully proved of any case,
+except that of interchange between heat and mechanical motion. It does
+seem to be ascertained, not only that these two are convertible into
+each other, but that after any number of conversions the original
+quantities reappear without addition or diminution, like the original
+quantities of hydrogen and oxygen after passing through the condition of
+water. If the same thing comes to be proved true of all the other
+forces, in relation to these two and to one another, the law of
+Conservation will be established; and it will be a legitimate mode of
+expressing the fact, to speak of Force, as we already speak of Matter,
+as indestructible. But Force will not the less remain, to the
+philosopher, a mere abstraction of the mind. All that will have been
+proved is, that in the phenomena of Nature, nothing actually ceases
+without generating a calculable, and always the same, quantity of some
+other natural phenomenon, which again, when it ceases, will in its turn
+either generate a calculable, and always the same, quantity of some
+third phenomenon, or reproduce the original quantity of the first.
+
+In these cases, where the heteropathic effect (as we called it in a
+former chapter)[44] is but a transformation of its cause, or in other
+words, where the effect and its cause are reciprocally such, and
+mutually convertible into each other; the problem of finding the cause
+resolves itself into the far easier one of finding an effect, which is
+the kind of inquiry that admits of being prosecuted by direct
+experiment. But there are other cases of heteropathic effects to which
+this mode of investigation is not applicable. Take, for instance, the
+heteropathic laws of mind; that portion of the phenomena of our mental
+nature which are analogous to chemical rather than to dynamical
+phenomena; as when a complex passion is formed by the coalition of
+several elementary impulses, or a complex emotion by several simple
+pleasures or pains, of which it is the result without being the
+aggregate, or in any respect homogeneous with them. The product, in
+these cases, is generated by its various factors; but the factors cannot
+be reproduced from the product; just as a youth can grow into an old
+man, but an old man cannot grow into a youth. We cannot ascertain from
+what simple feelings any of our complex states of mind are generated, as
+we ascertain the ingredients of a chemical compound, by making it, in
+its turn, generate them. We can only, therefore, discover these laws by
+the slow process of studying the simple feelings themselves, and
+ascertaining synthetically, by experimenting on the various combinations
+of which they are susceptible, what they, by their mutual action upon
+one another, are capable of generating.
+
+
+§ 5. It might have been supposed that the other, and apparently simpler
+variety of the mutual interference of causes, where each cause continues
+to produce its own proper effect according to the same laws to which it
+conforms in its separate state, would have presented fewer difficulties
+to the inductive inquirer than that of which we have just finished the
+consideration. It presents, however, so far as direct induction apart
+from deduction is concerned, infinitely greater difficulties. When a
+concurrence of causes gives rise to a new effect, bearing no relation to
+the separate effects of those causes, the resulting phenomenon stands
+forth undisguised, inviting attention to its peculiarity, and presenting
+no obstacle to our recognising its presence or absence among any number
+of surrounding phenomena. It admits therefore of being easily brought
+under the canons of Induction, provided instances can be obtained such
+as those canons require: and the non-occurrence of such instances, or
+the want of means to produce them artificially, is the real and only
+difficulty in such investigations; a difficulty not logical, but in some
+sort physical. It is otherwise with cases of what, in a preceding
+chapter, has been denominated the Composition of Causes. There, the
+effects of the separate causes do not terminate and give place to
+others, thereby ceasing to form any part of the phenomenon to be
+investigated; on the contrary, they still take place, but are
+intermingled with, and disguised by, the homogeneous and closely allied
+effects of other causes. They are no longer _a_, _b_, _c_, _d_, _e_,
+existing side by side, and continuing to be separately discernible; they
+are + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of which cancel one
+another, while many others do not appear distinguishably, but merge in
+one sum: forming altogether a result, between which and the causes
+whereby it was produced there is often an insurmountable difficulty in
+tracing by observation any fixed relation whatever.
+
+The general idea of the Composition of Causes has been seen to be, that
+though two or more laws interfere with one another, and apparently
+frustrate or modify one another's operation, yet in reality all are
+fulfilled, the collective effect being the exact sum of the effects of
+the causes taken separately. A familiar instance is that of a body kept
+in equilibrium by two equal and contrary forces. One of the forces if
+acting alone would carry the body in a given time a certain distance to
+the west, the other if acting alone would carry it exactly as far
+towards the east; and the result is the same as if it had been first
+carried to the west as far as the one force would carry it, and then
+back towards the east as far as the other would carry it, that is,
+precisely the same distance; being ultimately left where it was found at
+first.
+
+All laws of causation are liable to be in this manner counteracted, and
+seemingly frustrated, by coming into conflict with other laws, the
+separate result of which is opposite to theirs, or more or less
+inconsistent with it. And hence, with almost every law, many instances
+in which it really is entirely fulfilled, do not, at first sight, appear
+to be cases of its operation at all. It is so in the example just
+adduced: a force, in mechanics, means neither more nor less than a cause
+of motion, yet the sum of the effects of two causes of motion may be
+rest. Again, a body solicited by two forces in directions making an
+angle with one another, moves in the diagonal; and it seems a paradox to
+say that motion in the diagonal is the sum of two motions in two other
+lines. Motion, however, is but change of place, and at every instant the
+body is in the exact place it would have been in if the forces had acted
+during alternate instants instead of acting in the same instant; (saving
+that if we suppose two forces to act successively which are in truth
+simultaneous, we must of course allow them double the time.) It is
+evident, therefore, that each force has had, during each instant, all
+the effect which belonged to it; and that the modifying influence which
+one of two concurrent causes is said to exercise with respect to the
+other, may be considered as exerted not over the action of the cause
+itself, but over the effect after it is completed. For all purposes of
+predicting, calculating, or explaining their joint result, causes which
+compound their effects may be treated as if they produced simultaneously
+each of them its own effect, and all these effects coexisted visibly.
+
+Since the laws of causes are as really fulfilled when the causes are
+said to be counteracted by opposing causes, as when they are left to
+their own undisturbed action, we must be cautious not to express the
+laws in such terms as would render the assertion of their being
+fulfilled in those cases a contradiction. If, for instance, it were
+stated as a law of nature that a body to which a force is applied moves
+in the direction of the force, with a velocity proportioned to the force
+directly, and to its own mass inversely; when in point of fact some
+bodies to which a force is applied do not move at all, and those which
+do move (at least in the region of our earth) are, from the very first,
+retarded by the action of gravity and other resisting forces, and at
+last stopped altogether; it is clear that the general proposition,
+though it would be true under a certain hypothesis, would not express
+the facts as they actually occur. To accommodate the expression of the
+law to the real phenomena, we must say, not that the object moves, but
+that it _tends_ to move, in the direction and with the velocity
+specified. We might, indeed, guard our expression in a different mode,
+by saying that the body moves in that manner unless prevented, or except
+in so far as prevented, by some counteracting cause. But the body does
+not only move in that manner unless counteracted; it _tends_ to move in
+that manner even when counteracted; it still exerts, in the original
+direction, the same energy of movement as if its first impulse had been
+undisturbed, and produces, by that energy, an exactly equivalent
+quantity of effect. This is true even when the force leaves the body as
+it found it, in a state of absolute rest; as when we attempt to raise a
+body of three tons weight with a force equal to one ton. For if, while
+we are applying this force, wind or water or any other agent supplies an
+additional force just exceeding two tons, the body will be raised; thus
+proving that the force we applied exerted its full effect, by
+neutralizing an equivalent portion of the weight which it was
+insufficient altogether to overcome. And if while we are exerting this
+force of one ton upon the object in a direction contrary to that of
+gravity, it be put into a scale and weighed, it will be found to have
+lost a ton of its weight, or in other words, to press downwards with a
+force only equal to the difference of the two forces.
+
+These facts are correctly indicated by the expression _tendency_. All
+laws of causation, in consequence of their liability to be counteracted,
+require to be stated in words affirmative of tendencies only, and not of
+actual results. In those sciences of causation which have an accurate
+nomenclature, there are special words which signify a tendency to the
+particular effect with which the science is conversant; thus _pressure_,
+in mechanics, is synonymous with tendency to motion, and forces are not
+reasoned on as causing actual motion, but as exerting pressure. A
+similar improvement in terminology would be very salutary in many other
+branches of science.
+
+The habit of neglecting this necessary element in the precise expression
+of the laws of nature, has given birth to the popular prejudice that all
+general truths have exceptions; and much unmerited distrust has thence
+accrued to the conclusions of science, when they have been submitted to
+the judgment of minds insufficiently disciplined and cultivated. The
+rough generalizations suggested by common observation usually have
+exceptions; but principles of science, or in other words, laws of
+causation, have not. "What is thought to be an exception to a
+principle," (to quote words used on a different occasion,) "is always
+some other and distinct principle cutting into the former; some other
+force which impinges[45] against the first force, and deflects it from
+its direction. There are not a law and an exception to that law, the law
+acting in ninety-nine cases, and the exception in one. There are two
+laws, each possibly acting in the whole hundred cases, and bringing
+about a common effect by their conjunct operation. If the force which,
+being the less conspicuous of the two, is called the _disturbing_ force,
+prevails sufficiently over the other force in some one case, to
+constitute that case what is commonly called an exception, the same
+disturbing force probably acts as a modifying cause in many other cases
+which no one will call exceptions.
+
+"Thus if it were stated to be a law of nature that all heavy bodies fall
+to the ground, it would probably be said that the resistance of the
+atmosphere, which prevents a balloon from falling, constitutes the
+balloon an exception to that pretended law of nature. But the real law
+is, that all heavy bodies _tend_ to fall; and to this there is no
+exception, not even the sun and moon; for even they, as every astronomer
+knows, tend towards the earth, with a force exactly equal to that with
+which the earth tends towards them. The resistance of the atmosphere
+might, in the particular case of the balloon, from a misapprehension of
+what the law of gravitation is, be said to _prevail over_ the law; but
+its disturbing effect is quite as real in every other case, since though
+it does not prevent, it retards the fall of all bodies whatever. The
+rule, and the so-called exception, do not divide the cases between them;
+each of them is a comprehensive rule extending to all cases. To call one
+of these concurrent principles an exception to the other, is
+superficial, and contrary to the correct principles of nomenclature and
+arrangement. An effect of precisely the same kind, and arising from the
+same cause, ought not to be placed in two different categories, merely
+as there does or does not exist another cause preponderating over
+it."[46]
+
+
+§ 6. We have now to consider according to what method these complex
+effects, compounded of the effects of many causes, are to be studied;
+how we are enabled to trace each effect to the concurrence of causes in
+which it originated, and ascertain the conditions of its recurrence--the
+circumstances in which it may be expected again to occur. The conditions
+of a phenomenon which arises from a composition of causes, may be
+investigated either deductively or experimentally.
+
+The case, it is evident, is naturally susceptible of the deductive mode
+of investigation. The law of an effect of this description is a result
+of the laws of the separate causes on the combination of which it
+depends, and is therefore in itself capable of being deduced from these
+laws. This is called the method _à priori_. The other, or _à posteriori_
+method, professes to proceed according to the canons of experimental
+inquiry. Considering the whole assemblage of concurrent causes which
+produced the phenomenon, as one single cause, it attempts to ascertain
+the cause in the ordinary manner, by a comparison of instances. This
+second method subdivides itself into two different varieties. If it
+merely collates instances of the effect, it is a method of pure
+observation. If it operates upon the causes, and tries different
+combinations of them, in hopes of ultimately hitting the precise
+combination which will produce the given total effect, it is a method of
+experiment.
+
+In order more completely to clear up the nature of each of these three
+methods, and determine which of them deserves the preference, it will be
+expedient (conformably to a favourite maxim of Lord Chancellor Eldon, to
+which, though it has often incurred philosophical ridicule, a deeper
+philosophy will not refuse its sanction) to "clothe them in
+circumstances." We shall select for this purpose a case which as yet
+furnishes no very brilliant example of the success of any of the three
+methods, but which is all the more suited to illustrate the difficulties
+inherent in them. Let the subject of inquiry be, the conditions of
+health and disease in the human body; or (for greater simplicity) the
+conditions of recovery from a given disease; and in order to narrow the
+question still more, let it be limited, in the first instance, to this
+one inquiry: Is, or is not some particular medicament (mercury, for
+instance) a remedy for the given disease.
+
+Now, the deductive method would set out from known properties of
+mercury, and known laws of the human body, and by reasoning from these,
+would attempt to discover whether mercury will act upon the body when in
+the morbid condition supposed, in such a manner as to restore health.
+The experimental method would simply administer mercury in as many cases
+as possible, noting the age, sex, temperament, and other peculiarities
+of bodily constitution, the particular form or variety of the disease,
+the particular stage of its progress, &c., remarking in which of these
+cases it produced a salutary effect, and with what circumstances it was
+on those occasions combined. The method of simple observation would
+compare instances of recovery, to find whether they agreed in having
+been preceded by the administration of mercury; or would compare
+instances of recovery with instances of failure, to find cases which,
+agreeing in all other respects, differed only in the fact that mercury
+had been administered, or that it had not.
+
+
+§ 7. That the last of these three modes of investigation is applicable
+to the case, no one has ever seriously contended. No conclusions of
+value on a subject of such intricacy, ever were obtained in that way.
+The utmost that could result would be a vague general impression for or
+against the efficacy of mercury, of no avail for guidance unless
+confirmed by one of the other two methods. Not that the results, which
+this method strives to obtain, would not be of the utmost possible value
+if they could be obtained. If all the cases of recovery which presented
+themselves, in an examination extending to a great number of instances,
+were cases in which mercury had been administered, we might generalize
+with confidence from this experience, and should have obtained a
+conclusion of real value. But no such basis for generalization can we,
+in a case of this description, hope to obtain. The reason is that which
+we have spoken of as constituting the characteristic imperfection of the
+Method of Agreement; Plurality of Causes. Supposing even that mercury
+does tend to cure the disease, so many other causes, both natural and
+artificial, also tend to cure it, that there are sure to be abundant
+instances of recovery in which mercury has not been administered:
+unless, indeed, the practice be to administer it in all cases; on which
+supposition it will equally be found in the cases of failure.
+
+When an effect results from the union of many causes, the share which
+each has in the determination of the effect cannot in general be great:
+and the effect is not likely, even in its presence or absence, still
+less in its variations, to follow, even approximately, any one of the
+causes. Recovery from a disease is an event to which, in every case,
+many influences must concur. Mercury may be one such influence; but from
+the very fact that there are many other such, it will necessarily happen
+that although mercury is administered, the patient, for want of other
+concurring influences, will often not recover, and that he often will
+recover when it is not administered, the other favourable influences
+being sufficiently powerful without it. Neither, therefore, will the
+instances of recovery agree in the administration of mercury, nor will
+the instances of failure agree in its non-administration. It is much if,
+by multiplied and accurate returns from hospitals and the like, we can
+collect that there are rather more recoveries and rather fewer failures
+when mercury is administered than when it is not; a result of very
+secondary value even as a guide to practice, and almost worthless as a
+contribution to the theory of the subject.
+
+
+§ 8. The inapplicability of the method of simple observation to
+ascertain the conditions of effects dependent on many concurring
+causes, being thus recognised; we shall next inquire whether any greater
+benefit can be expected from the other branch of the _à posteriori_
+method, that which proceeds by directly trying different combinations of
+causes, either artificially produced or found in nature, and taking
+notice what is their effect: as, for example, by actually trying the
+effect of mercury, in as many different circumstances as possible. This
+method differs from the one which we have just examined, in turning our
+attention directly to the causes or agents, instead of turning it to the
+effect, recovery from the disease. And since, as a general rule, the
+effects of causes are far more accessible to our study than the causes
+of effects, it is natural to think that this method has a much better
+chance of proving successful than the former.
+
+The method now under consideration is called the Empirical Method; and
+in order to estimate it fairly, we must suppose it to be completely, not
+incompletely, empirical. We must exclude from it everything which
+partakes of the nature not of an experimental but of a deductive
+operation. If for instance we try experiments with mercury upon a person
+in health, in order to ascertain the general laws of its action upon the
+human body, and then reason from these laws to determine how it will act
+upon persons affected with a particular disease, this may be a really
+effectual method, but this is deduction. The experimental method does
+not derive the law of a complex case from the simpler laws which
+conspire to produce it, but makes its experiments directly upon the
+complex case. We must make entire abstraction of all knowledge of the
+simpler tendencies, the _modi operandi_ of mercury in detail. Our
+experimentation must aim at obtaining a direct answer to the specific
+question, Does or does not mercury tend to cure the particular disease?
+
+Let us see, therefore, how far the case admits of the observance of
+those rules of experimentation, which it is found necessary to observe
+in other cases. When we devise an experiment to ascertain the effect of
+a given agent, there are certain precautions which we never, if we can
+help it, omit. In the first place, we introduce the agent into the midst
+of a set of circumstances which we have exactly ascertained. It needs
+hardly be remarked how far this condition is from being realized in any
+case connected with the phenomena of life; how far we are from knowing
+what are all the circumstances which pre-exist in any instance in which
+mercury is administered to a living being. This difficulty, however,
+though insuperable in most cases, may not be so in all; there are
+sometimes concurrences of many causes, in which we yet know accurately
+what the causes are. Moreover, the difficulty may be attenuated by
+sufficient multiplication of experiments, in circumstances rendering it
+improbable that any of the unknown causes should exist in them all. But
+when we have got clear of this obstacle, we encounter another still more
+serious. In other cases, when we intend to try an experiment, we do not
+reckon it enough that there be no circumstance in the case the presence
+of which is unknown to us. We require also that none of the
+circumstances which we do know, shall have effects susceptible of being
+confounded with those of the agent whose properties we wish to study. We
+take the utmost pains to exclude all causes capable of composition with
+the given cause; or if forced to let in any such causes, we take care to
+make them such that we can compute and allow for their influence, so
+that the effect of the given cause may, after the subduction of those
+other effects, be apparent as a residual phenomenon.
+
+These precautions are inapplicable to such cases as we are now
+considering. The mercury of our experiment being tried with an unknown
+multitude (or even let it be a known multitude) of other influencing
+circumstances, the mere fact of their being influencing circumstances
+implies that they disguise the effect of the mercury, and preclude us
+from knowing whether it has any effect or not. Unless we already knew
+what and how much is owing to every other circumstance, (that is, unless
+we suppose the very problem solved which we are considering the means of
+solving,) we cannot tell that those other circumstances may not have
+produced the whole of the effect, independently or even in spite of the
+mercury. The Method of Difference, in the ordinary mode of its use,
+namely by comparing the state of things following the experiment with
+the state which preceded it, is thus, in the case of intermixture of
+effects, entirely unavailing; because other causes than that whose
+effect we are seeking to determine, have been operating during the
+transition. As for the other mode of employing the Method of Difference,
+namely by comparing, not the same case at two different periods, but
+different cases, this in the present instance is quite chimerical. In
+phenomena so complicated it is questionable if two cases, similar in all
+respects but one, ever occurred; and were they to occur, we could not
+possibly know that they were so exactly similar.
+
+Anything like a scientific use of the method of experiment, in these
+complicated cases, is therefore out of the question. We can in the most
+favourable cases only discover, by a succession of trials, that a
+certain cause is _very often_ followed by a certain effect. For, in one
+of these conjunct effects, the portion which is determined by any one of
+the influencing agents, is generally, as we before remarked, but small;
+and it must be a more potent cause than most, if even the tendency which
+it really exerts is not thwarted by other tendencies in nearly as many
+cases as it is fulfilled.
+
+If so little can be done by the experimental method to determine the
+conditions of an effect of many combined causes, in the case of medical
+science; still less is this method applicable to a class of phenomena
+more complicated than even those of physiology, the phenomena of
+politics and history. There, Plurality of Causes exists in almost
+boundless excess, and effects are, for the most part, inextricably
+interwoven with one another. To add to the embarrassment, most of the
+inquiries in political science relate to the production of effects of a
+most comprehensive description, such as the public wealth, public
+security, public morality, and the like: results liable to be affected
+directly or indirectly either in _plus_ or in _minus_ by nearly every
+fact which exists, or event which occurs, in human society. The vulgar
+notion, that the safe methods on political subjects are those of
+Baconian induction--that the true guide is not general reasoning, but
+specific experience--will one day be quoted as among the most
+unequivocal marks of a low state of the speculative faculties in any
+age in which it is accredited. Nothing can be more ludicrous than the
+sort of parodies on experimental reasoning which one is accustomed to
+meet with, not in popular discussion only, but in grave treatises, when
+the affairs of nations are the theme. "How," it is asked, "can an
+institution be bad, when the country has prospered under it?" "How can
+such or such causes have contributed to the prosperity of one country,
+when another has prospered without them?" Whoever makes use of an
+argument of this kind, not intending to deceive, should be sent back to
+learn the elements of some one of the more easy physical sciences. Such
+reasoners ignore the fact of Plurality of Causes in the very case which
+affords the most signal example of it. So little could be concluded, in
+such a case, from any possible collation of individual instances, that
+even the impossibility, in social phenomena, of making artificial
+experiments, a circumstance otherwise so prejudicial to directly
+inductive inquiry, hardly affords, in this case, additional reason of
+regret. For even if we could try experiments upon a nation or upon the
+human race, with as little scruple as M. Magendie tried them on dogs and
+rabbits, we should never succeed in making two instances identical in
+every respect except the presence or absence of some one definite
+circumstance. The nearest approach to an experiment in the philosophical
+sense, which takes place in politics, is the introduction of a new
+operative element into national affairs by some special and assignable
+measure of government, such as the enactment or repeal of a particular
+law. But where there are so many influences at work, it requires some
+time for the influence of any new cause upon national phenomena to
+become apparent; and as the causes operating in so extensive a sphere
+are not only infinitely numerous, but in a state of perpetual
+alteration, it is always certain that before the effect of the new cause
+becomes conspicuous enough to be a subject of induction, so many of the
+other influencing circumstances will have changed as to vitiate the
+experiment.
+
+Two, therefore, of the three possible methods for the study of phenomena
+resulting from the composition of many causes, being, from the very
+nature of the case, inefficient and illusory, there remains only the
+third,--that which considers the causes separately, and infers the
+effect from the balance of the different tendencies which produce it: in
+short, the deductive, or _à priori_ method. The more particular
+consideration of this intellectual process requires a chapter to itself.
+
+
+
+
+CHAPTER XI.
+
+OF THE DEDUCTIVE METHOD.
+
+
+§ 1. The mode of investigation which, from the proved inapplicability of
+direct methods of observation and experiment, remains to us as the main
+source of the knowledge we possess or can acquire respecting the
+conditions, and laws of recurrence, of the more complex phenomena, is
+called, in its most general expression, the Deductive Method; and
+consists of three operations: the first, one of direct induction; the
+second, of ratiocination; the third, of verification.
+
+I call the first step in the process an inductive operation, because
+there must be a direct induction as the basis of the whole; though in
+many particular investigations the place of the induction may be
+supplied by a prior deduction; but the premises of this prior deduction
+must have been derived from induction.
+
+The problem of the Deductive Method is, to find the law of an effect,
+from the laws of the different tendencies of which it is the joint
+result. The first requisite, therefore, is to know the laws of those
+tendencies; the law of each of the concurrent causes: and this supposes
+a previous process of observation or experiment upon each cause
+separately; or else a previous deduction, which also must depend for its
+ultimate premises on observation or experiment. Thus, if the subject be
+social or historical phenomena, the premises of the Deductive Method
+must be the laws of the causes which determine that class of phenomena;
+and those causes are human actions, together with the general outward
+circumstances under the influence of which mankind are placed, and which
+constitute man's position on the earth. The Deductive Method, applied to
+social phenomena, must begin, therefore, by investigating, or must
+suppose to have been already investigated, the laws of human action,
+and those properties of outward things by which the actions of human
+beings in society are determined. Some of these general truths will
+naturally be obtained by observation and experiment, others by
+deduction: the more complex laws of human action, for example, may be
+deduced from the simpler ones; but the simple or elementary laws will
+always, and necessarily, have been obtained by a directly inductive
+process.
+
+To ascertain, then, the laws of each separate cause which takes a share
+in producing the effect, is the first desideratum of the Deductive
+Method. To know what the causes are, which must be subjected to this
+process of study, may or may not be difficult. In the case last
+mentioned, this first condition is of easy fulfilment. That social
+phenomena depend on the acts and mental impressions of human beings,
+never could have been a matter of any doubt, however imperfectly it may
+have been known either by what laws those impressions and actions are
+governed, or to what social consequences their laws naturally lead.
+Neither, again, after physical science had attained a certain
+development, could there be any real doubt where to look for the laws on
+which the phenomena of life depend, since they must be the mechanical
+and chemical laws of the solid and fluid substances composing the
+organized body and the medium in which it subsists, together with the
+peculiar vital laws of the different tissues constituting the organic
+structure. In other cases, really far more simple than these, it was
+much less obvious in what quarter the causes were to be looked for: as
+in the case of the celestial phenomena. Until, by combining the laws of
+certain causes, it was found that those laws explained all the facts
+which experience had proved concerning the heavenly motions, and led to
+predictions which it always verified, mankind never knew that those
+_were_ the causes. But whether we are able to put the question before,
+or not until after, we have become capable of answering it, in either
+case it must be answered; the laws of the different causes must be
+ascertained, before we can proceed to deduce from them the conditions of
+the effect.
+
+The mode of ascertaining those laws neither is, nor can be, any other
+than the fourfold method of experimental inquiry, already discussed. A
+few remarks on the application of that method to cases of the
+Composition of Causes, are all that is requisite.
+
+It is obvious that we cannot expect to find the law of a tendency, by an
+induction from cases in which the tendency is counteracted. The laws of
+motion could never have been brought to light from the observation of
+bodies kept at rest by the equilibrium of opposing forces. Even where
+the tendency is not, in the ordinary sense of the word, counteracted,
+but only modified, by having its effects compounded with the effects
+arising from some other tendency or tendencies, we are still in an
+unfavourable position for tracing, by means of such cases, the law of
+the tendency itself. It would have been scarcely possible to discover
+the law that every body in motion tends to continue moving in a straight
+line, by an induction from instances in which the motion is deflected
+into a curve, by being compounded with the effect of an accelerating
+force. Notwithstanding the resources afforded in this description of
+cases by the Method of Concomitant Variations, the principles of a
+judicious experimentation prescribe that the law of each of the
+tendencies should be studied, if possible, in cases in which that
+tendency operates alone, or in combination with no agencies but those of
+which the effect can, from previous knowledge, be calculated and allowed
+for.
+
+Accordingly, in the cases, unfortunately very numerous and important, in
+which the causes do not suffer themselves to be separated and observed
+apart, there is much difficulty in laying down with due certainty the
+inductive foundation necessary to support the deductive method. This
+difficulty is most of all conspicuous in the case of physiological
+phenomena; it being seldom possible to separate the different agencies
+which collectively compose an organized body, without destroying the
+very phenomena which it is our object to investigate:
+
+    --following life, in creatures we dissect,
+    We lose it, in the moment we detect.
+
+And for this reason I am inclined to the opinion, that physiology
+(greatly and rapidly progressive as it now is) is embarrassed by
+greater natural difficulties, and is probably susceptible of a less
+degree of ultimate perfection, than even the social science; inasmuch as
+it is possible to study the laws and operations of one human mind apart
+from other minds, much less imperfectly than we can study the laws of
+one organ or tissue of the human body apart from the other organs or
+tissues.
+
+It has been judiciously remarked that pathological facts, or, to speak
+in common language, diseases in their different forms and degrees,
+afford in the case of physiological investigation the most valuable
+equivalent to experimentation properly so called; inasmuch as they often
+exhibit to us a definite disturbance in some one organ or organic
+function, the remaining organs and functions being, in the first
+instance at least, unaffected. It is true that from the perpetual
+actions and reactions which are going on among all parts of the organic
+economy, there can be no prolonged disturbance in any one function
+without ultimately involving many of the others; and when once it has
+done so, the experiment for the most part loses its scientific value.
+All depends on observing the early stages of the derangement; which,
+unfortunately, are of necessity the least marked. If, however, the
+organs and functions not disturbed in the first instance, become
+affected in a fixed order of succession, some light is thereby thrown
+upon the action which one organ exercises over another: and we
+occasionally obtain a series of effects which we can refer with some
+confidence to the original local derangement; but for this it is
+necessary that we should know that the original derangement _was_ local.
+If it was what is termed constitutional, that is, if we do not know in
+what part of the animal economy it took its rise, or the precise nature
+of the disturbance which took place in that part, we are unable to
+determine which of the various derangements was cause and which effect;
+which of them were produced by one another, and which by the direct,
+though perhaps tardy, action of the original cause.
+
+Besides natural pathological facts, we can produce pathological facts
+artificially; we can try experiments, even in the popular sense of the
+term, by subjecting the living being to some external agent, such as the
+mercury of our former example, or the section of a nerve to ascertain
+the functions of different parts of the nervous system. As this
+experimentation is not intended to obtain a direct solution of any
+practical question, but to discover general laws, from which afterwards
+the conditions of any particular effect may be obtained by deduction;
+the best cases to select are those of which the circumstances can be
+best ascertained: and such are generally not those in which there is any
+practical object in view. The experiments are best tried, not in a state
+of disease, which is essentially a changeable state, but in the
+condition of health, comparatively a fixed state. In the one, unusual
+agencies are at work, the results of which we have no means of
+predicting; in the other, the course of the accustomed physiological
+phenomena would, it may generally be presumed, remain undisturbed, were
+it not for the disturbing cause which we introduce.
+
+Such, with the occasional aid of the Method of Concomitant Variations,
+(the latter not less incumbered than the more elementary methods by the
+peculiar difficulties of the subject,) are our inductive resources for
+ascertaining the laws of the causes considered separately, when we have
+it not in our power to make trial of them in a state of actual
+separation. The insufficiency of these resources is so glaring, that no
+one can be surprised at the backward state of the science of physiology;
+in which indeed our knowledge of causes is so imperfect, that we can
+neither explain, nor could without specific experience have predicted,
+many of the facts which are certified to us by the most ordinary
+observation. Fortunately, we are much better informed as to the
+empirical laws of the phenomena, that is, the uniformities respecting
+which we cannot yet decide whether they are cases of causation, or mere
+results of it. Not only has the order in which the facts of organization
+and life successively manifest themselves, from the first germ of
+existence to death, been found to be uniform, and very accurately
+ascertainable; but, by a great application of the Method of Concomitant
+Variations to the entire facts of comparative anatomy and physiology,
+the characteristic organic structure corresponding to each class of
+functions has been determined with considerable precision. Whether these
+organic conditions are the whole of the conditions, and in many cases
+whether they are conditions at all, or mere collateral effects of some
+common cause, we are quite ignorant: nor are we ever likely to know,
+unless we could construct an organized body, and try whether it would
+live.
+
+Under such disadvantages do we, in cases of this description, attempt
+the initial, or inductive step, in the application of the Deductive
+Method to complex phenomena. But such, fortunately, is not the common
+case. In general, the laws of the causes on which the effect depends may
+be obtained by an induction from comparatively simple instances, or, at
+the worst, by deduction from the laws of simpler causes, so obtained. By
+simple instances are meant, of course, those in which the action of each
+cause was not intermixed or interfered with, or not to any great extent,
+by other causes whose laws were unknown. And only when the induction
+which furnished the premises to the Deductive method rested on such
+instances, has the application of such a method to the ascertainment of
+the laws of a complex effect, been attended with brilliant results.
+
+
+§ 2. When the laws of the causes have been ascertained, and the first
+stage of the great logical operation now under discussion satisfactorily
+accomplished, the second part follows; that of determining from the laws
+of the causes, what effect any given combination of those causes will
+produce. This is a process of calculation, in the wider sense of the
+term; and very often involves processes of calculation in the narrowest
+sense. It is a ratiocination; and when our knowledge of the causes is so
+perfect, as to extend to the exact numerical laws which they observe in
+producing their effects, the ratiocination may reckon among its premises
+the theorems of the science of number, in the whole immense extent of
+that science. Not only are the most advanced truths of mathematics often
+required to enable us to compute an effect, the numerical law of which
+we already know; but, even by the aid of those most advanced truths, we
+can go but a little way. In so simple a case as the common problem of
+three bodies gravitating towards one another, with a force directly as
+their mass and inversely as the square of the distance, all the
+resources of the calculus have not hitherto sufficed to obtain any
+general solution but an approximate one. In a case a little more
+complex, but still one of the simplest which arise in practice, that of
+the motion of a projectile, the causes which affect the velocity and
+range (for example) of a cannon-ball may be all known and estimated; the
+force of the gunpowder, the angle of elevation, the density of the air,
+the strength and direction of the wind; but it is one of the most
+difficult of mathematical problems to combine all these, so as to
+determine the effect resulting from their collective action.
+
+Besides the theorems of number, those of geometry also come in as
+premises, where the effects take place in space, and involve motion and
+extension, as in mechanics, optics, acoustics, astronomy. But when the
+complication increases, and the effects are under the influence of so
+many and such shifting causes as to give no room either for fixed
+numbers, or for straight lines and regular curves, (as in the case of
+physiological, to say nothing of mental and social phenomena,) the laws
+of number and extension are applicable, if at all, only on that large
+scale on which precision of details becomes unimportant. Although these
+laws play a conspicuous part in the most striking examples of the
+investigation of nature by the Deductive Method, as for example in the
+Newtonian theory of the celestial motions, they are by no means an
+indispensable part of every such process. All that is essential in it is
+reasoning from a general law to a particular case, that is, determining
+by means of the particular circumstances of that case, what result is
+required in that instance to fulfil the law. Thus in the Torricellian
+experiment, if the fact that air has weight had been previously known,
+it would have been easy, without any numerical data, to deduce from the
+general law of equilibrium, that the mercury would stand in the tube at
+such a height that the column of mercury would exactly balance a column
+of the atmosphere of equal diameter; because, otherwise, equilibrium
+would not exist.
+
+By such ratiocinations from the separate laws of the causes, we may, to
+a certain extent, succeed in answering either of the following
+questions: Given a certain combination of causes, what effect will
+follow? and, What combination of causes, if it existed, would produce a
+given effect? In the one case, we determine the effect to be expected in
+any complex circumstances of which the different elements are known: in
+the other case we learn, according to what law--under what antecedent
+conditions--a given complex effect will occur.
+
+
+§ 3. But (it may here be asked) are not the same arguments by which the
+methods of direct observation and experiment were set aside as illusory
+when applied to the laws of complex phenomena, applicable with equal
+force against the Method of Deduction? When in every single instance a
+multitude, often an unknown multitude, of agencies, are clashing and
+combining, what security have we that in our computation _à priori_ we
+have taken all these into our reckoning? How many must we not generally
+be ignorant of? Among those which we know, how probable that some have
+been overlooked; and, even were all included, how vain the pretence of
+summing up the effects of many causes, unless we know accurately the
+numerical law of each,--a condition in most cases not to be fulfilled;
+and even when fulfilled, to make the calculation transcends, in any but
+very simple cases, the utmost power of mathematical science with all its
+most modern improvements.
+
+These objections have real weight, and would be altogether unanswerable,
+if there were no test by which, when we employ the Deductive Method, we
+might judge whether an error of any of the above descriptions had been
+committed or not. Such a test however there is: and its application
+forms, under the name of Verification, the third essential component
+part of the Deductive Method; without which all the results it can give
+have little other value than that of conjecture. To warrant reliance on
+the general conclusions arrived at by deduction, these conclusions must
+be found, on careful comparison, to accord with the results of direct
+observation wherever it can be had. If, when we have experience to
+compare with them, this experience confirms them, we may safely trust to
+them in other cases of which our specific experience is yet to come. But
+if our deductions have led to the conclusion that from a particular
+combination of causes a given effect would result, then in all known
+cases where that combination can be shown to have existed, and where the
+effect has not followed, we must be able to show (or at least to make a
+probable surmise) what frustrated it: if we cannot, the theory is
+imperfect, and not yet to be relied upon. Nor is the verification
+complete, unless some of the cases in which the theory is borne out by
+the observed result, are of at least equal complexity with any other
+cases in which its application could be called for.
+
+If direct observation and collation of instances have furnished us with
+any empirical laws of the effect (whether true in all observed cases, or
+only true for the most part), the most effectual verification of which
+the theory could be susceptible would be, that it led deductively to
+those empirical laws; that the uniformities, whether complete or
+incomplete, which were observed to exist among the phenomena, were
+accounted for by the laws of the causes--were such as could not but
+exist if those be really the causes by which the phenomena are produced.
+Thus it was very reasonably deemed an essential requisite of any true
+theory of the causes of the celestial motions, that it should lead by
+deduction to Kepler's laws: which, accordingly, the Newtonian theory
+did.
+
+In order, therefore, to facilitate the verification of theories obtained
+by deduction, it is important that as many as possible of the empirical
+laws of the phenomena should be ascertained, by a comparison of
+instances, conformably to the Method of Agreement: as well as (it must
+be added) that the phenomena themselves should be described, in the most
+comprehensive as well as accurate manner possible; by collecting from
+the observation of parts, the simplest possible correct expressions for
+the corresponding wholes: as when the series of the observed places of a
+planet was first expressed by a circle, then by a system of epicycles,
+and subsequently by an ellipse.
+
+It is worth remarking, that complex instances which would have been of
+no use for the discovery of the simple laws into which we ultimately
+analyse their phenomena, nevertheless, when they have served to verify
+the analysis, become additional evidence of the laws themselves.
+Although we could not have got at the law from complex cases, still when
+the law, got at otherwise, is found to be in accordance with the result
+of a complex case, that case becomes a new experiment on the law, and
+helps to confirm what it did not assist to discover. It is a new trial
+of the principle in a different set of circumstances; and occasionally
+serves to eliminate some circumstance not previously excluded, and the
+exclusion of which might require an experiment impossible to be
+executed. This was strikingly conspicuous in the example formerly
+quoted, in which the difference between the observed and the calculated
+velocity of sound was ascertained to result from the heat extricated by
+the condensation which takes place in each sonorous vibration. This was
+a trial, in new circumstances, of the law of the development of heat by
+compression; and it added materially to the proof of the universality of
+that law. Accordingly any law of nature is deemed to have gained in
+point of certainty, by being found to explain some complex case which
+had not previously been thought of in connexion with it; and this indeed
+is a consideration to which it is the habit of scientific inquirers to
+attach rather too much value than too little.
+
+To the Deductive Method, thus characterized in its three constituent
+parts, Induction, Ratiocination, and Verification, the human mind is
+indebted for its most conspicuous triumphs in the investigation of
+nature. To it we owe all the theories by which vast and complicated
+phenomena are embraced under a few simple laws, which, considered as the
+laws of those great phenomena, could never have been detected by their
+direct study. We may form some conception of what the method has done
+for us, from the case of the celestial motions; one of the simplest
+among the greater instances of the Composition of Causes, since (except
+in a few cases not of primary importance) each of the heavenly bodies
+may be considered, without material inaccuracy, to be never at one time
+influenced by the attraction of more than two bodies, the sun and one
+other planet or satellite; making, with the reaction of the body itself,
+and the force generated by the body's own motion and acting in the
+direction of the tangent, only four different agents on the concurrence
+of which the motions of that body depend; a much smaller number, no
+doubt, than that by which any other of the great phenomena of nature is
+determined or modified. Yet how could we ever have ascertained the
+combination of forces on which the motions of the earth and planets are
+dependent, by merely comparing the orbits or velocities of different
+planets, or the different velocities or positions of the same planet?
+Notwithstanding the regularity which manifests itself in those motions,
+in a degree so rare among the effects of a concurrence of causes; and
+although the periodical recurrence of exactly the same effect, affords
+positive proof that all the combinations of causes which occur at all,
+recur periodically; we should not have known what the causes were, if
+the existence of agencies precisely similar on our own earth had not,
+fortunately, brought the causes themselves within the reach of
+experimentation under simple circumstances. As we shall have occasion to
+analyse, further on, this great example of the Method of Deduction, we
+shall not occupy any time with it here, but shall proceed to that
+secondary application of the Deductive Method, the result of which is
+not to prove laws of phenomena, but to explain them.
+
+
+
+
+CHAPTER XII.
+
+OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+§ 1. The deductive operation by which we derive the law of an effect
+from the laws of the causes, the concurrence of which gives rise to it,
+may be undertaken either for the purpose of discovering the law, or of
+explaining a law already discovered. The word _explanation_ occurs so
+continually and holds so important a place in philosophy, that a little
+time spent in fixing the meaning of it will be profitably employed.
+
+An individual fact is said to be explained, by pointing out its cause,
+that is, by stating the law or laws of causation, of which its
+production is an instance. Thus, a conflagration is explained, when it
+is proved to have arisen from a spark falling into the midst of a heap
+of combustibles. And in a similar manner, a law or uniformity in nature
+is said to be explained, when another law or laws are pointed out, of
+which that law itself is but a case, and from which it could be deduced.
+
+
+§ 2. There are three distinguishable sets of circumstances in which a
+law of causation may be explained from, or, as it also is often
+expressed, resolved into, other laws.
+
+The first is the case already so fully considered; an intermixture of
+laws, producing a joint effect equal to the sum of the effects of the
+causes taken separately. The law of the complex effect is explained, by
+being resolved into the separate laws of the causes which contribute to
+it. Thus, the law of the motion of a planet is resolved into the law of
+the acquired force, which tends to produce an uniform motion in the
+tangent, and the law of the centripetal force which tends to produce an
+accelerating motion towards the sun; the real motion being a compound of
+the two.
+
+It is necessary here to remark, that in this resolution of the law of a
+complex effect, the laws of which it is compounded are not the only
+elements. It is resolved into the laws of the separate causes, together
+with the fact of their coexistence. The one is as essential an
+ingredient as the other; whether the object be to discover the law of
+the effect, or only to explain it. To deduce the laws of the heavenly
+motions, we require not only to know the law of a rectilineal and that
+of a gravitative force, but the existence of both these forces in the
+celestial regions, and even their relative amount. The complex laws of
+causation are thus resolved into two distinct kinds of elements: the
+one, simpler laws of causation, the other (in the aptly selected
+expression of Dr. Chalmers) collocations; the collocations consisting in
+the existence of certain agents or powers, in certain circumstances of
+place and time. We shall hereafter have occasion to return to this
+distinction, and to dwell on it at such length as dispenses with the
+necessity of further insisting on it here. The first mode, then, of the
+explanation of Laws of Causation, is when the law of an effect is
+resolved into the various tendencies of which it is the result, together
+with the laws of those tendencies.
+
+
+§ 3. A second case is when, between what seemed the cause and what was
+supposed to be its effect, further observation detects an intermediate
+link; a fact caused by the antecedent, and in its turn causing the
+consequent; so that the cause at first assigned is but the remote cause,
+operating through the intermediate phenomenon. A seemed the cause of C,
+but it subsequently appeared that A was only the cause of B, and that it
+is B which was the cause of C. For example: mankind were aware that the
+act of touching an outward object caused a sensation. It was
+subsequently discovered, that after we have touched the object, and
+before we experience the sensation, some change takes place in a kind of
+thread called a nerve, which extends from our outward organs to the
+brain. Touching the object, therefore, is only the remote cause of our
+sensation; that is, not the cause, properly speaking, but the cause of
+the cause;--the real cause of the sensation is the change in the state
+of the nerve. Future experience may not only give us more knowledge than
+we now have of the particular nature of this change, but may also
+interpolate another link: between the contact (for example) of the
+object with our outward organs, and the production of the change of
+state in the nerve, there may take place some electric phenomenon; or
+some phenomenon of a nature not resembling the effects of any known
+agency. Hitherto, however, no such intermediate link has been
+discovered; and the touch of the object must be considered,
+provisionally, as the proximate cause of the affection of the nerve. The
+sequence, therefore, of a sensation of touch on contact with an object,
+is ascertained not to be an ultimate law; it is resolved, as the phrase
+is, into two other laws,--the law, that contact with an object produces
+an affection of the nerve; and the law, that an affection of the nerve
+produces sensation.
+
+To take another example: the more powerful acids corrode or blacken
+organic compounds. This is a case of causation, but of remote causation;
+and is said to be explained when it is shown that there is an
+intermediate link, namely, the separation of some of the chemical
+elements of the organic structure from the rest, and their entering into
+combination with the acid. The acid causes this separation of the
+elements, and the separation of the elements causes the disorganization,
+and often the charring of the structure. So, again, chlorine extracts
+colouring matters, (whence its efficacy in bleaching,) and purifies the
+air from infection. This law is resolved into the two following laws.
+Chlorine has a powerful affinity for bases of all kinds, particularly
+metallic bases and hydrogen. Such bases are essential elements of
+colouring matters and contagious compounds: which substances, therefore,
+are decomposed and destroyed by chlorine.
+
+
+§ 4. It is of importance to remark, that when a sequence of phenomena is
+thus resolved into other laws, they are always laws more general than
+itself. The law that A is followed by C, is less general than either of
+the laws which connect B with C and A with B. This will appear from very
+simple considerations.
+
+All laws of causation are liable to be counteracted or frustrated, by
+the non-fulfilment of some negative condition: the tendency, therefore,
+of B to produce C may be defeated. Now the law that A produces B, is
+equally fulfilled whether B is followed by C or not; but the law that A
+produces C by means of B, is of course only fulfilled when B is really
+followed by C, and is therefore less general than the law that A
+produces B. It is also less general than the law that B produces C. For
+B may have other causes besides A; and as A produces C only by means of
+B, while B produces C whether it has itself been produced by A or by
+anything else, the second law embraces a greater number of instances,
+covers as it were a greater space of ground, than the first.
+
+Thus, in our former example, the law that the contact of an object
+causes a change in the state of the nerve, is more general than the law
+that contact with an object causes sensation, since, for aught we know,
+the change in the nerve may equally take place when, from a
+counteracting cause, as for instance, strong mental excitement, the
+sensation does not follow; as in a battle, where wounds are sometimes
+received without any consciousness of receiving them. And again, the law
+that change in the state of a nerve produces sensation, is more general
+than the law that contact with an object produces sensation; since the
+sensation equally follows the change in the nerve when not produced by
+contact with an object, but by some other cause; as in the well-known
+case, when a person who has lost a limb, feels the same sensation which
+he has been accustomed to call a pain in the limb.
+
+Not only are the laws of more immediate sequence into which the law of a
+remote sequence is resolved, laws of greater generality than that law
+is, but (as a consequence of, or rather as implied in, their greater
+generality) they are more to be relied on; there are fewer chances of
+their being ultimately found not to be universally true. From the moment
+when the sequence of A and C is shown not to be immediate, but to
+depend on an intervening phenomenon, then, however constant and
+invariable the sequence of A and C has hitherto been found,
+possibilities arise of its failure, exceeding those which can affect
+either of the more immediate sequences, A, B, and B, C. The tendency of
+A to produce C may be defeated by whatever is capable of defeating
+either the tendency of A to produce B, or the tendency of B to produce
+C; it is therefore twice as liable to failure as either of those more
+elementary tendencies; and the generalization that A is always followed
+by C, is twice as likely to be found erroneous. And so of the converse
+generalization, that C is always preceded and caused by A; which will be
+erroneous not only if there should happen to be a second immediate mode
+of production of C itself, but moreover if there be a second mode of
+production of B, the immediate antecedent of C in the sequence.
+
+The resolution of the one generalization into the other two, not only
+shows that there are possible limitations of the former, from which its
+two elements are exempt, but shows also where these are to be looked
+for. As soon as we know that B intervenes between A and C, we also know
+that if there be cases in which the sequence of A and C does not hold,
+these are most likely to be found by studying the effects or the
+conditions of the phenomenon B.
+
+It appears, then, that in the second of the three modes in which a law
+may be resolved into other laws, the latter are more general, that is,
+extend to more cases, and are also less likely to require limitation
+from subsequent experience, than the law which they serve to explain.
+They are more nearly unconditional; they are defeated by fewer
+contingencies; they are a nearer approach to the universal truth of
+nature. The same observations are still more evidently true with regard
+to the first of the three modes of resolution. When the law of an effect
+of combined causes is resolved into the separate laws of the causes, the
+nature of the case implies that the law of the effect is less general
+than the law of any of the causes, since it only holds when they are
+combined; while the law of any one of the causes holds good both then,
+and also when that cause acts apart from the rest. It is also manifest
+that the complex law is liable to be oftener unfulfilled than any one
+of the simpler laws of which it is the result, since every contingency
+which defeats any of the laws prevents so much of the effect as depends
+on it, and thereby defeats the complex law. The mere rusting, for
+example, of some small part of a great machine, often suffices entirely
+to prevent the effect which ought to result from the joint action of all
+the parts. The law of the effect of a combination of causes is always
+subject to the whole of the negative conditions which attach to the
+action of all the causes severally.
+
+There is another and an equally strong reason why the law of a complex
+effect must be less general than the laws of the causes which conspire
+to produce it. The same causes, acting according to the same laws, and
+differing only in the proportions in which they are combined, often
+produce effects which differ not merely in quantity, but in kind. The
+combination of a centripetal with a projectile force, in the proportions
+which obtain in all the planets and satellites of our solar system,
+gives rise to an elliptical motion; but if the ratio of the two forces
+to each other were slightly altered, it is demonstrated that the motion
+produced would be in a circle, or a parabola, or an hyperbola: and it is
+thought that in the case of some comets one of these is probably the
+fact. Yet the law of the parabolic motion would be resolvable into the
+very same simple laws into which that of the elliptical motion is
+resolved, namely, the law of the permanence of rectilineal motion, and
+the law of gravitation. If, therefore, in the course of ages, some
+circumstance were to manifest itself which, without defeating the law of
+either of those forces, should merely alter their proportion to one
+another, (such as the shock of some solid body, or even the accumulating
+effect of the resistance of the medium in which astronomers have been
+led to surmise that the motions of the heavenly bodies take place,) the
+elliptical motion might be changed into a motion in some other conic
+section; and the complex law, that the planetary motions take place in
+ellipses, would be deprived of its universality, though the discovery
+would not at all detract from the universality of the simpler laws into
+which that complex law is resolved. The law, in short, of each of the
+concurrent causes remains the same, however their collocations may vary;
+but the law of their joint effect varies with every difference in the
+collocations. There needs no more to show how much more general the
+elementary laws must be, than any of the complex laws which are derived
+from them.
+
+
+§ 5. Besides the two modes which have been treated of, there is a third
+mode in which laws are resolved into one another; and in this it is
+self-evident that they are resolved into laws more general than
+themselves. This third mode is the _subsumption_ (as it has been called)
+of one law under another: or (what comes to the same thing) the
+gathering up of several laws into one more general law which includes
+them all. The most splendid example of this operation was when
+terrestrial gravity and the central force of the solar system were
+brought together under the general law of gravitation. It had been
+proved antecedently that the earth and the other planets tend to the
+sun; and it had been known from the earliest times that terrestrial
+bodies tend towards the earth. These were similar phenomena; and to
+enable them both to be subsumed under one law, it was only necessary to
+prove that, as the effects were similar in quality, so also they, as to
+quantity, conform to the same rules. This was first shown to be true of
+the moon, which agreed with terrestrial objects not only in tending to a
+centre, but in the fact that this centre was the earth. The tendency of
+the moon towards the earth being ascertained to vary as the inverse
+square of the distance, it was deduced from this, by direct calculation,
+that if the moon were as near to the earth as terrestrial objects are,
+and the acquired force in the direction of the tangent were suspended,
+the moon would fall towards the earth through exactly as many feet in a
+second as those objects do by virtue of their weight. Hence the
+inference was irresistible, that the moon also tends to the earth by
+virtue of its weight: and that the two phenomena, the tendency of the
+moon to the earth and the tendency of terrestrial objects to the earth,
+being not only similar in quality, but, when in the same circumstances,
+identical in quantity, are cases of one and the same law of causation.
+But the tendency of the moon to the earth, and the tendency of the earth
+and planets to the sun, were already known to be cases of the same law
+of causation: and thus the law of all these tendencies, and the law of
+terrestrial gravity, were recognised as identical, and were subsumed
+under one general law, that of gravitation.
+
+In a similar manner, the laws of magnetic phenomena have more recently
+been subsumed under known laws of electricity. It is thus that the most
+general laws of nature are usually arrived at: we mount to them by
+successive steps. For, to arrive by correct induction at laws which hold
+under such an immense variety of circumstances, laws so general as to be
+independent of any varieties of space or time which we are able to
+observe, requires for the most part many distinct sets of experiments or
+observations, conducted at different times and by different people. One
+part of the law is first ascertained, afterwards another part: one set
+of observations teaches us that the law holds good under some
+conditions, another that it holds good under other conditions, by
+combining which observations we find that it holds good under conditions
+much more general, or even universally. The general law, in this case,
+is literally the sum of all the partial ones; it is the recognition of
+the same sequence in different sets of instances; and may, in fact, be
+regarded as merely one step in the process of elimination. That tendency
+of bodies towards one another, which we now call gravity, had at first
+been observed only on the earth's surface, where it manifested itself
+only as a tendency of all bodies towards the earth, and might,
+therefore, be ascribed to a peculiar property of the earth itself: one
+of the circumstances, namely, the proximity of the earth, had not been
+eliminated. To eliminate this circumstance required a fresh set of
+instances in other parts of the universe: these we could not ourselves
+create; and though nature had created them for us, we were placed in
+very unfavourable circumstances for observing them. To make these
+observations, fell naturally to the lot of a different set of persons
+from those who studied terrestrial phenomena; and had, indeed, been a
+matter of great interest at a time when the idea of explaining celestial
+facts by terrestrial laws was looked upon as the confounding of an
+indefeasible distinction. When, however, the celestial motions were
+accurately ascertained, and the deductive processes performed, from
+which it appeared that their laws and those of terrestrial gravity
+corresponded, those celestial observations became a set of instances
+which exactly eliminated the circumstance of proximity to the earth; and
+proved that in the original case, that of terrestrial objects, it was
+not the earth, as such, that caused the motion or the pressure, but the
+circumstance common to that case with the celestial instances, namely,
+the presence of some great body within certain limits of distance.
+
+
+§ 6. There are, then, three modes of explaining laws of causation, or,
+which is the same thing, resolving them into other laws. First, when the
+law of an effect of combined causes is resolved into the separate laws
+of the causes, together with the fact of their combination. Secondly,
+when the law which connects any two links, not proximate, in a chain of
+causation, is resolved into the laws which connect each with the
+intermediate links. Both of these are cases of resolving one law into
+two or more; in the third, two or more are resolved into one: when,
+after the law has been shown to hold good in several different classes
+of cases, we decide that what is true in each of these classes of cases,
+is true under some more general supposition, consisting of what all
+those classes of cases have in common. We may here remark that this last
+operation involves none of the uncertainties attendant on induction by
+the Method of Agreement, since we need not suppose the result to be
+extended by way of inference to any new class of cases, different from
+those by the comparison of which it was engendered.
+
+In all these three processes, laws are, as we have seen, resolved into
+laws more general than themselves; laws extending to all the cases which
+the former extended to, and others besides. In the first two modes they
+are also resolved into laws more certain, in other words, more
+universally true than themselves; they are, in fact, proved not to be
+themselves laws of nature, the character of which is to be universally
+true, but _results_ of laws of nature, which may be only true
+conditionally, and for the most part. No difference of this sort exists
+in the third case; since here the partial laws are, in fact, the very
+same law as the general one, and any exception to them would be an
+exception to it too.
+
+By all the three processes, the range of deductive science is extended;
+since the laws, thus resolved, may be thenceforth deduced
+demonstratively from the laws into which they are resolved. As already
+remarked, the same deductive process which proves a law or fact of
+causation if unknown, serves to explain it when known.
+
+The word explanation is here used in its philosophical sense. What is
+called explaining one law of nature by another, is but substituting one
+mystery for another; and does nothing to render the general course of
+nature other than mysterious: we can no more assign a _why_ for the more
+extensive laws than for the partial ones. The explanation may substitute
+a mystery which has become familiar, and has grown to _seem_ not
+mysterious, for one which is still strange. And this is the meaning of
+explanation, in common parlance. But the process with which we are here
+concerned often does the very contrary: it resolves a phenomenon with
+which we are familiar, into one of which we previously knew little or
+nothing; as when the common fact of the fall of heavy bodies was
+resolved into the tendency of all particles of matter towards one
+another. It must be kept constantly in view, therefore, that in science,
+those who speak of explaining any phenomenon mean (or should mean)
+pointing out not some more familiar, but merely some more general,
+phenomenon, of which it is a partial exemplification; or some laws of
+causation which produce it by their joint or successive action, and from
+which, therefore, its conditions may be determined deductively. Every
+such operation brings us a step nearer towards answering the question
+which was stated in a previous chapter as comprehending the whole
+problem of the investigation of nature, viz. What are the fewest
+assumptions, which being granted, the order of nature as it exists
+would be the result? What are the fewest general propositions from which
+all the uniformities existing in nature could be deduced?
+
+The laws, thus explained or resolved, are sometimes said to be
+_accounted for_; but the expression is incorrect, if taken to mean
+anything more than what has been already stated. In minds not habituated
+to accurate thinking, there is often a confused notion that the general
+laws are the _causes_ of the partial ones; that the law of general
+gravitation, for example, causes the phenomenon of the fall of bodies to
+the earth. But to assert this, would be a misuse of the word cause:
+terrestrial gravity is not an effect of general gravitation, but a
+_case_ of it; that is, one kind of the particular instances in which
+that general law obtains. To account for a law of nature means, and can
+mean, nothing more than to assign other laws more general, together with
+collocations, which laws and collocations being supposed, the partial
+law follows without any additional supposition.
+
+
+
+
+CHAPTER XIII.
+
+MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+§ 1. The most striking example which the history of science presents, of
+the explanation of laws of causation and other uniformities of sequence
+among special phenomena, by resolving them into laws of greater
+simplicity and generality, is the great Newtonian generalization:
+respecting which typical instance so much having already been said, it
+is sufficient to call attention to the great number and variety of the
+special observed uniformities which are in this case accounted for,
+either as particular cases or as consequences of one very simple law of
+universal nature. The simple fact of a tendency of every particle of
+matter towards every other particle, varying inversely as the square of
+the distance, explains the fall of bodies to the earth, the revolutions
+of the planets and satellites, the motions (so far as known) of comets,
+and all the various regularities which have been observed in these
+special phenomena; such as the elliptical orbits, and the variations
+from exact ellipses; the relation between the solar distances of the
+planets and the duration of their revolutions; the precession of the
+equinoxes; the tides, and a vast number of minor astronomical truths.
+
+Mention has also been made in the preceding chapter of the explanation
+of the phenomena of magnetism from laws of electricity; the special laws
+of magnetic agency having been affiliated by deduction to observed laws
+of electric action, in which they have ever since been considered to be
+included as special cases. An example not so complete in itself, but
+even more fertile in consequences, having been the starting point of the
+really scientific study of physiology, is the affiliation, commenced by
+Bichat, and carried on by subsequent biologists, of the properties of
+the bodily organs, to the elementary properties of the tissues into
+which they are anatomically decomposed.
+
+Another striking instance is afforded by Dalton's generalization,
+commonly known as the atomic theory. It had been known from the very
+commencement of accurate chemical observation, that any two bodies
+combine chemically with one another in only a certain number of
+proportions; but those proportions were in each case expressed by a
+percentage--so many parts (by weight) of each ingredient, in 100 of the
+compound; (say 35 and a fraction of one element, 64 and a fraction of
+the other): in which mode of statement no relation was perceived between
+the proportion in which a given element combines with one substance, and
+that in which it combines with others. The great step made by Dalton
+consisted in perceiving, that a unit of weight might be established for
+each substance, such that by supposing the substance to enter into all
+its combinations in the ratio either of that unit, or of some low
+multiple of that unit, all the different proportions, previously
+expressed by percentages, were found to result. Thus 1 being assumed as
+the unit of hydrogen, if 8 were then taken as that of oxygen, the
+combination of one unit of hydrogen with one unit of oxygen would
+produce the exact proportion of weight between the two substances which
+is known to exist in water; the combination of one unit of hydrogen with
+two units of oxygen would produce the proportion which exists in the
+other compound of the same two elements, called peroxide of hydrogen;
+and the combinations of hydrogen and of oxygen with all other
+substances, would correspond with the supposition that those elements
+enter into combination by single units, or twos, or threes, of the
+numbers assigned to them, 1 and 8, and the other substances by ones or
+twos or threes of other determinate numbers proper to each. The result
+is that a table of the equivalent numbers, or, as they are called,
+atomic weights, of all the elementary substances, comprises in itself,
+and scientifically explains, all the proportions in which any substance,
+elementary or compound, is found capable of entering into chemical
+combination with any other substance whatever.
+
+
+§ 2. Some interesting cases of the explanation of old uniformities by
+newly ascertained laws are afforded by the researches of Professor
+Graham. That eminent chemist was the first who drew attention to the
+distinction which may be made of all substances into two classes, termed
+by him crystalloids and colloids; or rather, of all states of matter
+into the crystalloid and the colloidal states, for many substances are
+capable of existing in either. When in the colloidal state, their
+sensible properties are very different from those of the same substance
+when crystallized, or when in a state easily susceptible of
+crystallization. Colloid substances pass with extreme difficulty and
+slowness into the crystalline state, and are extremely inert in all the
+ordinary chemical relations. Substances in the colloid state are almost
+always, when combined with water, more or less viscous or gelatinous.
+The most prominent examples of the state are certain animal and
+vegetable substances, particularly gelatine, albumen, starch, the gums,
+caramel, tannin, and some others. Among substances not of organic
+origin, the most notable instances are hydrated silicic acid, and
+hydrated alumina, with other metallic peroxides of the aluminous class.
+
+Now it is found, that while colloidal substances are easily penetrated
+by water, and by the solutions of crystalloid substances, they are very
+little penetrable by one another: which enabled Professor Graham to
+introduce a highly effective process (termed dialysis) for separating
+the crystalloid substances contained in any liquid mixture, by passing
+them through a thin septum of colloidal matter, which does not suffer
+anything colloidal to pass, or suffers it only in very minute quantity.
+This property of colloids enabled Mr. Graham to account for a number of
+special results of observation, not previously explained.
+
+For instance, "while soluble crystalloids are always highly sapid,
+soluble colloids are singularly insipid," as might be expected; for, as
+the sentient extremities of the nerves of the palate "are probably
+protected by a colloidal membrane," impermeable to other colloids, a
+colloid, when tasted, probably never reaches those nerves. Again, "it
+has been observed that vegetable gum is not digested in the stomach; the
+coats of that organ dialyse the soluble food, absorbing crystalloids,
+and rejecting all colloids." One of the mysterious processes
+accompanying digestion, the secretion of free muriatic acid by the coats
+of the stomach, obtains a probable hypothetical explanation through the
+same law. Finally, much light is thrown upon the observed phenomena of
+osmose (the passage of fluids outward and inward through animal
+membranes) by the fact that the membranes are colloidal. In consequence,
+the water and saline solutions contained in the animal body pass easily
+and rapidly through the membranes, while the substances directly
+applicable to nutrition, which are mostly colloidal, are detained by
+them.[47]
+
+The property which salt possesses of preserving animal substances from
+putrefaction is resolved by Liebig into two more general laws, the
+strong attraction of salt for water, and the necessity of the presence
+of water as a condition of putrefaction. The intermediate phenomenon
+which is interpolated between the remote cause and the effect, can here
+be not merely inferred but seen; for it is a familiar fact, that flesh
+upon which salt has been thrown is speedily found swimming in brine.
+
+The second of the two factors (as they may be termed) into which the
+preceding law has been resolved, the necessity of water to putrefaction,
+itself affords an additional example of the Resolution of Laws. The law
+itself is proved by the Method of Difference, since flesh completely
+dried and kept in a dry atmosphere does not putrefy; as we see in the
+case of dried provisions, and human bodies in very dry climates. A
+deductive explanation of this same law results from Liebig's
+speculations. The putrefaction of animal and other azotised bodies is a
+chemical process, by which they are gradually dissipated in a gaseous
+form, chiefly in that of carbonic acid and ammonia; now to convert the
+carbon of the animal substance into carbonic acid requires oxygen, and
+to convert the azote into ammonia requires hydrogen, which are the
+elements of water. The extreme rapidity of the putrefaction of azotised
+substances, compared with the gradual decay of non-azotised bodies (such
+as wood and the like) by the action of oxygen alone, he explains from
+the general law that substances are much more easily decomposed by the
+action of two different affinities upon two of their elements, than by
+the action of only one.
+
+
+§ 3. Among the many important properties of the nervous system, which
+have either been first discovered or strikingly illustrated by Dr.
+Brown-Séquard, I select the reflex influence of the nervous system on
+nutrition and secretion. By reflex nervous action is meant, action which
+one part of the nervous system exerts over another part, without any
+intermediate action on the brain, and consequently without
+consciousness; or which, if it does pass through the brain, at least
+produces its effects independently of the will. There are many
+experiments which prove that irritation of a nerve in one part of the
+body may in this manner excite powerful action in another part; for
+example, food injected into the stomach through a divided œsophagus,
+nevertheless produces secretion of saliva; warm water injected into the
+bowels, and various other irritations of the lower intestines, have been
+found to excite secretion of the gastric juice, and so forth. The
+reality of the power being thus proved, its agency explains a great
+variety of apparently anomalous phenomena; of which I select the
+following from Dr. Brown-Séquard's _Lectures on the Nervous System_.
+
+The production of tears by irritation of the eye, or of the mucous
+membrane of the nose:
+
+The secretions of the eye and nose increased by exposure of other parts
+of the body to cold:
+
+Inflammation of the eye, especially when of traumatic origin, very
+frequently excites a similar affection in the other eye, which may be
+cured by section of the intervening nerve:
+
+Loss of sight sometimes produced by neuralgia; and has been known to be
+at once cured by the extirpation (for instance) of a carious tooth:
+
+Even cataract has been produced in a healthy eye by cataract in the
+other eye, or by neuralgia, or by a wound of the frontal nerve:
+
+The well-known phenomenon of a sudden stoppage of the heart's action,
+and consequent death, produced by irritation of some of the nervous
+extremities: _e.g._, by drinking very cold water; or by a blow on the
+abdomen, or other sudden excitation of the abdominal sympathetic nerve;
+though this nerve may be irritated to any extent without stopping the
+heart's action, if a section be made of the communicating nerves:
+
+The extraordinary effects produced on the internal organs by an
+extensive burn on the surface of the body; consisting in violent
+inflammation of the tissues of the abdomen, chest, or head: which, when
+death ensues from this kind of injury, is one of the most frequent
+causes of it:
+
+Paralysis and anæsthesia of one part of the body from neuralgia in
+another part; and muscular atrophy from neuralgia, even when there is no
+paralysis:
+
+Tetanus produced by the lesion of a nerve; Dr. Brown-Séquard thinks it
+highly probable that hydrophobia is a phenomenon of a similar nature:
+
+Morbid changes in the nutrition of the brain and spinal cord,
+manifesting themselves by epilepsy, chorea, hysteria, and other
+diseases, occasioned by lesion of some of the nervous extremities in
+remote places, as by worms, calculi, tumours, carious bones, and in some
+cases even by very slight irritations of the skin.
+
+
+§ 4. From the foregoing and similar instances, we may see the
+importance, when a law of nature previously unknown has been brought to
+light, or when new light has been thrown upon a known law by experiment,
+of examining all cases which present the conditions necessary for
+bringing that law into action; a process fertile in demonstrations of
+special laws previously unsuspected, and explanations of others already
+empirically known.
+
+For instance, Faraday discovered by experiment, that voltaic electricity
+could be evolved from a natural magnet, provided a conducting body were
+set in motion at right angles to the direction of the magnet: and this
+he found to hold not only of small magnets, but of that great magnet,
+the earth. The law being thus established experimentally, that
+electricity is evolved, by a magnet, and a conductor moving at right
+angles to the direction of its poles, we may now look out for fresh
+instances in which these conditions meet. Wherever a conductor moves or
+revolves at right angles to the direction of the earth's magnetic poles,
+there we may expect an evolution of electricity. In the northern
+regions, where the polar direction is nearly perpendicular to the
+horizon, all horizontal motions of conductors will produce electricity;
+horizontal wheels, for example, made of metal; likewise all running
+streams will evolve a current of electricity, which will circulate round
+them; and the air thus charged with electricity may be one of the causes
+of the Aurora Borealis. In the equatorial regions, on the contrary,
+upright wheels placed parallel to the equator will originate a voltaic
+circuit, and waterfalls will naturally become electric.
+
+For a second example; it has been proved, chiefly by the researches of
+Professor Graham, that gases have a strong tendency to permeate animal
+membranes, and diffuse themselves through the spaces which such
+membranes inclose, notwithstanding the presence of other gases in those
+spaces. Proceeding from this general law, and reviewing a variety of
+cases in which gases lie contiguous to membranes, we are enabled to
+demonstrate or to explain the following more special laws: 1st. The
+human or animal body, when surrounded with any gas not already contained
+within the body, absorbs it rapidly; such, for instance, as the gases of
+putrefying matters: which helps to explain malaria. 2nd. The carbonic
+acid gas of effervescing drinks, evolved in the stomach, permeates its
+membranes, and rapidly spreads through the system. 3rd. Alcohol taken
+into the stomach passes into vapour and spreads through the system with
+great rapidity; (which, combined with the high combustibility of
+alcohol, or in other words its ready combination with oxygen, may
+perhaps help to explain the bodily warmth immediately consequent on
+drinking spirituous liquors.) 4th. In any state of the body in which
+peculiar gases are formed within it, these will rapidly exhale through
+all parts of the body; and hence the rapidity with which, in certain
+states of disease, the surrounding atmosphere becomes tainted. 5th. The
+putrefaction of the interior parts of a carcase will proceed as rapidly
+as that of the exterior, from the ready passage outwards of the gaseous
+products. 6th. The exchange of oxygen and carbonic acid in the lungs is
+not prevented, but rather promoted, by the intervention of the membrane
+of the lungs and the coats of the blood-vessels between the blood and
+the air. It is necessary, however, that there should be a substance in
+the blood with which the oxygen of the air may immediately combine;
+otherwise instead of passing into the blood, it would permeate the whole
+organism: and it is necessary that the carbonic acid, as it is formed in
+the capillaries, should also find a substance in the blood with which it
+can combine; otherwise it would leave the body at all points, instead of
+being discharged through the lungs.
+
+
+§ 5. The following is a deduction which confirms, by explaining, the old
+but not undisputed empirical generalization, that soda powders weaken
+the human system. These powders, consisting of a mixture of tartaric
+acid with bicarbonate of soda, from which the carbonic acid is set free,
+must pass into the stomach as tartrate of soda. Now, neutral tartrates,
+citrates, and acetates of the alkalis are found, in their passage
+through the system, to be changed into carbonates; and to convert a
+tartrate into a carbonate requires an additional quantity of oxygen, the
+abstraction of which must lessen the oxygen destined for assimilation
+with the blood, on the quantity of which the vigorous action of the
+human system partly depends.
+
+The instances of new theories agreeing with and explaining old
+empiricisms, are innumerable. All the just remarks made by experienced
+persons on human character and conduct, are so many special laws, which
+the general laws of the human mind explain and resolve. The empirical
+generalizations on which the operations of the arts have usually been
+founded, are continually justified and confirmed on the one hand, or
+corrected and improved on the other, by the discovery of the simpler
+scientific laws on which the efficacy of those operations depends. The
+effects of the rotation of crops, of the various manures, and other
+processes of improved agriculture, have been for the first time resolved
+in our own day into known laws of chemical and organic action, by Davy,
+Liebig, and others. The processes of the medical art are even now mostly
+empirical: their efficacy is concluded, in each instance, from a special
+and most precarious experimental generalization: but as science advances
+in discovering the simple laws of chemistry and physiology, progress is
+made in ascertaining the intermediate links in the series of phenomena,
+and the more general laws on which they depend; and thus, while the old
+processes are either exploded, or their efficacy, in so far as real,
+explained, better processes, founded on the knowledge of proximate
+causes, are continually suggested and brought into use.[48] Many even of
+the truths of geometry were generalizations from experience before they
+were deduced from first principles. The quadrature of the cycloid is
+said to have been first effected by measurement, or rather by weighing a
+cycloidal card, and comparing its weight with that of a piece of similar
+card of known dimensions.
+
+
+§ 6. To the foregoing examples from physical science, let us add another
+from mental. The following is one of the simple laws of mind: Ideas of a
+pleasurable or painful character form associations more easily and
+strongly than other ideas, that is, they become associated after fewer
+repetitions, and the association is more durable. This is an
+experimental law, grounded on the Method of Difference. By deduction
+from this law, many of the more special laws which experience shows to
+exist among particular mental phenomena may be demonstrated and
+explained:--the ease and rapidity, for instance, with which thoughts
+connected with our passions or our more cherished interests are excited,
+and the firm hold which the facts relating to them have on our memory;
+the vivid recollection we retain of minute circumstances which
+accompanied any object or event that deeply interested us, and of the
+times and places in which we have been very happy or very miserable; the
+horror with which we view the accidental instrument of any occurrence
+which shocked us, or the locality where it took place, and the pleasure
+we derive from any memorial of past enjoyment; all these effects being
+proportional to the sensibility of the individual mind, and to the
+consequent intensity of the pain or pleasure from which the association
+originated. It has been suggested by the able writer of a biographical
+sketch of Dr. Priestley in a monthly periodical,[49] that the same
+elementary law of our mental constitution, suitably followed out, would
+explain a variety of mental phenomena previously inexplicable, and in
+particular some of the fundamental diversities of human character and
+genius. Associations being of two sorts, either between synchronous, or
+between successive impressions; and the influence of the law which
+renders associations stronger in proportion to the pleasurable or
+painful character of the impressions, being felt with peculiar force in
+the synchronous class of associations; it is remarked by the writer
+referred to, that in minds of strong organic sensibility synchronous
+associations will be likely to predominate, producing a tendency to
+conceive things in pictures and in the concrete, richly clothed in
+attributes and circumstances, a mental habit which is commonly called
+Imagination, and is one of the peculiarities of the painter and the
+poet; while persons of more moderate susceptibility to pleasure and pain
+will have a tendency to associate facts chiefly in the order of their
+succession, and such persons, if they possess mental superiority, will
+addict themselves to history or science rather than to creative art.
+This interesting speculation the author of the present work has
+endeavoured, on another occasion, to pursue farther, and to examine how
+far it will avail towards explaining the peculiarities of the poetical
+temperament.[50] It is at least an example which may serve, instead of
+many others, to show the extensive scope which exists for deductive
+investigation in the important and hitherto so imperfect Science of
+Mind.
+
+
+§ 7. The copiousness with which the discovery and explanation of special
+laws of phenomena by deduction from simpler and more general ones has
+here been exemplified, was prompted by a desire to characterize clearly,
+and place in its due position of importance, the Deductive Method;
+which, in the present state of knowledge, is destined henceforth
+irrevocably to predominate in the course of scientific investigation. A
+revolution is peaceably and progressively effecting itself in
+philosophy, the reverse of that to which Bacon has attached his name.
+That great man changed the method of the sciences from deductive to
+experimental, and it is now rapidly reverting from experimental to
+deductive. But the deductions which Bacon abolished were from premises
+hastily snatched up, or arbitrarily assumed. The principles were neither
+established by legitimate canons of experimental inquiry, nor the
+results tested by that indispensable element of a rational Deductive
+Method, verification by specific experience. Between the primitive
+method of Deduction and that which I have attempted to characterize,
+there is all the difference which exists between the Aristotelian
+physics and the Newtonian theory of the heavens.
+
+It would, however, be a mistake to expect that those great
+generalizations, from which the subordinate truths of the more backward
+sciences will probably at some future period be deduced by reasoning (as
+the truths of astronomy are deduced from the generalities of the
+Newtonian theory), will be found, in all, or even in most cases, among
+truths now known and admitted. We may rest assured, that many of the
+most general laws of nature are as yet entirely unthought of; and that
+many others, destined hereafter to assume the same character, are known,
+if at all, only as laws or properties of some limited class of
+phenomena; just as electricity, now recognised as one of the most
+universal of natural agencies, was once known only as a curious property
+which certain substances acquired by friction, of first attracting and
+then repelling light bodies. If the theories of heat, cohesion,
+crystallization, and chemical action, are destined, as there can be
+little doubt that they are, to become deductive, the truths which will
+then be regarded as the _principia_ of those sciences would probably, if
+now announced, appear quite as novel[51] as the law of gravitation
+appeared to the cotemporaries of Newton; possibly even more so, since
+Newton's law, after all, was but an extension of the law of weight--that
+is, of a generalization familiar from of old, and which already
+comprehended a not inconsiderable body of natural phenomena. The general
+laws of a similarly commanding character, which we still look forward to
+the discovery of, may not always find so much of their foundations
+already laid.
+
+These general truths will doubtless make their first appearance in the
+character of hypotheses; not proved, nor even admitting of proof, in
+the first instance, but assumed as premises for the purpose of deducing
+from them the known laws of concrete phenomena. But this, though their
+initial, cannot be their final state. To entitle an hypothesis to be
+received as one of the truths of nature, and not as a mere technical
+help to the human faculties, it must be capable of being tested by the
+canons of legitimate induction, and must actually have been submitted to
+that test. When this shall have been done, and done successfully,
+premises will have been obtained from which all the other propositions
+of the science will thenceforth be presented as conclusions, and the
+science will, by means of a new and unexpected Induction, be rendered
+Deductive.
+
+FOOTNOTES:
+
+[1] Dr. Whewell thinks it improper to apply the term Induction to any
+operation not terminating in the establishment of a general truth.
+Induction, he says (_Philosophy of Discovery_, p. 245), "is not the same
+thing as experience and observation. Induction is experience or
+observation _consciously_ looked at in a _general_ form. This
+consciousness and generality are necessary parts of that knowledge which
+is science." And he objects (p. 241) to the mode in which the word
+Induction is employed in this work, as an undue extension of that term
+"not only to the cases in which the general induction is consciously
+applied to a particular instance, but to the cases in which the
+particular instance is dealt with by means of experience in that rude
+sense in which experience can be asserted of brutes, and in which of
+course we can in no way imagine that the law is possessed or understood
+as a general proposition." This use of the term he deems a "confusion of
+knowledge with practical tendencies."
+
+I disclaim, as strongly as Dr. Whewell can do, the application of such
+terms as induction, inference, or reasoning, to operations performed by
+mere instinct, that is, from an animal impulse, without the exertion of
+any intelligence. But I perceive no ground for confining the use of
+those terms to cases in which the inference is drawn in the forms and
+with the precautions required by scientific propriety. To the idea of
+Science, an express recognition and distinct apprehension of general
+laws as such, is essential: but nine-tenths of the conclusions drawn
+from experience in the course of practical life, are drawn without any
+such recognition: they are direct inferences from known cases, to a case
+supposed to be similar. I have endeavoured to show that this is not only
+as legitimate an operation, but substantially the same operation, as
+that of ascending from known cases to a general proposition; except that
+the latter process has one great security for correctness which the
+former does not possess. In Science, the inference must necessarily pass
+through the intermediate stage of a general proposition, because Science
+wants its conclusions for record, and not for instantaneous use. But the
+inferences drawn for the guidance of practical affairs, by persons who
+would often be quite incapable of expressing in unexceptionable terms
+the corresponding generalizations, may and frequently do exhibit
+intellectual powers quite equal to any which have ever been displayed in
+Science: and if these inferences are not inductive, what are they? The
+limitation imposed on the term by Dr. Whewell seems perfectly arbitrary;
+neither justified by any fundamental distinction between what he
+includes and what he desires to exclude, nor sanctioned by usage, at
+least from the time of Reid and Stewart, the principal legislators (as
+far as the English language is concerned) of modern metaphysical
+terminology.
+
+[2] Supra, p. 214.
+
+[3] _Novum Organum Renovatum_, pp. 72, 73.
+
+[4] _Novum Organum Renovatum_, p. 32.
+
+[5] _Cours de Philosophie Positive_, vol. ii. p. 202.
+
+[6] Dr. Whewell, in his reply, contests the distinction here drawn, and
+maintains, that not only different descriptions, but different
+explanations of a phenomenon, may all be true. Of the three theories
+respecting the motions of the heavenly bodies, he says (_Philosophy of
+Discovery_, p. 231): "Undoubtedly all these explanations may be true and
+consistent with each other, and would be so if each had been followed
+out so as to show in what manner it could be made consistent with the
+facts. And this was, in reality, in a great measure done. The doctrine
+that the heavenly bodies were moved by vortices was successfully
+modified, so that it came to coincide in its results with the doctrine
+of an inverse-quadratic centripetal force.... When this point was
+reached, the vortex was merely a machinery, well or ill devised, for
+producing such a centripetal force, and therefore did not contradict the
+doctrine of a centripetal force. Newton himself does not appear to have
+been averse to explaining gravity by impulse. So little is it true that
+if one theory be true the other must be false. The attempt to explain
+gravity by the impulse of streams of particles flowing through the
+universe in all directions, which I have mentioned in the _Philosophy_,
+is so far from being inconsistent with the Newtonian theory, that it is
+founded entirely upon it. And even with regard to the doctrine, that the
+heavenly bodies move by an inherent virtue; if this doctrine had been
+maintained in any such way that it was brought to agree with the facts,
+the inherent virtue must have had its laws determined; and then it would
+have been found that the virtue had a reference to the central body; and
+so, the 'inherent virtue' must have coincided in its effect with the
+Newtonian force; and then, the two explanations would agree, except so
+far as the word 'inherent' was concerned. And if such a part of an
+earlier theory as this word _inherent_ indicates, is found to be
+untenable, it is of course rejected in the transition to later and more
+exact theories, in Inductions of this kind, as well as in what Mr. Mill
+calls Descriptions. There is, therefore, still no validity discoverable
+in the distinction which Mr. Mill attempts to draw between descriptions
+like Kepler's law of elliptical orbits, and other examples of
+induction."
+
+If the doctrine of vortices had meant, not that vortices existed, but
+only that the planets moved _in the same manner_ as if they had been
+whirled by vortices; if the hypothesis had been merely a mode of
+representing the facts, not an attempt to account for them; if, in
+short, it had been only a Description; it would, no doubt, have been
+reconcileable with the Newtonian theory. The vortices, however, were not
+a mere aid to conceiving the motions of the planets, but a supposed
+physical agent, actively impelling them; a material fact, which might be
+true or not true, but could not be both true and not true. According to
+Descartes' theory it was true, according to Newton's it was not true.
+Dr. Whewell probably means that since the phrases, centripetal and
+projectile force, do not declare the nature but only the direction of
+the forces, the Newtonian theory does not absolutely contradict any
+hypothesis which may be framed respecting the mode of their production.
+The Newtonian theory, regarded as a mere _description_ of the planetary
+motions, does not; but the Newtonian theory as an _explanation_ of them
+does. For in what does the explanation consist? In ascribing those
+motions to a general law which obtains between all particles of matter,
+and in identifying this with the law by which bodies fall to the ground.
+If the planets are kept in their orbits by a force which draws the
+particles composing them towards every other particle of matter in the
+solar system, they are not kept in those orbits by the impulsive force
+of certain streams of matter which whirl them round. The one explanation
+absolutely excludes the other. Either the planets are not moved by
+vortices, or they do not move by a law common to all matter. It is
+impossible that both opinions can be true. As well might it be said that
+there is no contradiction between the assertions, that a man died
+because somebody killed him, and that he died a natural death.
+
+So, again, the theory that the planets move by a virtue inherent in
+their celestial nature, is incompatible with either of the two others:
+either that of their being moved by vortices, or that which regards them
+as moving by a property which they have in common with the earth and all
+terrestrial bodies. Dr. Whewell says that the theory of an inherent
+virtue agrees with Newton's when the word inherent is left out, which of
+course it would be (he says) if "found to be untenable." But leave that
+out, and where is the theory? The word inherent _is_ the theory. When
+that is omitted, there remains nothing except that the heavenly bodies
+move by "a virtue," _i.e._ by a power of some sort; or by virtue of
+their celestial nature, which directly contradicts the doctrine that
+terrestrial bodies fall by the same law.
+
+If Dr. Whewell is not yet satisfied, any other subject will serve
+equally well to test his doctrine. He will hardly say that there is no
+contradiction between the emission theory and the undulatory theory of
+light; or that there can be both one and two electricities; or that the
+hypothesis of the production of the higher organic forms by development
+from the lower, and the supposition of separate and successive acts of
+creation, are quite reconcileable; or that the theory that volcanoes are
+fed from a central fire, and the doctrines which ascribe them to
+chemical action at a comparatively small depth below the earth's
+surface, are consistent with one another, and all true as far as they
+go.
+
+If different explanations of the same fact cannot both be true, still
+less, surely, can different predictions. Dr. Whewell quarrels (on what
+ground it is not necessary here to consider) with the example I had
+chosen on this point, and thinks an objection to an illustration a
+sufficient answer to a theory. Examples not liable to his objection are
+easily found, if the proposition that conflicting predictions cannot
+both be true, can be made clearer by any examples. Suppose the
+phenomenon to be a newly-discovered comet, and that one astronomer
+predicts its return once in every 300 years--another once in every 400:
+can they both be right? When Columbus predicted that by sailing
+constantly westward he should in time return to the point from which he
+set out, while others asserted that he could never do so except by
+turning back, were both he and his opponents true prophets? Were the
+predictions which foretold the wonders of railways and steamships, and
+those which averred that the Atlantic could never be crossed by steam
+navigation, nor a railway train propelled ten miles an hour, both (in
+Dr. Whewell's words) "true, and consistent with one another"?
+
+Dr. Whewell sees no distinction between holding contradictory opinions
+on a question of fact, and merely employing different analogies to
+facilitate the conception of the same fact. The case of different
+Inductions belongs to the former class, that of different Descriptions
+to the latter.
+
+[7] _Phil. of Discov._ p. 256.
+
+[8] _Essays on the Pursuit of Truth._
+
+[9] In the first edition a note was appended at this place, containing
+some criticism on Archbishop Whately's mode of conceiving the relation
+between Syllogism and Induction. In a subsequent issue of his _Logic_,
+the Archbishop made a reply to the criticism, which induced me to cancel
+part of the note, incorporating the remainder in the text. In a still
+later edition, the Archbishop observes in a tone of something like
+disapprobation, that the objections, "doubtless from their being fully
+answered and found untenable, were silently suppressed," and that hence
+he might appear to some of his readers to be combating a shadow. On this
+latter point, the Archbishop need give himself no uneasiness. His
+readers, I make bold to say, will fully credit his mere affirmation that
+the objections have actually been made.
+
+But as he seems to think that what he terms the suppression of the
+objections ought not to have been made "silently," I now break that
+silence, and state exactly what it is that I suppressed, and why. I
+suppressed that alone which might be regarded as personal criticism on
+the Archbishop. I had imputed to him the having omitted to ask himself a
+particular question. I found that he had asked himself the question, and
+could give it an answer consistent with his own theory. I had also,
+within the compass of a parenthesis, hazarded some remarks on certain
+general characteristics of Archbishop Whately as a philosopher. These
+remarks, though their tone, I hope, was neither disrespectful nor
+arrogant, I felt, on reconsideration, that I was hardly entitled to
+make; least of all, when the instance which I had regarded as an
+illustration of them, failed, as I now saw, to bear them out. The real
+matter at the bottom of the whole dispute, the different view we take of
+the function of the major premise, remains exactly where it was; and so
+far was I from thinking that my opinion had been "fully answered" and
+was "untenable," that in the same edition in which I cancelled the note,
+I not only enforced the opinion by further arguments, but answered
+(though without naming him) those of the Archbishop.
+
+For not having made this statement before, I do not think it needful to
+apologize. It would be attaching very great importance to one's smallest
+sayings, to think a formal retractation requisite every time that one
+commits an error. Nor is Archbishop Whately's well-earned fame of so
+tender a quality as to require, that in withdrawing a slight criticism
+on him I should have been bound to offer a public _amende_ for having
+made it.
+
+[10] But though it is a condition of the validity of every induction
+that there be uniformity in the course of nature, it is not a necessary
+condition that the uniformity should pervade all nature. It is enough
+that it pervades the particular class of phenomena to which the
+induction relates. An induction concerning the motions of the planets,
+or the properties of the magnet, would not be vitiated though we were to
+suppose that wind and weather are the sport of chance, provided it be
+assumed that astronomical and magnetic phenomena are under the dominion
+of general laws. Otherwise the early experience of mankind would have
+rested on a very weak foundation; for in the infancy of science it could
+not be known that _all_ phenomena are regular in their course.
+
+Neither would it be correct to say that every induction by which we
+infer any truth, implies the general fact of uniformity _as foreknown_,
+even in reference to the kind of phenomena concerned. It implies,
+_either_ that this general fact is already known, _or_ that we may now
+know it: as the conclusion, the Duke of Wellington is mortal, drawn from
+the instances A, B, and C, implies either that we have already concluded
+all men to be mortal, or that we are now entitled to do so from the same
+evidence. A vast amount of confusion and paralogism respecting the
+grounds of Induction would be dispelled by keeping in view these simple
+considerations.
+
+[11] Infra, chap. xxi.
+
+[12] Infra, chap. xxi. xxii.
+
+[13] Dr. Whewell (_Phil. of Discov._ p. 246) will not allow these and
+similar erroneous judgments to be called inductions; inasmuch as such
+superstitious fancies "were not collected from the facts by seeking a
+law of their occurrence, but were suggested by an imagination of the
+anger of superior powers, shown by such deviations from the ordinary
+course of nature." I conceive the question to be, not in what manner
+these notions were at first suggested, but by what evidence they have,
+from time to time, been supposed to be substantiated. If the believers
+in these erroneous opinions had been put on their defence, they would
+have referred to experience: to the comet which preceded the
+assassination of Julius Cæsar, or to oracles and other prophecies known
+to have been fulfilled. It is by such appeals to facts that all
+analogous superstitions, even in our day, attempt to justify themselves;
+the supposed evidence of experience is necessary to their hold on the
+mind. I quite admit that the influence of such coincidences would not be
+what it is, if strength were not lent to it by an antecedent
+presumption; but this is not peculiar to such cases; preconceived
+notions of probability form part of the explanation of many other cases
+of belief on insufficient evidence. The _à priori_ prejudice does not
+prevent the erroneous opinion from being sincerely regarded as a
+legitimate conclusion from experience; though it improperly predisposes
+the mind to that interpretation of experience.
+
+Thus much in defence of the sort of examples objected to. But it would
+be easy to produce instances, equally adapted to the purpose, and in
+which no antecedent prejudice is at all concerned. "For many ages," says
+Archbishop Whately, "all farmers and gardeners were firmly
+convinced--and convinced of their knowing it by experience--that the
+crops would never turn out good unless the seed were sown during the
+increase of the moon." This was induction, but bad induction: just as a
+vicious syllogism is reasoning, but bad reasoning.
+
+[14] The assertion, that any and every one of the conditions of a
+phenomenon may be and is, on some occasions and for some purposes,
+spoken of as the cause, has been disputed by an intelligent reviewer of
+this work in the _Prospective Review_ (the predecessor of the justly
+esteemed _National Review_), who maintains that "we always apply the
+word cause rather to that element in the antecedents which exercises
+_force_, and which would _tend_ at all times to produce the same or a
+similar effect to that which, under certain conditions, it would
+actually produce." And he says, that "every one would feel" the
+expression, that the cause of a surprise was the sentinel's being off
+his post, to be incorrect; but that the "allurement or force which
+_drew_ him off his post, might be so called, because in doing so it
+removed a resisting power which would have prevented the surprise." I
+cannot think that it would be wrong to say, that the event took place
+because the sentinel was absent, and yet right to say that it took place
+because he was bribed to be absent. Since the only direct effect of the
+bribe was his absence, the bribe could be called the remote cause of the
+surprise, only on the supposition that the absence was the proximate
+cause; nor does it seem to me that any one (who had not a theory to
+support) would use the one expression and reject the other.
+
+The reviewer observes, that when a person dies of poison, his possession
+of bodily organs is a necessary condition, but that no one would ever
+speak of it as the cause. I admit the fact; but I believe the reason to
+be, that the occasion could never arise for so speaking of it; for when
+in the inaccuracy of common discourse we are led to speak of some one
+condition of a phenomenon as its cause, the condition so spoken of is
+always one which it is at least possible that the hearer may require to
+be informed of. The possession of bodily organs is a known condition,
+and to give that as the answer, when asked the cause of a person's
+death, would not supply the information sought. Once conceive that a
+doubt could exist as to his having bodily organs, or that he were to be
+compared with some being who had them not, and cases may be imagined in
+which it might be said that his possession of them was the cause of his
+death. If Faust and Mephistopheles together took poison, it might be
+said that Faust died because he was a human being, and had a body, while
+Mephistopheles survived because he was a spirit.
+
+It is for the same reason that no one (as the reviewer remarks) "calls
+the cause of a leap, the muscles or sinews of the body, though they are
+necessary conditions; nor the cause of a self-sacrifice, the knowledge
+which was necessary for it; nor the cause of writing a book, that a man
+has time for it, which is a necessary condition." These conditions
+(besides that they are antecedent _states_, and not proximate antecedent
+_events_, and are therefore never the conditions in closest apparent
+proximity to the effect) are all of them so obviously implied, that it
+is hardly possible there should exist that necessity for insisting on
+them, which alone gives occasion for speaking of a single condition as
+if it were the cause. Wherever this necessity exists in regard to some
+one condition, and does not exist in regard to any other, I conceive
+that it is consistent with usage, when scientific accuracy is not aimed
+at, to apply the name cause to that one condition. If the only condition
+which can be supposed to be unknown is a negative condition, the
+negative condition may be spoken of as the cause. It might be said that
+a person died for want of medical advice: though this would not be
+likely to be said, unless the person was already understood to be ill,
+and in order to indicate that this negative circumstance was what made
+the illness fatal, and not the weakness of his constitution, or the
+original virulence of the disease. It might be said that a person was
+drowned because he could not swim; the positive condition, namely, that
+he fell into the water, being already implied in the word drowned. And
+here let me remark, that his falling into the water is in this case the
+only positive condition: all the conditions not expressly or virtually
+included in this (as that he could not swim, that nobody helped him, and
+so forth) are negative. Yet, if it were simply said that the cause of a
+man's death was falling into the water, there would be quite as great a
+sense of impropriety in the expression, as there would be if it were
+said that the cause was his inability to swim; because, though the one
+condition is positive and the other negative, it would be felt that
+neither of them was sufficient, without the other, to produce death.
+
+With regard to the assertion that nothing is termed the cause, except
+the element which exerts active force; I wave the question as to the
+meaning of active force, and accepting the phrase in its popular sense,
+I revert to a former example, and I ask, would it be more agreeable to
+custom to say that a man fell because his foot slipped in climbing a
+ladder, or that he fell because of his weight? for his weight, and not
+the motion of his foot, was the active force which determined his fall.
+If a person walking out in a frosty day, stumbled and fell, it might be
+said that he stumbled because the ground was slippery, or because he was
+not sufficiently careful; but few people, I suppose, would say, that he
+stumbled because he walked. Yet the only active force concerned was that
+which he exerted in walking: the others were mere negative conditions;
+but they happened to be the only ones which there could be any necessity
+to state; for he walked, most likely, in exactly his usual manner, and
+the negative conditions made all the difference. Again, if a person were
+asked why the army of Xerxes defeated that of Leonidas, he would
+probably say, because they were a thousand times the number; but I do
+not think he would say, it was because they fought, though that was the
+element of active force. To borrow another example, used by Mr. Grove
+and by Mr. Baden Powell, the opening of floodgates is said to be the
+cause of the flow of water; yet the active force is exerted by the water
+itself, and opening the floodgates merely supplies a negative condition.
+The reviewer adds, "there are some conditions absolutely passive, and
+yet absolutely necessary to physical phenomena, viz. the relations of
+space and time; and to these no one ever applies the word cause without
+being immediately arrested by those who hear him." Even from this
+statement I am compelled to dissent. Few persons would feel it
+incongruous to say (for example) that a secret became known because it
+was spoken of when A. B. was within hearing; which is a condition of
+space: or that the cause why one of two particular trees is taller than
+the other, is that it has been longer planted; which is a condition of
+time.
+
+[15] There are a few exceptions; for there are some properties of
+objects which seem to be purely preventive; as the property of opaque
+bodies, by which they intercept the passage of light. This, as far as we
+are able to understand it, appears an instance not of one cause
+counteracting another by the same law whereby it produces its own
+effects, but of an agency which manifests itself in no other way than in
+defeating the effects of another agency. If we knew on what other
+relations to light, or on what peculiarities of structure, opacity
+depends, we might find that this is only an apparent, not a real,
+exception to the general proposition in the text. In any case it needs
+not affect the practical application. The formula which includes all the
+negative conditions of an effect in the single one of the absence of
+counteracting causes, is not violated by such cases as this; though, if
+all counteracting agencies were of this description, there would be no
+purpose served by employing the formula, since we should still have to
+enumerate specially the negative conditions of each phenomenon, instead
+of regarding them as implicitly contained in the positive laws of the
+various other agencies in nature.
+
+[16] I mean by this expression, the ultimate laws of nature (whatever
+they may be) as distinguished from the derivative laws and from the
+collocations. The diurnal revolution of the earth (for example) is not a
+part of the constitution of things, because nothing can be so called
+which might possibly be terminated or altered by natural causes.
+
+[17] I use the words "straight line" for brevity and simplicity. In
+reality the line in question is not exactly straight, for, from the
+effect of refraction, we actually see the sun for a short interval
+during which the opaque mass of the earth is interposed in a direct line
+between the sun and our eyes; thus realizing, though but to a limited
+extent, the coveted desideratum of seeing round a corner.
+
+[18] _Second Burnett Prize Essay_, by Principal Tulloch, p. 25.
+
+[19] _Letters on the Philosophy of the Human Mind_, First Series, p.
+219.
+
+[20] _Essays_, pp. 206-208.
+
+[21] To the universality which mankind are agreed in ascribing to the
+Law of Causation, there is one claim of exception, one disputed case,
+that of the Human Will; the determinations of which, a large class of
+metaphysicians are not willing to regard as following the causes called
+motives, according to as strict laws as those which they suppose to
+exist in the world of mere matter. This controverted point will undergo
+a special examination when we come to treat particularly of the Logic of
+the Moral Sciences (Book vi. ch. 2). In the mean time I may remark that
+these metaphysicians, who, it must be observed, ground the main part of
+their objection on the supposed repugnance of the doctrine in question
+to our consciousness, seem to me to mistake the fact which consciousness
+testifies against. What is really in contradiction to consciousness,
+they would, I think, on strict self-examination, find to be, the
+application to human actions and volitions of the ideas involved in the
+common use of the term Necessity; which I agree with them in objecting
+to. But if they would consider that by saying that a person's actions
+_necessarily_ follow from his character, all that is really meant (for
+no more is meant in any case whatever of causation) is that he
+invariably _does_ act in conformity to his character, and that any one
+who thoroughly knew his character would certainly predict how he would
+act in any supposable case; they probably would not find this doctrine
+either contrary to their experience or revolting to their feelings. And
+no more than this is contended for by any one but an Asiatic fatalist.
+
+[22] _Lectures on Metaphysics_, vol. ii. Lect. xxxix. pp. 391-2.
+
+I regret that I cannot invoke the authority of Sir William Hamilton in
+favour of my own opinions on Causation, as I can against the particular
+theory which I am now combating. But that acute thinker has a theory of
+Causation peculiar to himself, which has never yet, as far as I know,
+been analytically examined, but which, I venture to think, admits of as
+complete refutation as any one of the false or insufficient
+psychological theories which strew the ground in such numbers under his
+potent metaphysical scythe. (Since examined and controverted in the
+sixteenth chapter of _An Examination of Sir William Hamilton's
+Philosophy_).
+
+[23] Unless we are to consider as such the following statement, by one
+of the writers quoted in the text: "In the case of mental exertion, the
+result to be accomplished is preconsidered or meditated, and is
+therefore known _à priori_, or before experience."--(Bowen's _Lowell
+Lectures on the Application of Metaphysical and Ethical Science to the
+Evidence of Religion_, Boston, 1849.) This is merely saying that when we
+will a thing we have an idea of it. But to have an idea of what we wish
+to happen, does not imply a prophetic knowledge that it will happen.
+Perhaps it will be said that the _first time_ we exerted our will, when
+we had of course no experience of any of the powers residing in us, we
+nevertheless must already have known that we possessed them, since we
+cannot will that which we do not believe to be in our power. But the
+impossibility is perhaps in the words only, and not in the facts; for we
+may _desire_ what we do not know to be in our power; and finding by
+experience that our bodies move according to our _desire_, we may then,
+and only then, pass into the more complicated mental state which is
+termed will.
+
+After all, even if we had an instinctive knowledge that our actions
+would follow our will, this, as Brown remarks, would prove nothing as to
+the nature of Causation. Our knowing, previous to experience, that an
+antecedent will be followed by a certain consequent, would not prove the
+relation between them to be anything more than antecedence and
+consequence.
+
+[24] Reid's _Essays on the Active Powers_, Essay iv. ch. 3.
+
+[25] _Prospective Review_ for February 1850.
+
+[26] Vide supra, p. 270, note.
+
+[27] _Westminster Review_ for October 1855.
+
+[28] See the whole doctrine in Aristotle _de Animâ_: where the _θρεπτικὴ
+ψυχὴ_ is treated as exactly equivalent to _θρεπτικὴ δύναμις_.
+
+[29] It deserves notice that the parts of nature, which Aristotle
+regards as presenting evidence of design, are the Uniformities: the
+phenomena in so far as reducible to law. _Τύχη_ and _τὸ αὐτομάτον_
+satisfy him as explanations of the variable element in phenomena, but
+their occurring according to a fixed rule can only, to his conceptions,
+be accounted for by an Intelligent Will. The common, or what may be
+called the instinctive, religious interpretation of nature, is the
+reverse of this. The events in which men spontaneously see the hand of a
+supernatural being, are those which cannot, as they think, be reduced to
+a physical law. What they can distinctly connect with physical causes,
+and especially what they can predict, though of course ascribed to an
+Author of Nature if they already recognise such an author, might be
+conceived, they think, to arise from a blind fatality, and in any case
+do not appear to them to bear so obviously the mark of a divine will.
+And this distinction has been countenanced by eminent writers on Natural
+Theology, in particular by Dr. Chalmers: who thinks that though design
+is present everywhere, the irresistible evidence of it is to be found
+not in the _laws_ of nature but in the collocations, _i.e._ in the part
+of nature in which it is impossible to trace any law. A few properties
+of dead matter might, he thinks, conceivably account for the regular and
+invariable succession of effects and causes; but that the different
+kinds of matter have been so placed as to promote beneficent ends, is
+what he regards as the proof of a Divine Providence. Mr. Baden Powell,
+in his Essay entitled "Philosophy of Creation," has returned to the
+point of view of Aristotle and the ancients, and vigorously reasserts
+the doctrine that the indication of design in the universe is not
+special adaptations, but Uniformity and Law, these being the evidences
+of mind, and not what appears to us to be a provision for our uses.
+While I decline to express any opinion here on this _vexata quæstio_, I
+ought not to mention Mr. Powell's volume without the acknowledgment due
+to the philosophic spirit which pervades generally the three Essays
+composing it, forming in the case of one of them (the "Unity of Worlds")
+an honourable contrast with the other dissertations, so far as they have
+come under my notice, which have appeared on either side of that
+controversy.
+
+[30] In the words of Fontenelle, another celebrated Cartesian, "les
+philosophes aussi bien que le peuple avaient cru que l'âme et le corps
+agissaient réellement et physiquement l'un sur l'autre. Descartes vint,
+qui prouva que leur nature ne permettait point cette sorte de
+communication véritable, et qu'ils n'en pouvaient avoir qu'une
+apparente, dont Dieu était le Médiateur."--_Œuvres de Fontenelle_,
+ed. 1767, tom. v. p. 534.
+
+[31] I omit, for simplicity, to take into account the effect, in this
+latter case, of the diminution of pressure, in diminishing the flow of
+water through the drain; which evidently in no way affects the truth or
+applicability of the principle, since when the two causes act
+simultaneously the conditions of that diminution of pressure do not
+arise.
+
+[32] Unless, indeed, the consequent was generated not by the antecedent,
+but by the means employed to produce the antecedent. As, however, these
+means are under our power, there is so far a probability that they are
+also sufficiently within our knowledge, to enable us to judge whether
+that could be the case or not.
+
+[33] _Discourse on the Study of Natural Philosophy_, p. 179.
+
+[34] For this speculation, as for many other of my scientific
+illustrations, I am indebted to Professor Bain, of Aberdeen, who has
+since, in his profound treatises entitled "The Senses and the
+Intellect," and "The Emotions and the Will," carried the analytic
+investigation of the mental phenomena according to the methods of
+physical science, to the most advanced point which it has yet reached,
+and has worthily inscribed his name among the successive constructors of
+an edifice to which Hartley, Brown, and James Mill had each contributed
+their part.
+
+[35] This view of the necessary coexistence of opposite excitements
+involves a great extension of the original doctrine of two
+electricities. The early theorists assumed that, when amber was rubbed,
+the amber was made positive and the rubber negative to the same degree;
+but it never occurred to them to suppose that the existence of the amber
+charge was dependent on an opposite charge in the bodies with which the
+amber was contiguous, while the existence of the negative charge on the
+rubber was equally dependent on a contrary state of the surfaces that
+might accidentally be confronted with it; that, in fact, in a case of
+electrical excitement by friction, four charges were the minimum that
+could exist. But this double electrical action is essentially implied in
+the explanation now universally adopted in regard to the phenomena of
+the common electric machine.
+
+[36] Pp. 159-162.
+
+[37] Infra, book iv. ch. ii. On Abstraction.
+
+[38] I must, however, remark, that this example, which seems to militate
+against the assertion we made of the comparative inapplicability of the
+Method of Difference to cases of pure observation, is really one of
+those exceptions which, according to a proverbial expression, prove the
+general rule. For in this case, in which Nature, in her experiment,
+seems to have imitated the type of the experiments made by man, she has
+only succeeded in producing the likeness of man's most imperfect
+experiments; namely, those in which, though he succeeds in producing the
+phenomenon, he does so by employing complex means, which he is unable
+perfectly to analyse, and can form therefore no sufficient judgment what
+portion of the effects may be due, not to the supposed cause, but to
+some unknown agency of the means by which that cause was produced. In
+the natural experiment which we are speaking of, the means used was the
+clearing off a canopy of clouds; and we certainly do not know
+sufficiently in what this process consists, or on what it depends, to be
+certain _à priori_ that it might not operate upon the deposition of dew
+independently of any thermometric effect at the earth's surface. Even,
+therefore, in a case so favourable as this to Nature's experimental
+talents, her experiment is of little value except in corroboration of a
+conclusion already attained through other means.
+
+[39] In his subsequent work, _Outlines of Astronomy_ (§ 570), Sir John
+Herschel suggests another possible explanation of the acceleration of
+the revolution of a comet.
+
+[40] Discourse, pp. 156-8, and 171.
+
+[41] _Outlines of Astronomy_, § 856.
+
+[42] _Philosophy of Discovery_, pp. 263, 264.
+
+[43] See, on this point, the second chapter of the present Book.
+
+[44] Ante, ch. vii. § 1.
+
+[45] It seems hardly necessary to say that the word _impinge_, as a
+general term to express collision of forces, is here used by a figure of
+speech, and not as expressive of any theory respecting the nature of
+force.
+
+[46] _Essays on some Unsettled Questions of Political Economy_, Essay V.
+
+[47] _Vide_ Memoir by Thomas Graham, F.R.S., Master of the Mint, "On
+Liquid Diffusion Applied to Analysis," in the _Philosophical
+Transactions_ for 1862, reprinted in the _Journal of the Chemical
+Society_, and also separately as a pamphlet.
+
+[48] It was an old generalization in surgery, that tight bandaging had a
+tendency to prevent or dissipate local inflammation. This sequence,
+being, in the progress of physiological knowledge, resolved into more
+general laws, led to the important surgical invention made by Dr.
+Arnott, the treatment of local inflammation and tumours by means of an
+equable pressure, produced by a bladder partially filled with air. The
+pressure, by keeping back the blood from the part, prevents the
+inflammation, or the tumour, from being nourished: in the case of
+inflammation, it removes the stimulus, which the organ is unfit to
+receive; in the case of tumours, by keeping back the nutritive fluid, it
+causes the absorption of matter to exceed the supply, and the diseased
+mass is gradually absorbed and disappears.
+
+[49] Since acknowledged and reprinted in Mr. Martineau's _Miscellanies_.
+
+[50] _Dissertations and Discussions_, vol. i., fourth paper.
+
+[51] Written before the rise of the new views respecting the relation of
+heat to mechanical force; but confirmed rather than contradicted by
+them.
+
+
+END OF VOL. I.
+
+
+
+
+  LONDON:
+  SAVILL, EDWARDS AND CO., PRINTERS, CHANDOS STREET,
+  COVENT GARDEN.
+
+
+
+
+Transcriber's Notes
+
+
+Spelling irregularities where there was no obviously preferred version
+were left as is. Variants include: "alkalies" and "alkalis;" "apprise"
+and "apprize;" "coexistent" and "co-existent" (along with derivatives);
+"coextensive" and "co-extensive;" "e. g." and "e.g."; "encumbered" and
+"incumbered;" "formulæ" and "formulas;" "i. e." and "i.e."; "nonentity"
+and "non-entity;" "recal" and "recall" (and derivatives); "rectilinear"
+and "rectilineal;" "stopt" and "stopped."
+
+Changed "3" to "4" on page xiii: "4. --and from descriptions."
+
+Volume I. contains "το ὄν," while Volume II. spells it "τὸ ὄν." The
+spellings were left as is, in each case.
+
+Inserted missing page number, "167," for Chapter VIII, section 7 on page
+xiii.
+
+Moved the semi-colon inside the quotation marks in the footnote on page
+14: "the Science of the Formal Laws of Thought;".
+
+Changed "sub-divisions" to "subdivisions" on page 59: "three
+subdivisions."
+
+Changed "pre-supposed" to "presupposed" on page 75: "they are
+presupposed."
+
+In the footnote to page 122, changed the Greek character upsilon with
+dasia and oxia to upsilon with psili and oxia, making the
+transliteration "deuterai ousiai."
+
+Changed "he" to "be" on page 189: "to which it may be reduced."
+
+Changed "cb." to "ch." in footnote on page 227: "Theory of Reasoning,
+ch. iv."
+
+Changed "reconcilable" to "reconcileable" on page 240: "not easily
+reconcileable."
+
+Preserved the hyphen in "counter-acting" on page 280. Usually this is
+spelled without the hyphen, but this instance is in a quotation.
+
+Moved parenthesis that was after "to" to before it on page 321: "(to
+return to a former example)."
+
+Put "i.e." in italics on page 335: "_i.e._ by a power of some sort."
+
+Changed "paralyzed" to "paralysed" on page 389: "nerves of motion were
+paralysed."
+
+The footnote from page 396 refers to the footnote on page 270. There is
+no such footnote. The intent may be to refer to the footnote on page
+268. However, the text was not changed.
+
+Added the dropped "w" in "which" on page 420: "which the progress of the
+inquiry."
+
+Changed "developes" to "develops" on page 456: "the prime conductor
+develops."
+
+Removed the additional period at the end of the footnote on page 457:
+"Pp. 159-162."
+
+Added the dropped "l" to "essential" on page 515: "an essential
+requisite."
+
+Removed extra opening quotation mark before "gum" on page 532:
+"vegetable gum is not digested."
+
+
+
+
+
+
+End of the Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
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diff --git a/35420-0.zip b/35420-0.zip
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+The Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A System of Logic: Ratiocinative and Inductive
+       7th Edition, Vol. I
+
+Author: John Stuart Mill
+
+Release Date: February 27, 2011 [EBook #35420]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL 1 ***
+
+
+
+
+Produced by David Clarke, Stephen H. Sentoff and the Online
+Distributed Proofreading Team at https://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+VOL. I.
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+BEING A CONNECTED VIEW OF THE
+PRINCIPLES OF EVIDENCE
+AND THE
+METHODS OF SCIENTIFIC INVESTIGATION
+
+BY
+
+JOHN STUART MILL
+
+
+IN TWO VOLUMES
+
+VOL. I.
+
+SEVENTH EDITION
+
+
+LONDON:
+LONGMANS, GREEN, READER, AND DYER
+
+MDCCCLXVIII
+
+
+
+
+PREFACE TO THE FIRST EDITION.
+
+
+This book makes no pretence of giving to the world a new theory of the
+intellectual operations. Its claim to attention, if it possess any, is
+grounded on the fact that it is an attempt not to supersede, but to
+embody and systematize, the best ideas which have been either
+promulgated on its subject by speculative writers, or conformed to by
+accurate thinkers in their scientific inquiries.
+
+To cement together the detached fragments of a subject, never yet
+treated as a whole; to harmonize the true portions of discordant
+theories, by supplying the links of thought necessary to connect them,
+and by disentangling them from the errors with which they are always
+more or less interwoven; must necessarily require a considerable amount
+of original speculation. To other originality than this, the present
+work lays no claim. In the existing state of the cultivation of the
+sciences, there would be a very strong presumption against any one who
+should imagine that he had effected a revolution in the theory of the
+investigation of truth, or added any fundamentally new process to the
+practice of it. The improvement which remains to be effected in the
+methods of philosophizing (and the author believes that they have much
+need of improvement) can only consist in performing, more systematically
+and accurately, operations with which, at least in their elementary
+form, the human intellect in some one or other of its employments is
+already familiar.
+
+In the portion of the work which treats of Ratiocination, the author has
+not deemed it necessary to enter into technical details which may be
+obtained in so perfect a shape from the existing treatises on what is
+termed the Logic of the Schools. In the contempt entertained by many
+modern philosophers for the syllogistic art, it will be seen that he by
+no means participates; though the scientific theory on which its defence
+is usually rested appears to him erroneous: and the view which he has
+suggested of the nature and functions of the Syllogism may, perhaps,
+afford the means of conciliating the principles of the art with as much
+as is well grounded in the doctrines and objections of its assailants.
+
+The same abstinence from details could not be observed in the First
+Book, on Names and Propositions; because many useful principles and
+distinctions which were contained in the old Logic, have been gradually
+omitted from the writings of its later teachers; and it appeared
+desirable both to revive these, and to reform and rationalize the
+philosophical foundation on which they stood. The earlier chapters of
+this preliminary Book will consequently appear, to some readers,
+needlessly elementary and scholastic. But those who know in what
+darkness the nature of our knowledge, and of the processes by which it
+is obtained, is often involved by a confused apprehension of the import
+of the different classes of Words and Assertions, will not regard these
+discussions as either frivolous, or irrelevant to the topics considered
+in the later Books.
+
+On the subject of Induction, the task to be performed was that of
+generalizing the modes of investigating truth and estimating evidence,
+by which so many important and recondite laws of nature have, in the
+various sciences, been aggregated to the stock of human knowledge. That
+this is not a task free from difficulty may be presumed from the fact,
+that even at a very recent period, eminent writers (among whom it is
+sufficient to name Archbishop Whately, and the author of a celebrated
+article on Bacon in the _Edinburgh Review_) have not scrupled to
+pronounce it impossible.[1] The author has endeavoured to combat their
+theory in the manner in which Diogenes confuted the sceptical reasonings
+against the possibility of motion; remembering that Diogenes' argument
+would have been equally conclusive, though his individual perambulations
+might not have extended beyond the circuit of his own tub.
+
+Whatever may be the value of what the author has succeeded in effecting
+on this branch of his subject, it is a duty to acknowledge that for much
+of it he has been indebted to several important treatises, partly
+historical and partly philosophical, on the generalities and processes
+of physical science, which have been published within the last few
+years. To these treatises, and to their authors, he has endeavoured to
+do justice in the body of the work. But as with one of these writers,
+Dr. Whewell, he has occasion frequently to express differences of
+opinion, it is more particularly incumbent on him in this place to
+declare, that without the aid derived from the facts and ideas contained
+in that gentleman's _History of the Inductive Sciences_, the
+corresponding portion of this work would probably not have been written.
+
+The concluding Book is an attempt to contribute towards the solution of
+a question, which the decay of old opinions, and the agitation that
+disturbs European society to its inmost depths, render as important in
+the present day to the practical interests of human life, as it must at
+all times be to the completeness of our speculative knowledge: viz.
+Whether moral and social phenomena are really exceptions to the general
+certainty and uniformity of the course of nature; and how far the
+methods, by which so many of the laws of the physical world have been
+numbered among truths irrevocably acquired and universally assented to,
+can be made instrumental to the formation of a similar body of received
+doctrine in moral and political science.
+
+
+
+
+PREFACE TO THE THIRD AND FOURTH EDITIONS.
+
+
+Several criticisms, of a more or less controversial character, on this
+work, have appeared since the publication of the second edition; and Dr.
+Whewell has lately published a reply to those parts of it in which some
+of his opinions were controverted.[2]
+
+I have carefully reconsidered all the points on which my conclusions
+have been assailed. But I have not to announce a change of opinion on
+any matter of importance. Such minor oversights as have been detected,
+either by myself or by my critics, I have, in general silently,
+corrected: but it is not to be inferred that I agree with the objections
+which have been made to a passage, in every instance in which I have
+altered or cancelled it. I have often done so, merely that it might not
+remain a stumbling-block, when the amount of discussion necessary to
+place the matter in its true light would have exceeded what was suitable
+to the occasion.
+
+To several of the arguments which have been urged against me, I have
+thought it useful to reply with some degree of minuteness; not from any
+taste for controversy, but because the opportunity was favourable for
+placing my own conclusions, and the grounds of them, more clearly and
+completely before the reader. Truth, on these subjects, is militant, and
+can only establish itself by means of conflict. The most opposite
+opinions can make a plausible show of evidence while each has the
+statement of its own case; and it is only possible to ascertain which of
+them is in the right, after hearing and comparing what each can say
+against the other, and what the other can urge in its defence.
+
+Even the criticisms from which I most dissent have been of great service
+to me, by showing in what places the exposition most needed to be
+improved, or the argument strengthened. And I should have been well
+pleased if the book had undergone a much greater amount of attack; as in
+that case I should probably have been enabled to improve it still more
+than I believe I have now done.
+
+       *       *       *       *       *
+
+In the subsequent editions, the attempt to improve the work by additions
+and corrections, suggested by criticism or by thought, has been
+continued. In the present (seventh) edition, a few further corrections
+have been made, but no material additions.
+
+FOOTNOTES:
+
+[1] In the later editions of Archbishop Whately's _Logic_, he states his
+meaning to be, not that "rules" for the ascertainment of truths by
+inductive investigation cannot be laid down, or that they may not be "of
+eminent service," but that they "must always be comparatively vague and
+general, and incapable of being built up into a regular demonstrative
+theory like that of the Syllogism." (Book IV. ch. iv. � 3.) And he
+observes, that to devise a system for this purpose, capable of being
+"brought into a scientific form," would be an achievement which "he must
+be more sanguine than scientific who expects." (Book IV. ch. ii. � 4.)
+To effect this, however, being the express object of the portion of the
+present work which treats of Induction, the words in the text are no
+overstatement of the difference of opinion between Archbishop Whately
+and me on the subject.
+
+[2] Now forming a chapter in his volume on _The Philosophy of
+Discovery_.
+
+
+
+
+CONTENTS
+OF
+THE FIRST VOLUME.
+
+
+  INTRODUCTION.
+
+
+  � 1. A definition at the commencement of a subject must be
+       provisional                                                    1
+
+    2. Is logic the art and science of reasoning?                     2
+
+    3. Or the art and science of the pursuit of truth?                3
+
+    4. Logic is concerned with inferences, not with intuitive truths  5
+
+    5. Relation of logic to the other sciences                        8
+
+    6. Its utility, how shown                                        10
+
+    7. Definition of logic stated and illustrated                    11
+
+
+  BOOK I.
+
+  OF NAMES AND PROPOSITIONS.
+
+
+  CHAPTER I. _Of the Necessity of commencing with an
+  Analysis of Language._
+
+  � 1. Theory of names, why a necessary part of logic                17
+
+    2. First step in the analysis of Propositions                    18
+
+    3. Names must be studied before Things                           21
+
+
+  CHAPTER II. _Of Names._
+
+  � 1. Names are names of things, not of our ideas                   23
+
+    2. Words which are not names, but parts of names                 24
+
+    3. General and Singular names                                    26
+
+    4. Concrete and Abstract                                         29
+
+    5. Connotative and Non-connotative                               31
+
+    6. Positive and Negative                                         42
+
+    7. Relative and Absolute                                         44
+
+    8. Univocal and �quivocal                                        47
+
+
+  CHAPTER III. _Of the Things denoted by Names._
+
+  � 1. Necessity of an enumeration of Nameable Things. The
+       Categories of Aristotle                                       49
+
+    2. Ambiguity of the most general names                           51
+
+    3. Feelings, or states of consciousness                          54
+
+    4. Feelings must be distinguished from their physical
+       antecedents. Perceptions, what                                56
+
+    5. Volitions, and Actions, what                                  58
+
+    6. Substance and Attribute                                       59
+
+    7. Body                                                          61
+
+    8. Mind                                                          67
+
+    9. Qualities                                                     69
+
+   10. Relations                                                     72
+
+   11. Resemblance                                                   74
+
+   12. Quantity                                                      78
+
+   13. All attributes of bodies are grounded on states of
+       consciousness                                                 79
+
+   14. So also all attributes of mind                                80
+
+   15. Recapitulation                                                81
+
+
+  CHAPTER IV. _Of Propositions._
+
+  � 1. Nature and office of the copula                               85
+
+    2. Affirmative and Negative propositions                         87
+
+    3. Simple and Complex                                            89
+
+    4. Universal, Particular, and Singular                           93
+
+
+  CHAPTER V. _Of the Import of Propositions._
+
+  � 1. Doctrine that a proposition is the expression of a relation
+       between two ideas                                             96
+
+    2. Doctrine that it is the expression of a relation between the
+       meanings of two names                                         99
+
+    3. Doctrine that it consists in referring something to, or
+       excluding something from, a class                            103
+
+    4. What it really is                                            107
+
+    5. It asserts (or denies) a sequence, a coexistence, a simple
+       existence, a causation                                       110
+
+    6. --or a resemblance                                           112
+
+    7. Propositions of which the terms are abstract                 115
+
+
+  CHAPTER VI. _Of Propositions merely Verbal._
+
+  � 1. Essential and Accidental propositions                        119
+
+    2. All essential propositions are identical propositions        120
+
+    3. Individuals have no essences                                 124
+
+    4. Real propositions, how distinguished from verbal             126
+
+    5. Two modes of representing the import of a Real proposition   127
+
+
+  CHAPTER VII. _Of the Nature of Classification, and
+  the Five Predicables._
+
+  � 1. Classification, how connected with Naming                    129
+
+    2. The Predicables, what                                        131
+
+    3. Genus and Species                                            131
+
+    4. Kinds have a real existence in nature                        134
+
+    5. Differentia                                                  139
+
+    6. Differenti� for general purposes, and differenti� for
+       special or technical purposes                                141
+
+    7. Proprium                                                     144
+
+    8. Accidens                                                     146
+
+
+  CHAPTER VIII. _Of Definition._
+
+  � 1. A definition, what                                           148
+
+    2. Every name can be defined, whose meaning is susceptible
+       of analysis                                                  150
+
+    3. Complete, how distinguished from incomplete definitions      152
+
+    4. --and from descriptions                                      154
+
+    5. What are called definitions of Things, are definitions of
+       Names with an implied assumption of the existence of
+       Things corresponding to them                                 157
+
+    6. --even when such things do not in reality exist              165
+
+    7. Definitions, though of names only, must be grounded on
+       knowledge of the corresponding Things                        167
+
+
+  BOOK II.
+
+  OF REASONING.
+
+
+  CHAPTER I. _Of Inference, or Reasoning, in general._
+
+  � 1. Retrospect of the preceding book                             175
+
+    2. Inferences improperly so called                              177
+
+    3. Inferences proper, distinguished into inductions and
+       ratiocinations                                               181
+
+
+  CHAPTER II. _Of Ratiocination, or Syllogism._
+
+  � 1. Analysis of the Syllogism                                    184
+
+    2. The _dictum de omni_ not the foundation of reasoning,
+       but a mere identical proposition                             191
+
+    3. What is the really fundamental axiom of Ratiocination        196
+
+    4. The other form of the axiom                                  199
+
+
+  CHAPTER III. _Of the Functions, and Logical Value, of the
+  Syllogism._
+
+  � 1. Is the syllogism a _petitio principii_?                      202
+
+    2. Insufficiency of the common theory                           203
+
+    3. All inference is from particulars to particulars             205
+
+    4. General propositions are a record of such inferences, and
+       the rules of the syllogism are rules for the interpretation
+       of the record                                                214
+
+    5. The syllogism not the type of reasoning, but a test of it    218
+
+    6. The true type, what                                          222
+
+    7. Relation between Induction and Deduction                     226
+
+    8. Objections answered                                          227
+
+    9. Of Formal Logic, and its relation to the Logic of Truth      231
+
+
+  CHAPTER IV. _Of Trains of Reasoning, and Deductive
+  Sciences._
+
+  � 1. For what purpose trains of reasoning exist                   234
+
+    2. A train of reasoning is a series of inductive inferences     234
+
+    3. --from particulars to particulars through marks of marks     237
+
+    4. Why there are deductive sciences                             240
+
+    5. Why other sciences still remain experimental                 244
+
+    6. Experimental sciences may become deductive by the progress
+       of experiment                                                246
+
+    7. In what manner this usually takes place                      247
+
+
+  CHAPTER V. _Of Demonstration, and Necessary Truths._
+
+  � 1. The Theorems of geometry are necessary truths only in
+       the sense of necessarily following from hypotheses           251
+
+    2. Those hypotheses are real facts with some of their
+       circumstances exaggerated or omitted                         255
+
+    3. Some of the first principles of geometry are axioms, and
+       these are not hypothetical                                   256
+
+    4. --but are experimental truths                                258
+
+    5. An objection answered                                        261
+
+    6. Dr. Whewell's opinions on axioms examined                    264
+
+
+  CHAPTER VI. _The same Subject continued._
+
+  � 1. All deductive sciences are inductive                         281
+
+    2. The propositions of the science of number are not verbal,
+       but generalizations from experience                          284
+
+    3. In what sense hypothetical                                   289
+
+    4. The characteristic property of demonstrative science is to
+       be hypothetical                                              290
+
+    5. Definition of demonstrative evidence                         292
+
+
+  CHAPTER VII. _Examination of some Opinions opposed to
+  the preceding doctrines._
+
+  � 1. Doctrine of the Universal Postulate                          294
+
+    2. The test of inconceivability does not represent the
+       aggregate of past experience                                 296
+
+    3. --nor is implied in every process of thought                 299
+
+    4. Sir W. Hamilton's opinion on the Principles of
+       Contradiction and Excluded Middle                            306
+
+
+  BOOK III.
+
+  OF INDUCTION.
+
+
+  CHAPTER I. _Preliminary Observations on Induction in general._
+
+  � 1. Importance of an Inductive Logic                             313
+
+    2. The logic of science is also that of business and life       314
+
+
+  CHAPTER II. _Of Inductions improperly so called._
+
+  � 1. Inductions distinguished from verbal transformations         319
+
+    2. --from inductions, falsely so called, in mathematics         321
+
+    3. --and from descriptions                                      323
+
+    4. Examination of Dr. Whewell's theory of Induction             326
+
+    5. Further illustration of the preceding remarks                336
+
+
+  CHAPTER III. _On the Ground of Induction._
+
+  � 1. Axiom of the uniformity of the course of nature              341
+
+    2. Not true in every sense. Induction _per enumerationem
+       simplicem_                                                   346
+
+    3. The question of Inductive Logic stated                       348
+
+
+  CHAPTER IV. _Of Laws of Nature._
+
+  � 1. The general regularity in nature is a tissue of partial
+       regularities, called laws                                    351
+
+    2. Scientific induction must be grounded on previous
+       spontaneous inductions                                       355
+
+    3. Are there any inductions fitted to be a test of all others?  357
+
+
+  CHAPTER V. _Of the Law of Universal Causation._
+
+  � 1. The universal law of successive phenomena is the Law of
+       Causation                                                    360
+
+    2. --_i.e._ the law that every consequent has an invariable
+       antecedent                                                   363
+
+    3. The cause of a phenomenon is the assemblage of its
+       conditions                                                   365
+
+    4. The distinction of agent and patient illusory                373
+
+    5. The cause is not the invariable antecedent, but the
+       _unconditional_ invariable antecedent                        375
+
+    6. Can a cause be simultaneous with its effect?                 380
+
+    7. Idea of a Permanent Cause, or original natural agent         383
+
+    8. Uniformities of coexistence between effects of different
+       permanent causes, are not laws                               386
+
+    9. Doctrine that volition is an efficient cause, examined       387
+
+
+  CHAPTER VI. _Of the Composition of Causes._
+
+  � 1. Two modes of the conjunct action of causes, the mechanical
+       and the chemical                                             405
+
+    2. The composition of causes the general rule; the other case
+       exceptional                                                  408
+
+    3. Are effects proportional to their causes?                    412
+
+
+  CHAPTER VII. _Of Observation and Experiment._
+
+  � 1. The first step of inductive inquiry is a mental analysis of
+       complex phenomena into their elements                        414
+
+    2. The next is an actual separation of those elements           416
+
+    3. Advantages of experiment over observation                    417
+
+    4. Advantages of observation over experiment                    420
+
+
+  CHAPTER VIII. _Of the Four Methods of Experimental
+  Inquiry._
+
+  � 1. Method of Agreement                                          425
+
+    2. Method of Difference                                         428
+
+    3. Mutual relation of these two methods                         429
+
+    4. Joint Method of Agreement and Difference                     433
+
+    5. Method of Residues                                           436
+
+    6. Method of Concomitant Variations                             437
+
+    7. Limitations of this last method                              443
+
+
+  CHAPTER IX. _Miscellaneous Examples of the Four Methods._
+
+  � 1. Liebig's theory of metallic poisons                          449
+
+    2. Theory of induced electricity                                453
+
+    3. Dr. Wells' theory of dew                                     457
+
+    4. Dr. Brown-S�quard's theory of cadaveric rigidity             465
+
+    5. Examples of the Method of Residues                           471
+
+    6. Dr. Whewell's objections to the Four Methods                 475
+
+
+  CHAPTER X. _Of Plurality of Causes; and of the Intermixture
+  of Effects._
+
+  � 1. One effect may have several causes                           482
+
+    2. --which is the source of a characteristic imperfection of
+       the Method of Agreement                                      483
+
+    3. Plurality of Causes, how ascertained                         487
+
+    4. Concurrence of Causes which do not compound their effects    489
+
+    5. Difficulties of the investigation, when causes compound
+       their effects                                                494
+
+    6. Three modes of investigating the laws of complex effects     499
+
+    7. The method of simple observation inapplicable                500
+
+    8. The purely experimental method inapplicable                  501
+
+
+  CHAPTER XI. _Of the Deductive Method._
+
+  � 1. First stage; ascertainment of the laws of the separate
+       causes by direct induction                                   507
+
+    2. Second stage; ratiocination from the simple laws of the
+       complex cases                                                512
+
+    3. Third stage; verification by specific experience             514
+
+
+  CHAPTER XII. _Of the Explanation of Laws of Nature._
+
+  � 1. Explanation defined                                          518
+
+    2. First mode of explanation, by resolving the law of a complex
+       effect into the laws of the concurrent causes and
+       the fact of their coexistence                                518
+
+    3. Second mode; by the detection of an intermediate link in
+       the sequence                                                 519
+
+    4. Laws are always resolved into laws more general than
+       themselves                                                   520
+
+    5. Third mode; the subsumption of less general laws under
+       a more general one                                           524
+
+    6. What the explanation of a law of nature amounts to           526
+
+
+  CHAPTER XIII. _Miscellaneous Examples of the Explanation of
+  Laws of Nature._
+
+  � 1. The general theories of the sciences                         529
+
+    2. Examples from chemical speculations                          531
+
+    3. Example from Dr. Brown-S�quard's researches on the
+       nervous system                                               533
+
+    4. Examples of following newly-discovered laws into their
+       complex manifestations                                       534
+
+    5. Examples of empirical generalizations, afterwards confirmed
+       and explained deductively                                    536
+
+    6. Example from mental science                                  538
+
+    7. Tendency of all the sciences to become deductive             539
+
+
+
+
+INTRODUCTION.
+
+
+� 1. There is as great diversity among authors in the modes which they
+have adopted of defining logic, as in their treatment of the details of
+it. This is what might naturally be expected on any subject on which
+writers have availed themselves of the same language as a means of
+delivering different ideas. Ethics and jurisprudence are liable to the
+remark in common with logic. Almost every writer having taken a
+different view of some of the particulars which these branches of
+knowledge are usually understood to include; each has so framed his
+definition as to indicate beforehand his own peculiar tenets, and
+sometimes to beg the question in their favour.
+
+This diversity is not so much an evil to be complained of, as an
+inevitable and in some degree a proper result of the imperfect state of
+those sciences. It is not to be expected that there should be agreement
+about the definition of anything, until there is agreement about the
+thing itself. To define, is to select from among all the properties of a
+thing, those which shall be understood to be designated and declared by
+its name; and the properties must be well known to us before we can be
+competent to determine which of them are fittest to be chosen for this
+purpose. Accordingly, in the case of so complex an aggregation of
+particulars as are comprehended in anything which can be called a
+science, the definition we set out with is seldom that which a more
+extensive knowledge of the subject shows to be the most appropriate.
+Until we know the particulars themselves, we cannot fix upon the most
+correct and compact mode of circumscribing them by a general
+description. It was not until after an extensive and accurate
+acquaintance with the details of chemical phenomena, that it was found
+possible to frame a rational definition of chemistry; and the definition
+of the science of life and organization is still a matter of dispute. So
+long as the sciences are imperfect, the definitions must partake of
+their imperfection; and if the former are progressive, the latter ought
+to be so too. As much, therefore, as is to be expected from a definition
+placed at the commencement of a subject, is that it should define the
+scope of our inquiries: and the definition which I am about to offer of
+the science of logic, pretends to nothing more, than to be a statement
+of the question which I have put to myself, and which this book is an
+attempt to resolve. The reader is at liberty to object to it as a
+definition of logic; but it is at all events a correct definition of the
+subject of these volumes.
+
+
+� 2. Logic has often been called the Art of Reasoning. A writer[1] who
+has done more than any other person to restore this study to the rank
+from which it had fallen in the estimation of the cultivated class in
+our own country, has adopted the above definition with an amendment; he
+has defined Logic to be the Science, as well as the Art, of reasoning;
+meaning by the former term, the analysis of the mental process which
+takes place whenever we reason, and by the latter, the rules, grounded
+on that analysis, for conducting the process correctly. There can be no
+doubt as to the propriety of the emendation. A right understanding of
+the mental process itself, of the conditions it depends on, and the
+steps of which it consists, is the only basis on which a system of
+rules, fitted for the direction of the process, can possibly be founded.
+Art necessarily presupposes knowledge; art, in any but its infant state,
+presupposes scientific knowledge: and if every art does not bear the
+name of a science, it is only because several sciences are often
+necessary to form the groundwork of a single art. So complicated are the
+conditions which govern our practical agency, that to enable one thing
+to be _done_, it is often requisite to _know_ the nature and properties
+of many things.
+
+Logic, then, comprises the science of reasoning, as well as an art,
+founded on that science. But the word Reasoning, again, like most other
+scientific terms in popular use, abounds in ambiguities. In one of its
+acceptations, it means syllogizing; or the mode of inference which may
+be called (with sufficient accuracy for the present purpose) concluding
+from generals to particulars. In another of its senses, to reason is
+simply to infer any assertion, from assertions already admitted: and in
+this sense induction is as much entitled to be called reasoning as the
+demonstrations of geometry.
+
+Writers on logic have generally preferred the former acceptation of the
+term: the latter, and more extensive signification is that in which I
+mean to use it. I do this by virtue of the right I claim for every
+author, to give whatever provisional definition he pleases of his own
+subject. But sufficient reasons will, I believe, unfold themselves as we
+advance, why this should be not only the provisional but the final
+definition. It involves, at all events, no arbitrary change in the
+meaning of the word; for, with the general usage of the English
+language, the wider signification, I believe, accords better than the
+more restricted one.
+
+
+� 3. But Reasoning, even in the widest sense of which the word is
+susceptible, does not seem to comprehend all that is included, either in
+the best, or even in the most current, conception of the scope and
+province of our science. The employment of the word Logic to denote the
+theory of argumentation, is derived from the Aristotelian, or, as they
+are commonly termed, the scholastic, logicians. Yet even with them, in
+their systematic treatises, argumentation was the subject only of the
+third part: the two former treated of Terms, and of Propositions; under
+one or other of which heads were also included Definition and Division.
+By some, indeed, these previous topics were professedly introduced only
+on account of their connexion with reasoning, and as a preparation for
+the doctrine and rules of the syllogism. Yet they were treated with
+greater minuteness, and dwelt on at greater length, than was required
+for that purpose alone. More recent writers on logic have generally
+understood the term as it was employed by the able author of the Port
+Royal Logic; viz. as equivalent to the Art of Thinking. Nor is this
+acceptation confined to books, and scientific inquiries. Even in
+ordinary conversation, the ideas connected with the word Logic include
+at least precision of language, and accuracy of classification: and we
+perhaps oftener hear persons speak of a logical arrangement, or of
+expressions logically defined, than of conclusions logically deduced
+from premises. Again, a man is often called a great logician, or a man
+of powerful logic, not for the accuracy of his deductions, but for the
+extent of his command over premises; because the general propositions
+required for explaining a difficulty or refuting a sophism, copiously
+and promptly occur to him: because, in short, his knowledge, besides
+being ample, is well under his command for argumentative use. Whether,
+therefore, we conform to the practice of those who have made the subject
+their particular study, or to that of popular writers and common
+discourse, the province of logic will include several operations of the
+intellect not usually considered to fall within the meaning of the terms
+Reasoning and Argumentation.
+
+These various operations might be brought within the compass of the
+science, and the additional advantage be obtained of a very simple
+definition, if, by an extension of the term, sanctioned by high
+authorities, we were to define logic as the science which treats of the
+operations of the human understanding in the pursuit of truth. For to
+this ultimate end, naming, classification, definition, and all other
+operations over which logic has ever claimed jurisdiction, are
+essentially subsidiary. They may all be regarded as contrivances for
+enabling a person to know the truths which are needful to him, and to
+know them at the precise moment at which they are needful. Other
+purposes, indeed, are also served by these operations; for instance,
+that of imparting our knowledge to others. But, viewed with regard to
+this purpose, they have never been considered as within the province of
+the logician. The sole object of Logic is the guidance of one's own
+thoughts: the communication of those thoughts to others falls under the
+consideration of Rhetoric, in the large sense in which that art was
+conceived by the ancients; or of the still more extensive art of
+Education. Logic takes cognizance of our intellectual operations, only
+as they conduce to our own knowledge, and to our command over that
+knowledge for our own uses. If there were but one rational being in the
+universe, that being might be a perfect logician; and the science and
+art of logic would be the same for that one person as for the whole
+human race.
+
+
+� 4. But, if the definition which we formerly examined included too
+little, that which is now suggested has the opposite fault of including
+too much.
+
+Truths are known to us in two ways: some are known directly, and of
+themselves; some through the medium of other truths. The former are the
+subject of Intuition, or Consciousness;[2] the latter, of Inference. The
+truths known by intuition are the original premises from which all
+others are inferred. Our assent to the conclusion being grounded on the
+truth of the premises, we never could arrive at any knowledge by
+reasoning, unless something could be known antecedently to all
+reasoning.
+
+Examples of truths known to us by immediate consciousness, are our own
+bodily sensations and mental feelings. I know directly, and of my own
+knowledge, that I was vexed yesterday, or that I am hungry to-day.
+Examples of truths which we know only by way of inference, are
+occurrences which took place while we were absent, the events recorded
+in history, or the theorems of mathematics. The two former we infer from
+the testimony adduced, or from the traces of those past occurrences
+which still exist; the latter, from the premises laid down in books of
+geometry, under the title of definitions and axioms. Whatever we are
+capable of knowing must belong to the one class or to the other; must
+be in the number of the primitive data, or of the conclusions which can
+be drawn from these.
+
+With the original data, or ultimate premises of our knowledge; with
+their number or nature, the mode in which they are obtained, or the
+tests by which they may be distinguished; logic, in a direct way at
+least, has, in the sense in which I conceive the science, nothing to do.
+These questions are partly not a subject of science at all, partly that
+of a very different science.
+
+Whatever is known to us by consciousness, is known beyond possibility of
+question. What one sees or feels, whether bodily or mentally, one cannot
+but be sure that one sees or feels. No science is required for the
+purpose of establishing such truths; no rules of art can render our
+knowledge of them more certain than it is in itself. There is no logic
+for this portion of our knowledge.
+
+But we may fancy that we see or feel what we in reality infer. A truth,
+or supposed truth, which is really the result of a very rapid inference,
+may seem to be apprehended intuitively. It has long been agreed by
+thinkers of the most opposite schools, that this mistake is actually
+made in so familiar an instance as that of the eyesight. There is
+nothing of which we appear to ourselves to be more directly conscious,
+than the distance of an object from us. Yet it has long been
+ascertained, that what is perceived by the eye, is at most nothing more
+than a variously coloured surface; that when we fancy we see distance,
+all we really see is certain variations of apparent size, and degrees of
+faintness of colour; that our estimate of the object's distance from us
+is the result partly of a rapid inference from the muscular sensations
+accompanying the adjustment of the focal distance of the eye to objects
+unequally remote from us, and partly of a comparison (made with so much
+rapidity that we are unconscious of making it) between the size and
+colour of the object as they appear at the time, and the size and colour
+of the same or of similar objects as they appeared when close at hand,
+or when their degree of remoteness was known by other evidence. The
+perception of distance by the eye, which seems so like intuition, is
+thus, in reality, an inference grounded on experience; an inference,
+too, which we learn to make; and which we make with more and more
+correctness as our experience increases; though in familiar cases it
+takes place so rapidly as to appear exactly on a par with those
+perceptions of sight which are really intuitive, our perceptions of
+colour.[3]
+
+Of the science, therefore, which expounds the operations of the human
+understanding in the pursuit of truth, one essential part is the
+inquiry: What are the facts which are the objects of intuition or
+consciousness, and what are those which we merely infer? But this
+inquiry has never been considered a portion of logic. Its place is in
+another and a perfectly distinct department of science, to which the
+name metaphysics more particularly belongs: that portion of mental
+philosophy which attempts to determine what part of the furniture of the
+mind belongs to it originally, and what part is constructed out of
+materials furnished to it from without. To this science appertain the
+great and much debated questions of the existence of matter; the
+existence of spirit, and of a distinction between it and matter; the
+reality of time and space, as things without the mind, and
+distinguishable from the objects which are said to exist in them. For in
+the present state of the discussion on these topics, it is almost
+universally allowed that the existence of matter or of spirit, of space
+or of time, is in its nature unsusceptible of being proved; and that if
+anything is known of them, it must be by immediate intuition. To the
+same science belong the inquiries into the nature of Conception,
+Perception, Memory, and Belief; all of which are operations of the
+understanding in the pursuit of truth; but with which, as phenomena of
+the mind, or with the possibility which may or may not exist of
+analysing any of them into simpler phenomena, the logician as such has
+no concern. To this science must also be referred the following, and all
+analogous questions: To what extent our intellectual faculties and our
+emotions are innate--to what extent the result of association: Whether
+God, and duty, are realities, the existence of which is manifest to us
+_� priori_ by the constitution of our rational faculty; or whether our
+ideas of them are acquired notions, the origin of which we are able to
+trace and explain; and the reality of the objects themselves a question
+not of consciousness or intuition, but of evidence and reasoning.
+
+The province of logic must be restricted to that portion of our
+knowledge which consists of inferences from truths previously known;
+whether those antecedent data be general propositions, or particular
+observations and perceptions. Logic is not the science of Belief, but
+the science of Proof, or Evidence. In so far as belief professes to be
+founded on proof, the office of logic is to supply a test for
+ascertaining whether or not the belief is well grounded. With the claims
+which any proposition has to belief on the evidence of consciousness,
+that is, without evidence in the proper sense of the word, logic has
+nothing to do.
+
+
+� 5. By far the greatest portion of our knowledge, whether of general
+truths or of particular facts, being avowedly matter of inference,
+nearly the whole, not only of science, but of human conduct, is amenable
+to the authority of logic. To draw inferences has been said to be the
+great business of life. Every one has daily, hourly, and momentary need
+of ascertaining facts which he has not directly observed; not from any
+general purpose of adding to his stock of knowledge, but because the
+facts themselves are of importance to his interests or to his
+occupations. The business of the magistrate, of the military commander,
+of the navigator, of the physician, of the agriculturist, is merely to
+judge of evidence, and to act accordingly. They all have to ascertain
+certain facts, in order that they may afterwards apply certain rules,
+either devised by themselves, or prescribed for their guidance by
+others; and as they do this well or ill, so they discharge well or ill
+the duties of their several callings. It is the only occupation in
+which the mind never ceases to be engaged; and is the subject, not of
+logic, but of knowledge in general.
+
+Logic, however, is not the same thing with knowledge, though the field
+of logic is coextensive with the field of knowledge. Logic is the common
+judge and arbiter of all particular investigations. It does not
+undertake to find evidence, but to determine whether it has been found.
+Logic neither observes, nor invents, nor discovers; but judges. It is no
+part of the business of logic to inform the surgeon what appearances are
+found to accompany a violent death. This he must learn from his own
+experience and observation, or from that of others, his predecessors in
+his peculiar pursuit. But logic sits in judgment on the sufficiency of
+that observation and experience to justify his rules, and on the
+sufficiency of his rules to justify his conduct. It does not give him
+proofs, but teaches him what makes them proofs, and how he is to judge
+of them. It does not teach that any particular fact proves any other,
+but points out to what conditions all facts must conform, in order that
+they may prove other facts. To decide whether any given fact fulfils
+these conditions, or whether facts can be found which fulfil them in a
+given case, belongs exclusively to the particular art or science, or to
+our knowledge of the particular subject.
+
+It is in this sense that logic is, what Bacon so expressively called it,
+_ars artium_; the science of science itself. All science consists of
+data and conclusions from those data, of proofs and what they prove: now
+logic points out what relations must subsist between data and whatever
+can be concluded from them, between proof and everything which it can
+prove. If there be any such indispensable relations, and if these can be
+precisely determined, every particular branch of science, as well as
+every individual in the guidance of his conduct, is bound to conform to
+those relations, under the penalty of making false inferences, of
+drawing conclusions which are not grounded in the realities of things.
+Whatever has at any time been concluded justly, whatever knowledge has
+been acquired otherwise than by immediate intuition, depended on the
+observance of the laws which it is the province of logic to investigate.
+If the conclusions are just, and the knowledge real, those laws, whether
+known or not, have been observed.
+
+
+� 6. We need not, therefore, seek any farther for a solution of the
+question, so often agitated, respecting the utility of logic. If a
+science of logic exists, or is capable of existing, it must be useful.
+If there be rules to which every mind consciously or unconsciously
+conforms in every instance in which it infers rightly, there seems
+little necessity for discussing whether a person is more likely to
+observe those rules, when he knows the rules, than when he is
+unacquainted with them.
+
+A science may undoubtedly be brought to a certain, not inconsiderable,
+stage of advancement, without the application of any other logic to it
+than what all persons, who are said to have a sound understanding,
+acquire empirically in the course of their studies. Mankind judged of
+evidence, and often correctly, before logic was a science, or they never
+could have made it one. And they executed great mechanical works before
+they understood the laws of mechanics. But there are limits both to what
+mechanicians can do without principles of mechanics, and to what
+thinkers can do without principles of logic. A few individuals, by
+extraordinary genius, or by the accidental acquisition of a good set of
+intellectual habits, may work without principles in the same way, or
+nearly the same way, in which they would have worked if they had been in
+possession of principles. But the bulk of mankind require either to
+understand the theory of what they are doing, or to have rules laid down
+for them by those who have understood the theory. In the progress of
+science from its easiest to its more difficult problems, each great step
+in advance has usually had either as its precursor, or as its
+accompaniment and necessary condition, a corresponding improvement in
+the notions and principles of logic received among the most advanced
+thinkers. And if several of the more difficult sciences are still in so
+defective a state; if not only so little is proved, but disputation has
+not terminated even about the little which seemed to be so; the reason
+perhaps is, that men's logical notions have not yet acquired the degree
+of extension, or of accuracy, requisite for the estimation of the
+evidence proper to those particular departments of knowledge.
+
+
+� 7. Logic, then, is the science of the operations of the understanding
+which are subservient to the estimation of evidence: both the process
+itself of advancing from known truths to unknown, and all other
+intellectual operations in so far as auxiliary to this. It includes,
+therefore, the operation of Naming; for language is an instrument of
+thought, as well as a means of communicating our thoughts. It includes,
+also, Definition, and Classification. For, the use of these operations
+(putting all other minds than one's own out of consideration) is to
+serve not only for keeping our evidences and the conclusions from them
+permanent and readily accessible in the memory, but for so marshalling
+the facts which we may at any time be engaged in investigating, as to
+enable us to perceive more clearly what evidence there is, and to judge
+with fewer chances of error whether it be sufficient. These, therefore,
+are operations specially instrumental to the estimation of evidence,
+and, as such, are within the province of Logic. There are other more
+elementary processes, concerned in all thinking, such as Conception,
+Memory, and the like; but of these it is not necessary that Logic should
+take any peculiar cognizance, since they have no special connexion with
+the problem of Evidence, further than that, like all other problems
+addressed to the understanding, it presupposes them.
+
+Our object, then, will be, to attempt a correct analysis of the
+intellectual process called Reasoning or Inference, and of such other
+mental operations as are intended to facilitate this; as well as, on the
+foundation of this analysis, and _pari passu_ with it, to bring together
+or frame a set of rules or canons for testing the sufficiency of any
+given evidence to prove any given proposition.
+
+With respect to the first part of this undertaking, I do not attempt to
+decompose the mental operations in question into their ultimate
+elements. It is enough if the analysis as far as it goes is correct,
+and if it goes far enough for the practical purposes of logic considered
+as an art. The separation of a complicated phenomenon into its component
+parts is not like a connected and interdependent chain of proof. If one
+link of an argument breaks, the whole drops to the ground; but one step
+towards an analysis holds good and has an independent value, though we
+should never be able to make a second. The results which have been
+obtained by analytical chemistry are not the less valuable, though it
+should be discovered that all which we now call simple substances are
+really compounds. All other things are at any rate compounded of those
+elements: whether the elements themselves admit of decomposition, is an
+important inquiry, but does not affect the certainty of the science up
+to that point.
+
+I shall, accordingly, attempt to analyse the process of inference, and
+the processes subordinate to inference, so far only as may be requisite
+for ascertaining the difference between a correct and an incorrect
+performance of those processes. The reason for thus limiting our design,
+is evident. It has been said by objectors to logic, that we do not learn
+to use our muscles by studying their anatomy. The fact is not quite
+fairly stated; for if the action of any of our muscles were vitiated by
+local weakness, or other physical defect, a knowledge of their anatomy
+might be very necessary for effecting a cure. But we should be justly
+liable to the criticism involved in this objection, were we, in a
+treatise on logic, to carry the analysis of the reasoning process beyond
+the point at which any inaccuracy which may have crept into it must
+become visible. In learning bodily exercises (to carry on the same
+illustration) we do, and must, analyse the bodily motions so far as is
+necessary for distinguishing those which ought to be performed from
+those which ought not. To a similar extent, and no further, it is
+necessary that the logician should analyse the mental processes with
+which Logic is concerned. Logic has no interest in carrying the analysis
+beyond the point at which it becomes apparent whether the operations
+have in any individual case been rightly or wrongly performed: in the
+same manner as the science of music teaches us to discriminate between
+musical notes, and to know the combinations of which they are
+susceptible, but not what number of vibrations in a second correspond to
+each; which, though useful to be known, is useful for totally different
+purposes. The extension of Logic as a Science is determined by its
+necessities as an Art: whatever it does not need for its practical ends,
+it leaves to the larger science which may be said to correspond, not to
+any particular art, but to art in general; the science which deals with
+the constitution of the human faculties; and to which, in the part of
+our mental nature which concerns Logic, as well as in all other parts,
+it belongs to decide what are ultimate facts, and what are resolvable
+into other facts. And I believe it will be found that most of the
+conclusions arrived at in this work have no necessary connexion with any
+particular views respecting the ulterior analysis. Logic is common
+ground on which the partisans of Hartley and of Reid, of Locke and of
+Kant, may meet and join hands. Particular and detached opinions of all
+these thinkers will no doubt occasionally be controverted, since all of
+them were logicians as well as metaphysicians; but the field on which
+their principal battles have been fought, lies beyond the boundaries of
+our science.
+
+It cannot, indeed, be pretended that logical principles can be
+altogether irrelevant to those more abstruse discussions; nor is it
+possible but that the view we are led to take of the problem which logic
+proposes, must have a tendency favourable to the adoption of some one
+opinion, on these controverted subjects, rather than another. For
+metaphysics, in endeavouring to solve its own peculiar problem, must
+employ means, the validity of which falls under the cognizance of logic.
+It proceeds, no doubt, as far as possible, merely by a closer and more
+attentive interrogation of our consciousness, or more properly speaking,
+of our memory; and so far is not amenable to logic. But wherever this
+method is insufficient to attain the end of its inquiries, it must
+proceed, like other sciences, by means of evidence. Now, the moment this
+science begins to draw inferences from evidence, logic becomes the
+sovereign judge whether its inferences are well grounded, or what other
+inferences would be so.
+
+This, however, constitutes no nearer or other relation between logic
+and metaphysics, than that which exists between logic and every other
+science. And I can conscientiously affirm, that no one proposition laid
+down in this work has been adopted for the sake of establishing, or with
+any reference to its fitness for being employed in establishing,
+preconceived opinions in any department of knowledge or of inquiry on
+which the speculative world is still undecided.[4]
+
+FOOTNOTES:
+
+[1] Archbishop Whately.
+
+[2] I use these terms indiscriminately, because, for the purpose in
+view, there is no need for making any distinction between them. But
+metaphysicians usually restrict the name Intuition to the direct
+knowledge we are supposed to have of things external to our minds, and
+Consciousness to our knowledge of our own mental phenomena.
+
+[3] This important theory has of late been called in question by a
+writer of deserved reputation, Mr. Samuel Bailey; but I do not conceive
+that the grounds on which it has been admitted as an established
+doctrine for a century past, have been at all shaken by that gentleman's
+objections. I have elsewhere said what appeared to me necessary in reply
+to his arguments. (_Westminster Review_ for October 1842; reprinted in
+_Dissertations and Discussions_, vol. ii.)
+
+[4] The view taken in the text, of the definition and purpose of Logic,
+stands in marked opposition to that of the school of philosophy which,
+in this country, is represented by the writings of Sir William Hamilton
+and of his numerous pupils. Logic, as this school conceives it, is "the
+Science of the Formal Laws of Thought;" a definition framed for the
+express purpose of excluding, as irrelevant to Logic, whatever relates
+to Belief and Disbelief, or to the pursuit of truth as such, and
+restricting the science to that very limited portion of its total
+province, which has reference to the conditions, not of Truth, but of
+Consistency. What I have thought it useful to say in opposition to this
+limitation of the field of Logic, has been said at some length in a
+separate work, first published in 1865, and entitled _An Examination of
+Sir William Hamilton's Philosophy, and of the Principal Philosophical
+Questions discussed in his Writings_. For the purposes of the present
+Treatise, I am content that the justification of the larger extension
+which I give to the domain of the science, should rest on the sequel of
+the Treatise itself. Some remarks on the relation which the Logic of
+Consistency bears to the Logic of Truth, and on the place which that
+particular part occupies in the whole to which it belongs, will be found
+in the present volume (Book II. chap. iii. � 9).
+
+
+
+
+BOOK I.
+
+OF NAMES AND PROPOSITIONS.
+
+
+'La scolastique, qui produisit dans la logique, comme dans la morale,
+et dans une partie de la m�taphysique, une subtilit�, une pr�cision
+d'id�es, dont l'habitude inconnue aux anciens, a contribu� plus qu'on ne
+croit au progr�s de la bonne philosophie.'--CONDORCET, _Vie de Turgot_.
+
+'To the schoolmen the vulgar languages are principally indebted for what
+precision and analytic subtlety they possess.'--SIR W. HAMILTON,
+_Discussions in Philosophy_.
+
+
+
+
+CHAPTER I.
+
+OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.
+
+
+� 1. It is so much the established practice of writers on logic to
+commence their treatises by a few general observations (in most cases,
+it is true, rather meagre) on Terms and their varieties, that it will,
+perhaps, scarcely be required from me in merely following the common
+usage, to be as particular in assigning my reasons, as it is usually
+expected that those should be who deviate from it.
+
+The practice, indeed, is recommended by considerations far too obvious
+to require a formal justification. Logic is a portion of the Art of
+Thinking: Language is evidently, and by the admission of all
+philosophers, one of the principal instruments or helps of thought; and
+any imperfection in the instrument, or in the mode of employing it, is
+confessedly liable, still more than in almost any other art, to confuse
+and impede the process, and destroy all ground of confidence in the
+result. For a mind not previously versed in the meaning and right use of
+the various kinds of words, to attempt the study of methods of
+philosophizing, would be as if some one should attempt to become an
+astronomical observer, having never learned to adjust the focal distance
+of his optical instruments so as to see distinctly.
+
+Since Reasoning, or Inference, the principal subject of logic, is an
+operation which usually takes place by means of words, and in
+complicated cases can take place in no other way; those who have not a
+thorough insight into the signification and purposes of words, will be
+under chances, amounting almost to certainty, of reasoning or inferring
+incorrectly. And logicians have generally felt that unless, in the very
+first stage, they removed this source of error; unless they taught their
+pupil to put away the glasses which distort the object, and to use
+those which are adapted to his purpose in such a manner as to assist,
+not perplex, his vision; he would not be in a condition to practise the
+remaining part of their discipline with any prospect of advantage.
+Therefore it is that an inquiry into language, so far as is needful to
+guard against the errors to which it gives rise, has at all times been
+deemed a necessary preliminary to the study of logic.
+
+But there is another reason, of a still more fundamental nature, why the
+import of words should be the earliest subject of the logician's
+consideration: because without it he cannot examine into the import of
+Propositions. Now this is a subject which stands on the very threshold
+of the science of logic.
+
+The object of logic, as defined in the Introductory Chapter, is to
+ascertain how we come by that portion of our knowledge (much the
+greatest portion) which is not intuitive: and by what criterion we can,
+in matters not self-evident, distinguish between things proved and
+things not proved, between what is worthy and what is unworthy of
+belief. Of the various questions which present themselves to our
+inquiring faculties, some receive an answer from direct consciousness,
+others, if resolved at all, can only be resolved by means of evidence.
+Logic is concerned with these last. But before inquiring into the mode
+of resolving questions, it is necessary to inquire what are those which
+offer themselves; what questions are conceivable; what inquiries are
+there, to which mankind have either obtained, or been able to imagine it
+possible that they should obtain, an answer. This point is best
+ascertained by a survey and analysis of Propositions.
+
+
+� 2. The answer to every question which it is possible to frame, must be
+contained in a Proposition, or Assertion. Whatever can be an object of
+belief, or even of disbelief, must, when put into words, assume the form
+of a proposition. All truth and all error lie in propositions. What, by
+a convenient misapplication of an abstract term, we call a Truth, means
+simply a True Proposition; and errors are false propositions. To know
+the import of all possible propositions, would be to know all questions
+which can be raised, all matters which are susceptible of being either
+believed or disbelieved. How many kinds of inquiries can be propounded;
+how many kinds of judgments can be made; and how many kinds of
+propositions it is possible to frame with a meaning; are but different
+forms of one and the same question. Since, then, the objects of all
+Belief and of all Inquiry express themselves in propositions; a
+sufficient scrutiny of Propositions and of their varieties will apprize
+us what questions mankind have actually asked of themselves, and what,
+in the nature of answers to those questions, they have actually thought
+they had grounds to believe.
+
+Now the first glance at a proposition shows that it is formed by putting
+together two names. A proposition, according to the common simple
+definition, which is sufficient for our purpose, is, _discourse, in
+which something is affirmed or denied of something_. Thus, in the
+proposition, Gold is yellow, the quality _yellow_ is affirmed of the
+substance _gold_. In the proposition, Franklin was not born in England,
+the fact expressed by the words _born in England_ is denied of the man
+Franklin.
+
+Every proposition consists of three parts: the Subject, the Predicate,
+and the Copula. The predicate is the name denoting that which is
+affirmed or denied. The subject is the name denoting the person or thing
+which something is affirmed or denied of. The copula is the sign
+denoting that there is an affirmation or denial; and thereby enabling
+the hearer or reader to distinguish a proposition from any other kind of
+discourse. Thus, in the proposition, The earth is round, the Predicate
+is the word _round_, which denotes the quality affirmed, or (as the
+phrase is) predicated: _the earth_, words denoting the object which that
+quality is affirmed of, compose the Subject; the word _is_, which serves
+as the connecting mark between the subject and predicate, to show that
+one of them is affirmed of the other, is called the Copula.
+
+Dismissing, for the present, the copula, of which more will be said
+hereafter, every proposition, then, consists of at least two names;
+brings together two names, in a particular manner. This is already a
+first step towards what we are in quest of. It appears from this, that
+for an act of belief, _one_ object is not sufficient; the simplest act
+of belief supposes, and has something to do with, _two_ objects: two
+names, to say the least; and (since the names must be names of
+something) two _nameable things_. A large class of thinkers would cut
+the matter short by saying, two _ideas_. They would say, that the
+subject and predicate are both of them names of ideas; the idea of gold,
+for instance, and the idea of yellow; and that what takes place (or part
+of what takes place) in the act of belief, consists in bringing (as it
+is often expressed) one of these ideas under the other. But this we are
+not yet in a condition to say: whether such be the correct mode of
+describing the phenomenon, is an after consideration. The result with
+which for the present we must be contented, is, that in every act of
+belief _two_ objects are in some manner taken cognizance of; that there
+can be no belief claimed, or question propounded, which does not embrace
+two distinct (either material or intellectual) subjects of thought; each
+of them capable, or not, of being conceived by itself, but incapable of
+being believed by itself.
+
+I may say, for instance, "the sun." The word has a meaning, and suggests
+that meaning to the mind of any one who is listening to me. But suppose
+I ask him, Whether it is true: whether he believes it? He can give no
+answer. There is as yet nothing to believe, or to disbelieve. Now,
+however, let me make, of all possible assertions respecting the sun, the
+one which involves the least of reference to any object besides itself;
+let me say, "the sun exists." Here, at once, is something which a person
+can say he believes. But here, instead of only one, we find two distinct
+objects of conception: the sun is one object; existence is another. Let
+it not be said that this second conception, existence, is involved in
+the first; for the sun may be conceived as no longer existing. "The sun"
+does not convey all the meaning that is conveyed by "the sun exists:"
+"my father" does not include all the meaning of "my father exists," for
+he may be dead; "a round square" does not include the meaning of "a
+round square exists," for it does not and cannot exist. When I say "the
+sun," "my father," or a "round square," I do not call upon the hearer
+for any belief or disbelief, nor can either the one or the other be
+afforded me; but if I say, "the sun exists," "my father exists," or "a
+round square exists," I call for belief; and should, in the first of the
+three instances, meet with it; in the second, with belief or disbelief,
+as the case might be; in the third, with disbelief.
+
+
+� 3. This first step in the analysis of the object of belief, which,
+though so obvious, will be found to be not unimportant, is the only one
+which we shall find it practicable to make without a preliminary survey
+of language. If we attempt to proceed further in the same path, that is,
+to analyse any further the import of Propositions; we find forced upon
+us, as a subject of previous consideration, the import of Names. For
+every proposition consists of two names; and every proposition affirms
+or denies one of these names, of the other. Now what we do, what passes
+in our mind, when we affirm or deny two names of one another, must
+depend on what they are names of; since it is with reference to that,
+and not to the mere names themselves, that we make the affirmation or
+denial. Here, therefore, we find a new reason why the signification of
+names, and the relation generally between names and the things signified
+by them, must occupy the preliminary stage of the inquiry we are engaged
+in.
+
+It may be objected that the meaning of names can guide us at most only
+to the opinions, possibly the foolish and groundless opinions, which
+mankind have formed concerning things, and that as the object of
+philosophy is truth, not opinion, the philosopher should dismiss words
+and look into things themselves, to ascertain what questions can be
+asked and answered in regard to them. This advice (which no one has it
+in his power to follow) is in reality an exhortation to discard the
+whole fruits of the labours of his predecessors, and conduct himself as
+if he were the first person who had ever turned an inquiring eye upon
+nature. What does any one's personal knowledge of Things amount to,
+after subtracting all which he has acquired by means of the words of
+other people? Even after he has learned as much as people usually do
+learn from others, will the notions of things contained in his
+individual mind afford as sufficient a basis for a _catalogue raisonn�_
+as the notions which are in the minds of all mankind?
+
+In any enumeration and classification of Things, which does not set out
+from their names, no varieties of things will of course be comprehended
+but those recognised by the particular inquirer; and it will still
+remain to be established, by a subsequent examination of names, that the
+enumeration has omitted nothing which ought to have been included. But
+if we begin with names, and use them as our clue to the things, we bring
+at once before us all the distinctions which have been recognised, not
+by a single inquirer, but by all inquirers taken together. It doubtless
+may, and I believe it will, be found, that mankind have multiplied the
+varieties unnecessarily, and have imagined distinctions among things,
+where there were only distinctions in the manner of naming them. But we
+are not entitled to assume this in the commencement. We must begin by
+recognising the distinctions made by ordinary language. If some of these
+appear, on a close examination, not to be fundamental, the enumeration
+of the different kinds of realities may be abridged accordingly. But to
+impose upon the facts in the first instance the yoke of a theory, while
+the grounds of the theory are reserved for discussion in a subsequent
+stage, is not a course which a logician can reasonably adopt.
+
+
+
+
+CHAPTER II.
+
+OF NAMES.
+
+
+� 1. "A name," says Hobbes,[1] "is a word taken at pleasure to serve for
+a mark which may raise in our mind a thought like to some thought we had
+before, and which being pronounced to others, may be to them a sign of
+what thought the speaker had[2] before in his mind." This simple
+definition of a name, as a word (or set of words) serving the double
+purpose of a mark to recall to ourselves the likeness of a former
+thought, and a sign to make it known to others, appears unexceptionable.
+Names, indeed, do much more than this; but whatever else they do, grows
+out of, and is the result of this: as will appear in its proper place.
+
+Are names more properly said to be the names of things, or of our ideas
+of things? The first is the expression in common use; the last is that
+of some metaphysicians, who conceived that in adopting it they were
+introducing a highly important distinction. The eminent thinker, just
+quoted, seems to countenance the latter opinion. "But seeing," he
+continues, "names ordered in speech (as is defined) are signs of our
+conceptions, it is manifest they are not signs of the things themselves;
+for that the sound of this word _stone_ should be the sign of a stone,
+cannot be understood in any sense but this, that he that hears it
+collects that he that pronounces it thinks of a stone."
+
+If it be merely meant that the conception alone, and not the thing
+itself, is recalled by the name, or imparted to the hearer, this of
+course cannot be denied. Nevertheless, there seems good reason for
+adhering to the common usage, and calling the word _sun_ the name of
+the sun, and not the name of our idea of the sun. For names are not
+intended only to make the hearer conceive what we conceive, but also to
+inform him what we believe. Now, when I use a name for the purpose of
+expressing a belief, it is a belief concerning the thing itself, not
+concerning my idea of it. When I say, "the sun is the cause of day," I
+do not mean that my idea of the sun causes or excites in me the idea of
+day; or in other words, that thinking of the sun makes me think of day.
+I mean, that a certain physical fact, which is called the sun's presence
+(and which, in the ultimate analysis, resolves itself into sensations,
+not ideas) causes another physical fact, which is called day. It seems
+proper to consider a word as the _name_ of that which we intend to be
+understood by it when we use it; of that which any fact that we assert
+of it is to be understood of; that, in short, concerning which, when we
+employ the word, we intend to give information. Names, therefore, shall
+always be spoken of in this work as the names of things themselves, and
+not merely of our ideas of things.
+
+But the question now arises, of what things? and to answer this it is
+necessary to take into consideration the different kinds of names.
+
+
+� 2. It is usual, before examining the various classes into which names
+are commonly divided, to begin by distinguishing from names of every
+description, those words which are not names, but only parts of names.
+Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
+inflected cases of nouns substantive, as _me_, _him_, _John's_; and even
+adjectives, as _large_, _heavy_. These words do not express things of
+which anything can be affirmed or denied. We cannot say, Heavy fell, or
+A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
+room. Unless, indeed, we are speaking of the mere words themselves, as
+when we say, Truly is an English word, or, Heavy is an adjective. In
+that case they are complete names, viz. names of those particular
+sounds, or of those particular collections of written characters. This
+employment of a word to denote the mere letters and syllables of which
+it is composed, was termed by the schoolmen the _suppositio materialis_
+of the word. In any other sense we cannot introduce one of these words
+into the subject of a proposition, unless in combination with other
+words; as, A heavy _body_ fell, A truly _important fact_ was asserted, A
+_member_ of _parliament_ was in the room.
+
+An adjective, however, is capable of standing by itself as the predicate
+of a proposition; as when we say, Snow is white; and occasionally even
+as the subject, for we may say, White is an agreeable colour. The
+adjective is often said to be so used by a grammatical ellipsis: Snow is
+white, instead of Snow is a white object; White is an agreeable colour,
+instead of, A white colour, or, The colour white, is agreeable. The
+Greeks and Romans were allowed, by the rules of their language, to
+employ this ellipsis universally in the subject as well as in the
+predicate of a proposition. In English this cannot, generally speaking,
+be done. We may say, The earth is round; but we cannot say, Round is
+easily moved; we must say, A round object. This distinction, however, is
+rather grammatical than logical. Since there is no difference of meaning
+between _round_, and _a round object_, it is only custom which
+prescribes that on any given occasion one shall be used, and not the
+other. We shall, therefore, without scruple, speak of adjectives as
+names, whether in their own right, or as representative of the more
+circuitous forms of expression above exemplified. The other classes of
+subsidiary words have no title whatever to be considered as names. An
+adverb, or an accusative case, cannot under any circumstances (except
+when their mere letters and syllables are spoken of) figure as one of
+the terms of a proposition.
+
+Words which are not capable of being used as names, but only as parts of
+names, were called by some of the schoolmen Syncategorematic terms: from
+[Greek: syn], with, and [Greek: kat�gore�], to predicate, because it was
+only _with_ some other word that they could be predicated. A word which
+could be used either as the subject or predicate of a proposition
+without being accompanied by any other word, was termed by the same
+authorities a Categorematic term. A combination of one or more
+Categorematic, and one or more Syncategorematic words, as A heavy body,
+or A court of justice, they sometimes called a _mixed_ term; but this
+seems a needless multiplication of technical expressions. A mixed term
+is, in the only useful sense of the word, Categorematic. It belongs to
+the class of what have been called many-worded names.
+
+For, as one word is frequently not a name, but only part of a name, so a
+number of words often compose one single name, and no more. These words,
+"the place which the wisdom or policy of antiquity had destined for the
+residence of the Abyssinian princes," form in the estimation of the
+logician only one name; one Categorematic term. A mode of determining
+whether any set of words makes only one name, or more than one, is by
+predicating something of it, and observing whether, by this predication,
+we make only one assertion or several. Thus, when we say, John Nokes,
+who was the mayor of the town, died yesterday--by this predication we
+make but one assertion; whence it appears that "John Nokes, who was the
+mayor of the town," is no more than one name. It is true that in this
+proposition, besides the assertion that John Nokes died yesterday, there
+is included another assertion, namely, that John Nokes was mayor of the
+town. But this last assertion was already made: we did not make it by
+adding the predicate, "died yesterday." Suppose, however, that the words
+had been, John Nokes _and_ the mayor of the town, they would have formed
+two names instead of one. For when we say, John Nokes and the mayor of
+the town died yesterday, we make two assertions; one, that John Nokes
+died yesterday; the other, that the mayor of the town died yesterday.
+
+It being needless to illustrate at any greater length the subject of
+many-worded names, we proceed to the distinctions which have been
+established among names, not according to the words they are composed
+of, but according to their signification.
+
+
+� 3. All names are names of something, real or imaginary; but all things
+have not names appropriated to them individually. For some individual
+objects we require, and consequently have, separate distinguishing
+names; there is a name for every person, and for every remarkable place.
+Other objects, of which we have not occasion to speak so frequently, we
+do not designate by a name of their own; but when the necessity arises
+for naming them, we do so by putting together several words, each of
+which, by itself, might be and is used for an indefinite number of other
+objects; as when I say, _this stone_: "this" and "stone" being, each of
+them, names that may be used of many other objects besides the
+particular one meant, though the only object of which they can both be
+used at the given moment, consistently with their signification, may be
+the one of which I wish to speak.
+
+Were this the sole purpose for which names, that are common to more
+things than one, could be employed; if they only served, by mutually
+limiting each other, to afford a designation for such individual objects
+as have no names of their own; they could only be ranked among
+contrivances for economizing the use of language. But it is evident that
+this is not their sole function. It is by their means that we are
+enabled to assert _general_ propositions; to affirm or deny any
+predicate of an indefinite number of things at once. The distinction,
+therefore, between _general_ names, and _individual_ or _singular_
+names, is fundamental; and may be considered as the first grand division
+of names.
+
+A general name is familiarly defined, a name which is capable of being
+truly affirmed, in the same sense, of each of an indefinite number of
+things. An individual or singular name is a name which is only capable
+of being truly affirmed, in the same sense, of one thing.
+
+Thus, _man_ is capable of being truly affirmed of John, George, Mary,
+and other persons without assignable limit; and it is affirmed of all of
+them in the same sense; for the word man expresses certain qualities,
+and when we predicate it of those persons, we assert that they all
+possess those qualities. But _John_ is only capable of being truly
+affirmed of one single person, at least in the same sense. For though
+there are many persons who bear that name, it is not conferred upon
+them to indicate any qualities, or anything which belongs to them in
+common; and cannot be said to be affirmed of them in any _sense_ at all,
+consequently not in the same sense. "The king who succeeded William the
+Conqueror," is also an individual name. For, that there cannot be more
+than one person of whom it can be truly affirmed, is implied in the
+meaning of the words. Even "_the_ king," when the occasion or the
+context defines the individual of whom it is to be understood, may
+justly be regarded as an individual name.
+
+It is not unusual, by way of explaining what is meant by a general name,
+to say that it is the name of a _class_. But this, though a convenient
+mode of expression for some purposes, is objectionable as a definition,
+since it explains the clearer of two things by the more obscure. It
+would be more logical to reverse the proposition, and turn it into a
+definition of the word _class_: "A class is the indefinite multitude of
+individuals denoted by a general name."
+
+It is necessary to distinguish _general_ from _collective_ names. A
+general name is one which can be predicated of _each_ individual of a
+multitude; a collective name cannot be predicated of each separately,
+but only of all taken together. "The 76th regiment of foot in the
+British army," which is a collective name, is not a general but an
+individual name; for though it can be predicated of a multitude of
+individual soldiers taken jointly, it cannot be predicated of them
+severally. We may say, Jones is a soldier, and Thompson is a soldier,
+and Smith is a soldier, but we cannot say, Jones is the 76th regiment,
+and Thompson is the 76th regiment, and Smith is the 76th regiment. We
+can only say, Jones, and Thompson, and Smith, and Brown, and so forth
+(enumerating all the soldiers), are the 76th regiment.
+
+"The 76th regiment" is a collective name, but not a general one: "a
+regiment" is both a collective and a general name. General with respect
+to all individual regiments, of each of which separately it can be
+affirmed; collective with respect to the individual soldiers of whom any
+regiment is composed.
+
+
+� 4. The second general division of names is into _concrete_ and
+_abstract_. A concrete name is a name which stands for a thing; an
+abstract name is a name which stands for an attribute of a thing. Thus
+_John_, _the sea_, _this table_, are names of things. _White_, also, is
+a name of a thing, or rather of things. Whiteness, again, is the name of
+a quality or attribute of those things. Man is a name of many things;
+humanity is a name of an attribute of those things. _Old_ is a name of
+things; _old age_ is a name of one of their attributes.
+
+I have used the words concrete and abstract in the sense annexed to them
+by the schoolmen, who, notwithstanding the imperfections of their
+philosophy, were unrivalled in the construction of technical language,
+and whose definitions, in logic at least, though they never went more
+than a little way into the subject, have seldom, I think, been altered
+but to be spoiled. A practice, however, has grown up in more modern
+times, which, if not introduced by Locke, has gained currency chiefly
+from his example, of applying the expression "abstract name" to all
+names which are the result of abstraction or generalization, and
+consequently to all general names, instead of confining it to the names
+of attributes. The metaphysicians of the Condillac school,--whose
+admiration of Locke, passing over the profoundest speculations of that
+truly original genius, usually fastens with peculiar eagerness upon his
+weakest points,--have gone on imitating him in this abuse of language,
+until there is now some difficulty in restoring the word to its original
+signification. A more wanton alteration in the meaning of a word is
+rarely to be met with; for the expression _general name_, the exact
+equivalent of which exists in all languages I am acquainted with, was
+already available for the purpose to which _abstract_ has been
+misappropriated, while the misappropriation leaves that important class
+of words, the names of attributes, without any compact distinctive
+appellation. The old acceptation, however, has not gone so completely
+out of use, as to deprive those who still adhere to it of all chance of
+being understood. By _abstract_, then, I shall always, in Logic, mean
+the opposite of _concrete_: by an abstract name, the name of an
+attribute; by a concrete name, the name of an object.
+
+Do abstract names belong to the class of general, or to that of singular
+names? Some of them are certainly general. I mean those which are names
+not of one single and definite attribute, but of a class of attributes.
+Such is the word _colour_, which is a name common to whiteness, redness,
+&c. Such is even the word whiteness, in respect of the different shades
+of whiteness to which it is applied in common; the word magnitude, in
+respect of the various degrees of magnitude and the various dimensions
+of space; the word weight, in respect of the various degrees of weight.
+Such also is the word _attribute_ itself, the common name of all
+particular attributes. But when only one attribute, neither variable in
+degree nor in kind, is designated by the name; as visibleness;
+tangibleness; equality; squareness; milkwhiteness; then the name can
+hardly be considered general; for though it denotes an attribute of many
+different objects, the attribute itself is always conceived as one, not
+many.[3] To avoid needless logomachies, the best course would probably
+be to consider these names as neither general nor individual, and to
+place them in a class apart.
+
+It may be objected to our definition of an abstract name, that not only
+the names which we have called abstract, but adjectives, which we have
+placed in the concrete class, are names of attributes; that _white_, for
+example, is as much the name of the colour as _whiteness_ is. But (as
+before remarked) a word ought to be considered as the name of that which
+we intend to be understood by it when we put it to its principal use,
+that is, when we employ it in predication. When we say snow is white,
+milk is white, linen is white, we do not mean it to be understood that
+snow, or linen, or milk, is a colour. We mean that they are things
+having the colour. The reverse is the case with the word whiteness; what
+we affirm to _be_ whiteness is not snow, but the colour of snow.
+Whiteness, therefore, is the name of the colour exclusively: white is a
+name of all things whatever having the colour; a name, not of the
+quality whiteness, but of every white object. It is true, this name was
+given to all those various objects on account of the quality; and we may
+therefore say, without impropriety, that the quality forms part of its
+signification; but a name can only be said to stand for, or to be a name
+of, the things of which it can be predicated. We shall presently see
+that all names which can be said to have any signification, all names by
+applying which to an individual we give any information respecting that
+individual, may be said to _imply_ an attribute of some sort; but they
+are not names of the attribute; it has its own proper abstract name.
+
+
+� 5. This leads to the consideration of a third great division of names,
+into _connotative_ and _non-connotative_, the latter sometimes, but
+improperly, called _absolute_. This is one of the most important
+distinctions which we shall have occasion to point out, and one of those
+which go deepest into the nature of language.
+
+A non-connotative term is one which signifies a subject only, or an
+attribute only. A connotative term is one which denotes a subject, and
+implies an attribute. By a subject is here meant anything which
+possesses attributes. Thus John, or London, or England, are names which
+signify a subject only. Whiteness, length, virtue, signify an attribute
+only. None of these names, therefore, are connotative. But _white_,
+_long_, _virtuous_, are connotative. The word white, denotes all white
+things, as snow, paper, the foam of the sea, &c., and implies, or as it
+was termed by the schoolmen, _connotes_[4], the attribute _whiteness_.
+The word white is not predicated of the attribute, but of the subjects,
+snow, &c.; but when we predicate it of them, we imply, or connote, that
+the attribute whiteness belongs to them. The same may be said of the
+other words above cited. Virtuous, for example, is the name of a class,
+which includes Socrates, Howard, the Man of Ross, and an undefinable
+number of other individuals, past, present, and to come. These
+individuals, collectively and severally, can alone be said with
+propriety to be denoted by the word: of them alone can it properly be
+said to be a name. But it is a name applied to all of them in
+consequence of an attribute which they are supposed to possess in
+common, the attribute which has received the name of virtue. It is
+applied to all beings that are considered to possess this attribute; and
+to none which are not so considered.
+
+All concrete general names are connotative. The word _man_, for example,
+denotes Peter, Jane, John, and an indefinite number of other
+individuals, of whom, taken as a class, it is the name. But it is
+applied to them, because they possess, and to signify that they possess,
+certain attributes. These seem to be, corporeity, animal life,
+rationality, and a certain external form, which for distinction we call
+the human. Every existing thing, which possessed all these attributes,
+would be called a man; and anything which possessed none of them, or
+only one, or two, or even three of them without the fourth, would not be
+so called. For example, if in the interior of Africa there were to be
+discovered a race of animals possessing reason equal to that of human
+beings, but with the form of an elephant, they would not be called men.
+Swift's Houyhnhnms would not be so called. Or if such newly-discovered
+beings possessed the form of man without any vestige of reason, it is
+probable that some other name than that of man would be found for them.
+How it happens that there can be any doubt about the matter, will appear
+hereafter. The word _man_, therefore, signifies all these attributes,
+and all subjects which possess these attributes. But it can be
+predicated only of the subjects. What we call men, are the subjects, the
+individual Stiles and Nokes; not the qualities by which their humanity
+is constituted. The name, therefore, is said to signify the subjects
+_directly_, the attributes _indirectly_; it _denotes_ the subjects, and
+implies, or involves, or indicates, or as we shall say henceforth
+_connotes_, the attributes. It is a connotative name.
+
+Connotative names have hence been also called _denominative_, because
+the subject which they denote is denominated by, or receives a name
+from, the attribute which they connote. Snow, and other objects, receive
+the name white, because they possess the attribute which is called
+whiteness; Peter, James, and others receive the name man, because they
+possess the attributes which are considered to constitute humanity. The
+attribute, or attributes, may therefore be said to denominate those
+objects, or to give them a common name.[5]
+
+It has been seen that all concrete general names are connotative. Even
+abstract names, though the names only of attributes, may in some
+instances be justly considered as connotative; for attributes themselves
+may have attributes ascribed to them; and a word which denotes
+attributes may connote an attribute of those attributes. Of this
+description, for example, is such a word as _fault_; equivalent to _bad_
+or _hurtful quality_. This word is a name common to many attributes, and
+connotes hurtfulness, an attribute of those various attributes. When,
+for example, we say that slowness, in a horse, is a fault, we do not
+mean that the slow movement, the actual change of place of the slow
+horse, is a bad thing, but that the property or peculiarity of the
+horse, from which it derives that name, the quality of being a slow
+mover, is an undesirable peculiarity.
+
+In regard to those concrete names which are not general but individual,
+a distinction must be made.
+
+Proper names are not connotative: they denote the individuals who are
+called by them; but they do not indicate or imply any attributes as
+belonging to those individuals. When we name a child by the name Paul,
+or a dog by the name C�sar, these names are simply marks used to enable
+those individuals to be made subjects of discourse. It may be said,
+indeed, that we must have had some reason for giving them those names
+rather than any others; and this is true; but the name, once given, is
+independent of the reason. A man may have been named John, because that
+was the name of his father; a town may have been named Dartmouth,
+because it is situated at the mouth of the Dart. But it is no part of
+the signification of the word John, that the father of the person so
+called bore the same name; nor even of the word Dartmouth, to be
+situated at the mouth of the Dart. If sand should choke up the mouth of
+the river, or an earthquake change its course, and remove it to a
+distance from the town, the name of the town would not necessarily be
+changed. That fact, therefore, can form no part of the signification of
+the word; for otherwise, when the fact confessedly ceased to be true, no
+one would any longer think of applying the name. Proper names are
+attached to the objects themselves, and are not dependent on the
+continuance of any attribute of the object.
+
+But there is another kind of names, which, although they are individual
+names, that is, predicable only of one object, are really connotative.
+For, though we may give to an individual a name utterly unmeaning, which
+we call a proper name,--a word which answers the purpose of showing what
+thing it is we are talking about, but not of telling anything about it;
+yet a name peculiar to an individual is not necessarily of this
+description. It may be significant of some attribute, or some union of
+attributes, which, being possessed by no object but one, determines the
+name exclusively to that individual. "The sun" is a name of this
+description; "God," when used by a monotheist, is another. These,
+however, are scarcely examples of what we are now attempting to
+illustrate, being, in strictness of language, general, not individual
+names: for, however they may be _in fact_ predicable only of one object,
+there is nothing in the meaning of the words themselves which implies
+this: and, accordingly, when we are imagining and not affirming, we may
+speak of many suns; and the majority of mankind have believed, and still
+believe, that there are many gods. But it is easy to produce words which
+are real instances of connotative individual names. It may be part of
+the meaning of the connotative name itself, that there can exist but
+one individual possessing the attribute which it connotes: as, for
+instance, "the _only_ son of John Stiles;" "the _first_ emperor of
+Rome." Or the attribute connoted may be a connexion with some
+determinate event, and the connexion may be of such a kind as only one
+individual could have; or may at least be such as only one individual
+actually had; and this may be implied in the form of the expression.
+"The father of Socrates" is an example of the one kind (since Socrates
+could not have had two fathers); "the author of the Iliad," "the
+murderer of Henri Quatre," of the second. For, though it is conceivable
+that more persons than one might have participated in the authorship of
+the Iliad, or in the murder of Henri Quatre, the employment of the
+article _the_ implies that, in fact, this was not the case. What is here
+done by the word _the_, is done in other cases by the context: thus,
+"C�sar's army" is an individual name, if it appears from the context
+that the army meant is that which C�sar commanded in a particular
+battle. The still more general expressions, "the Roman army," or "the
+Christian army," may be individualized in a similar manner. Another case
+of frequent occurrence has already been noticed; it is the following.
+The name, being a many-worded one, may consist, in the first place, of a
+_general_ name, capable therefore in itself of being affirmed of more
+things than one, but which is, in the second place, so limited by other
+words joined with it, that the entire expression can only be predicated
+of one object, consistently with the meaning of the general term. This
+is exemplified in such an instance as the following: "the present prime
+minister of England." Prime Minister of England is a general name; the
+attributes which it connotes may be possessed by an indefinite number of
+persons: in succession however, not simultaneously; since the meaning of
+the name itself imports (among other things) that there can be only one
+such person at a time. This being the case, and the application of the
+name being afterwards limited by the article and the word _present_, to
+such individuals as possess the attributes at one indivisible point of
+time, it becomes applicable only to one individual. And as this appears
+from the meaning of the name, without any extrinsic proof, it is
+strictly an individual name.
+
+From the preceding observations it will easily be collected, that
+whenever the names given to objects convey any information, that is,
+whenever they have properly any meaning, the meaning resides not in what
+they _denote_, but in what they _connote_. The only names of objects
+which connote nothing are _proper_ names; and these have, strictly
+speaking, no signification.[6]
+
+If, like the robber in the Arabian Nights, we make a mark with chalk on
+a house to enable us to know it again, the mark has a purpose, but it
+has not properly any meaning. The chalk does not declare anything about
+the house; it does not mean, This is such a person's house, or This is a
+house which contains booty. The object of making the mark is merely
+distinction. I say to myself, All these houses are so nearly alike that
+if I lose sight of them I shall not again be able to distinguish that
+which I am now looking at, from any of the others; I must therefore
+contrive to make the appearance of this one house unlike that of the
+others, that I may hereafter know, when I see the mark--not indeed any
+attribute of the house--but simply that it is the same house which I am
+now looking at. Morgiana chalked all the other houses in a similar
+manner, and defeated the scheme: how? simply by obliterating the
+difference of appearance between that house and the others. The chalk
+was still there, but it no longer served the purpose of a distinctive
+mark.
+
+When we impose a proper name, we perform an operation in some degree
+analogous to what the robber intended in chalking the house. We put a
+mark, not indeed upon the object itself, but, so to speak, upon the idea
+of the object. A proper name is but an unmeaning mark which we connect
+in our minds with the idea of the object, in order that whenever the
+mark meets our eyes or occurs to our thoughts, we may think of that
+individual object. Not being attached to the thing itself, it does not,
+like the chalk, enable us to distinguish the object when we see it; but
+it enables us to distinguish it when it is spoken of, either in the
+records of our own experience, or in the discourse of others; to know
+that what we find asserted in any proposition of which it is the
+subject, is asserted of the individual thing with which we were
+previously acquainted.
+
+When we predicate of anything its proper name; when we say, pointing to
+a man, this is Brown or Smith, or pointing to a city, that it is York,
+we do not, merely by so doing, convey to the hearer any information
+about them, except that those are their names. By enabling him to
+identify the individuals, we may connect them with information
+previously possessed by him; by saying, This is York, we may tell him
+that it contains the Minster. But this is in virtue of what he has
+previously heard concerning York; not by anything implied in the name.
+It is otherwise when objects are spoken of by connotative names. When we
+say, The town is built of marble, we give the hearer what may be
+entirely new information, and this merely by the signification of the
+many-worded connotative name, "built of marble." Such names are not
+signs of the mere objects, invented because we have occasion to think
+and speak of those objects individually; but signs which accompany an
+attribute: a kind of livery in which the attribute clothes all objects
+which are recognised as possessing it. They are not mere marks, but
+more, that is to say, significant marks; and the connotation is what
+constitutes their significance.
+
+As a proper name is said to be the name of the one individual which it
+is predicated of, so (as well from the importance of adhering to
+analogy, as for the other reasons formerly assigned) a connotative name
+ought to be considered a name of all the various individuals which it is
+predicable of, or in other words _denotes_, and not of what it connotes.
+But by learning what things it is a name of, we do not learn the meaning
+of the name: for to the same thing we may, with equal propriety, apply
+many names, not equivalent in meaning. Thus, I call a certain man by the
+name Sophroniscus: I call him by another name, The father of Socrates.
+Both these are names of the same individual, but their meaning is
+altogether different; they are applied to that individual for two
+different purposes; the one, merely to distinguish him from other
+persons who are spoken of; the other to indicate a fact relating to him,
+the fact that Socrates was his son. I further apply to him these other
+expressions: a man, a Greek, an Athenian, a sculptor, an old man, an
+honest man, a brave man. All these are, or may be, names of
+Sophroniscus, not indeed of him alone, but of him and each of an
+indefinite number of other human beings. Each of these names is applied
+to Sophroniscus for a different reason, and by each whoever understands
+its meaning is apprised of a distinct fact or number of facts concerning
+him; but those who knew nothing about the names except that they were
+applicable to Sophroniscus, would be altogether ignorant of their
+meaning. It is even possible that I might know every single individual
+of whom a given name could be with truth affirmed, and yet could not be
+said to know the meaning of the name. A child knows who are its brothers
+and sisters, long before it has any definite conception of the nature of
+the facts which are involved in the signification of those words.
+
+In some cases it is not easy to decide precisely how much a particular
+word does or does not connote; that is, we do not exactly know (the case
+not having arisen) what degree of difference in the object would
+occasion a difference in the name. Thus, it is clear that the word man,
+besides animal life and rationality, connotes also a certain external
+form; but it would be impossible to say precisely what form; that is, to
+decide how great a deviation from the form ordinarily found in the
+beings whom we are accustomed to call men, would suffice in a
+newly-discovered race to make us refuse them the name of man.
+Rationality, also, being a quality which admits of degrees, it has never
+been settled what is the lowest degree of that quality which would
+entitle any creature to be considered a human being. In all such cases,
+the meaning of the general name is so far unsettled and vague; mankind
+have not come to any positive agreement about the matter. When we come
+to treat of Classification, we shall have occasion to show under what
+conditions this vagueness may exist without practical inconvenience; and
+cases will appear in which the ends of language are better promoted by
+it than by complete precision; in order that, in natural history for
+instance, individuals or species of no very marked character may be
+ranged with those more strongly characterized individuals or species to
+which, in all their properties taken together, they bear the nearest
+resemblance.
+
+But this partial uncertainty in the connotation of names can only be
+free from mischief when guarded by strict precautions. One of the chief
+sources, indeed, of lax habits of thought, is the custom of using
+connotative terms without a distinctly ascertained connotation, and with
+no more precise notion of their meaning than can be loosely collected
+from observing what objects they are used to denote. It is in this
+manner that we all acquire, and inevitably so, our first knowledge of
+our vernacular language. A child learns the meaning of the words _man_,
+or _white_, by hearing them applied to a variety of individual objects,
+and finding out, by a process of generalization and analysis which he
+could not himself describe, what those different objects have in common.
+In the case of these two words the process is so easy as to require no
+assistance from culture; the objects called human beings, and the
+objects called white, differing from all others by qualities of a
+peculiarly definite and obvious character. But in many other cases,
+objects bear a general resemblance to one another, which leads to their
+being familiarly classed together under a common name, while, without
+more analytic habits than the generality of mankind possess, it is not
+immediately apparent what are the particular attributes, upon the
+possession of which in common by them all, their general resemblance
+depends. When this is the case, people use the name without any
+recognised connotation, that is, without any precise meaning; they talk,
+and consequently think, vaguely, and remain contented to attach only the
+same degree of significance to their own words, which a child three
+years old attaches to the words brother and sister. The child at least
+is seldom puzzled by the starting up of new individuals, on whom he is
+ignorant whether or not to confer the title; because there is usually an
+authority close at hand competent to solve all doubts. But a similar
+resource does not exist in the generality of cases; and new objects are
+continually presenting themselves to men, women, and children, which
+they are called upon to class _proprio motu_. They, accordingly, do this
+on no other principle than that of superficial similarity, giving to
+each new object the name of that familiar object, the idea of which it
+most readily recalls, or which, on a cursory inspection, it seems to
+them most to resemble: as an unknown substance found in the ground will
+be called, according to its texture, earth, sand, or a stone. In this
+manner, names creep on from subject to subject, until all traces of a
+common meaning sometimes disappear, and the word comes to denote a
+number of things not only independently of any common attribute, but
+which have actually no attribute in common; or none but what is shared
+by other things to which the name is capriciously refused. Even
+scientific writers have aided in this perversion of general language
+from its purpose; sometimes because, like the vulgar, they knew no
+better; and sometimes in deference to that aversion to admit new words,
+which induces mankind, on all subjects not considered technical, to
+attempt to make the original stock of names serve with but little
+augmentation to express a constantly increasing number of objects and
+distinctions, and, consequently, to express them in a manner
+progressively more and more imperfect.
+
+To what a degree this loose mode of classing and denominating objects
+has rendered the vocabulary of mental and moral philosophy unfit for the
+purposes of accurate thinking, is best known to whoever has most
+meditated on the present condition of those branches of knowledge.
+Since, however, the introduction of a new technical language as the
+vehicle of speculations on subjects belonging to the domain of daily
+discussion, is extremely difficult to effect, and would not be free from
+inconvenience even if effected, the problem for the philosopher, and one
+of the most difficult which he has to resolve, is, in retaining the
+existing phraseology, how best to alleviate its imperfections. This can
+only be accomplished by giving to every general concrete name which
+there is frequent occasion to predicate, a definite and fixed
+connotation; in order that it may be known what attributes, when we call
+an object by that name, we really mean to predicate of the object. And
+the question of most nicety is, how to give this fixed connotation to a
+name, with the least possible change in the objects which the name is
+habitually employed to denote; with the least possible disarrangement,
+either by adding or subtraction, of the group of objects which, in
+however imperfect a manner, it serves to circumscribe and hold together;
+and with the least vitiation of the truth of any propositions which are
+commonly received as true.
+
+This desirable purpose, of giving a fixed connotation where it is
+wanting, is the end aimed at whenever any one attempts to give a
+definition of a general name already in use; every definition of a
+connotative name being an attempt either merely to declare, or to
+declare and analyse, the connotation of the name. And the fact, that no
+questions which have arisen in the moral sciences have been subjects of
+keener controversy than the definitions of almost all the leading
+expressions, is a proof how great an extent the evil to which we have
+adverted has attained.
+
+Names with indeterminate connotation are not to be confounded with names
+which have more than one connotation, that is to say, ambiguous words. A
+word may have several meanings, but all of them fixed and recognised
+ones; as the word _post_, for example, or the word _box_, the various
+senses of which it would be endless to enumerate. And the paucity of
+existing names, in comparison with the demand for them, may often render
+it advisable and even necessary to retain a name in this multiplicity
+of acceptations, distinguishing these so clearly as to prevent their
+being confounded with one another. Such a word may be considered as two
+or more names, accidentally written and spoken alike.[7]
+
+
+� 6. The fourth principal division of names, is into _positive_ and
+_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,
+_not-tree_, _not-good_. To every positive concrete name, a corresponding
+negative one might be framed. After giving a name to any one thing, or
+to any plurality of things, we might create a second name which should
+be a name of all things whatever, except that particular thing or
+things. These negative names are employed whenever we have occasion to
+speak collectively of all things other than some thing or class of
+things. When the positive name is connotative, the corresponding
+negative name is connotative likewise; but in a peculiar way, connoting
+not the presence but the absence of an attribute. Thus, _not-white_
+denotes all things whatever except white things; and connotes the
+attribute of not possessing whiteness. For the non-possession of any
+given attribute is also an attribute, and may receive a name as such;
+and thus negative concrete names may obtain negative abstract names to
+correspond to them.
+
+Names which are positive in form are often negative in reality, and
+others are really positive though their form is negative. The word
+_inconvenient_, for example, does not express the mere absence of
+convenience; it expresses a positive attribute, that of being the cause
+of discomfort or annoyance. So the word _unpleasant_, notwithstanding
+its negative form, does not connote the mere absence of pleasantness,
+but a less degree of what is signified by the word _painful_, which, it
+is hardly necessary to say, is positive. _Idle_, on the other hand, is a
+word which, though positive in form, expresses nothing but what would be
+signified either by the phrase _not working_, or by the phrase _not
+disposed to work_; and _sober_, either by _not drunk_ or by _not
+drunken_.
+
+There is a class of names called _privative_. A privative name is
+equivalent in its signification to a positive and a negative name taken
+together; being the name of something which has once had a particular
+attribute, or for some other reason might have been expected to have it,
+but which has it not. Such is the word _blind_, which is not equivalent
+to _not seeing_, or to _not capable of seeing_, for it would not, except
+by a poetical or rhetorical figure, be applied to stocks and stones. A
+thing is not usually said to be blind, unless the class to which it is
+most familiarly referred, or to which it is referred on the particular
+occasion, be chiefly composed of things which can see, as in the case of
+a blind man, or a blind horse; or unless it is supposed for any reason
+that it ought to see; as in saying of a man, that he rushed blindly into
+an abyss, or of philosophers or the clergy that the greater part of them
+are blind guides. The names called privative, therefore, connote two
+things: the absence of certain attributes, and the presence of others,
+from which the presence also of the former might naturally have been
+expected.
+
+
+� 7. The fifth leading division of names is into _relative_ and
+_absolute_, or let us rather say, _relative_ and _non-relative_; for the
+word absolute is put upon much too hard duty in metaphysics, not to be
+willingly spared when its services can be dispensed with. It resembles
+the word _civil_ in the language of jurisprudence, which stands for the
+opposite of criminal, the opposite of ecclesiastical, the opposite of
+military, the opposite of political--in short, the opposite of any
+positive word which wants a negative.
+
+Relative names are such as father, son; ruler, subject; like; equal;
+unlike; unequal; longer, shorter; cause, effect. Their characteristic
+property is, that they are always given in pairs. Every relative name
+which is predicated of an object, supposes another object (or objects),
+of which we may predicate either that same name or another relative name
+which is said to be the _correlative_ of the former. Thus, when we call
+any person a son, we suppose other persons who must be called parents.
+When we call any event a cause, we suppose another event which is an
+effect. When we say of any distance that it is longer, we suppose
+another distance which is shorter. When we say of any object that it is
+like, we mean that it is like some other object, which is also said to
+be like the first. In this last case both objects receive the same name;
+the relative term is its own correlative.
+
+It is evident that these words, when concrete, are, like other concrete
+general names, connotative; they denote a subject, and connote an
+attribute; and each of them has or might have a corresponding abstract
+name, to denote the attribute connoted by the concrete. Thus the
+concrete _like_ has its abstract _likeness_; the concretes, father and
+son, have, or might have, the abstracts, paternity, and filiety, or
+sonship. The concrete name connotes an attribute, and the abstract name
+which answers to it denotes that attribute. But of what nature is the
+attribute? Wherein consists the peculiarity in the connotation of a
+relative name?
+
+The attribute signified by a relative name, say some, is a relation; and
+this they give, if not as a sufficient explanation, at least as the only
+one attainable. If they are asked, What then is a relation? they do not
+profess to be able to tell. It is generally regarded as something
+peculiarly recondite and mysterious. I cannot, however, perceive in what
+respect it is more so than any other attribute; indeed, it appears to me
+to be so in a somewhat less degree. I conceive, rather, that it is by
+examining into the signification of relative names, or, in other words,
+into the nature of the attribute which they connote, that a clear
+insight may best be obtained into the nature of all attributes: of all
+that is meant by an attribute.
+
+It is obvious, in fact, that if we take any two correlative names,
+_father_ and _son_ for instance, though the objects _de_noted by the
+names are different, they both, in a certain sense, connote the same
+thing. They cannot, indeed, be said to connote the same _attribute_: to
+be a father, is not the same thing as to be a son. But when we call one
+man a father, another a son, what we mean to affirm is a set of facts,
+which are exactly the same in both cases. To predicate of A that he is
+the father of B, and of B that he is the son of A, is to assert one and
+the same fact in different words. The two propositions are exactly
+equivalent: neither of them asserts more or asserts less than the
+other. The paternity of A and the filiety of B are not two facts, but
+two modes of expressing the same fact. That fact, when analysed,
+consists of a series of physical events or phenomena, in which both A
+and B are parties concerned, and from which they both derive names. What
+those names really connote, is this series of events: that is the
+meaning, and the whole meaning, which either of them is intended to
+convey. The series of events may be said to _constitute_ the relation;
+the schoolmen called it the foundation of the relation, _fundamentum
+relationis_.
+
+In this manner any fact, or series of facts, in which two different
+objects are implicated, and which is therefore predicable of both of
+them, may be either considered as constituting an attribute of the one,
+or an attribute of the other. According as we consider it in the former,
+or in the latter aspect, it is connoted by the one or the other of the
+two correlative names. _Father_ connotes the fact, regarded as
+constituting an attribute of A: _son_ connotes the same fact, as
+constituting an attribute of B. It may evidently be regarded with equal
+propriety in either light. And all that appears necessary to account for
+the existence of relative names, is, that whenever there is a fact in
+which two individuals are concerned, an attribute grounded on that fact
+may be ascribed to either of these individuals.
+
+A name, therefore, is said to be relative, when, over and above the
+object which it denotes, it implies in its signification the existence
+of another object, also deriving a denomination from the same fact which
+is the ground of the first name. Or (to express the same meaning in
+other words) a name is relative, when, being the name of one thing, its
+signification cannot be explained but by mentioning another. Or we may
+state it thus--when the name cannot be employed in discourse so as to
+have a meaning, unless the name of some other thing than what it is
+itself the name of, be either expressed or understood. These definitions
+are all, at bottom, equivalent, being modes of variously expressing this
+one distinctive circumstance--that every other attribute of an object
+might, without any contradiction, be conceived still to exist if no
+object besides that one had ever existed;[8] but those of its
+attributes which are expressed by relative names, would on that
+supposition be swept away.
+
+
+� 8. Names have been further distinguished into _univocal_ and
+_�quivocal_: these, however, are not two kinds of names, but two
+different modes of employing names. A name is univocal, or applied
+univocally, with respect to all things of which it can be predicated _in
+the same sense_: it is �quivocal, or applied �quivocally, as respects
+those things of which it is predicated in different senses. It is
+scarcely necessary to give instances of a fact so familiar as the double
+meaning of a word. In reality, as has been already observed, an
+�quivocal or ambiguous word is not one name, but two names, accidentally
+coinciding in sound. _File_ meaning a steel instrument, and _file_
+meaning a line of soldiers, have no more title to be considered one
+word, because written alike, than _grease_ and _Greece_ have, because
+they are pronounced alike. They are one sound, appropriated to form two
+different words.
+
+An intermediate case is that of a name used _analogically_ or
+metaphorically; that is, a name which is predicated of two things, not
+univocally, or exactly in the same signification, but in significations
+somewhat similar, and which being derived one from the other, one of
+them may be considered the primary, and the other a secondary
+signification. As when we speak of a brilliant light and a brilliant
+achievement. The word is not applied in the same sense to the light and
+to the achievement; but having been applied to the light in its original
+sense, that of brightness to the eye, it is transferred to the
+achievement in a derivative signification, supposed to be somewhat like
+the primitive one. The word, however, is just as properly two names
+instead of one, in this case, as in that of the most perfect ambiguity.
+And one of the commonest forms of fallacious reasoning arising from
+ambiguity, is that of arguing from a metaphorical expression as if it
+were literal; that is, as if a word, when applied metaphorically, were
+the same name as when taken in its original sense: which will be seen
+more particularly in its place.
+
+
+
+
+CHAPTER III.
+
+OF THE THINGS DENOTED BY NAMES.
+
+
+� 1. Looking back now to the commencement of our inquiry, let us attempt
+to measure how far it has advanced. Logic, we found, is the Theory of
+Proof. But proof supposes something provable, which must be a
+Proposition or Assertion; since nothing but a Proposition can be an
+object of belief, or therefore of proof. A Proposition is, discourse
+which affirms or denies something of some other thing. This is one step:
+there must, it seems, be two things concerned in every act of belief.
+But what are these Things? They can be no other than those signified by
+the two names, which being joined together by a copula constitute the
+Proposition. If, therefore, we knew what all names signify, we should
+know everything which in the existing state of human knowledge, is
+capable either of being made a subject of affirmation or denial, or of
+being itself affirmed or denied of a subject. We have accordingly, in
+the preceding chapter, reviewed the various kinds of Names, in order to
+ascertain what is signified by each of them. And we have now carried
+this survey far enough to be able to take an account of its results, and
+to exhibit an enumeration of all kinds of Things which are capable of
+being made predicates, or of having anything predicated of them: after
+which to determine the import of Predication, that is, of Propositions,
+can be no arduous task.
+
+The necessity of an enumeration of Existences, as the basis of Logic,
+did not escape the attention of the schoolmen, and of their master
+Aristotle, the most comprehensive, if not also the most sagacious, of
+the ancient philosophers. The Categories, or Predicaments--the former a
+Greek word, the latter its literal translation in the Latin
+language--were intended by him and his followers as an enumeration of
+all things capable of being named; an enumeration by the _summa
+genera_, _i.e._ the most extensive classes into which things could be
+distributed; which, therefore, were so many highest Predicates, one or
+other of which was supposed capable of being affirmed with truth of
+every nameable thing whatsoever. The following are the classes into
+which, according to this school of philosophy, Things in general might
+be reduced:--
+
+  [Greek: Ousia],       Substantia.
+  [Greek: Poson],       Quantitas.
+  [Greek: Poion],       Qualitas.
+  [Greek: Pros ti],     Relatio.
+  [Greek: Poiein],      Actio.
+  [Greek: Paschein],    Passio.
+  [Greek: Pou],         Ubi.
+  [Greek: Pote],        Quando.
+  [Greek: Keisthai],    Situs.
+  [Greek: Echein],      Habitus.
+
+The imperfections of this classification are too obvious to require, and
+its merits are not sufficient to reward, a minute examination. It is a
+mere catalogue of the distinctions rudely marked out by the language of
+familiar life, with little or no attempt to penetrate, by philosophic
+analysis, to the _rationale_ even of those common distinctions. Such an
+analysis, however superficially conducted, would have shown the
+enumeration to be both redundant and defective. Some objects are
+omitted, and others repeated several times under different heads. It is
+like a division of animals into men, quadrupeds, horses, asses, and
+ponies. That, for instance, could not be a very comprehensive view of
+the nature of Relation which could exclude action, passivity, and local
+situation from that category. The same observation applies to the
+categories Quando (or position in time), and Ubi (or position in space);
+while the distinction between the latter and Situs is merely verbal. The
+incongruity of erecting into a _summum genus_ the class which forms the
+tenth category is manifest. On the other hand, the enumeration takes no
+notice of anything besides substances and attributes. In what category
+are we to place sensations, or any other feelings and states of mind; as
+hope, joy, fear; sound, smell, taste; pain, pleasure; thought, judgment,
+conception, and the like? Probably all these would have been placed by
+the Aristotelian school in the categories of _actio_ and _passio_; and
+the relation of such of them as are active, to their objects, and of
+such of them as are passive, to their causes, would rightly be so
+placed; but the things themselves, the feelings or states of mind,
+wrongly. Feelings, or states of consciousness, are assuredly to be
+counted among realities, but they cannot be reckoned either among
+substances or attributes.
+
+
+� 2. Before recommencing, under better auspices, the attempt made with
+such imperfect success by the great founder of the science of logic, we
+must take notice of an unfortunate ambiguity in all the concrete names
+which correspond to the most general of all abstract terms, the word
+Existence. When we have occasion for a name which shall be capable of
+denoting whatever exists, as contradistinguished from non-entity or
+Nothing, there is hardly a word applicable to the purpose which is not
+also, and even more familiarly, taken in a sense in which it denotes
+only substances. But substances are not all that exists; attributes, if
+such things are to be spoken of, must be said to exist; feelings
+certainly exist. Yet when we speak of an _object_, or of a _thing_, we
+are almost always supposed to mean a substance. There seems a kind of
+contradiction in using such an expression as that one _thing_ is merely
+an attribute of another thing. And the announcement of a Classification
+of Things would, I believe, prepare most readers for an enumeration like
+those in natural history, beginning with the great divisions of animal,
+vegetable, and mineral, and subdividing them into classes and orders.
+If, rejecting the word Thing, we endeavour to find another of a more
+general import, or at least more exclusively confined to that general
+import, a word denoting all that exists, and connoting only simple
+existence; no word might be presumed fitter for such a purpose than
+_being_: originally the present participle of a verb which in one of its
+meanings is exactly equivalent to the verb _exists_; and therefore
+suitable, even by its grammatical formation, to be the concrete of the
+abstract _existence_. But this word, strange as the fact may appear, is
+still more completely spoiled for the purpose which it seemed expressly
+made for, than the word Thing. _Being_ is, by custom, exactly synonymous
+with substance; except that it is free from a slight taint of a second
+ambiguity; being applied impartially to matter and to mind, while
+substance, though originally and in strictness applicable to both, is
+apt to suggest in preference the idea of matter. Attributes are never
+called Beings; nor are feelings. A Being is that which excites feelings,
+and which possesses attributes. The soul is called a Being; God and
+angels are called Beings; but if we were to say, extension, colour,
+wisdom, virtue, are beings, we should perhaps be suspected of thinking
+with some of the ancients, that the cardinal virtues are animals; or, at
+the least, of holding with the Platonic school the doctrine of
+self-existent Ideas, or with the followers of Epicurus that of Sensible
+Forms, which detach themselves in every direction from bodies, and by
+coming in contact with our organs, cause our perceptions. We should be
+supposed, in short, to believe that Attributes are Substances.
+
+In consequence of this perversion of the word Being, philosophers
+looking about for something to supply its place, laid their hands upon
+the word Entity, a piece of barbarous Latin, invented by the schoolmen
+to be used as an abstract name, in which class its grammatical form
+would seem to place it; but being seized by logicians in distress to
+stop a leak in their terminology, it has ever since been used as a
+concrete name. The kindred word _essence_, born at the same time and of
+the same parents, scarcely underwent a more complete transformation
+when, from being the abstract of the verb _to be_, it came to denote
+something sufficiently concrete to be enclosed in a glass bottle. The
+word Entity, since it settled down into a concrete name, has retained
+its universality of signification somewhat less impaired than any of the
+names before mentioned. Yet the same gradual decay to which, after a
+certain age, all the language of psychology seems liable, has been at
+work even here. If you call virtue an _entity_, you are indeed somewhat
+less strongly suspected of believing it to be a substance than if you
+called it a _being_; but you are by no means free from the suspicion.
+Every word which was originally intended to connote mere existence,
+seems, after a long time, to enlarge its connotation to _separate_
+existence, or existence freed from the condition of belonging to a
+substance; which condition being precisely what constitutes an
+attribute, attributes are gradually shut out; and along with them
+feelings, which in ninety-nine cases out of a hundred have no other name
+than that of the attribute which is grounded on them. Strange that when
+the greatest embarrassment felt by all who have any considerable number
+of thoughts to express, is to find a sufficient variety of precise words
+fitted to express them, there should be no practice to which even
+scientific thinkers are more addicted than that of taking valuable words
+to express ideas which are sufficiently expressed by other words already
+appropriated to them.
+
+When it is impossible to obtain good tools, the next best thing is to
+understand thoroughly the defects of those we have. I have therefore
+warned the reader of the ambiguity of the names which, for want of
+better, I am necessitated to employ. It must now be the writer's
+endeavour so to employ them as in no case to leave the meaning doubtful
+or obscure. No one of the above terms being altogether unambiguous, I
+shall not confine myself to any one, but shall employ on each occasion
+the word which seems least likely in the particular case to lead to
+misunderstanding; nor do I pretend to use either these or any other
+words with a rigorous adherence to one single sense. To do so would
+often leave us without a word to express what is signified by a known
+word in some one or other of its senses: unless authors had an unlimited
+licence to coin new words, together with (what it would be more
+difficult to assume) unlimited power of making readers understand them.
+Nor would it be wise in a writer, on a subject involving so much of
+abstraction, to deny himself the advantage derived from even an improper
+use of a term, when, by means of it, some familiar association is called
+up which brings the meaning home to the mind, as it were by a flash.
+
+The difficulty both to the writer and reader, of the attempt which must
+be made to use vague words so as to convey a precise meaning, is not
+wholly a matter of regret. It is not unfitting that logical treatises
+should afford an example of that, to facilitate which is among the most
+important uses of logic. Philosophical language will for a long time,
+and popular language still longer, retain so much of vagueness and
+ambiguity, that logic would be of little value if it did not, among its
+other advantages, exercise the understanding in doing its work neatly
+and correctly with these imperfect tools.
+
+After this preamble it is time to proceed to our enumeration. We shall
+commence with Feelings, the simplest class of nameable things; the term
+Feeling being of course understood in its most enlarged sense.
+
+
+I. FEELINGS, OR STATES OF CONSCIOUSNESS.
+
+� 3. A Feeling and a State of Consciousness are, in the language of
+philosophy, equivalent expressions: everything is a feeling of which the
+mind is conscious; everything which it _feels_, or, in other words,
+which forms a part of its own sentient existence. In popular language
+Feeling is not always synonymous with State of Consciousness; being
+often taken more peculiarly for those states which are conceived as
+belonging to the sensitive, or to the emotional, phasis of our nature,
+and sometimes, with a still narrower restriction, to the emotional
+alone, as distinguished from what are conceived as belonging to the
+percipient or to the intellectual phasis. But this is an admitted
+departure from correctness of language; just as, by a popular perversion
+the exact converse of this, the word Mind is withdrawn from its rightful
+generality of signification, and restricted to the intellect. The still
+greater perversion by which Feeling is sometimes confined not only to
+bodily sensations, but to the sensations of a single sense, that of
+touch, needs not be more particularly adverted to.
+
+Feeling, in the proper sense of the term, is a genus, of which
+Sensation, Emotion, and Thought, are subordinate species. Under the word
+Thought is here to be included whatever we are internally conscious of
+when we are said to think; from the consciousness we have when we think
+of a red colour without having it before our eyes, to the most recondite
+thoughts of a philosopher or poet. Be it remembered, however, that by a
+thought is to be understood what passes in the mind itself, and not any
+object external to the mind, which the person is commonly said to be
+thinking of. He may be thinking of the sun, or of God, but the sun and
+God are not thoughts; his mental image, however, of the sun, and his
+idea of God, are thoughts; states of his mind, not of the objects
+themselves; and so also is his belief of the existence of the sun, or of
+God; or his disbelief, if the case be so. Even imaginary objects (which
+are said to exist only in our ideas) are to be distinguished from our
+ideas of them. I may think of a hobgoblin, as I may think of the loaf
+which was eaten yesterday, or of the flower which will bloom to-morrow.
+But the hobgoblin which never existed is not the same thing with my idea
+of a hobgoblin, any more than the loaf which once existed is the same
+thing with my idea of a loaf, or the flower which does not yet exist,
+but which will exist, is the same with my idea of a flower. They are
+all, not thoughts, but objects of thought; though at the present time
+all the objects are alike non-existent.
+
+In like manner, a Sensation is to be carefully distinguished from the
+object which causes the sensation; our sensation of white from a white
+object: nor is it less to be distinguished from the attribute whiteness,
+which we ascribe to the object in consequence of its exciting the
+sensation. Unfortunately for clearness and due discrimination in
+considering these subjects, our sensations seldom receive separate
+names. We have a name for the objects which produce in us a certain
+sensation: the word _white_. We have a name for the quality in those
+objects, to which we ascribe the sensation: the name _whiteness_. But
+when we speak of the sensation itself (as we have not occasion to do
+this often except in our scientific speculations), language, which
+adapts itself for the most part only to the common uses of life, has
+provided us with no single-worded or immediate designation; we must
+employ a circumlocution, and say, The sensation of white, or The
+sensation of whiteness; we must denominate the sensation either from the
+object, or from the attribute, by which it is excited. Yet the
+sensation, though it never _does_, might very well be _conceived_ to
+exist, without anything whatever to excite it. We can conceive it as
+arising spontaneously in the mind. But if it so arose, we should have no
+name to denote it which would not be a misnomer. In the case of our
+sensations of hearing we are better provided; we have the word Sound,
+and a whole vocabulary of words to denote the various kinds of sounds.
+For as we are often conscious of these sensations in the absence of any
+perceptible object, we can more easily conceive having them in the
+absence of any object whatever. We need only shut our eyes and listen to
+music, to have a conception of an universe with nothing in it except
+sounds, and ourselves hearing them: and what is easily conceived
+separately, easily obtains a separate name. But in general our names of
+sensations denote indiscriminately the sensation and the attribute.
+Thus, _colour_ stands for the sensations of white, red, &c., but also
+for the quality in the coloured object. We talk of the colours of things
+as among their _properties_.
+
+
+� 4. In the case of sensations, another distinction has also to be kept
+in view, which is often confounded, and never without mischievous
+consequences. This is, the distinction between the sensation itself, and
+the state of the bodily organs which precedes the sensation, and which
+constitutes the physical agency by which it is produced. One of the
+sources of confusion on this subject is the division commonly made of
+feelings into Bodily and Mental. Philosophically speaking, there is no
+foundation at all for this distinction: even sensations are states of
+the sentient mind, not states of the body, as distinguished from it.
+What I am conscious of when I see the colour blue, is a feeling of blue
+colour, which is one thing; the picture on my retina, or the phenomenon
+of hitherto mysterious nature which takes place in my optic nerve or in
+my brain, is another thing, of which I am not at all conscious, and
+which scientific investigation alone could have apprised me of. These
+are states of my body; but the sensation of blue, which is the
+consequence of these states of body, is not a state of body: that which
+perceives and is conscious is called Mind. When sensations are called
+bodily feelings, it is only as being the class of feelings which are
+immediately occasioned by bodily states; whereas the other kinds of
+feelings, thoughts, for instance, or emotions, are immediately excited
+not by anything acting upon the bodily organs, but by sensations, or by
+previous thoughts. This, however, is a distinction not in our feelings,
+but in the agency which produces our feelings: all of them when actually
+produced are states of mind.
+
+Besides the affection of our bodily organs from without, and the
+sensation thereby produced in our minds, many writers admit a third link
+in the chain of phenomena, which they call a Perception, and which
+consists in the recognition of an external object as the exciting cause
+of the sensation. This perception, they say, is an _act_ of the mind,
+proceeding from its own spontaneous activity; while in a sensation the
+mind is passive, being merely acted upon by the outward object. And
+according to some metaphysicians, it is by an act of the mind, similar
+to perception, except in not being preceded by any sensation, that the
+existence of God, the soul, and other hyper-physical objects is
+recognised.
+
+These acts of what is termed perception, whatever be the conclusion
+ultimately come to respecting their nature, must, I conceive, take their
+place among the varieties of feelings or states of mind. In so classing
+them, I have not the smallest intention of declaring or insinuating any
+theory as to the law of mind in which these mental processes may be
+supposed to originate, or the conditions under which they may be
+legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
+suppose must be meant in an analogous case[9]) to indicate that as they
+are "_merely_ states of mind," it is superfluous to inquire into their
+distinguishing peculiarities. I abstain from the inquiry as irrelevant
+to the science of logic. In these so-called perceptions, or direct
+recognitions by the mind, of objects, whether physical or spiritual,
+which are external to itself, I can see only cases of belief; but of
+belief which claims to be intuitive, or independent of external
+evidence. When a stone lies before me, I am conscious of certain
+sensations which I receive from it; but if I say that these sensations
+come to me from an external object which I _perceive_, the meaning of
+these words is, that receiving the sensations, I intuitively _believe_
+that an external cause of those sensations exists. The laws of intuitive
+belief, and the conditions under which it is legitimate, are a subject
+which, as we have already so often remarked, belongs not to logic, but
+to the science of the ultimate laws of the human mind.
+
+To the same region of speculation belongs all that can be said
+respecting the distinction which the German metaphysicians and their
+French and English followers so elaborately draw between the _acts_ of
+the mind and its merely passive _states_; between what it receives from,
+and what it gives to, the crude materials of its experience. I am aware
+that with reference to the view which those writers take of the primary
+elements of thought and knowledge, this distinction is fundamental. But
+for the present purpose, which is to examine, not the original
+groundwork of our knowledge, but how we come by that portion of it which
+is not original; the difference between active and passive states of
+mind is of secondary importance. For us, they all are states of mind,
+they all are feelings; by which, let it be said once more, I mean to
+imply nothing of passivity, but simply that they are psychological
+facts, facts which take place in the mind, and are to be carefully
+distinguished from the external or physical facts with which they may be
+connected either as effects or as causes.
+
+
+� 5. Among active states of mind, there is, however, one species which
+merits particular attention, because it forms a principal part of the
+connotation of some important classes of names. I mean _volitions_, or
+acts of the will. When we speak of sentient beings by relative names, a
+large portion of the connotation of the name usually consists of the
+actions of those beings; actions past, present, and possible or probable
+future. Take, for instance, the words Sovereign and Subject. What
+meaning do these words convey, but that of innumerable actions, done or
+to be done by the sovereign and the subjects, to or in regard to one
+another reciprocally? So with the words physician and patient, leader
+and follower, tutor and pupil. In many cases the words also connote
+actions which would be done under certain contingencies by persons other
+than those denoted: as the words mortgagor and mortgagee, obligor and
+obligee, and many other words expressive of legal relation, which
+connote what a court of justice would do to enforce the legal obligation
+if not fulfilled. There are also words which connote actions previously
+done by persons other than those denoted either by the name itself or by
+its correlative; as the word brother. From these instances, it may be
+seen how large a portion of the connotation of names consists of
+actions. Now what is an action? Not one thing, but a series of two
+things: the state of mind called a volition, followed by an effect. The
+volition or intention to produce the effect, is one thing; the effect
+produced in consequence of the intention, is another thing; the two
+together constitute the action. I form the purpose of instantly moving
+my arm; that is a state of my mind: my arm (not being tied or paralytic)
+moves in obedience to my purpose; that is a physical fact, consequent on
+a state of mind. The intention, followed by the fact, or (if we prefer
+the expression) the fact when preceded and caused by the intention, is
+called the action of moving my arm.
+
+
+� 6. Of the first leading division of nameable things, viz. Feelings or
+States of Consciousness, we began by recognising three subdivisions;
+Sensations, Thoughts, and Emotions. The first two of these we have
+illustrated at considerable length; the third, Emotions, not being
+perplexed by similar ambiguities, does not require similar
+exemplification. And, finally, we have found it necessary to add to
+these three a fourth species, commonly known by the name Volitions.
+Without seeking to prejudge the metaphysical question whether any mental
+state or phenomenon can be found which is not included in one or other
+of these four species, it appears to me that the amount of illustration
+bestowed upon these may, so far as we are concerned, suffice for the
+whole genus. We shall, therefore, proceed to the two remaining classes
+of nameable things; all things which are external to the mind being
+considered as belonging either to the class of Substances or to that of
+Attributes.
+
+II. SUBSTANCES.
+
+Logicians have endeavoured to define Substance and Attribute; but their
+definitions are not so much attempts to draw a distinction between the
+things themselves, as instructions what difference it is customary to
+make in the grammatical structure of the sentence, according as we are
+speaking of substances or of attributes. Such definitions are rather
+lessons of English, or of Greek, Latin, or German, than of mental
+philosophy. An attribute, say the school logicians, must be the
+attribute _of_ something; colour, for example, must be the colour _of_
+something; goodness must be the goodness _of_ something: and if this
+something should cease to exist, or should cease to be connected with
+the attribute, the existence of the attribute would be at an end. A
+substance, on the contrary, is self-existent; in speaking about it, we
+need not put _of_ after its name. A stone is not the stone _of_
+anything; the moon is not the moon _of_ anything, but simply the moon.
+Unless, indeed, the name which we choose to give to the substance be a
+relative name; if so, it must be followed either by _of_, or by some
+other particle, implying, as that preposition does, a reference to
+something else: but then the other characteristic peculiarity of an
+attribute would fail; the _something_ might be destroyed, and the
+substance might still subsist. Thus, a father must be the father _of_
+something, and so far resembles an attribute, in being referred to
+something besides himself: if there were no child, there would be no
+father: but this, when we look into the matter, only means that we
+should not call him father. The man called father might still exist
+though there were no child, as he existed before there was a child: and
+there would be no contradiction in supposing him to exist, though the
+whole universe except himself were destroyed. But destroy all white
+substances, and where would be the attribute whiteness? Whiteness,
+without any white thing, is a contradiction in terms.
+
+This is the nearest approach to a solution of the difficulty, that will
+be found in the common treatises on logic. It will scarcely be thought
+to be a satisfactory one. If an attribute is distinguished from a
+substance by being the attribute _of_ something, it seems highly
+necessary to understand what is meant by _of_; a particle which needs
+explanation too much itself, to be placed in front of the explanation of
+anything else. And as for the self-existence of substance, it is very
+true that a substance may be conceived to exist without any other
+substance, but so also may an attribute without any other attribute: and
+we can no more imagine a substance without attributes than we can
+imagine attributes without a substance.
+
+Metaphysicians, however, have probed the question deeper, and given an
+account of Substance considerably more satisfactory than this.
+Substances are usually distinguished as Bodies or Minds. Of each of
+these, philosophers have at length provided us with a definition which
+seems unexceptionable.
+
+
+� 7. A Body, according to the received doctrine of modern
+metaphysicians, may be defined, the external cause to which we ascribe
+our sensations. When I see and touch a piece of gold, I am conscious of
+a sensation of yellow colour, and sensations of hardness and weight; and
+by varying the mode of handling, I may add to these sensations many
+others completely distinct from them. The sensations are all of which I
+am directly conscious; but I consider them as produced by something not
+only existing independently of my will, but external to my bodily organs
+and to my mind. This external something I call a body.
+
+It may be asked, how come we to ascribe our sensations to any external
+cause? And is there sufficient ground for so ascribing them? It is
+known, that there are metaphysicians who have raised a controversy on
+the point; maintaining that we are not warranted in referring our
+sensations to a cause such as we understand by the word Body, or to any
+external cause whatever. Though we have no concern here with this
+controversy, nor with the metaphysical niceties on which it turns, one
+of the best ways of showing what is meant by Substance is, to consider
+what position it is necessary to take up, in order to maintain its
+existence against opponents.
+
+It is certain, then, that a part of our notion of a body consists of the
+notion of a number of sensations of our own, or of other sentient
+beings, habitually occurring simultaneously. My conception of the table
+at which I am writing is compounded of its visible form and size, which
+are complex sensations of sight; its tangible form and size, which are
+complex sensations of our organs of touch and of our muscles; its
+weight, which is also a sensation of touch and of the muscles; its
+colour, which is a sensation of sight; its hardness, which is a
+sensation of the muscles; its composition, which is another word for all
+the varieties of sensation which we receive under various circumstances
+from the wood of which it is made, and so forth. All or most of these
+various sensations frequently are, and, as we learn by experience,
+always might be, experienced simultaneously, or in many different orders
+of succession, at our own choice: and hence the thought of any one of
+them makes us think of the others, and the whole becomes mentally
+amalgamated into one mixed state of consciousness, which, in the
+language of the school of Locke and Hartley, is termed a Complex Idea.
+
+Now, there are philosophers who have argued as follows. If we conceive
+an orange to be divested of its natural colour without acquiring any new
+one; to lose its softness without becoming hard, its roundness without
+becoming square or pentagonal, or of any other regular or irregular
+figure whatever; to be deprived of size, of weight, of taste, of smell;
+to lose all its mechanical and all its chemical properties, and acquire
+no new ones; to become, in short, invisible, intangible, imperceptible
+not only by all our senses, but by the senses of all other sentient
+beings, real or possible; nothing, say these thinkers, would remain.
+For of what nature, they ask, could be the residuum? and by what token
+could it manifest its presence? To the unreflecting its existence seems
+to rest on the evidence of the senses. But to the senses nothing is
+apparent except the sensations. We know, indeed, that these sensations
+are bound together by some law; they do not come together at random, but
+according to a systematic order, which is part of the order established
+in the universe. When we experience one of these sensations, we usually
+experience the others also, or know that we have it in our power to
+experience them. But a fixed law of connexion, making the sensations
+occur together, does not, say these philosophers, necessarily require
+what is called a substratum to support them. The conception of a
+substratum is but one of many possible forms in which that connexion
+presents itself to our imagination; a mode of, as it were, realizing the
+idea. If there be such a substratum, suppose it this instant
+miraculously annihilated, and let the sensations continue to occur in
+the same order, and how would the substratum be missed? By what signs
+should we be able to discover that its existence had terminated? Should
+we not have as much reason to believe that it still existed as we now
+have? And if we should not then be warranted in believing it, how can we
+be so now? A body, therefore, according to these metaphysicians, is not
+anything intrinsically different from the sensations which the body is
+said to produce in us; it is, in short, a set of sensations, or rather,
+of possibilities of sensation, joined together according to a fixed law.
+
+The controversies to which these speculations have given rise, and the
+doctrines which have been developed in the attempt to find a conclusive
+answer to them, have been fruitful of important consequences to the
+Science of Mind. The sensations (it was answered) which we are conscious
+of, and which we receive, not at random, but joined together in a
+certain uniform manner, imply not only a law or laws of connexion, but a
+cause external to our mind, which cause, by its own laws, determines the
+laws according to which the sensations are connected and experienced.
+The schoolmen used to call this external cause by the name we have
+already employed, a _substratum_; and its attributes (as they expressed
+themselves) _inhered_, literally _stuck_, in it. To this substratum the
+name Matter is usually given in philosophical discussions. It was soon,
+however, acknowledged by all who reflected on the subject, that the
+existence of matter cannot be proved by extrinsic evidence. The answer,
+therefore, now usually made to Berkeley and his followers, is, that the
+belief is intuitive; that mankind, in all ages, have felt themselves
+compelled, by a necessity of their nature, to refer their sensations to
+an external cause: that even those who deny it in theory, yield to the
+necessity in practice, and both in speech, thought, and feeling, do,
+equally with the vulgar, acknowledge their sensations to be the effects
+of something external to them: this knowledge, therefore, it is
+affirmed, is as evidently intuitive as our knowledge of our sensations
+themselves is intuitive. And here the question merges in the fundamental
+problem of metaphysics properly so called; to which science we leave it.
+
+But although the extreme doctrine of the Idealist metaphysicians, that
+objects are nothing but our sensations and the laws which connect them,
+has not been generally adopted by subsequent thinkers; the point of most
+real importance is one on which those metaphysicians are now very
+generally considered to have made out their case: viz., that _all we
+know_ of objects is the sensations which they give us, and the order of
+the occurrence of those sensations. Kant himself, on this point, is as
+explicit as Berkeley or Locke. However firmly convinced that there
+exists an universe of "Things in themselves," totally distinct from the
+universe of phenomena, or of things as they appear to our senses; and
+even when bringing into use a technical expression (_Noumenon_) to
+denote what the thing is in itself, as contrasted with the
+_representation_ of it in our minds; he allows that this representation
+(the matter of which, he says, consists of our sensations, though the
+form is given by the laws of the mind itself) is all we know of the
+object: and that the real nature of the Thing is, and by the
+constitution of our faculties ever must remain, at least in the present
+state of existence, an impenetrable mystery to us. "Of things absolutely
+or in themselves," says Sir William Hamilton,[10] "be they external, be
+they internal, we know nothing, or know them only as incognisable; and
+become aware of their incomprehensible existence, only as this is
+indirectly and accidentally revealed to us, through certain qualities
+related to our faculties of knowledge, and which qualities, again, we
+cannot think as unconditioned, irrelative, existent in and of
+themselves. All that we know is therefore ph�nomenal,--ph�nomenal of the
+unknown."[11] The same doctrine is laid down in the clearest and
+strongest terms by M. Cousin, whose observations on the subject are the
+more worthy of attention, as, in consequence of the ultra-German and
+ontological character of his philosophy in other respects, they may be
+regarded as the admissions of an opponent.[12]
+
+There is not the slightest reason for believing that what we call the
+sensible qualities of the object are a type of anything inherent in
+itself, or bear any affinity to its own nature. A cause does not, as
+such, resemble its effects; an east wind is not like the feeling of
+cold, nor heat like the steam of boiling water. Why then should matter
+resemble our sensations? Why should the inmost nature of fire or water
+resemble the impressions made by those objects upon our senses?[13] Or
+on what principle are we authorized to deduce from the effects, anything
+concerning the cause, except that it is a cause adequate to produce
+those effects? It may, therefore, safely be laid down as a truth both
+obvious in itself, and admitted by all whom it is at present necessary
+to take into consideration, that, of the outward world, we know and can
+know absolutely nothing, except the sensations which we experience from
+it.[14]
+
+
+� 8. Body having now been defined the external cause, and (according to
+the more reasonable opinion) the unknown external cause, to which we
+refer our sensations; it remains to frame a definition of Mind. Nor,
+after the preceding observations, will this be difficult. For, as our
+conception of a body is that of an unknown exciting cause of sensations,
+so our conception of a mind is that of an unknown recipient, or
+percipient, of them; and not of them alone, but of all our other
+feelings. As body is understood to be the mysterious something which
+excites the mind to feel, so mind is the mysterious something which
+feels and thinks. It is unnecessary to give in the case of mind, as we
+gave in the case of matter, a particular statement of the sceptical
+system by which its existence as a Thing in itself, distinct from the
+series of what are denominated its states, is called in question. But it
+is necessary to remark, that on the inmost nature (whatever be meant by
+inmost nature) of the thinking principle, as well as on the inmost
+nature of matter, we are, and with our faculties must always remain,
+entirely in the dark. All which we are aware of, even in our own minds,
+is (in the words of Mr. James Mill) a certain "thread of consciousness;"
+a series of feelings, that is, of sensations, thoughts, emotions, and
+volitions, more or less numerous and complicated. There is a something I
+call Myself, or, by another form of expression, my mind, which I
+consider as distinct from these sensations, thoughts, &c.; a something
+which I conceive to be not the thoughts, but the being that has the
+thoughts, and which I can conceive as existing for ever in a state of
+quiescence, without any thoughts at all. But what this being is, though
+it is myself, I have no knowledge, other than the series of its states
+of consciousness. As bodies manifest themselves to me only through the
+sensations of which I regard them as the causes, so the thinking
+principle, or mind, in my own nature, makes itself known to me only by
+the feelings of which it is conscious. I know nothing about myself, save
+my capacities of feeling or being conscious (including, of course,
+thinking and willing): and were I to learn anything new concerning my
+own nature, I cannot with my present faculties conceive this new
+information to be anything else, than that I have some additional
+capacities, as yet unknown to me, of feeling, thinking, or willing.
+
+Thus, then, as body is the unsentient cause to which we are naturally
+prompted to refer a certain portion of our feelings, so mind may be
+described as the sentient _subject_ (in the scholastic sense of the
+term) of all feelings; that which has or feels them. But of the nature
+of either body or mind, further than the feelings which the former
+excites, and which the latter experiences, we do not, according to the
+best existing doctrine, know anything; and if anything, logic has
+nothing to do with it, or with the manner in which the knowledge is
+acquired. With this result we may conclude this portion of our subject,
+and pass to the third and only remaining class or division of Nameable
+Things.
+
+
+III. ATTRIBUTES: AND, FIRST, QUALITIES.
+
+� 9. From what has already been said of Substance, what is to be said of
+Attribute is easily deducible. For if we know not, and cannot know,
+anything of bodies but the sensations which they excite in us or in
+others, those sensations must be all that we can, at bottom, mean by
+their attributes; and the distinction which we verbally make between the
+properties of things and the sensations we receive from them, must
+originate in the convenience of discourse rather than in the nature of
+what is signified by the terms.
+
+Attributes are usually distributed under the three heads of Quality,
+Quantity, and Relation. We shall come to the two latter presently: in
+the first place we shall confine ourselves to the former.
+
+Let us take, then, as our example, one of what are termed the sensible
+qualities of objects, and let that example be whiteness. When we ascribe
+whiteness to any substance, as, for instance, snow; when we say that
+snow has the quality whiteness, what do we really assert? Simply, that
+when snow is present to our organs, we have a particular sensation,
+which we are accustomed to call the sensation of white. But how do I
+know that snow is present? Obviously by the sensations which I derive
+from it, and not otherwise. I infer that the object is present, because
+it gives me a certain assemblage or series of sensations. And when I
+ascribe to it the attribute whiteness, my meaning is only, that, of the
+sensations composing this group or series, that which I call the
+sensation of white colour is one.
+
+This is one view which may be taken of the subject. But there is also
+another and a different view. It may be said, that it is true we _know_
+nothing of sensible objects, except the sensations they excite in us;
+that the fact of our receiving from snow the particular sensation which
+is called a sensation of white, is the _ground_ on which we ascribe to
+that substance the quality whiteness; the sole proof of its possessing
+that quality. But because one thing may be the sole evidence of the
+existence of another thing, it does not follow that the two are one and
+the same. The attribute whiteness (it may be said) is not the fact of
+receiving the sensation, but something in the object itself; a _power_
+inherent in it; something _in virtue_ of which the object produces the
+sensation. And when we affirm that snow possesses the attribute
+whiteness, we do not merely assert that the presence of snow produces in
+us that sensation, but that it does so through, and by reason of, that
+power or quality.
+
+For the purposes of logic it is not of material importance which of
+these opinions we adopt. The full discussion of the subject belongs to
+the other department of scientific inquiry, so often alluded to under
+the name of metaphysics; but it may be said here, that for the doctrine
+of the existence of a peculiar species of entities called qualities, I
+can see no foundation except in a tendency of the human mind which is
+the cause of many delusions. I mean, the disposition, wherever we meet
+with two names which are not precisely synonymous, to suppose that they
+must be the names of two different things; whereas in reality they may
+be names of the same thing viewed in two different lights, or under
+different suppositions as to surrounding circumstances. Because
+_quality_ and _sensation_ cannot be put indiscriminately one for the
+other, it is supposed that they cannot both signify the same thing,
+namely, the impression or feeling with which we are affected through our
+senses by the presence of an object; though there is at least no
+absurdity in supposing that this identical impression or feeling may be
+called a sensation when considered merely in itself, and a quality when
+looked at in relation to any one of the numerous objects, the presence
+of which to our organs excites in our minds that among various other
+sensations or feelings. And if this be admissible as a supposition, it
+rests with those who contend for an entity _per se_ called a quality, to
+show that their opinion is preferable, or is anything in fact but a
+lingering remnant of the scholastic doctrine of occult causes; the very
+absurdity which Moli�re so happily ridiculed when he made one of his
+pedantic physicians account for the fact that "l'opium endormit," by the
+maxim "parcequ'il a une vertu soporifique."
+
+It is evident that when the physician stated that opium had "une vertu
+soporifique," he did not account for, but merely asserted over again,
+the fact that it _endormit_. In like manner, when we say that snow is
+white because it has the quality of whiteness, we are only re-asserting
+in more technical language the fact that it excites in us the sensation
+of white. If it be said that the sensation must have some cause, I
+answer, its cause is the presence of the assemblage of phenomena which
+is termed the object. When we have asserted that as often as the object
+is present, and our organs in their normal state, the sensation takes
+place, we have stated all that we know about the matter. There is no
+need, after assigning a certain and intelligible cause, to suppose an
+occult cause besides, for the purpose of enabling the real cause to
+produce its effect. If I am asked, why does the presence of the object
+cause this sensation in me, I cannot tell: I can only say that such is
+my nature, and the nature of the object; that the fact forms a part of
+the constitution of things. And to this we must at last come, even after
+interpolating the imaginary entity. Whatever number of links the chain
+of causes and effects may consist of, how any one link produces the one
+which is next to it, remains equally inexplicable to us. It is as easy
+to comprehend that the object should produce the sensation directly and
+at once, as that it should produce the same sensation by the aid of
+something else called the _power_ of producing it.
+
+But, as the difficulties which may be felt in adopting this view of the
+subject cannot be removed without discussions transcending the bounds of
+our science, I content myself with a passing indication, and shall, for
+the purposes of logic, adopt a language compatible with either view of
+the nature of qualities. I shall say,--what at least admits of no
+dispute,--that the quality of whiteness ascribed to the object snow, is
+_grounded_ on its exciting in us the sensation of white; and adopting
+the language already used by the school logicians in the case of the
+kind of attributes called Relations, I shall term the sensation of
+white the foundation of the quality whiteness. For logical purposes the
+sensation is the only essential part of what is meant by the word; the
+only part which we ever can be concerned in proving. When that is
+proved, the quality is proved; if an object excites a sensation, it has,
+of course, the power of exciting it.
+
+
+IV. RELATIONS.
+
+� 10. The _qualities_ of a body, we have said, are the attributes
+grounded on the sensations which the presence of that particular body to
+our organs excites in our minds. But when we ascribe to any object the
+kind of attribute called a Relation, the foundation of the attribute
+must be something in which other objects are concerned besides itself
+and the percipient.
+
+As there may with propriety be said to be a relation between any two
+things to which two correlative names are or may be given, we may expect
+to discover what constitutes a relation in general, if we enumerate the
+principal cases in which mankind have imposed correlative names, and
+observe what these cases have in common.
+
+What, then, is the character which is possessed in common by states of
+circumstances so heterogeneous and discordant as these: one thing _like_
+another; one thing _unlike_ another; one thing _near_ another; one thing
+_far from_ another; one thing _before_, _after_, _along with_ another;
+one thing _greater_, _equal_, _less_, than another; one thing the
+_cause_ of another, the _effect_ of another; one person the _master_,
+_servant_, _child_, _parent_, _debtor_, _creditor_, _sovereign_,
+_subject_, _attorney_, _client_, of another, and so on?
+
+Omitting, for the present, the case of Resemblance, (a relation which
+requires to be considered separately,) there seems to be one thing
+common to all these cases, and only one; that in each of them there
+exists or occurs, or has existed or occurred, or may be expected to
+exist or occur, some fact or phenomenon, into which the two things which
+are said to be related to each other, both enter as parties concerned.
+This fact, or phenomenon, is what the Aristotelian logicians called the
+_fundamentum relationis_. Thus in the relation of greater and less
+between two magnitudes, the _fundamentum relationis_ is the fact that
+one of the two magnitudes could, under certain conditions, be included
+in, without entirely filling, the space occupied by the other magnitude.
+In the relation of master and servant, the _fundamentum relationis_ is
+the fact that the one has undertaken, or is compelled, to perform
+certain services for the benefit and at the bidding of the other.
+Examples might be indefinitely multiplied; but it is already obvious
+that whenever two things are said to be related, there is some fact, or
+series of facts, into which they both enter; and that whenever any two
+things are involved in some one fact, or series of facts, we may ascribe
+to those two things a mutual relation grounded on the fact. Even if they
+have nothing in common but what is common to all things, that they are
+members of the universe, we call that a relation, and denominate them
+fellow-creatures, fellow-beings, or fellow-denizens of the universe. But
+in proportion as the fact into which the two objects enter as parts is
+of a more special and peculiar, or of a more complicated nature, so also
+is the relation grounded upon it. And there are as many conceivable
+relations as there are conceivable kinds of fact in which two things can
+be jointly concerned.
+
+In the same manner, therefore, as a quality is an attribute grounded on
+the fact that a certain sensation or sensations are produced in us by
+the object, so an attribute grounded on some fact into which the object
+enters jointly with another object, is a relation between it and that
+other object. But the fact in the latter case consists of the very same
+kind of elements as the fact in the former; namely, states of
+consciousness. In the case, for example, of any legal relation, as
+debtor and creditor, principal and agent, guardian and ward, the
+_fundamentum relationis_ consists entirely of thoughts, feelings, and
+volitions (actual or contingent), either of the persons themselves or of
+other persons concerned in the same series of transactions; as, for
+instance, the intentions which would be formed by a judge, in case a
+complaint were made to his tribunal of the infringement of any of the
+legal obligations imposed by the relation; and the acts which the judge
+would perform in consequence; acts being (as we have already seen)
+another word for intentions followed by an effect, and that effect being
+but another word for sensations, or some other feelings, occasioned
+either to the agent himself or to somebody else. There is no part of
+what the names expressive of the relation imply, that is not resolvable
+into states of consciousness; outward objects being, no doubt, supposed
+throughout as the causes by which some of those states of consciousness
+are excited, and minds as the subjects by which all of them are
+experienced, but neither the external objects nor the minds making their
+existence known otherwise than by the states of consciousness.
+
+Cases of relation are not always so complicated as those to which we
+last alluded. The simplest of all cases of relation are those expressed
+by the words antecedent and consequent, and by the word simultaneous. If
+we say, for instance, that dawn preceded sunrise, the fact in which the
+two things, dawn and sunrise, were jointly concerned, consisted only of
+the two things themselves; no third thing entered into the fact or
+phenomenon at all. Unless, indeed, we choose to call the succession of
+the two objects a third thing; but their succession is not something
+added to the things themselves; it is something involved in them. Dawn
+and sunrise announce themselves to our consciousness by two successive
+sensations. Our consciousness of the succession of these sensations is
+not a third sensation or feeling added to them; we have not first the
+two feelings, and then a feeling of their succession. To have two
+feelings at all, implies having them either successively, or else
+simultaneously. Sensations, or other feelings, being given, succession
+and simultaneousness are the two conditions, to the alternative of which
+they are subjected by the nature of our faculties; and no one has been
+able, or needs expect, to analyse the matter any farther.
+
+
+� 11. In a somewhat similar position are two other sorts of relations,
+Likeness and Unlikeness. I have two sensations; we will suppose them to
+be simple ones; two sensations of white, or one sensation of white and
+another of black. I call the first two sensations _like_; the last two
+_unlike_. What is the fact or phenomenon constituting the _fundamentum_
+of this relation? The two sensations first, and then what we call a
+feeling of resemblance, or of want of resemblance. Let us confine
+ourselves to the former case. Resemblance is evidently a feeling; a
+state of the consciousness of the observer. Whether the feeling of the
+resemblance of the two colours be a third state of consciousness, which
+I have _after_ having the two sensations of colour, or whether (like the
+feeling of their succession) it is involved in the sensations
+themselves, may be a matter of discussion. But in either case, these
+feelings of resemblance, and of its opposite dissimilarity, are parts of
+our nature; and parts so far from being capable of analysis, that they
+are presupposed in every attempt to analyse any of our other feelings.
+Likeness and unlikeness, therefore, as well as antecedence, sequence,
+and simultaneousness, must stand apart among relations, as things _sui
+generis_. They are attributes grounded on facts, that is, on states of
+consciousness, but on states which are peculiar, unresolvable, and
+inexplicable.
+
+But, though likeness or unlikeness cannot be resolved into anything
+else, complex cases of likeness or unlikeness can be resolved into
+simpler ones. When we say of two things which consist of parts, that
+they are like one another, the likeness of the wholes does admit of
+analysis; it is compounded of likenesses between the various parts
+respectively, and of likeness in their arrangement. Of how vast a
+variety of resemblances of parts must that resemblance be composed,
+which induces us to say that a portrait, or a landscape, is like its
+original. If one person mimics another with any success, of how many
+simple likenesses must the general or complex likeness be compounded:
+likeness in a succession of bodily postures; likeness in voice, or in
+the accents and intonations of the voice; likeness in the choice of
+words, and in the thoughts or sentiments expressed, whether by word,
+countenance, or gesture.
+
+All likeness and unlikeness of which we have any cognizance, resolve
+themselves into likeness and unlikeness between states of our own, or
+some other, mind. When we say that one body is like another, (since we
+know nothing of bodies but the sensations which they excite,) we mean
+really that there is a resemblance between the sensations excited by the
+two bodies, or between some portions at least of those sensations. If we
+say that two attributes are like one another, (since we know nothing of
+attributes except the sensations or states of feeling on which they are
+grounded,) we mean really that those sensations, or states of feeling,
+resemble each other. We may also say that two relations are alike. The
+fact of resemblance between relations is sometimes called _analogy_,
+forming one of the numerous meanings of that word. The relation in which
+Priam stood to Hector, namely, that of father and son, resembles the
+relation in which Philip stood to Alexander; resembles it so closely
+that they are called the same relation. The relation in which Cromwell
+stood to England resembles the relation in which Napoleon stood to
+France, though not so closely as to be called the same relation. The
+meaning in both these instances must be, that a resemblance existed
+between the facts which constituted the _fundamentum relationis_.
+
+This resemblance may exist in all conceivable gradations, from perfect
+undistinguishableness to something extremely slight. When we say, that a
+thought suggested to the mind of a person of genius is like a seed cast
+into the ground, because the former produces a multitude of other
+thoughts, and the latter a multitude of other seeds, this is saying that
+between the relation of an inventive mind to a thought contained in it,
+and the relation of a fertile soil to a seed contained in it, there
+exists a resemblance: the real resemblance being in the two _fundamenta
+relationis_, in each of which there occurs a germ, producing by its
+development a multitude of other things similar to itself. And as,
+whenever two objects are jointly concerned in a phenomenon, this
+constitutes a relation between those objects, so, if we suppose a second
+pair of objects concerned in a second phenomenon, the slightest
+resemblance between the two phenomena is sufficient to admit of its
+being said that the two relations resemble; provided, of course, the
+points of resemblance are found in those portions of the two phenomena
+respectively which are connoted by the relative names.
+
+While speaking of resemblance, it is necessary to take notice of an
+ambiguity of language, against which scarcely any one is sufficiently on
+his guard. Resemblance, when it exists in the highest degree of all,
+amounting to undistinguishableness, is often called identity, and the
+two similar things are said to be the same. I say often, not always; for
+we do not say that two visible objects, two persons for instance, are
+the same, because they are so much alike that one might be mistaken for
+the other: but we constantly use this mode of expression when speaking
+of feelings; as when I say that the sight of any object gives me the
+_same_ sensation or emotion to-day that it did yesterday, or the _same_
+which it gives to some other person. This is evidently an incorrect
+application of the word _same_; for the feeling which I had yesterday is
+gone, never to return; what I have to-day is another feeling, exactly
+like the former perhaps, but distinct from it; and it is evident that
+two different persons cannot be experiencing the same feeling, in the
+sense in which we say that they are both sitting at the same table. By a
+similar ambiguity we say, that two persons are ill of the _same_
+disease; that two persons hold the _same_ office; not in the sense in
+which we say that they are engaged in the same adventure, or sailing in
+the same ship, but in the sense that they fill offices exactly similar,
+though, perhaps, in distant places. Great confusion of ideas is often
+produced, and many fallacies engendered, in otherwise enlightened
+understandings, by not being sufficiently alive to the fact (in itself
+not always to be avoided), that they use the same name to express ideas
+so different as those of identity and undistinguishable resemblance.
+Among modern writers, Archbishop Whately stands almost alone in having
+drawn attention to this distinction, and to the ambiguity connected with
+it.
+
+Several relations, generally called by other names, are really cases of
+resemblance. As, for example, equality; which is but another word for
+the exact resemblance commonly called identity, considered as subsisting
+between things in respect of their _quantity_. And this example forms a
+suitable transition to the third and last of the three heads under
+which, as already remarked, Attributes are commonly arranged.
+
+
+V. QUANTITY.
+
+� 12. Let us imagine two things, between which there is no difference
+(that is, no dissimilarity), except in quantity alone: for instance, a
+gallon of water, and more than a gallon of water. A gallon of water,
+like any other external object, makes its presence known to us by a set
+of sensations which it excites. Ten gallons of water are also an
+external object, making its presence known to us in a similar manner;
+and as we do not mistake ten gallons of water for a gallon of water, it
+is plain that the set of sensations is more or less different in the two
+cases. In like manner, a gallon of water, and a gallon of wine, are two
+external objects, making their presence known by two sets of sensations,
+which sensations are different from each other. In the first case,
+however, we say that the difference is in quantity; in the last there is
+a difference in quality, while the quantity of the water and of the wine
+is the same. What is the real distinction between the two cases? It is
+not the province of Logic to analyse it; nor to decide whether it is
+susceptible of analysis or not. For us the following considerations are
+sufficient. It is evident that the sensations I receive from the gallon
+of water, and those I receive from the gallon of wine, are not the same,
+that is, not precisely alike; neither are they altogether unlike: they
+are partly similar, partly dissimilar; and that in which they resemble
+is precisely that in which alone the gallon of water and the ten gallons
+do not resemble. That in which the gallon of water and the gallon of
+wine are like each other, and in which the gallon and the ten gallons of
+water are unlike each other, is called their quantity. This likeness
+and unlikeness I do not pretend to explain, no more than any other kind
+of likeness or unlikeness. But my object is to show, that when we say of
+two things that they differ in quantity, just as when we say that they
+differ in quality, the assertion is always grounded on a difference in
+the sensations which they excite. Nobody, I presume, will say, that to
+see, or to lift, or to drink, ten gallons of water, does not include in
+itself a different set of sensations from those of seeing, lifting, or
+drinking one gallon; or that to see or handle a foot-rule, and to see or
+handle a yard-measure made exactly like it, are the same sensations. I
+do not undertake to say what the difference in the sensations is.
+Everybody knows, and nobody can tell; no more than any one could tell
+what white is to a person who had never had the sensation. But the
+difference, so far as cognizable by our faculties, lies in the
+sensations. Whatever difference we say there is in the things
+themselves, is, in this as in all other cases, grounded, and grounded
+exclusively, on a difference in the sensations excited by them.
+
+
+VI. ATTRIBUTES CONCLUDED.
+
+� 13. Thus, then, all the attributes of bodies which are classed under
+Quality or Quantity, are grounded on the sensations which we receive
+from those bodies, and may be defined, the powers which the bodies have
+of exciting those sensations. And the same general explanation has been
+found to apply to most of the attributes usually classed under the head
+of Relation. They, too, are grounded on some fact or phenomenon into
+which the related objects enter as parts; that fact or phenomenon having
+no meaning and no existence to us, except the series of sensations or
+other states of consciousness by which it makes itself known; and the
+relation being simply the power or capacity which the object possesses
+of taking part along with the correlated object in the production of
+that series of sensations or states of consciousness. We have been
+obliged, indeed, to recognise a somewhat different character in certain
+peculiar relations, those of succession and simultaneity, of likeness
+and unlikeness. These, not being grounded on any fact or phenomenon
+distinct from the related objects themselves, do not admit of the same
+kind of analysis. But these relations, though not, like other relations,
+grounded on states of consciousness, are themselves states of
+consciousness: resemblance is nothing but our feeling of resemblance;
+succession is nothing but our feeling of succession. Or, if this be
+disputed (and we cannot, without transgressing the bounds of our
+science, discuss it here), at least our knowledge of these relations,
+and even our possibility of knowledge, is confined to those which
+subsist between sensations, or other states of consciousness; for,
+though we ascribe resemblance, or succession, or simultaneity, to
+objects and to attributes, it is always in virtue of resemblance or
+succession or simultaneity in the sensations or states of consciousness
+which those objects excite, and on which those attributes are grounded.
+
+
+� 14. In the preceding investigation we have, for the sake of
+simplicity, considered bodies only, and omitted minds. But what we have
+said, is applicable, _mutatis mutandis_, to the latter. The attributes
+of minds, as well as those of bodies, are grounded on states of feeling
+or consciousness. But in the case of a mind, we have to consider its own
+states, as well as those which it produces in other minds. Every
+attribute of a mind consists either in being itself affected in a
+certain way, or affecting other minds in a certain way. Considered in
+itself, we can predicate nothing of it but the series of its own
+feelings. When we say of any mind, that it is devout, or superstitious,
+or meditative, or cheerful, we mean that the ideas, emotions, or
+volitions implied in those words, form a frequently recurring part of
+the series of feelings, or states of consciousness, which fill up the
+sentient existence of that mind.
+
+In addition, however, to those attributes of a mind which are grounded
+on its own states of feeling, attributes may also be ascribed to it, in
+the same manner as to a body, grounded on the feelings which it excites
+in other minds. A mind does not, indeed, like a body, excite
+sensations, but it may excite thoughts or emotions. The most important
+example of attributes ascribed on this ground, is the employment of
+terms expressive of approbation or blame. When, for example, we say of
+any character, or (in other words) of any mind, that it is admirable, we
+mean that the contemplation of it excites the sentiment of admiration;
+and indeed somewhat more, for the word implies that we not only feel
+admiration, but approve that sentiment in ourselves. In some cases,
+under the semblance of a single attribute, two are really predicated:
+one of them, a state of the mind itself; the other, a state with which
+other minds are affected by thinking of it. As when we say of any one
+that he is generous. The word generosity expresses a certain state of
+mind, but being a term of praise, it also expresses that this state of
+mind excites in us another mental state, called approbation. The
+assertion made, therefore, is twofold, and of the following purport:
+Certain feelings form habitually a part of this person's sentient
+existence; and the idea of those feelings of his, excites the sentiment
+of approbation in ourselves or others.
+
+As we thus ascribe attributes to minds on the ground of ideas and
+emotions, so may we to bodies on similar grounds, and not solely on the
+ground of sensations: as in speaking of the beauty of a statue; since
+this attribute is grounded on the peculiar feeling of pleasure which the
+statue produces in our minds; which is not a sensation, but an emotion.
+
+
+VII. GENERAL RESULTS.
+
+� 15. Our survey of the varieties of Things which have been, or which
+are capable of being, named--which have been, or are capable of being,
+either predicated of other Things, or themselves made the subject of
+predications--is now concluded.
+
+Our enumeration commenced with Feelings. These we scrupulously
+distinguished from the objects which excite them, and from the organs by
+which they are, or may be supposed to be, conveyed. Feelings are of
+four sorts: Sensations, Thoughts, Emotions, and Volitions. What are
+called Perceptions are merely a particular case of Belief, and belief is
+a kind of thought. Actions are merely volitions followed by an effect.
+If there be any other kind of mental state not included under these
+subdivisions, we did not think it necessary or proper in this place to
+discuss its existence, or the rank which ought to be assigned to it.
+
+After Feelings we proceeded to Substances. These are either Bodies or
+Minds. Without entering into the grounds of the metaphysical doubts
+which have been raised concerning the existence of Matter and Mind as
+objective realities, we stated as sufficient for us the conclusion in
+which the best thinkers are now for the most part agreed, that all we
+can know of Matter is the sensations which it gives us, and the order of
+occurrence of those sensations; and that while the substance Body is the
+unknown cause of our sensations, the substance Mind is the unknown
+recipient.
+
+The only remaining class of Nameable Things is Attributes; and these are
+of three kinds, Quality, Relation, and Quantity. Qualities, like
+substances, are known to us no otherwise than by the sensations or other
+states of consciousness which they excite: and while, in compliance with
+common usage, we have continued to speak of them as a distinct class of
+Things, we showed that in predicating them no one means to predicate
+anything but those sensations or states of consciousness, on which they
+may be said to be grounded, and by which alone they can be defined or
+described. Relations, except the simple cases of likeness and
+unlikeness, succession and simultaneity, are similarly grounded on some
+fact or phenomenon, that is, on some series of sensations or states of
+consciousness, more or less complicated. The third species of Attribute,
+Quantity, is also manifestly grounded on something in our sensations or
+states of feeling, since there is an indubitable difference in the
+sensations excited by a larger and a smaller bulk, or by a greater or a
+less degree of intensity, in any object of sense or of consciousness.
+All attributes, therefore, are to us nothing but either our sensations
+and other states of feeling, or something inextricably involved
+therein; and to this even the peculiar and simple relations just
+adverted to are not exceptions. Those peculiar relations, however, are
+so important, and, even if they might in strictness be classed among
+states of consciousness, are so fundamentally distinct from any other of
+those states, that it would be a vain subtlety to bring them under that
+common description, and it is necessary that they should be classed
+apart.
+
+As the result, therefore, of our analysis, we obtain the following as an
+enumeration and classification of all Nameable Things:--
+
+1st. Feelings, or States of Consciousness.
+
+2nd. The Minds which experience those feelings.
+
+3rd. The Bodies, or external objects, which excite certain of those
+feelings, together with the powers or properties whereby they excite
+them; these last being included rather in compliance with common
+opinion, and because their existence is taken for granted in the common
+language from which I cannot prudently deviate, than because the
+recognition of such powers or properties as real existences appears to
+be warranted by a sound philosophy.
+
+4th, and last. The Successions and Co-existences, the Likenesses and
+Unlikenesses, between feelings or states of consciousness. Those
+relations, when considered as subsisting between other things, exist in
+reality only between the states of consciousness which those things, if
+bodies, excite, if minds, either excite or experience.
+
+This, until a better can be suggested, may serve as a substitute for the
+abortive Classification of Existences, termed the Categories of
+Aristotle. The practical application of it will appear when we commence
+the inquiry into the Import of Propositions; in other words, when we
+inquire what it is which the mind actually believes, when it gives what
+is called its assent to a proposition.
+
+These four classes comprising, if the classification be correct, all
+Nameable Things, these or some of them must of course compose the
+signification of all names; and of these, or some of them, is made up
+whatever we call a fact.
+
+For distinction's sake, every fact which is solely composed of feelings
+or states of consciousness considered as such, is often called a
+Psychological or Subjective fact; while every fact which is composed,
+either wholly or in part, of something different from these, that is, of
+substances and attributes, is called an Objective fact. We may say,
+then, that every objective fact is grounded on a corresponding
+subjective one; and has no meaning to us, (apart from the subjective
+fact which corresponds to it,) except as a name for the unknown and
+inscrutable process by which that subjective or psychological fact is
+brought to pass.
+
+
+
+
+CHAPTER IV.
+
+OF PROPOSITIONS.
+
+
+� 1. In treating of Propositions, as already in treating of Names, some
+considerations of a comparatively elementary nature respecting their
+form and varieties must be premised, before entering upon that analysis
+of the import conveyed by them, which is the real subject and purpose of
+this preliminary book.
+
+A proposition, we have before said, is a portion of discourse in which a
+predicate is affirmed or denied of a subject. A predicate and a subject
+are all that is necessarily required to make up a proposition: but as we
+cannot conclude from merely seeing two names put together, that they are
+a predicate and a subject, that is, that one of them is intended to be
+affirmed or denied of the other, it is necessary that there should be
+some mode or form of indicating that such is the intention; some sign to
+distinguish a predication from any other kind of discourse. This is
+sometimes done by a slight alteration of one of the words, called an
+_inflection_; as when we say, Fire burns; the change of the second word
+from _burn_ to _burns_ showing that we mean to affirm the predicate burn
+of the subject fire. But this function is more commonly fulfilled by the
+word _is_, when an affirmation is intended, _is not_, when a negation;
+or by some other part of the verb _to be_. The word which thus serves
+the purpose of a sign of predication is called, as we formerly observed,
+the _copula_. It is important that there should be no indistinctness in
+our conception of the nature and office of the copula; for confused
+notions respecting it are among the causes which have spread mysticism
+over the field of logic, and perverted its speculations into
+logomachies.
+
+It is apt to be supposed that the copula is something more than a mere
+sign of predication; that it also signifies existence. In the
+proposition, Socrates is just, it may seem to be implied not only that
+the quality _just_ can be affirmed of Socrates, but moreover that
+Socrates _is_, that is to say, exists. This, however, only shows that
+there is an ambiguity in the word _is_; a word which not only performs
+the function of the copula in affirmations, but has also a meaning of
+its own, in virtue of which it may itself be made the predicate of a
+proposition. That the employment of it as a copula does not necessarily
+include the affirmation of existence, appears from such a proposition as
+this, A centaur is a fiction of the poets; where it cannot possibly be
+implied that a centaur exists, since the proposition itself expressly
+asserts that the thing has no real existence.
+
+Many volumes might be filled with the frivolous speculations concerning
+the nature of Being, ([Greek: to on, ousia], Ens, Entitas, Essentia, and
+the like) which have arisen from overlooking this double meaning of the
+word _to be_; from supposing that when it signifies _to exist_, and when
+it signifies to _be_ some specified thing, as to _be_ a man, to _be_
+Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a
+nonentity, it must still, at bottom, answer to the same idea; and that a
+meaning must be found for it which shall suit all these cases. The fog
+which rose from this narrow spot diffused itself at an early period over
+the whole surface of metaphysics. Yet it becomes us not to triumph over
+the great intellects of Plato and Aristotle because we are now able to
+preserve ourselves from many errors into which they, perhaps inevitably,
+fell. The fire-teazer of a modern steam-engine produces by his exertions
+far greater effects than Milo of Crotona could, but he is not therefore
+a stronger man. The Greeks seldom knew any language but their own. This
+rendered it far more difficult for them than it is for us, to acquire a
+readiness in detecting ambiguities. One of the advantages of having
+accurately studied a plurality of languages, especially of those
+languages which eminent thinkers have used as the vehicle of their
+thoughts, is the practical lesson we learn respecting the ambiguities of
+words, by finding that the same word in one language corresponds, on
+different occasions, to different words in another. When not thus
+exercised, even the strongest understandings find it difficult to
+believe that things which have a common name, have not in some respect
+or other a common nature; and often expend much labour very unprofitably
+(as was frequently done by the two philosophers just mentioned) in vain
+attempts to discover in what this common nature consists. But, the habit
+once formed, intellects much inferior are capable of detecting even
+ambiguities which are common to many languages: and it is surprising
+that the one now under consideration, though it exists in the modern
+languages as well as in the ancient, should have been overlooked by
+almost all authors. The quantity of futile speculation which had been
+caused by a misapprehension of the nature of the copula, was hinted at
+by Hobbes; but Mr. James Mill[15] was, I believe, the first who
+distinctly characterized the ambiguity, and pointed out how many errors
+in the received systems of philosophy it has had to answer for. It has
+indeed misled the moderns scarcely less than the ancients, though their
+mistakes, because our understandings are not yet so completely
+emancipated from their influence, do not appear equally irrational.
+
+We shall now briefly review the principal distinctions which exist among
+propositions, and the technical terms most commonly in use to express
+those distinctions.
+
+
+� 2. A proposition being a portion of discourse in which something is
+affirmed or denied of something, the first division of propositions is
+into affirmative and negative. An affirmative proposition is that in
+which the predicate is _affirmed_ of the subject; as, C�sar is dead. A
+negative proposition is that in which the predicate is _denied_ of the
+subject; as, C�sar is not dead. The copula, in this last species of
+proposition, consists of the words _is not_, which are the sign of
+negation; _is_ being the sign of affirmation.
+
+Some logicians, among whom may be mentioned Hobbes, state this
+distinction differently; they recognise only one form of copula, _is_,
+and attach the negative sign to the predicate. "C�sar is dead," and
+"C�sar is not dead," according to these writers, are propositions
+agreeing not in the subject and predicate, but in the subject only. They
+do not consider "dead," but "not dead," to be the predicate of the
+second proposition, and they accordingly define a negative proposition
+to be one in which the predicate is a negative name. The point, though
+not of much practical moment, deserves notice as an example (not
+unfrequent in logic) where by means of an apparent simplification, but
+which is merely verbal, matters are made more complex than before. The
+notion of these writers was, that they could get rid of the distinction
+between affirming and denying, by treating every case of denying as the
+affirming of a negative name. But what is meant by a negative name? A
+name expressive of the _absence_ of an attribute. So that when we affirm
+a negative name, what we are really predicating is absence and not
+presence; we are asserting not that anything is, but that something is
+not; to express which operation no word seems so proper as the word
+denying. The fundamental distinction is between a fact and the
+non-existence of that fact; between seeing something and not seeing it,
+between C�sar's being dead and his not being dead; and if this were a
+merely verbal distinction, the generalization which brings both within
+the same form of assertion would be a real simplification: the
+distinction, however, being real, and in the facts, it is the
+generalization confounding the distinction that is merely verbal; and
+tends to obscure the subject, by treating the difference between two
+kinds of truths as if it were only a difference between two kinds of
+words. To put things together, and to put them or keep them asunder,
+will remain different operations, whatever tricks we may play with
+language.
+
+A remark of a similar nature may be applied to most of those
+distinctions among propositions which are said to have reference to
+their _modality_; as, difference of tense or time; the sun _did_ rise,
+the sun _is_ rising, the sun _will_ rise. These differences, like that
+between affirmation and negation, might be glossed over by considering
+the incident of time as a mere modification of the predicate: thus, The
+sun is _an object having risen_, The sun is _an object now rising_, The
+sun is _an object to rise hereafter_. But the simplification would be
+merely verbal. Past, present, and future, do not constitute so many
+different kinds of rising; they are designations belonging to the event
+asserted, to the _sun's_ rising to-day. They affect, not the predicate,
+but the applicability of the predicate to the particular subject. That
+which we affirm to be past, present, or future, is not what the subject
+signifies, nor what the predicate signifies, but specifically and
+expressly what the predication signifies; what is expressed only by the
+proposition as such, and not by either or both of the terms. Therefore
+the circumstance of time is properly considered as attaching to the
+copula, which is the sign of predication, and not to the predicate. If
+the same cannot be said of such modifications as these, C�sar _may_ be
+dead; C�sar is _perhaps_ dead; it is _possible_ that C�sar is dead; it
+is only because these fall altogether under another head, being properly
+assertions not of anything relating to the fact itself, but of the state
+of our own mind in regard to it; namely, our absence of disbelief of it.
+Thus "C�sar may be dead" means "I am not sure that C�sar is alive."
+
+
+� 3. The next division of propositions is into Simple and Complex. A
+simple proposition is that in which one predicate is affirmed or denied
+of one subject. A complex proposition is that in which there is more
+than one predicate, or more than one subject, or both.
+
+At first sight this division has the air of an absurdity; a solemn
+distinction of things into one and more than one; as if we were to
+divide horses into single horses and teams of horses. And it is true
+that what is called a complex proposition is often not a proposition at
+all, but several propositions, held together by a conjunction. Such, for
+example, is this: C�sar is dead, and Brutus is alive: or even this,
+C�sar is dead, _but_ Brutus is alive. There are here two distinct
+assertions; and we might as well call a street a complex house, as
+these two propositions a complex proposition. It is true that the
+syncategorematic words _and_ and _but_ have a meaning; but that meaning
+is so far from making the two propositions one, that it adds a third
+proposition to them. All particles are abbreviations, and generally
+abbreviations of propositions; a kind of short-hand, whereby something
+which, to be expressed fully, would have required a proposition or a
+series of propositions, is suggested to the mind at once. Thus the
+words, C�sar is dead and Brutus is alive, are equivalent to these: C�sar
+is dead; Brutus is alive; it is desired that the two preceding
+propositions should be thought of together. If the words were, C�sar is
+dead _but_ Brutus is alive, the sense would be equivalent to the same
+three propositions together with a fourth; "between the two preceding
+propositions there exists a contrast:" viz. either between the two facts
+themselves, or between the feelings with which it is desired that they
+should be regarded.
+
+In the instances cited the two propositions are kept visibly distinct,
+each subject having its separate predicate, and each predicate its
+separate subject. For brevity, however, and to avoid repetition, the
+propositions are often blended together: as in this, "Peter and James
+preached at Jerusalem and in Galilee," which contains four propositions:
+Peter preached at Jerusalem, Peter preached in Galilee, James preached
+at Jerusalem, James preached in Galilee.
+
+We have seen that when the two or more propositions comprised in what is
+called a complex proposition are stated absolutely, and not under any
+condition or proviso, it is not a proposition at all, but a plurality of
+propositions; since what it expresses is not a single assertion, but
+several assertions, which, if true when joined, are true also when
+separated. But there is a kind of proposition which, though it contains
+a plurality of subjects and of predicates, and may be said in one sense
+of the word to consist of several propositions, contains but one
+assertion; and its truth does not at all imply that of the simple
+propositions which compose it. An example of this is, when the simple
+propositions are connected by the particle _or_; as, Either A is B or C
+is D; or by the particle _if_; as, A is B if C is D. In the former case,
+the proposition is called _disjunctive_, in the latter, _conditional_:
+the name _hypothetical_ was originally common to both. As has been well
+remarked by Archbishop Whately and others, the disjunctive form is
+resolvable into the conditional; every disjunctive proposition being
+equivalent to two or more conditional ones. "Either A is B or C is D,"
+means, "if A is not B, C is D; and if C is not D, A is B." All
+hypothetical propositions, therefore, though disjunctive in form, are
+conditional in meaning; and the words hypothetical and conditional may
+be, as indeed they generally are, used synonymously. Propositions in
+which the assertion is not dependent on a condition, are said, in the
+language of logicians, to be _categorical_.
+
+An hypothetical proposition is not, like the pretended complex
+propositions which we previously considered, a mere aggregation of
+simple propositions. The simple propositions which form part of the
+words in which it is couched, form no part of the assertion which it
+conveys. When we say, If the Koran comes from God, Mahomet is the
+prophet of God, we do not intend to affirm either that the Koran does
+come from God, or that Mahomet is really his prophet. Neither of these
+simple propositions may be true, and yet the truth of the hypothetical
+proposition may be indisputable. What is asserted is not the truth of
+either of the propositions, but the inferribility of the one from the
+other. What, then, is the subject, and what the predicate of the
+hypothetical proposition? "The Koran" is not the subject of it, nor is
+"Mahomet:" for nothing is affirmed or denied either of the Koran or of
+Mahomet. The real subject of the predication is the entire proposition,
+"Mahomet is the prophet of God;" and the affirmation is, that this is a
+legitimate inference from the proposition, "The Koran comes from God."
+The subject and predicate, therefore, of an hypothetical proposition are
+names of propositions. The subject is some one proposition. The
+predicate is a general relative name applicable to propositions; of this
+form--"an inference from so and so." A fresh instance is here afforded
+of the remark, that particles are abbreviations; since "_If_ A is B, C
+is D," is found to be an abbreviation of the following: "The proposition
+C is D, is a legitimate inference from the proposition A is B."
+
+The distinction, therefore, between hypothetical and categorical
+propositions, is not so great as it at first appears. In the
+conditional, as well as in the categorical form, one predicate is
+affirmed of one subject, and no more: but a conditional proposition is a
+proposition concerning a proposition; the subject of the assertion is
+itself an assertion. Nor is this a property peculiar to hypothetical
+propositions. There are other classes of assertions concerning
+propositions. Like other things, a proposition has attributes which may
+be predicated of it. The attribute predicated of it in an hypothetical
+proposition, is that of being an inference from a certain other
+proposition. But this is only one of many attributes that might be
+predicated. We may say, That the whole is greater than its part, is an
+axiom in mathematics: That the Holy Ghost proceeds from the Father
+alone, is a tenet of the Greek Church: The doctrine of the divine right
+of kings was renounced by Parliament at the Revolution: The
+infallibility of the Pope has no countenance from Scripture. In all
+these cases the subject of the predication is an entire proposition.
+That which these different predicates are affirmed of, is _the
+proposition_, "the whole is greater than its part;" _the proposition_,
+"the Holy Ghost proceeds from the Father alone;" _the proposition_,
+"kings have a divine right;" _the proposition_, "the Pope is
+infallible."
+
+Seeing, then, that there is much less difference between hypothetical
+propositions and any others, than one might be led to imagine from their
+form, we should be at a loss to account for the conspicuous position
+which they have been selected to fill in treatises on logic, if we did
+not remember that what they predicate of a proposition, namely, its
+being an inference from something else, is precisely that one of its
+attributes with which most of all a logician is concerned.
+
+
+� 4. The next of the common divisions of Propositions is into
+Universal, Particular, Indefinite, and Singular: a distinction founded
+on the degree of generality in which the name, which is the subject of
+the proposition, is to be understood. The following are examples:
+
+  _All men_ are mortal--       Universal.
+  _Some men_ are mortal--      Particular.
+  _Man_ is mortal--            Indefinite.
+  _Julius C�sar_ is mortal--   Singular.
+
+The proposition is Singular, when the subject is an individual name. The
+individual name needs not be a proper name. "The Founder of Christianity
+was crucified," is as much a singular proposition as "Christ was
+crucified."
+
+When the name which is the subject of the proposition is a general name,
+we may intend to affirm or deny the predicate, either of all the things
+that the subject denotes, or only of some. When the predicate is
+affirmed or denied of all and each of the things denoted by the subject,
+the proposition is universal; when of some undefined portion of them
+only, it is particular. Thus, All men are mortal; Every man is mortal;
+are universal propositions. No man is immortal, is also an universal
+proposition, since the predicate, immortal, is denied of each and every
+individual denoted by the term man; the negative proposition being
+exactly equivalent to the following, Every man is not-immortal. But
+"some men are wise," "some men are not wise," are particular
+propositions; the predicate _wise_ being in the one case affirmed and in
+the other denied not of each and every individual denoted by the term
+man, but only of each and every one of some portion of those
+individuals, without specifying what portion; for if this were
+specified, the proposition would be changed either into a singular
+proposition, or into an universal proposition with a different subject;
+as, for instance, "all _properly instructed_ men are wise." There are
+other forms of particular propositions; as, "_Most_ men are imperfectly
+educated:" it being immaterial how large a portion of the subject the
+predicate is asserted of, as long as it is left uncertain how that
+portion is to be distinguished from the rest.
+
+When the form of the expression does not clearly show whether the
+general name which is the subject of the proposition is meant to stand
+for all the individuals denoted by it, or only for some of them, the
+proposition is, by some logicians, called Indefinite; but this, as
+Archbishop Whately observes, is a solecism, of the same nature as that
+committed by some grammarians when in their list of genders they
+enumerate the _doubtful_ gender. The speaker must mean to assert the
+proposition either as an universal or as a particular proposition,
+though he has failed to declare which: and it often happens that though
+the words do not show which of the two he intends, the context, or the
+custom of speech, supplies the deficiency. Thus, when it is affirmed
+that "Man is mortal," nobody doubts that the assertion is intended of
+all human beings; and the word indicative of universality is commonly
+omitted, only because the meaning is evident without it. In the
+proposition, "Wine is good," it is understood with equal readiness,
+though for somewhat different reasons, that the assertion is not
+intended to be universal, but particular.[16]
+
+When a general name stands for each and every individual which it is a
+name of, or in other words, which it denotes, it is said by logicians to
+be _distributed_, or taken distributively. Thus, in the proposition, All
+men are mortal, the subject, Man, is distributed, because mortality is
+affirmed of each and every man. The predicate, Mortal, is not
+distributed, because the only mortals who are spoken of in the
+proposition are those who happen to be men; while the word may, for
+aught that appears, and in fact does, comprehend within it an indefinite
+number of objects besides men. In the proposition, Some men are mortal,
+both the predicate and the subject are undistributed. In the following,
+No men have wings, both the predicate and the subject are distributed.
+Not only is the attribute of having wings denied of the entire class
+Man, but that class is severed and cast out from the whole of the class
+Winged, and not merely from some part of that class.
+
+This phraseology, which is of great service in stating and
+demonstrating the rules of the syllogism, enables us to express very
+concisely the definitions of an universal and a particular proposition.
+An universal proposition is that of which the subject is distributed; a
+particular proposition is that of which the subject is undistributed.
+
+There are many more distinctions among propositions than those we have
+here stated, some of them of considerable importance. But, for
+explaining and illustrating these, more suitable opportunities will
+occur in the sequel.
+
+
+
+
+CHAPTER V.
+
+OF THE IMPORT OF PROPOSITIONS.
+
+
+� 1. An inquiry into the nature of propositions must have one of two
+objects: to analyse the state of mind called Belief, or to analyse what
+is believed. All language recognises a difference between a doctrine or
+opinion, and the fact of entertaining the opinion; between assent, and
+what is assented to.
+
+Logic, according to the conception here formed of it, has no concern
+with the nature of the act of judging or believing; the consideration of
+that act, as a phenomenon of the mind, belongs to another science.
+Philosophers, however, from Descartes downwards, and especially from the
+era of Leibnitz and Locke, have by no means observed this distinction;
+and would have treated with great disrespect any attempt to analyse the
+import of Propositions, unless founded on an analysis of the act of
+Judgment. A proposition, they would have said, is but the expression in
+words of a Judgment. The thing expressed, not the mere verbal
+expression, is the important matter. When the mind assents to a
+proposition, it judges. Let us find out what the mind does when it
+judges, and we shall know what propositions mean, and not otherwise.
+
+Conformably to these views, almost all the writers on Logic in the last
+two centuries, whether English, German, or French, have made their
+theory of Propositions, from one end to the other, a theory of
+Judgments. They considered a Proposition, or a Judgment, for they used
+the two words indiscriminately, to consist in affirming or denying one
+_idea_ of another. To judge, was to put two ideas together, or to bring
+one idea under another, or to compare two ideas, or to perceive the
+agreement or disagreement between two ideas: and the whole doctrine of
+Propositions, together with the theory of Reasoning, (always necessarily
+founded on the theory of Propositions,) was stated as if Ideas, or
+Conceptions, or whatever other term the writer preferred as a name for
+mental representations generally, constituted essentially the subject
+matter and substance of those operations.
+
+It is, of course, true, that in any case of judgment, as for instance
+when we judge that gold is yellow, a process takes place in our minds,
+of which some one or other of these theories is a partially correct
+account. We must have the idea of gold and the idea of yellow, and these
+two ideas must be brought together in our mind. But in the first place,
+it is evident that this is only a part of what takes place; for we may
+put two ideas together without any act of belief; as when we merely
+imagine something, such as a golden mountain; or when we actually
+disbelieve: for in order even to disbelieve that Mahomet was an apostle
+of God, we must put the idea of Mahomet and that of an apostle of God
+together. To determine what it is that happens in the case of assent or
+dissent besides putting two ideas together, is one of the most intricate
+of metaphysical problems. But whatever the solution may be, we may
+venture to assert that it can have nothing whatever to do with the
+import of propositions; for this reason, that propositions (except
+sometimes when the mind itself is the subject treated of) are not
+assertions respecting our ideas of things, but assertions respecting the
+things themselves. In order to believe that gold is yellow, I must,
+indeed, have the idea of gold, and the idea of yellow, and something
+having reference to those ideas must take place in my mind; but my
+belief has not reference to the ideas, it has reference to the things.
+What I believe, is a fact relating to the outward thing, gold, and to
+the impression made by that outward thing upon the human organs; not a
+fact relating to my conception of gold, which would be a fact in my
+mental history, not a fact of external nature. It is true, that in order
+to believe this fact in external nature, another fact must take place in
+my mind, a process must be performed upon my ideas; but so it must in
+everything else that I do. I cannot dig the ground unless I have the
+idea of the ground, and of a spade, and of all the other things I am
+operating upon, and unless I put those ideas together.[17] But it would
+be a very ridiculous description of digging the ground to say that it is
+putting one idea into another. Digging is an operation which is
+performed upon the things themselves, though it cannot be performed
+unless I have in my mind the ideas of them. And in like manner,
+believing is an act which has for its subject the facts themselves,
+though a previous mental conception of the facts is an indispensable
+condition. When I say that fire causes heat, do I mean that my idea of
+fire causes my idea of heat? No: I mean that the natural phenomenon,
+fire, causes the natural phenomenon, heat. When I mean to assert
+anything respecting the ideas, I give them their proper name, I call
+them ideas: as when I say, that a child's idea of a battle is unlike the
+reality, or that the ideas entertained of the Deity have a great effect
+on the characters of mankind.
+
+The notion that what is of primary importance to the logician in a
+proposition, is the relation between the two _ideas_ corresponding to
+the subject and predicate, (instead of the relation between the two
+_phenomena_ which they respectively express,) seems to me one of the
+most fatal errors ever introduced into the philosophy of Logic; and the
+principal cause why the theory of the science has made such
+inconsiderable progress during the last two centuries. The treatises on
+Logic, and on the branches of Mental Philosophy connected with Logic,
+which have been produced since the intrusion of this cardinal error,
+though sometimes written by men of extraordinary abilities and
+attainments, almost always tacitly imply a theory that the investigation
+of truth consists in contemplating and handling our ideas, or
+conceptions of things, instead of the things themselves: a doctrine
+tantamount to the assertion, that the only mode of acquiring knowledge
+of nature is to study it at second hand, as represented in our own
+minds. Meanwhile, inquiries into every kind of natural phenomena were
+incessantly establishing great and fruitful truths on most important
+subjects, by processes upon which these views of the nature of Judgment
+and Reasoning threw no light, and in which they afforded no assistance
+whatever. No wonder that those who knew by practical experience how
+truths are arrived at, should deem a science futile, which consisted
+chiefly of such speculations. What has been done for the advancement of
+Logic since these doctrines came into vogue, has been done not by
+professed logicians, but by discoverers in the other sciences; in whose
+methods of investigation many principles of logic, not previously
+thought of, have successively come forth into light, but who have
+generally committed the error of supposing that nothing whatever was
+known of the art of philosophizing by the old logicians, because their
+modern interpreters have written to so little purpose respecting it.
+
+We have to inquire, then, on the present occasion, not into Judgment,
+but judgments; not into the act of believing, but into the thing
+believed. What is the immediate object of belief in a Proposition? What
+is the matter of fact signified by it? What is it to which, when I
+assert the proposition, I give my assent, and call upon others to give
+theirs? What is that which is expressed by the form of discourse called
+a Proposition, and the conformity of which to fact constitutes the truth
+of the proposition?
+
+
+� 2. One of the clearest and most consecutive thinkers whom this country
+or the world has produced, I mean Hobbes, has given the following answer
+to this question. In every proposition (says he) what is signified is,
+the belief of the speaker that the predicate is a name of the same thing
+of which the subject is a name; and if it really is so, the proposition
+is true. Thus the proposition, All men are living beings (he would say)
+is true, because _living being_ is a name of everything of which _man_
+is a name. All men are six feet high, is not true, because _six feet
+high_ is not a name of everything (though it is of some things) of which
+_man_ is a name.
+
+What is stated in this theory as the definition of a true proposition,
+must be allowed to be a property which all true propositions possess.
+The subject and predicate being both of them names of things, if they
+were names of quite different things the one name could not,
+consistently with its signification, be predicated of the other. If it
+be true that some men are copper-coloured, it must be true--and the
+proposition does really assert--that among the individuals denoted by
+the name man, there are some who are also among those denoted by the
+name copper-coloured. If it be true that all oxen ruminate, it must be
+true that all the individuals denoted by the name ox are also among
+those denoted by the name ruminating; and whoever asserts that all oxen
+ruminate, undoubtedly does assert that this relation subsists between
+the two names.
+
+The assertion, therefore, which, according to Hobbes, is the only one
+made in any proposition, really is made in every proposition: and his
+analysis has consequently one of the requisites for being the true one.
+We may go a step farther; it is the only analysis that is rigorously
+true of all propositions without exception. What he gives as the meaning
+of propositions, is part of the meaning of all propositions, and the
+whole meaning of some. This, however, only shows what an extremely
+minute fragment of meaning it is quite possible to include within the
+logical formula of a proposition. It does not show that no proposition
+means more. To warrant us in putting together two words with a copula
+between them, it is really enough that the thing or things denoted by
+one of the names should be capable, without violation of usage, of being
+called by the other name also. If, then, this be all the meaning
+necessarily implied in the form of discourse called a Proposition, why
+do I object to it as the scientific definition of what a proposition
+means? Because, though the mere collocation which makes the proposition
+a proposition, conveys no more than this scanty amount of meaning, that
+same collocation combined with other circumstances, that _form_
+combined with other _matter_, does convey more, and much more.
+
+The only propositions of which Hobbes' principle is a sufficient
+account, are that limited and unimportant class in which both the
+predicate and the subject are proper names. For, as has already been
+remarked, proper names have strictly no meaning; they are mere marks for
+individual objects: and when a proper name is predicated of another
+proper name, all the signification conveyed is, that both the names are
+marks for the same object. But this is precisely what Hobbes produces as
+a theory of predication in general. His doctrine is a full explanation
+of such predications as these: Hyde was Clarendon, or, Tully is Cicero.
+It exhausts the meaning of those propositions. But it is a sadly
+inadequate theory of any others. That it should ever have been thought
+of as such, can be accounted for only by the fact, that Hobbes, in
+common with the other Nominalists, bestowed little or no attention upon
+the _connotation_ of words; and sought for their meaning exclusively in
+what they _denote_: as if all names had been (what none but proper names
+really are) marks put upon individuals; and as if there were no
+difference between a proper and a general name, except that the first
+denotes only one individual, and the last a greater number.
+
+It has been seen, however, that the meaning of all names, except proper
+names and that portion of the class of abstract names which are not
+connotative, resides in the connotation. When, therefore, we are
+analysing the meaning of any proposition in which the predicate and the
+subject, or either of them, are connotative names, it is to the
+connotation of those terms that we must exclusively look, and not to
+what they _denote_, or in the language of Hobbes (language so far
+correct) are names of.
+
+In asserting that the truth of a proposition depends on the conformity
+of import between its terms, as, for instance, that the proposition,
+Socrates is wise, is a true proposition, because Socrates and wise are
+names applicable to, or, as he expresses it, names of, the same person;
+it is very remarkable that so powerful a thinker should not have asked
+himself the question, But how came they to be names of the same person?
+Surely not because such was the intention of those who invented the
+words. When mankind fixed the meaning of the word wise, they were not
+thinking of Socrates, nor, when his parents gave him the name of
+Socrates, were they thinking of wisdom. The names _happen_ to fit the
+same person because of a certain _fact_, which fact was not known, nor
+in being, when the names were invented. If we want to know what the fact
+is, we shall find the clue to it in the _connotation_ of the names.
+
+A bird or a stone, a man, or a wise man, means simply, an object having
+such and such attributes. The real meaning of the word man, is those
+attributes, and not Smith, Brown, and the remainder of the individuals.
+The word _mortal_, in like manner connotes a certain attribute or
+attributes; and when we say, All men are mortal, the meaning of the
+proposition is, that all beings which possess the one set of attributes,
+possess also the other. If, in our experience, the attributes connoted
+by _man_ are always accompanied by the attribute connoted by _mortal_,
+it will follow as a consequence, that the class _man_ will be wholly
+included in the class _mortal_, and that _mortal_ will be a name of all
+things of which _man_ is a name: but why? Those objects are brought
+under the name, by possessing the attributes connoted by it: but their
+possession of the attributes is the real condition on which the truth of
+the proposition depends; not their being called by the name. Connotative
+names do not precede, but follow, the attributes which they connote. If
+one attribute happens to be always found in conjunction with another
+attribute, the concrete names which answer to those attributes will of
+course be predicable of the same subjects, and may be said, in Hobbes'
+language, (in the propriety of which on this occasion I fully concur,)
+to be two names for the same things. But the possibility of a concurrent
+application of the two names, is a mere consequence of the conjunction
+between the two attributes, and was, in most cases, never thought of
+when the names were introduced and their signification fixed. That the
+diamond is combustible, was a proposition certainly not dreamt of when
+the words Diamond and Combustible first received their meaning; and
+could not have been discovered by the most ingenious and refined
+analysis of the signification of those words. It was found out by a very
+different process, namely, by exerting the senses, and learning from
+them, that the attribute of combustibility existed in the diamonds upon
+which the experiment was tried; the number or character of the
+experiments being such, that what was true of those individuals might be
+concluded to be true of all substances "called by the name," that is, of
+all substances possessing the attributes which the name connotes. The
+assertion, therefore, when analysed, is, that wherever we find certain
+attributes, there will be found a certain other attribute: which is not
+a question of the signification of names, but of laws of nature; the
+order existing among phenomena.
+
+
+� 3. Although Hobbes' theory of Predication has not, in the terms in
+which he stated it, met with a very favourable reception from subsequent
+thinkers, a theory virtually identical with it, and not by any means so
+perspicuously expressed, may almost be said to have taken the rank of an
+established opinion. The most generally received notion of Predication
+decidedly is that it consists in referring something to a class, _i.e._,
+either placing an individual under a class, or placing one class under
+another class. Thus, the proposition, Man is mortal, asserts, according
+to this view of it, that the class man is included in the class mortal.
+"Plato is a philosopher," asserts that the individual Plato is one of
+those who compose the class philosopher. If the proposition is negative,
+then instead of placing something in a class, it is said to exclude
+something from a class. Thus, if the following be the proposition, The
+elephant is not carnivorous; what is asserted (according to this theory)
+is, that the elephant is excluded, from the class carnivorous, or is not
+numbered among the things comprising that class. There is no real
+difference, except in language, between this theory of Predication and
+the theory of Hobbes. For a class _is_ absolutely nothing but an
+indefinite number of individuals denoted by a general name. The name
+given to them in common, is what makes them a class. To refer anything
+to a class, therefore, is to look upon it as one of the things which are
+to be called by that common name. To exclude it from a class, is to say
+that the common name is not applicable to it.
+
+How widely these views of predication have prevailed, is evident from
+this, that they are the basis of the celebrated _dictum de omni et
+nullo_. When the syllogism is resolved, by all who treat of it, into an
+inference that what is true of a class is true of all things whatever
+that belong to the class; and when this is laid down by almost all
+professed logicians as the ultimate principle to which all reasoning
+owes its validity; it is clear that in the general estimation of
+logicians, the propositions of which reasonings are composed can be the
+expression of nothing but the process of dividing things into classes,
+and referring everything to its proper class.
+
+This theory appears to me a signal example of a logical error very often
+committed in logic, that of [Greek: hysteron proteron], or explaining a
+thing by something which presupposes it. When I say that snow is white,
+I may and ought to be thinking of snow as a class, because I am
+asserting a proposition as true of all snow: but I am certainly not
+thinking of white objects as a class; I am thinking of no white object
+whatever except snow, but only of that, and of the sensation of white
+which it gives me. When, indeed, I have judged, or assented to the
+propositions, that snow is white, and that several other things are also
+white, I gradually begin to think of white objects as a class, including
+snow and those other things. But this is a conception which followed,
+not preceded, those judgments, and therefore cannot be given as an
+explanation of them. Instead of explaining the effect by the cause, this
+doctrine explains the cause by the effect, and is, I conceive, founded
+on a latent misconception of the nature of classification.
+
+There is a sort of language very generally prevalent in these
+discussions, which seems to suppose that classification is an
+arrangement and grouping of definite and known individuals: that when
+names were imposed, mankind took into consideration all the individual
+objects in the universe, distributed them into parcels or lists, and
+gave to the objects of each list a common name, repeating this operation
+_toties quoties_ until they had invented all the general names of which
+language consists; which having been once done, if a question
+subsequently arises whether a certain general name can be truly
+predicated of a certain particular object, we have only (as it were) to
+read the roll of the objects upon which that name was conferred, and see
+whether the object about which the question arises is to be found among
+them. The framers of language (it would seem to be supposed) have
+predetermined all the objects that are to compose each class, and we
+have only to refer to the record of an antecedent decision.
+
+So absurd a doctrine will be owned by nobody when thus nakedly stated;
+but if the commonly received explanations of classification and naming
+do not imply this theory, it requires to be shown how they admit of
+being reconciled with any other.
+
+General names are not marks put upon definite objects; classes are not
+made by drawing a line round a given number of assignable individuals.
+The objects which compose any given class are perpetually fluctuating.
+We may frame a class without knowing the individuals, or even any of the
+individuals, of which it may be composed; we may do so while believing
+that no such individuals exist. If by the _meaning_ of a general name
+are to be understood the things which it is the name of, no general
+name, except by accident, has a fixed meaning at all, or ever long
+retains the same meaning. The only mode in which any general name has a
+definite meaning, is by being a name of an indefinite variety of things;
+namely, of all things, known or unknown, past, present, or future, which
+possess certain definite attributes. When, by studying not the meaning
+of words, but the phenomena of nature, we discover that these attributes
+are possessed by some object not previously known to possess them, (as
+when chemists found that the diamond was combustible), we include this
+new object in the class; but it did not already belong to the class. We
+place the individual in the class because the proposition is true; the
+proposition is not true because the object is placed in the class.
+
+It will appear hereafter, in treating of reasoning, how much the theory
+of that intellectual process has been vitiated by the influence of these
+erroneous notions, and by the habit which they exemplify of assimilating
+all the operations of the human understanding which have truth for their
+object, to processes of mere classification and naming. Unfortunately,
+the minds which have been entangled in this net are precisely those
+which have escaped the other cardinal error commented upon in the
+beginning of the present chapter. Since the revolution which dislodged
+Aristotle from the schools, logicians may almost be divided into those
+who have looked upon reasoning as essentially an affair of Ideas, and
+those who have looked upon it as essentially an affair of Names.
+
+Although, however, Hobbes' theory of Predication, according to the
+well-known remark of Leibnitz, and the avowal of Hobbes himself,[18]
+renders truth and falsity completely arbitrary, with no standard but the
+will of men, it must not be concluded that either Hobbes, or any of the
+other thinkers who have in the main agreed with him, did in fact
+consider the distinction between truth and error as less real, or
+attached less importance to it, than other people. To suppose that they
+did so would argue total unacquaintance with their other speculations.
+But this shows how little hold their doctrine possessed over their own
+minds. No person, at bottom, ever imagined that there was nothing more
+in truth than propriety of expression; than using language in conformity
+to a previous convention. When the inquiry was brought down from
+generals to a particular case, it has always been acknowledged that
+there is a distinction between verbal and real questions; that some
+false propositions are uttered from ignorance of the meaning of words,
+but that in others the source of the error is a misapprehension of
+things; that a person who has not the use of language at all may form
+propositions mentally, and that they may be untrue, that is, he may
+believe as matters of fact what are not really so. This last admission
+cannot be made in stronger terms than it is by Hobbes himself;[19]
+though he will not allow such erroneous belief to be called falsity, but
+only error. And he has himself laid down, in other places, doctrines in
+which the true theory of predication is by implication contained. He
+distinctly says that general names are given to things on account of
+their attributes, and that abstract names are the names of those
+attributes. "Abstract is that which in any subject denotes the cause of
+the concrete name.... And these causes of names are the same with the
+causes of our conceptions, namely, some power of action, or affection,
+of the thing conceived, which some call the manner by which anything
+works upon our senses, but by most men they are called _accidents_."[20]
+It is strange that having gone so far, he should not have gone one step
+farther, and seen that what he calls the cause of the concrete name, is
+in reality the meaning of it; and that when we predicate of any subject
+a name which is given _because_ of an attribute (or, as he calls it, an
+accident), our object is not to affirm the name, but, by means of the
+name, to affirm the attribute.
+
+
+� 4. Let the predicate be, as we have said, a connotative term; and to
+take the simplest case first, let the subject be a proper name: "The
+summit of Chimborazo is white." The word white connotes an attribute
+which is possessed by the individual object designated by the words
+"summit of Chimborazo;" which attribute consists in the physical fact,
+of its exciting in human beings the sensation which we call a sensation
+of white. It will be admitted that, by asserting the proposition, we
+wish to communicate information of that physical fact, and are not
+thinking of the names, except as the necessary means of making that
+communication. The meaning of the proposition, therefore, is, that the
+individual thing denoted by the subject, has the attributes connoted by
+the predicate.
+
+If we now suppose the subject also to be a connotative name, the meaning
+expressed by the proposition has advanced a step farther in
+complication. Let us first suppose the proposition to be universal, as
+well as affirmative: "All men are mortal." In this case, as in the last,
+what the proposition asserts (or expresses a belief of) is, of course,
+that the objects denoted by the subject (man) possess the attributes
+connoted by the predicate (mortal). But the characteristic of this case
+is, that the objects are no longer _individually_ designated. They are
+pointed out only by some of their attributes: they are the objects
+called men, that is, possessing the attributes connoted by the name man;
+and the only thing known of them may be those attributes: indeed, as the
+proposition is general, and the objects denoted by the subject are
+therefore indefinite in number, most of them are not known individually
+at all. The assertion, therefore, is not, as before, that the attributes
+which the predicate connotes are possessed by any given individual, or
+by any number of individuals previously known as John, Thomas, &c., but
+that those attributes are possessed by each and every individual
+possessing certain other attributes; that whatever has the attributes
+connoted by the subject, has also those connoted by the predicate; that
+the latter set of attributes _constantly accompany_ the former set.
+Whatever has the attributes of man has the attribute of mortality;
+mortality constantly accompanies the attributes of man.[21]
+
+If it be remembered that every attribute is _grounded_ on some fact or
+phenomenon, either of outward sense or of inward consciousness, and that
+to _possess_ an attribute is another phrase for being the cause of, or
+forming part of, the fact or phenomenon upon which the attribute is
+grounded; we may add one more step to complete the analysis. The
+proposition which asserts that one attribute always accompanies another
+attribute, really asserts thereby no other thing than this, that one
+phenomenon always accompanies another phenomenon; insomuch that where we
+find the one, we have assurance of the existence of the other. Thus, in
+the proposition, All men are mortal, the word man connotes the
+attributes which we ascribe to a certain kind of living creatures, on
+the ground of certain phenomena which they exhibit, and which are partly
+physical phenomena, namely the impressions made on our senses by their
+bodily form and structure, and partly mental phenomena, namely the
+sentient and intellectual life which they have of their own. All this is
+understood when we utter the word man, by any one to whom the meaning of
+the word is known. Now, when we say, Man is mortal, we mean that
+wherever these various physical and mental phenomena are all found,
+there we have assurance that the other physical and mental phenomenon,
+called death, will not fail to take place. The proposition does not
+affirm _when_; for the connotation of the word _mortal_ goes no farther
+than to the occurrence of the phenomenon at some time or other, leaving
+the precise time undecided.
+
+
+� 5. We have already proceeded far enough, not only to demonstrate the
+error of Hobbes, but to ascertain the real import of by far the most
+numerous class of propositions. The object of belief in a proposition,
+when it asserts anything more than the meaning of words, is generally,
+as in the cases which we have examined, either the co-existence or the
+sequence of two phenomena. At the very commencement of our inquiry, we
+found that every act of belief implied two Things: we have now
+ascertained what, in the most frequent case, these two things are,
+namely two Phenomena, in other words, two states of consciousness; and
+what it is which the proposition affirms (or denies) to subsist between
+them, namely either succession or co-existence. And this case includes
+innumerable instances which no one, previous to reflection, would think
+of referring to it. Take the following example: A generous person is
+worthy of honour. Who would expect to recognise here a case of
+co-existence between phenomena? But so it is. The attribute which causes
+a person to be termed generous, is ascribed to him on the ground of
+states of his mind, and particulars of his conduct: both are phenomena:
+the former are facts of internal consciousness; the latter, so far as
+distinct from the former, are physical facts, or perceptions of the
+senses. Worthy of honour admits of a similar analysis. Honour, as here
+used, means a state of approving and admiring emotion, followed on
+occasion by corresponding outward acts. "Worthy of honour" connotes all
+this, together with our approval of the act of showing honour. All these
+are phenomena; states of internal consciousness, accompanied or followed
+by physical facts. When we say, A generous person is worthy of honour,
+we affirm co-existence between the two complicated phenomena connoted by
+the two terms respectively. We affirm, that wherever and whenever the
+inward feelings and outward facts implied in the word generosity have
+place, then and there the existence and manifestation of an inward
+feeling, honour, would be followed in our minds by another inward
+feeling, approval.
+
+After the analysis, in a former chapter, of the import of names, many
+examples are not needed to illustrate the import of propositions. When
+there is any obscurity, or difficulty, it does not lie in the meaning of
+the proposition, but in the meaning of the names which compose it; in
+the extremely complicated connotation of many words; the immense
+multitude and prolonged series of facts which often constitute the
+phenomenon connoted by a name. But where it is seen what the phenomenon
+is, there is seldom any difficulty in seeing that the assertion conveyed
+by the proposition is, the co-existence of one such phenomenon with
+another; or the succession of one such phenomenon to another: their
+_conjunction_, in short, so that where the one is found, we may
+calculate on finding both.
+
+This, however, though the most common, is not the only meaning which
+propositions are ever intended to convey. In the first place, sequences
+and co-existences are not only asserted respecting Phenomena; we make
+propositions also respecting those hidden causes of phenomena, which are
+named substances and attributes. A substance, however, being to us
+nothing but either that which causes, or that which is conscious of,
+phenomena; and the same being true, _mutatis mutandis_, of attributes;
+no assertion can be made, at least with a meaning, concerning these
+unknown and unknowable entities, except in virtue of the Phenomena by
+which alone they manifest themselves to our faculties. When we say,
+Socrates was cotemporary with the Peloponnesian war, the foundation of
+this assertion, as of all assertions concerning substances, is an
+assertion concerning the phenomena which they exhibit,--namely, that the
+series of facts by which Socrates manifested himself to mankind, and the
+series of mental states which constituted his sentient existence, went
+on simultaneously with the series of facts known by the name of the
+Peloponnesian war. Still, the proposition does not assert that alone; it
+asserts that the Thing in itself, the _noumenon_ Socrates, was existing,
+and doing or experiencing those various facts during the same time.
+Co-existence and sequence, therefore, may be affirmed or denied not only
+between phenomena, but between noumena, or between a noumenon and
+phenomena. And both of noumena and of phenomena we may affirm simple
+existence. But what is a noumenon? An unknown cause. In affirming,
+therefore, the existence of a noumenon, we affirm causation. Here,
+therefore, are two additional kinds of fact, capable of being asserted
+in a proposition. Besides the propositions which assert Sequence or
+Coexistence, there are some which assert simple Existence; and others
+assert Causation, which, subject to the explanations which will follow
+in the Third Book, must be considered provisionally as a distinct and
+peculiar kind of assertion.
+
+
+� 6. To these four kinds of matter-of-fact or assertion, must be added a
+fifth, Resemblance. This was a species of attribute which we found it
+impossible to analyse; for which no _fundamentum_, distinct from the
+objects themselves, could be assigned. Besides propositions which assert
+a sequence or co-existence between two phenomena, there are therefore
+also propositions which assert resemblance between them: as, This colour
+is like that colour;--The heat of to-day is _equal_ to the heat of
+yesterday. It is true that such an assertion might with some
+plausibility be brought within the description of an affirmation of
+sequence, by considering it as an assertion that the simultaneous
+contemplation of the two colours is _followed_ by a specific feeling
+termed the feeling of resemblance. But there would be nothing gained by
+encumbering ourselves, especially in this place, with a generalization
+which may be looked upon as strained. Logic does not undertake to
+analyse mental facts into their ultimate elements. Resemblance between
+two phenomena is more intelligible in itself than any explanation could
+make it, and under any classification must remain specifically distinct
+from the ordinary cases of sequence and co-existence.
+
+It is sometimes said, that all propositions whatever, of which the
+predicate is a general name, do, in point of fact, affirm or deny
+resemblance. All such propositions affirm that a thing belongs to a
+class; but things being classed together according to their resemblance,
+everything is of course classed with the things which it is supposed to
+resemble most; and thence, it may be said, when we affirm that Gold is a
+metal, or that Socrates is a man, the affirmation intended is, that
+gold resembles other metals, and Socrates other men, more nearly than
+they resemble the objects contained in any other of the classes
+co-ordinate with these.
+
+There is some slight degree of foundation for this remark, but no more
+than a slight degree. The arrangement of things into classes, such as
+the class _metal_, or the class _man_, is grounded indeed on a
+resemblance among the things which are placed in the same class, but not
+on a mere general resemblance: the resemblance it is grounded on
+consists in the possession by all those things, of certain common
+peculiarities; and those peculiarities it is which the terms connote,
+and which the propositions consequently assert; not the resemblance: for
+though when I say, Gold is a metal, I say by implication that if there
+be any other metals it must resemble them, yet if there were no other
+metals I might still assert the proposition with the same meaning as at
+present, namely, that gold has the various properties implied in the
+word metal; just as it might be said, Christians are men, even if there
+were no men who were not Christians. Propositions, therefore, in which
+objects are referred to a class because they possess the attributes
+constituting the class, are so far from asserting nothing but
+resemblance, that they do not, properly speaking, assert resemblance at
+all.
+
+But we remarked some time ago (and the reasons of the remark will be
+more fully entered into in a subsequent Book[22]) that there is
+sometimes a convenience in extending the boundaries of a class so as to
+include things which possess in a very inferior degree, if in any, some
+of the characteristic properties of the class,--provided they resemble
+that class more than any other, insomuch that the general propositions
+which are true of the class, will be nearer to being true of those
+things than any other equally general propositions. For instance, there
+are substances called metals which have very few of the properties by
+which metals are commonly recognised; and almost every great family of
+plants or animals has a few anomalous genera or species on its borders,
+which are admitted into it by a sort of courtesy, and concerning which
+it has been matter of discussion to what family they properly belonged.
+Now when the class-name is predicated of any object of this description,
+we do, by so predicating it, affirm resemblance and nothing more. And in
+order to be scrupulously correct it ought to be said, that in every case
+in which we predicate a general name, we affirm, not absolutely that the
+object possesses the properties designated by the name, but that it
+_either_ possesses those properties, or if it does not, at any rate
+resembles the things which do so, more than it resembles any other
+things. In most cases, however, it is unnecessary to suppose any such
+alternative, the latter of the two grounds being very seldom that on
+which the assertion is made: and when it is, there is generally some
+slight difference in the form of the expression, as, This species (or
+genus) is _considered_, or _may be ranked_, as belonging to such and
+such a family: we should hardly say positively that it does belong to
+it, unless it possessed unequivocally the properties of which the
+class-name is scientifically significant.
+
+There is still another exceptional case, in which, though the predicate
+is the name of a class, yet in predicating it we affirm nothing but
+resemblance, the class being founded not on resemblance in any given
+particular, but on general unanalysable resemblance. The classes in
+question are those into which our simple sensations, or other simple
+feelings, are divided. Sensations of white, for instance, are classed
+together, not because we can take them to pieces, and say they are alike
+in this, and not alike in that, but because we feel them to be alike
+altogether, though in different degrees. When, therefore, I say, The
+colour I saw yesterday was a white colour, or, The sensation I feel is
+one of tightness, in both cases the attribute I affirm of the colour or
+of the other sensation is mere resemblance--simple _likeness_ to
+sensations which I have had before, and which have had those names
+bestowed upon them. The names of feelings, like other concrete general
+names, are connotative; but they connote a mere resemblance. When
+predicated of any individual feeling, the information they convey is
+that of its likeness to the other feelings which we have been accustomed
+to call by the same name. Thus much may suffice in illustration of the
+kind of propositions in which the matter-of-fact asserted (or denied) is
+simple Resemblance.
+
+Existence, Coexistence, Sequence, Causation, Resemblance: one or other
+of these is asserted (or denied) in every proposition which is not
+merely verbal. This five-fold division is an exhaustive classification
+of matters-of-fact; of all things that can be believed, or tendered for
+belief; of all questions that can be propounded, and all answers that
+can be returned to them. Instead of Coexistence and Sequence, we shall
+sometimes say, for greater particularity, Order in Place, and Order in
+Time: Order in Place being the specific mode of coexistence, not
+necessary to be more particularly analysed here; while the mere fact of
+coexistence, or simultaneousness, may be classed, together with
+Sequence, under the head of Order in Time.
+
+
+� 7. In the foregoing inquiry into the import of Propositions, we have
+thought it necessary to analyse directly those alone, in which the terms
+of the proposition (or the predicate at least) are concrete terms. But,
+in doing so, we have indirectly analysed those in which the terms are
+abstract. The distinction between an abstract term and its corresponding
+concrete, does not turn upon any difference in what they are appointed
+to signify; for the real signification of a concrete general name is, as
+we have so often said, its connotation; and what the concrete term
+connotes, forms the entire meaning of the abstract name. Since there is
+nothing in the import of an abstract name which is not in the import of
+the corresponding concrete, it is natural to suppose that neither can
+there be anything in the import of a proposition of which the terms are
+abstract, but what there is in some proposition which can be framed of
+concrete terms.
+
+And this presumption a closer examination will confirm. An abstract name
+is the name of an attribute, or combination of attributes. The
+corresponding concrete is a name given to things, because of, and in
+order to express, their possessing that attribute, or that combination
+of attributes. When, therefore, we predicate of anything a concrete
+name, the attribute is what we in reality predicate of it. But it has
+now been shown that in all propositions of which the predicate is a
+concrete name, what is really predicated is one of five things:
+Existence, Coexistence, Causation, Sequence, or Resemblance. An
+attribute, therefore, is necessarily either an existence, a coexistence,
+a causation, a sequence, or a resemblance. When a proposition consists
+of a subject and predicate which are abstract terms, it consists of
+terms which must necessarily signify one or other of these things. When
+we predicate of anything an abstract name, we affirm of the thing that
+it is one or other of these five things; that it is a case of Existence,
+or of Coexistence, or of Causation, or of Sequence, or of Resemblance.
+
+It is impossible to imagine any proposition expressed in abstract terms,
+which cannot be transformed into a precisely equivalent proposition in
+which the terms are concrete; namely, either the concrete names which
+connote the attributes themselves, or the names of the _fundamenta_ of
+those attributes; the facts or phenomena on which they are grounded. To
+illustrate the latter case, let us take this proposition, of which the
+subject only is an abstract name, "Thoughtlessness is dangerous."
+Thoughtlessness is an attribute, grounded on the facts which we call
+thoughtless actions; and the proposition is equivalent to this,
+Thoughtless actions are dangerous. In the next example the predicate as
+well as the subject are abstract names: "Whiteness is a colour;" or "The
+colour of snow is a whiteness." These attributes being grounded on
+sensations, the equivalent propositions in the concrete would be, The
+sensation of white is one of the sensations called those of colour,--The
+sensation of sight, caused by looking at snow, is one of the sensations
+called sensations of white. In these propositions, as we have before
+seen, the matter-of-fact asserted is a Resemblance. In the following
+examples, the concrete terms are those which directly correspond to the
+abstract names; connoting the attribute which these denote. "Prudence
+is a virtue:" this may be rendered, "All prudent persons, _in so far as_
+prudent, are virtuous:" "Courage is deserving of honour," thus, "All
+courageous persons are deserving of honour _in so far_ as they are
+courageous:" which is equivalent to this--"All courageous persons
+deserve an addition to the honour, or a diminution of the disgrace,
+which would attach to them on other grounds."
+
+In order to throw still further light upon the import of propositions of
+which the terms are abstract, we will subject one of the examples given
+above to a minuter analysis. The proposition we shall select is the
+following:--"Prudence is a virtue." Let us substitute for the word
+virtue an equivalent but more definite expression, such as "a mental
+quality beneficial to society," or "a mental quality pleasing to God,"
+or whatever else we adopt as the definition of virtue. What the
+proposition asserts is a sequence, accompanied with causation; namely,
+that benefit to society, or that the approval of God, is consequent on,
+and caused by, prudence. Here is a sequence; but between what? We
+understand the consequent of the sequence, but we have yet to analyse
+the antecedent. Prudence is an attribute; and, in connexion with it, two
+things besides itself are to be considered; prudent persons, who are the
+_subjects_ of the attribute, and prudential conduct, which may be called
+the _foundation_ of it. Now is either of these the antecedent? and,
+first, is it meant, that the approval of God, or benefit to society, is
+attendant upon all prudent _persons_? No; except _in so far_ as they are
+prudent; for prudent persons who are scoundrels can seldom on the whole
+be beneficial to society, nor can they be acceptable to a good being. Is
+it upon prudential _conduct_, then, that divine approbation and benefit
+to mankind are supposed to be invariably consequent? Neither is this the
+assertion meant, when it is said that prudence is a virtue; except with
+the same reservation as before, and for the same reason, namely, that
+prudential conduct, although in _so far as_ it is prudential it is
+beneficial to society, may yet, by reason of some other of its
+qualities, be productive of an injury outweighing the benefit, and
+deserve a displeasure exceeding the approbation which would be due to
+the prudence. Neither the substance, therefore, (viz. the person,) nor
+the phenomenon, (the conduct,) is an antecedent on which the other term
+of the sequence is universally consequent. But the proposition,
+"Prudence is a virtue," is an universal proposition. What is it, then,
+upon which the proposition affirms the effects in question to be
+universally consequent? Upon that in the person, and in the conduct,
+which causes them to be called prudent, and which is equally in them
+when the action, though prudent, is wicked; namely, a correct foresight
+of consequences, a just estimation of their importance to the object in
+view, and repression of any unreflecting impulse at variance with the
+deliberate purpose. These, which are states of the person's mind, are
+the real antecedent in the sequence, the real cause in the causation,
+asserted by the proposition. But these are also the real ground, or
+foundation, of the attribute Prudence; since wherever these states of
+mind exist we may predicate prudence, even before we know whether any
+conduct has followed. And in this manner every assertion respecting an
+attribute, may be transformed into an assertion exactly equivalent
+respecting the fact or phenomenon which is the ground of the attribute.
+And no case can be assigned, where that which is predicated of the fact
+or phenomenon, does not belong to one or other of the five species
+formerly enumerated: it is either simple Existence, or it is some
+Sequence, Coexistence, Causation, or Resemblance.
+
+And as these five are the only things which can be affirmed, so are they
+the only things which can be denied. "No horses are web-footed" denies
+that the attributes of a horse ever coexist with web-feet. It is
+scarcely necessary to apply the same analysis to Particular affirmations
+and negations. "Some birds are web-footed," affirms that, with the
+attributes connoted by _bird_, the phenomenon web-feet is sometimes
+co-existent: "Some birds are not web-footed," asserts that there are
+other instances in which this coexistence does not have place. Any
+further explanation of a thing which, if the previous exposition has
+been assented to, is so obvious, may here be spared.
+
+
+
+
+CHAPTER VI.
+
+OF PROPOSITIONS MERELY VERBAL.
+
+
+� 1. As a preparation for the inquiry which is the proper object of
+Logic, namely, in what manner propositions are to be proved, we have
+found it necessary to inquire what they contain which requires, or is
+susceptible of, proof; or (which is the same thing) what they assert. In
+the course of this preliminary investigation into the import of
+Propositions, we examined the opinion of the Conceptualists, that a
+proposition is the expression of a relation between two ideas; and the
+doctrine of the Nominalists, that it is the expression of an agreement
+or disagreement between the meanings of two names. We decided that, as
+general theories, both of these are erroneous; and that, though
+propositions may be made both respecting names and respecting ideas,
+neither the one nor the other are the subject-matter of Propositions
+considered generally. We then examined the different kinds of
+Propositions, and found that, with the exception of those which are
+merely verbal, they assert five different kinds of matters of fact,
+namely, Existence, Order in Place, Order in Time, Causation, and
+Resemblance; that in every proposition one of these five is either
+affirmed, or denied, of some fact or phenomenon, or of some object the
+unknown source of a fact or phenomenon.
+
+In distinguishing, however, the different kinds of matters of fact
+asserted in propositions, we reserved one class of propositions, which
+do not relate to any matter of fact, in the proper sense of the term, at
+all, but to the meaning of names. Since names and their signification
+are entirely arbitrary, such propositions are not, strictly speaking,
+susceptible of truth or falsity, but only of conformity or disconformity
+to usage or convention; and all the proof they are capable of, is proof
+of usage; proof that the words have been employed by others in the
+acceptation in which the speaker or writer desires to use them. These
+propositions occupy, however, a conspicuous place in philosophy; and
+their nature and characteristics are of as much importance in logic, as
+those of any of the other classes of propositions previously adverted
+to.
+
+If all propositions respecting the signification of words were as simple
+and unimportant as those which served us for examples when examining
+Hobbes' theory of predication, viz. those of which the subject and
+predicate are proper names, and which assert only that those names have,
+or that they have not, been conventionally assigned to the same
+individual, there would be little to attract to such propositions the
+attention of philosophers. But the class of merely verbal propositions
+embraces not only much more than these, but much more than any
+propositions which at first sight present themselves as verbal;
+comprehending a kind of assertions which have been regarded not only as
+relating to things, but as having actually a more intimate relation with
+them than any other propositions whatever. The student in philosophy
+will perceive that I allude to the distinction on which so much stress
+was laid by the schoolmen, and which has been retained either under the
+same or under other names by most metaphysicians to the present day,
+viz. between what were called _essential_, and what were called
+_accidental_, propositions, and between essential and accidental
+properties or attributes.
+
+
+� 2. Almost all metaphysicians prior to Locke, as well as many since his
+time, have made a great mystery of Essential Predication, and of
+predicates which are said to be of the _essence_ of the subject. The
+essence of a thing, they said, was that without which the thing could
+neither be, nor be conceived to be. Thus, rationality was of the essence
+of man, because without rationality, man could not be conceived to
+exist. The different attributes which made up the essence of the thing
+were called its essential properties; and a proposition in which any of
+these were predicated of it was called an Essential Proposition, and was
+considered to go deeper into the nature of the thing, and to convey more
+important information respecting it, than any other proposition could
+do. All properties, not of the essence of the thing, were called its
+accidents; were supposed to have nothing at all, or nothing
+comparatively, to do with its inmost nature; and the propositions in
+which any of these were predicated of it were called Accidental
+Propositions. A connexion may be traced between this distinction, which
+originated with the schoolmen, and the well-known dogmas of _substanti�
+secund�_ or general substances, and _substantial forms_, doctrines which
+under varieties of language pervaded alike the Aristotelian and the
+Platonic schools, and of which more of the spirit has come down to
+modern times than might be conjectured from the disuse of the
+phraseology. The false views of the nature of classification and
+generalization which prevailed among the schoolmen, and of which these
+dogmas were the technical expression, afford the only explanation which
+can be given of their having misunderstood the real nature of those
+Essences which held so conspicuous a place in their philosophy. They
+said, truly, that _man_ cannot be conceived without rationality. But
+though _man_ cannot, a being may be conceived exactly like a man in all
+points except that one quality, and those others which are the
+conditions or consequences of it. All therefore which is really true in
+the assertion that man cannot be conceived without rationality, is only,
+that if he had not rationality, he would not be reputed a man. There is
+no impossibility in conceiving the _thing_, nor, for aught we know, in
+its existing: the impossibility is in the conventions of language, which
+will not allow the thing, even if it exist, to be called by the name
+which is reserved for rational beings. Rationality, in short, is
+involved in the meaning of the word man: is one of the attributes
+connoted by the name. The essence of man, simply means the whole of the
+attributes connoted by the word; and any one of those attributes taken
+singly, is an essential property of man.
+
+But these reflections, so easy to us, would have been difficult to
+persons who thought, as most of the later Aristotelians did, that
+objects were made what they were called, that gold (for instance) was
+made gold, not by the possession of certain properties to which mankind
+have chosen to attach that name, but by participation in the nature of
+a certain general substance, called gold in general, which substance,
+together with all the properties that belonged to it, _inhered_ in every
+individual piece of gold.[23] As they did not consider these universal
+substances to be attached to all general names, but only to some, they
+thought that an object borrowed only a part of its properties from an
+universal substance, and that the rest belonged to it individually: the
+former they called its essence, and the latter its accidents. The
+scholastic doctrine of essences long survived the theory on which it
+rested, that of the existence of real entities corresponding to general
+terms; and it was reserved for Locke at the end of the seventeenth
+century, to convince philosophers that the supposed essences of classes
+were merely the signification of their names; nor, among the signal
+services which his writings rendered to philosophy, was there one more
+needful or more valuable.
+
+Now, as the most familiar of the general names by which an object is
+designated usually connotes not one only, but several attributes of the
+object, each of which attributes separately forms also the bond of union
+of some class, and the meaning of some general name; we may predicate of
+a name which connotes a variety of attributes, another name which
+connotes only one of these attributes, or some smaller number of them
+than all. In such cases, the universal affirmative proposition will be
+true; since whatever possesses the whole of any set of attributes, must
+possess any part of that same set. A proposition of this sort, however,
+conveys no information to any one who previously understood the whole
+meaning of the terms. The propositions, Every man is a corporeal being,
+Every man is a living creature, Every man is rational, convey no
+knowledge to any one who was already aware of the entire meaning of the
+word _man_, for the meaning of the word includes all this: and that
+every _man_ has the attributes connoted by all these predicates, is
+already asserted when he is called a man. Now, of this nature are all
+the propositions which have been called essential. They are, in fact,
+identical propositions.
+
+It is true that a proposition which predicates any attribute, even
+though it be one implied in the name, is in most cases understood to
+involve a tacit assertion that there _exists_ a thing corresponding to
+the name, and possessing the attributes connoted by it; and this implied
+assertion may convey information, even to those who understood the
+meaning of the name. But all information of this sort, conveyed by all
+the essential propositions of which man can be made the subject, is
+included in the assertion, Men exist. And this assumption of real
+existence is, after all, the result of an imperfection of language. It
+arises from the ambiguity of the copula, which, in addition to its
+proper office of a mark to show that an assertion is made, is also, as
+formerly remarked, a concrete word connoting existence. The actual
+existence of the subject of the proposition is therefore only
+apparently, not really, implied in the predication, if an essential one:
+we may say, A ghost is a disembodied spirit, without believing in
+ghosts. But an accidental, or non-essential, affirmation, does imply the
+real existence of the subject, because in the case of a non-existent
+subject there is nothing for the proposition to assert. Such a
+proposition as, The ghost of a murdered person haunts the couch of the
+murderer, can only have a meaning if understood as implying a belief in
+ghosts; for since the signification of the word ghost implies nothing of
+the kind, the speaker either means nothing, or means to assert a thing
+which he wishes to be believed to have really taken place.
+
+It will be hereafter seen that when any important consequences seem to
+follow, as in mathematics, from an essential proposition, or, in other
+words, from a proposition involved in the meaning of a name, what they
+really flow from is the tacit assumption of the real existence of the
+objects so named. Apart from this assumption of real existence, the
+class of propositions in which the predicate is of the essence of the
+subject (that is, in which the predicate connotes the whole or part of
+what the subject connotes, but nothing besides) answer no purpose but
+that of unfolding the whole or some part of the meaning of the name, to
+those who did not previously know it. Accordingly, the most useful, and
+in strictness the only useful kind of essential propositions, are
+Definitions: which, to be complete, should unfold the whole of what is
+involved in the meaning of the word defined; that is, (when it is a
+connotative word,) the whole of what it connotes. In defining a name,
+however, it is not usual to specify its entire connotation, but so much
+only as is sufficient to mark out the objects usually denoted by it from
+all other known objects. And sometimes a merely accidental property, not
+involved in the meaning of the name, answers this purpose equally well.
+The various kinds of definition which these distinctions give rise to,
+and the purposes to which they are respectively subservient, will be
+minutely considered in the proper place.
+
+
+� 3. According to the above view of essential propositions, no
+proposition can be reckoned such which relates to an individual by name,
+that is, in which the subject is a proper name. Individuals have no
+essences. When the schoolmen talked of the essence of an individual,
+they did not mean the properties implied in its name, for the names of
+individuals imply no properties. They regarded as of the essence of an
+individual, whatever was of the essence of the species in which they
+were accustomed to place that individual; _i.e._ of the class to which
+it was most familiarly referred, and to which, therefore, they conceived
+that it by nature belonged. Thus, because the proposition Man is a
+rational being, was an essential proposition, they affirmed the same
+thing of the proposition, Julius C�sar is a rational being. This
+followed very naturally if genera and species were to be considered as
+entities, distinct from, but _inhering_ in, the individuals composing
+them. If _man_ was a substance inhering in each individual man, the
+_essence_ of man (whatever that might mean) was naturally supposed to
+accompany it; to inhere in John Thompson, and to form the _common
+essence_ of Thompson and Julius C�sar. It might then be fairly said,
+that rationality, being of the essence of Man, was of the essence also
+of Thompson. But if Man altogether be only the individual men and a name
+bestowed upon them in consequence of certain common properties, what
+becomes of John Thompson's essence?
+
+A fundamental error is seldom expelled from philosophy by a single
+victory. It retreats slowly, defends every inch of ground, and often,
+after it has been driven from the open country, retains a footing in
+some remote fastness. The essences of individuals were an unmeaning
+figment arising from a misapprehension of the essences of classes, yet
+even Locke, when he extirpated the parent error, could not shake himself
+free from that which was its fruit. He distinguished two sorts of
+essences, Real and Nominal. His nominal essences were the essences of
+classes, explained nearly as we have now explained them. Nor is anything
+wanting to render the third book of Locke's Essay a nearly
+unexceptionable treatise on the connotation of names, except to free its
+language from the assumption of what are called Abstract Ideas, which
+unfortunately is involved in the phraseology, though not necessarily
+connected with the thoughts contained in that immortal Third Book.[24]
+But, besides nominal essences, he admitted real essences, or essences of
+individual objects, which he supposed to be the causes of the sensible
+properties of those objects. We know not (said he) what these are; (and
+this acknowledgment rendered the fiction comparatively innocuous;) but
+if we did, we could, from them alone, demonstrate the sensible
+properties of the object, as the properties of the triangle are
+demonstrated from the definition of the triangle. I shall have occasion
+to revert to this theory in treating of Demonstration, and of the
+conditions under which one property of a thing admits of being
+demonstrated from another property. It is enough here to remark that,
+according to this definition, the real essence of an object has, in the
+progress of physics, come to be conceived as nearly equivalent, in the
+case of bodies, to their corpuscular structure: what it is now supposed
+to mean in the case of any other entities, I would not take upon myself
+to define.
+
+
+� 4. An essential proposition, then, is one which is purely verbal;
+which asserts of a thing under a particular name, only what is asserted
+of it in the fact of calling it by that name; and which therefore either
+gives no information, or gives it respecting the name, not the thing.
+Non-essential, or accidental propositions, on the contrary, may be
+called Real Propositions, in opposition to Verbal. They predicate of a
+thing some fact not involved in the signification of the name by which
+the proposition speaks of it; some attribute not connoted by that name.
+Such are all propositions concerning things individually designated, and
+all general or particular propositions in which the predicate connotes
+any attribute not connoted by the subject. All these, if true, add to
+our knowledge: they convey information, not already involved in the
+names employed. When I am told that all, or even that some objects,
+which have certain qualities, or which stand in certain relations, have
+also certain other qualities, or stand in certain other relations, I
+learn from this proposition a new fact; a fact not included in my
+knowledge of the meaning of the words, nor even of the existence of
+Things answering to the signification of those words. It is this class
+of propositions only which are in themselves instructive, or from which
+any instructive propositions can be inferred.[25]
+
+Nothing has probably contributed more to the opinion so long prevalent
+of the futility of the school logic, than the circumstance that almost
+all the examples used in the common school books to illustrate the
+doctrine of predication and that of the syllogism, consist of essential
+propositions. They were usually taken either from the branches or from
+the main trunk of the Predicamental Tree, which included nothing but
+what was of the _essence_ of the species: _Omne corpus est substantia_,
+_Omne animal est corpus_, _Omnis homo est corpus_, _Omnis homo est
+animal_, _Omnis homo est rationalis_, and so forth. It is far from
+wonderful that the syllogistic art should have been thought to be of no
+use in assisting correct reasoning, when almost the only propositions
+which, in the hands of its professed teachers, it was employed to prove,
+were such as every one assented to without proof the moment he
+comprehended the meaning of the words; and stood exactly on a level, in
+point of evidence, with the premises from which they were drawn. I have,
+therefore, throughout this work, avoided the employment of essential
+propositions as examples, except where the nature of the principle to be
+illustrated specifically required them.
+
+
+� 5. With respect to propositions which do convey information--which
+assert something of a Thing, under a name that does not already
+presuppose what is about to be asserted; there are two different aspects
+in which these, or rather such of them as are general propositions, may
+be considered: we may either look at them as portions of speculative
+truth, or as memoranda for practical use. According as we consider
+propositions in one or the other of these lights, their import may be
+conveniently expressed in one or in the other of two formulas.
+
+According to the formula which we have hitherto employed, and which is
+best adapted to express the import of the proposition as a portion of
+our theoretical knowledge, All men are mortal, means that the attributes
+of man are always accompanied by the attribute mortality: No men are
+gods, means that the attributes of man are never accompanied by the
+attributes, or at least never by all the attributes, signified by the
+word god. But when the proposition is considered as a memorandum for
+practical use, we shall find a different mode of expressing the same
+meaning better adapted to indicate the office which the proposition
+performs. The practical use of a proposition is, to apprise or remind us
+what we have to expect, in any individual case which comes within the
+assertion contained in the proposition. In reference to this purpose,
+the proposition, All men are mortal, means that the attributes of man
+are _evidence of_, are a _mark_ of, mortality; an indication by which
+the presence of that attribute is made manifest. No men are gods, means
+that the attributes of man are a mark or evidence that some or all of
+the attributes understood to belong to a god are not there; that where
+the former are, we need not expect to find the latter.
+
+These two forms of expression are at bottom equivalent; but the one
+points the attention more directly to what a proposition means, the
+latter to the manner in which it is to be used.
+
+Now it is to be observed that Reasoning (the subject to which we are
+next to proceed) is a process into which propositions enter not as
+ultimate results, but as means to the establishment of other
+propositions. We may expect, therefore, that the mode of exhibiting the
+import of a general proposition which shows it in its application to
+practical use, will best express the function which propositions perform
+in Reasoning. And accordingly, in the theory of Reasoning, the mode of
+viewing the subject which considers a Proposition as asserting that one
+fact or phenomenon is a _mark_ or _evidence_ of another fact or
+phenomenon, will be found almost indispensable. For the purposes of that
+Theory, the best mode of defining the import of a proposition is not the
+mode which shows most clearly what it is in itself, but that which most
+distinctly suggests the manner in which it may be made available for
+advancing from it to other propositions.
+
+
+
+
+CHAPTER VII.
+
+OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
+
+
+� 1. In examining into the nature of general propositions, we have
+adverted much less than is usual with logicians to the ideas of a Class,
+and Classification; ideas which, since the Realist doctrine of General
+Substances went out of vogue, have formed the basis of almost every
+attempt at a philosophical theory of general terms and general
+propositions. We have considered general names as having a meaning,
+quite independently of their being the names of classes. That
+circumstance is in truth accidental, it being wholly immaterial to the
+signification of the name whether there are many objects, or only one,
+to which it happens to be applicable, or whether there be any at all.
+God is as much a general term to the Christian or Jew as to the
+Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much
+so as if real objects existed, corresponding to those names. Every name
+the signification of which is constituted by attributes, is potentially
+a name of an indefinite number of objects; but it needs not be actually
+the name of any; and if of any, it may be the name of only one. As soon
+as we employ a name to connote attributes, the things, be they more or
+fewer, which happen to possess those attributes, are constituted _ipso
+facto_ a class. But in predicating the name we predicate only the
+attributes; and the fact of belonging to a class does not, in many
+cases, come into view at all.
+
+Although, however, Predication does not presuppose Classification, and
+though the theory of Names and of Propositions is not cleared up, but
+only encumbered, by intruding the idea of classification into it, there
+is nevertheless a close connexion between Classification and the
+employment of General Names. By every general name which we introduce,
+we create a class, if there be any things, real or imaginary, to compose
+it; that is, any Things corresponding to the signification of the name.
+Classes, therefore, mostly owe their existence to general language. But
+general language, also, though that is not the most common case,
+sometimes owes its existence to classes. A general, which is as much as
+to say a significant, name, is indeed mostly introduced because we have
+a signification to express by it; because we need a word by means of
+which to predicate the attributes which it connotes. But it is also true
+that a name is sometimes introduced because we have found it convenient
+to create a class; because we have thought it useful for the regulation
+of our mental operations, that a certain group of objects should be
+thought of together. A naturalist, for purposes connected with his
+particular science, sees reason to distribute the animal or vegetable
+creation into certain groups rather than into any others, and he
+requires a name to bind, as it were, each of his groups together. It
+must not however be supposed that such names, when introduced, differ in
+any respect, as to their mode of signification, from other connotative
+names. The classes which they denote are, as much as any other classes,
+constituted by certain common attributes, and their names are
+significant of those attributes, and of nothing else. The names of
+Cuvier's classes and orders, _Plantigrades_, _Digitigrades_, &c., are as
+much the expression of attributes as if those names had preceded,
+instead of grown out of, his classification of animals. The only
+peculiarity of the case is, that the convenience of classification was
+here the primary motive for introducing the names; while in other cases
+the name is introduced as a means of predication, and the formation of a
+class denoted by it is only an indirect consequence.
+
+The principles which ought to regulate Classification as a logical
+process subservient to the investigation of truth, cannot be discussed
+to any purpose until a much later stage of our inquiry. But, of
+Classification as resulting from, and implied in, the fact of employing
+general language, we cannot forbear to treat here, without leaving the
+theory of general names and of their employment in predication,
+mutilated and formless.
+
+
+� 2. This portion of the theory of general language is the subject of
+what is termed the doctrine of the Predicables; a set of distinctions
+handed down from Aristotle, and his follower Porphyry, many of which
+have taken a firm root in scientific, and some of them even in popular,
+phraseology. The predicables are a five-fold division of General Names,
+not grounded as usual on a difference in their meaning, that is, in the
+attribute which they connote, but on a difference in the kind of class
+which they denote. We may predicate of a thing five different varieties
+of class-name:--
+
+  A _genus_ of the thing  ([Greek: genos]).
+  A _species_             ([Greek: eidos]).
+  A _differentia_         ([Greek: diaphora]).
+  A _proprium_            ([Greek: idion]).
+  An _accidens_           ([Greek: symbeb�kos]).
+
+It is to be remarked of these distinctions, that they express, not what
+the predicate is in its own meaning, but what relation it bears to the
+subject of which it happens on the particular occasion to be predicated.
+There are not some names which are exclusively genera, and others which
+are exclusively species, or differenti�; but the same name is referred
+to one or another predicable, according to the subject of which it is
+predicated on the particular occasion. _Animal_, for instance, is a
+genus with respect to man, or John; a species with respect to Substance,
+or Being. _Rectangular_ is one of the Differenti� of a geometrical
+square; it is merely one of the Accidentia of the table at which I am
+writing. The words genus, species, &c. are therefore relative terms;
+they are names applied to certain predicates, to express the relation
+between them and some given subject: a relation grounded, as we shall
+see, not on what the predicate connotes, but on the class which it
+denotes, and on the place which, in some given classification, that
+class occupies relatively to the particular subject.
+
+
+� 3. Of these five names, two, Genus and Species, are not only used by
+naturalists in a technical acceptation not precisely agreeing with their
+philosophical meaning, but have also acquired a popular acceptation,
+much more general than either. In this popular sense any two classes,
+one of which includes the whole of the other and more, may be called a
+Genus and a Species. Such, for instance, are Animal and Man; Man and
+Mathematician. Animal is a Genus; Man and Brute are its two species; or
+we may divide it into a greater number of species, as man, horse, dog,
+&c. _Biped_, or _two-footed animal_, may also be considered a genus, of
+which man and bird are two species. _Taste_ is a genus, of which sweet
+taste, sour taste, salt taste, &c. are species. _Virtue_ is a genus;
+justice, prudence, courage, fortitude, generosity, &c. are its species.
+
+The same class which is a genus with reference to the sub-classes or
+species included in it, may be itself a species with reference to a more
+comprehensive, or, as it is often called, a superior genus. Man is a
+species with reference to animal, but a genus with reference to the
+species Mathematician. Animal is a genus, divided into two species, man
+and brute; but animal is also a species, which, with another species,
+vegetable, makes up the genus, organized being. Biped is a genus with
+reference to man and bird, but a species with respect to the superior
+genus, animal. Taste is a genus divided into species, but also a species
+of the genus sensation. Virtue, a genus with reference to justice,
+temperance, &c., is one of the species of the genus, mental quality.
+
+In this popular sense the words Genus and Species have passed into
+common discourse. And it should be observed that in ordinary parlance,
+not the name of the class, but the class itself, is said to be the genus
+or species; not, of course, the class in the sense of each individual of
+the class, but the individuals collectively, considered as an aggregate
+whole; the name by which the class is designated being then called not
+the genus or species, but the generic or specific name. And this is an
+admissible form of expression; nor is it of any importance which of the
+two modes of speaking we adopt, provided the rest of our language is
+consistent with it; but, if we call the class itself the genus, we must
+not talk of predicating the genus. We predicate of man the _name_
+mortal; and by predicating the name, we may be said, in an intelligible
+sense, to predicate what the name expresses, the _attribute_ mortality;
+but in no allowable sense of the word predication do we predicate of man
+the _class_ mortal. We predicate of him the fact of belonging to the
+class.
+
+By the Aristotelian logicians, the terms genus and species were used in
+a more restricted sense. They did not admit every class which could be
+divided into other classes to be a genus, or every class which could be
+included in a larger class to be a species. Animal was by them
+considered a genus; man and brute co-ordinate species under that genus:
+_biped_, however, would not have been admitted to be a genus with
+reference to man, but a _proprium_ or _accidens_ only. It was requisite,
+according to their theory, that genus and species should be of the
+_essence_ of the subject. Animal was of the essence of man; biped was
+not. And in every classification they considered some one class as the
+lowest or _infima_ species. Man, for instance, was a lowest species. Any
+further divisions into which the class might be capable of being broken
+down, as man into white, black, and red man, or into priest and layman,
+they did not admit to be species.
+
+It has been seen, however, in the preceding chapter, that the
+distinction between the essence of a class, and the attributes or
+properties which are not of its essence--a distinction which has given
+occasion to so much abstruse speculation, and to which so mysterious a
+character was formerly, and by many writers is still, attached,--amounts
+to nothing more than the difference between those attributes of the
+class which are, and those which are not, involved in the signification
+of the class-name. As applied to individuals, the word Essence, we
+found, has no meaning, except in connexion with the exploded tenets of
+the Realists; and what the schoolmen chose to call the essence of an
+individual, was simply the essence of the class to which that individual
+was most familiarly referred.
+
+Is there no difference, then, save this merely verbal one, between the
+classes which the schoolmen admitted to be genera or species, and those
+to which they refused the title? Is it an error to regard some of the
+differences which exist among objects as differences _in kind_ (_genere_
+or _specie_), and others only as differences in the accidents? Were the
+schoolmen right or wrong in giving to some of the classes into which
+things may be divided, the name of _kinds_, and considering others as
+secondary divisions, grounded on differences of a comparatively
+superficial nature? Examination will show that the Aristotelians did
+mean something by this distinction, and something important; but which,
+being but indistinctly conceived, was inadequately expressed by the
+phraseology of essences, and the various other modes of speech to which
+they had recourse.
+
+
+� 4. It is a fundamental principle in logic, that the power of framing
+classes is unlimited, as long as there is any (even the smallest)
+difference to found a distinction upon. Take any attribute whatever, and
+if some things have it, and others have not, we may ground on the
+attribute a division of all things into two classes; and we actually do
+so, the moment we create a name which connotes the attribute. The number
+of possible classes, therefore, is boundless; and there are as many
+actual classes (either of real or of imaginary things) as there are
+general names, positive and negative together.
+
+But if we contemplate any one of the classes so formed, such as the
+class animal or plant, or the class sulphur or phosphorus, or the class
+white or red, and consider in what particulars the individuals included
+in the class differ from those which do not come within it, we find a
+very remarkable diversity in this respect between some classes and
+others. There are some classes, the things contained in which differ
+from other things only in certain particulars which may be numbered,
+while others differ in more than can be numbered, more even than we need
+ever expect to know. Some classes have little or nothing in common to
+characterize them by, except precisely what is connoted by the name:
+white things, for example, are not distinguished by any common
+properties, except whiteness; or if they are, it is only by such as are
+in some way dependent on, or connected with, whiteness. But a hundred
+generations have not exhausted the common properties of animals or of
+plants, of sulphur or of phosphorus; nor do we suppose them to be
+exhaustible, but proceed to new observations and experiments, in the
+full confidence of discovering new properties which were by no means
+implied in those we previously knew. While, if any one were to propose
+for investigation the common properties of all things which are of the
+same colour, the same shape, or the same specific gravity, the absurdity
+would be palpable. We have no ground to believe that any such common
+properties exist, except such as may be shown to be involved in the
+supposition itself, or to be derivable from it by some law of causation.
+It appears, therefore, that the properties, on which we ground our
+classes, sometimes exhaust all that the class has in common, or contain
+it all by some mode of implication; but in other instances we make a
+selection of a few properties from among not only a greater number, but
+a number inexhaustible by us, and to which as we know no bounds, they
+may, so far as we are concerned, be regarded as infinite.
+
+There is no impropriety in saying that, of these two classifications,
+the one answers to a much more radical distinction in the things
+themselves, than the other does. And if any one even chooses to say that
+the one classification is made by nature, the other by us for our
+convenience, he will be right; provided he means no more than this:
+Where a certain apparent difference between things (though perhaps in
+itself of little moment) answers to we know not what number of other
+differences, pervading not only their known properties, but properties
+yet undiscovered, it is not optional but imperative to recognise this
+difference as the foundation of a specific distinction; while, on the
+contrary, differences that are merely finite and determinate, like those
+designated by the words white, black, or red, may be disregarded if the
+purpose for which the classification is made does not require attention
+to those particular properties. The differences, however, are made by
+nature, in both cases; while the recognition of those differences as
+grounds of classification and of naming, is, equally in both cases, the
+act of man: only in the one case, the ends of language and of
+classification would be subverted if no notice were taken of the
+difference, while in the other case, the necessity of taking notice of
+it depends on the importance or unimportance of the particular qualities
+in which the difference happens to consist.
+
+Now, these classes, distinguished by unknown multitudes of properties,
+and not solely by a few determinate ones--which are parted off from one
+another by an unfathomable chasm, instead of a mere ordinary ditch with
+a visible bottom--are the only classes which, by the Aristotelian
+logicians, were considered as genera or species. Differences which
+extended only to a certain property or properties, and there terminated,
+they considered as differences only in the _accidents_ of things; but
+where any class differed from other things by an infinite series of
+differences, known and unknown, they considered the distinction as one
+of _kind_, and spoke of it as being an _essential_ difference, which is
+also one of the current meanings of that vague expression at the present
+day.
+
+Conceiving the schoolmen to have been justified in drawing a broad line
+of separation between these two kinds of classes and of
+class-distinctions, I shall not only retain the division itself, but
+continue to express it in their language. According to that language,
+the proximate (or lowest) Kind to which any individual is referrible, is
+called its species. Conformably to this, Sir Isaac Newton would be said
+to be of the species man. There are indeed numerous sub-classes included
+in the class man, to which Newton also belongs; for example, Christian,
+and Englishman, and Mathematician. But these, though distinct classes,
+are not, in our sense of the term, distinct Kinds of men. A Christian,
+for example, differs from other human beings; but he differs only in the
+attribute which the word expresses, namely, belief in Christianity, and
+whatever else that implies, either as involved in the fact itself, or
+connected with it through some law of cause and effect. We should never
+think of inquiring what properties, unconnected with Christianity either
+as cause or effect, are common to all Christians and peculiar to them;
+while in regard to all Men, physiologists are perpetually carrying on
+such an inquiry; nor is the answer ever likely to be completed. Man,
+therefore, we may call a species; Christian, or Mathematician, we
+cannot.
+
+Note here, that it is by no means intended to imply that there may not
+be different Kinds, or logical species, of man. The various races and
+temperaments, the two sexes, and even the various ages, may be
+differences of kind, within our meaning of the term. I do not say that
+they are so. For in the progress of physiology it may almost be said to
+be made out, that the differences which really exist between different
+races, sexes, &c., follow as consequences, under laws of nature, from a
+small number of primary differences which can be precisely determined,
+and which, as the phrase is, _account for_ all the rest. If this be so,
+these are not distinctions in kind; no more than Christian, Jew,
+Mussulman, and Pagan, a difference which also carries many consequences
+along with it. And in this way classes are often mistaken for real
+Kinds, which are afterwards proved not to be so. But if it turned out
+that the differences were not capable of being thus accounted for, then
+Caucasian, Mongolian, Negro, &c. would be really different Kinds of
+human beings, and entitled to be ranked as species by the logician;
+though not by the naturalist. For (as already noticed) the word species
+is used in a different signification in logic and in natural history. By
+the naturalist, organized beings are not usually said to be of different
+species, if it is supposed that they could possibly have descended from
+the same stock. That, however, is a sense artificially given to the
+word, for the technical purposes of a particular science. To the
+logician, if a negro and a white man differ in the same manner (however
+less in degree) as a horse and a camel do, that is, if their differences
+are inexhaustible, and not referrible to any common cause, they are
+different species, whether they are descended from common ancestors or
+not. But if their differences can all be traced to climate and habits,
+or to some one or a few special differences in structure, they are not,
+in the logician's view, specially distinct.
+
+When the _infima species_, or proximate Kind, to which an individual
+belongs, has been ascertained, the properties common to that Kind
+include necessarily the whole of the common properties of every other
+real Kind to which the individual can be referrible. Let the individual,
+for example, be Socrates, and the proximate Kind, man. Animal, or living
+creature, is also a real Kind, and includes Socrates; but, since it
+likewise includes man, or in other words, since all men are animals, the
+properties common to animals form a portion of the common properties of
+the sub-class, man. And if there be any class which includes Socrates
+without including man, that class is not a real Kind. Let the class for
+example, be _flat-nosed_; that being a class which includes Socrates,
+without including all men. To determine whether it is a real Kind, we
+must ask ourselves this question: Have all flat-nosed animals, in
+addition to whatever is implied in their flat noses, any common
+properties, other than those which are common to all animals whatever?
+If they had; if a flat nose were a mark or index to an indefinite number
+of other peculiarities, not deducible from the former by an
+ascertainable law, then out of the class man we might cut another class,
+flat-nosed man, which according to our definition, would be a Kind. But
+if we could do this, man would not be, as it was assumed to be, the
+proximate Kind. Therefore, the properties of the proximate Kind do
+comprehend those (whether known or unknown) of all other Kinds to which
+the individual belongs; which was the point we undertook to prove. And
+hence, every other Kind which is predicable of the individual, will be
+to the proximate Kind in the relation of a genus, according to even the
+popular acceptation of the terms genus and species; that is, it will be
+a larger class, including it and more.
+
+We are now able to fix the logical meaning of these terms. Every class
+which is a real Kind, that is, which is distinguished from all other
+classes by an indeterminate multitude of properties not derivable from
+one another, is either a genus or a species. A Kind which is not
+divisible into other Kinds, cannot be a genus, because it has no
+species under it; but it is itself a species, both with reference to the
+individuals below and to the genera above (Species Pr�dicabilis and
+Species Subjicibilis.) But every Kind which admits of division into real
+Kinds (as animal into mammal, bird, fish, &c., or bird into various
+species of birds) is a genus to all below it, a species to all genera in
+which it is itself included. And here we may close this part of the
+discussion, and pass to the three remaining predicables, Differentia,
+Proprium, and Accidens.
+
+
+� 5. To begin with Differentia. This word is correlative with the words
+genus and species, and as all admit, it signifies the attribute which
+distinguishes a given species from every other species of the same
+genus. This is so far clear: but we may still ask, which of the
+distinguishing attributes it signifies. For we have seen that every Kind
+(and a species must be a Kind) is distinguished from other Kinds not by
+any one attribute, but by an indefinite number. Man, for instance, is a
+species of the genus animal: Rational (or rationality, for it is of no
+consequence here whether we use the concrete or the abstract form) is
+generally assigned by logicians as the Differentia; and doubtless this
+attribute serves the purpose of distinction: but it has also been
+remarked of man, that he is a cooking animal; the only animal that
+dresses its food. This, therefore, is another of the attributes by which
+the species man is distinguished from other species of the same genus:
+would this attribute serve equally well for a differentia? The
+Aristotelians say No; having laid it down that the differentia must,
+like the genus and species, be of the _essence_ of the subject.
+
+And here we lose even that vestige of a meaning grounded in the nature
+of the things themselves, which may be supposed to be attached to the
+word essence when it is said that genus and species must be of the
+essence of the thing. There can be no doubt that when the schoolmen
+talked of the essences of things as opposed to their accidents, they had
+confusedly in view the distinction between differences of kind, and the
+differences which are not of kind; they meant to intimate that genera
+and species must be Kinds. Their notion of the essence of a thing was a
+vague notion of a something which makes it what it is, _i. e._ which
+makes it the Kind of thing that it is--which causes it to have all that
+variety of properties which distinguish its Kind. But when the matter
+came to be looked at more closely, nobody could discover what caused the
+thing to have all those properties, nor even that there was anything
+which caused it to have them. Logicians, however, not liking to admit
+this, and being unable to detect what made the thing to be what it was,
+satisfied themselves with what made it to be what it was called. Of the
+innumerable properties, known and unknown, that are common to the class
+man, a portion only, and of course a very small portion, are connoted by
+its name; these few, however, will naturally have been thus
+distinguished from the rest either for their greater obviousness, or for
+greater supposed importance. These properties, then, which were connoted
+by the name, logicians seized upon, and called them the essence of the
+species; and not stopping there, they affirmed them, in the case of the
+_infima species_, to be the essence of the individual too; for it was
+their maxim, that the species contained the "whole essence" of the
+thing. Metaphysics, that fertile field of delusion propagated by
+language, does not afford a more signal instance of such delusion. On
+this account it was that rationality, being connoted by the name man,
+was allowed to be a differentia of the class; but the peculiarity of
+cooking their food, not being connoted, was relegated to the class of
+accidental properties.
+
+The distinction, therefore, between Differentia, Proprium, and Accidens,
+is not grounded in the nature of things, but in the connotation of
+names; and we must seek it there, if we wish to find what it is.
+
+From the fact that the genus includes the species, in other words
+_de_notes more than the species, or is predicable of a greater number of
+individuals, it follows that the species must connote more than the
+genus. It must connote all the attributes which the genus connotes, or
+there would be nothing to prevent it from denoting individuals not
+included in the genus. And it must connote something besides, otherwise
+it would include the whole genus. Animal denotes all the individuals
+denoted by man, and many more. Man, therefore, must connote all that
+animal connotes, otherwise there might be men who are not animals; and
+it must connote something more than animal connotes, otherwise all
+animals would be men. This surplus of connotation--this which the
+species connotes over and above the connotation of the genus--is the
+Differentia, or specific difference; or, to state the same proposition
+in other words, the Differentia is that which must be added to the
+connotation of the genus, to complete the connotation of the species.
+
+The word man, for instance, exclusively of what it connotes in common
+with animal, also connotes rationality, and at least some approximation
+to that external form which we all know, but which as we have no name
+for it considered in itself, we are content to call the human. The
+Differentia, or specific difference, therefore, of man, as referred to
+the genus animal, is that outward form and the possession of reason. The
+Aristotelians said, the possession of reason, without the outward form.
+But if they adhered to this, they would have been obliged to call the
+Houyhnhnms men. The question never arose, and they were never called
+upon to decide how such a case would have affected their notion of
+essentiality. However this may be, they were satisfied with taking such
+a portion of the differentia as sufficed to distinguish the species from
+all other _existing_ things, though by so doing they might not exhaust
+the connotation of the name.
+
+
+� 6. And here, to prevent the notion of differentia from being
+restricted within too narrow limits, it is necessary to remark, that a
+species, even as referred to the same genus, will not always have the
+same differentia, but a different one, according to the principle and
+purpose which preside over the particular classification. For example, a
+naturalist surveys the various kinds of animals, and looks out for the
+classification of them most in accordance with the order in which, for
+zoological purposes, he considers it desirable that we should think of
+them. With this view he finds it advisable that one of his fundamental
+divisions should be into warm-blooded and cold-blooded animals; or into
+animals which breathe with lungs and those which breathe with gills; or
+into carnivorous, and frugivorous or graminivorous; or into those which
+walk on the flat part and those which walk on the extremity of the foot,
+a distinction on which two of Cuvier's families are founded. In doing
+this, the naturalist creates as many new classes; which are by no means
+those to which the individual animal is familiarly and spontaneously
+referred; nor should we ever think of assigning to them so prominent a
+position in our arrangement of the animal kingdom, unless for a
+preconceived purpose of scientific convenience. And to the liberty of
+doing this there is no limit. In the examples we have given, most of the
+classes are real Kinds, since each of the peculiarities is an index to a
+multitude of properties belonging to the class which it characterizes:
+but even if the case were otherwise--if the other properties of those
+classes could all be derived, by any process known to us, from the one
+peculiarity on which the class is founded--even then, if these
+derivative properties were of primary importance for the purposes of the
+naturalist, he would be warranted in founding his primary divisions on
+them.
+
+If, however, practical convenience is a sufficient warrant for making
+the main demarcations in our arrangement of objects run in lines not
+coinciding with any distinction of Kind, and so creating genera and
+species in the popular sense which are not genera or species in the
+rigorous sense at all, _� fortiori_ must we be warranted, when our
+genera and species _are_ real genera and species, in marking the
+distinction between them by those of their properties which
+considerations of practical convenience most strongly recommend. If we
+cut a species out of a given genus--the species man, for instance, out
+of the genus animal--with an intention on our part that the peculiarity
+by which we are to be guided in the application of the name man should
+be rationality, then rationality is the differentia of the species man.
+Suppose, however, that being naturalists, we, for the purposes of our
+particular study, cut out of the genus animal the same species man, but
+with an intention that the distinction between man and all other species
+of animal should be, not rationality, but the possession of "four
+incisors in each jaw, tusks solitary, and erect posture." It is evident
+that the word man, when used by us as naturalists, no longer connotes
+rationality, but connotes the three other properties specified; for that
+which we have expressly in view when we impose a name, assuredly forms
+part of the meaning of that name. We may, therefore, lay it down as a
+maxim, that wherever there is a Genus, and a Species marked out from
+that genus by an assignable differentia, the name of the species must be
+connotative, and must connote the differentia; but the connotation may
+be special--not involved in the signification of the term as ordinarily
+used, but given to it when employed as a term of art or science. The
+word Man in common use, connotes rationality and a certain form, but
+does not connote the number or character of the teeth; in the Linn�an
+system it connotes the number of incisor and canine teeth, but does not
+connote rationality nor any particular form. The word _man_ has,
+therefore, two different meanings; though not commonly considered as
+ambiguous, because it happens in both cases to _de_note the same
+individual objects. But a case is conceivable in which the ambiguity
+would become evident: we have only to imagine that some new kind of
+animal were discovered, having Linn�us's three characteristics of
+humanity, but not rational, or not of the human form. In ordinary
+parlance, these animals would not be called men; but in natural history
+they must still be called so by those, if any there be, who adhere to
+the Linn�an classification; and the question would arise, whether the
+word should continue to be used in two senses, or the classification be
+given up, and the technical sense of the term be abandoned along with
+it.
+
+Words not otherwise connotative may, in the mode just adverted to,
+acquire a special or technical connotation. Thus the word whiteness, as
+we have so often remarked, connotes nothing; it merely denotes the
+attribute corresponding to a certain sensation: but if we are making a
+classification of colours, and desire to justify, or even merely to
+point out, the particular place assigned to whiteness in our
+arrangement, we may define it "the colour produced by the mixture of all
+the simple rays;" and this fact, though by no means implied in the
+meaning of the word whiteness as ordinarily used, but only known by
+subsequent scientific investigation, is part of its meaning in the
+particular essay or treatise, and becomes the differentia of the
+species.[26]
+
+The differentia, therefore, of a species may be defined to be, that part
+of the connotation of the specific name, whether ordinary or special and
+technical, which distinguishes the species in question from all other
+species of the genus to which on the particular occasion we are
+referring it.
+
+
+� 7. Having disposed of Genus, Species, and Differentia, we shall not
+find much difficulty in attaining a clear conception of the distinction
+between the other two predicables, as well as between them and the first
+three.
+
+In the Aristotelian phraseology, Genus and Differentia are of the
+_essence_ of the subject; by which, as we have seen, is really meant
+that the properties signified by the genus and those signified by the
+differentia, form part of the connotation of the name denoting the
+species. Proprium and Accidens, on the other hand, form no part of the
+essence, but are predicated of the species only _accidentally_. Both are
+Accidents, in the wider sense in which the accidents of a thing are
+opposed to its essence; though, in the doctrine of the Predicables,
+Accidens is used for one sort of accident only, Proprium being another
+sort. Proprium, continue the schoolmen, is predicated _accidentally_,
+indeed, but _necessarily_; or, as they further explain it, signifies an
+attribute which is not indeed part of the essence, but which flows from,
+or is a consequence of, the essence, and is, therefore, inseparably
+attached to the species; _e. g._ the various properties of a triangle,
+which, though no part of its definition, must necessarily be possessed
+by whatever comes under that definition. Accidens, on the contrary, has
+no connexion whatever with the essence, but may come and go, and the
+species still remain what it was before. If a species could exist
+without its Propria, it must be capable of existing without that on
+which its Propria are necessarily consequent, and therefore without its
+essence, without that which constitutes it a species. But an Accidens,
+whether separable or inseparable from the species in actual experience,
+may be supposed separated, without the necessity of supposing any other
+alteration; or at least, without supposing any of the essential
+properties of the species to be altered, since with them an Accidens has
+no connexion.
+
+A Proprium, therefore, of the species, may be defined, any attribute
+which belongs to all the individuals included in the species, and which,
+though not connoted by the specific name, (either ordinarily if the
+classification we are considering be for ordinary purposes, or specially
+if it be for a special purpose,) yet follows from some attribute which
+the name either ordinarily or specially connotes.
+
+One attribute may follow from another in two ways; and there are
+consequently two kinds of Proprium. It may follow as a conclusion
+follows premises, or it may follow as an effect follows a cause. Thus,
+the attribute of having the opposite sides equal, which is not one of
+those connoted by the word Parallelogram, nevertheless follows from
+those connoted by it, namely, from having the opposite sides straight
+lines and parallel, and the number of sides four. The attribute,
+therefore, of having the opposite sides equal, is a Proprium of the
+class parallelogram; and a Proprium of the first kind, which follows
+from the connoted attributes by way of _demonstration_. The attribute of
+being capable of understanding language, is a Proprium of the species
+man, since without being connoted by the word, it follows from an
+attribute which the word does connote, viz. from the attribute of
+rationality. But this is a Proprium of the second kind, which follows by
+way of _causation_. How it is that one property of a thing follows, or
+can be inferred, from another; under what conditions this is possible,
+and what is the exact meaning of the phrase; are among the questions
+which will occupy us in the two succeeding Books. At present it needs
+only be said, that whether a Proprium follows by demonstration or by
+causation, it follows _necessarily_; that is to say, its not following
+would be inconsistent with some law which we regard as a part of the
+constitution either of our thinking faculty or of the universe.
+
+
+� 8. Under the remaining predicable, Accidens, are included all
+attributes of a thing which are neither involved in the signification of
+the name (whether ordinarily or as a term of art), nor have, so far as
+we know, any necessary connexion with attributes which are so involved.
+They are commonly divided into Separable and Inseparable Accidents.
+Inseparable accidents are those which--although we know of no connexion
+between them and the attributes constitutive of the species, and
+although, therefore, so far as we are aware, they might be absent
+without making the name inapplicable and the species a different
+species--are yet never in fact known to be absent. A concise mode of
+expressing the same meaning is, that inseparable accidents are
+properties which are universal to the species, but not necessary to it.
+Thus, blackness is an attribute of a crow, and, as far as we know, an
+universal one. But if we were to discover a race of white birds, in
+other respects resembling crows, we should not say, These are not crows;
+we should say, These are white crows. Crow, therefore, does not connote
+blackness; nor, from any of the attributes which it does connote,
+whether as a word in popular use or as a term of art, could blackness be
+inferred. Not only, therefore, can we conceive a white crow, but we know
+of no reason why such an animal should not exist. Since, however, none
+but black crows are known to exist, blackness, in the present state of
+our knowledge, ranks as an accident, but an inseparable accident, of
+the species crow.
+
+Separable Accidents are those which are found, in point of fact, to be
+sometimes absent from the species; which are not only not necessary, but
+not even universal. They are such as do not belong to every individual
+of the species, but only to some individuals; or if to all, not at all
+times. Thus the colour of an European is one of the separable accidents
+of the species man, because it is not an attribute of all human
+creatures. Being born, is also (speaking in the logical sense) a
+separable accident of the species man, because, though an attribute of
+all human beings, it is so only at one particular time. _� fortiori_
+those attributes which are not constant even in the same individual, as,
+to be in one or in another place, to be hot or cold, sitting or walking,
+must be ranked as separable accidents.
+
+
+
+
+CHAPTER VIII.
+
+OF DEFINITION.
+
+
+� 1. One necessary part of the theory of Names and of Propositions
+remains to be treated of in this place: the theory of Definitions. As
+being the most important of the class of propositions which we have
+characterized as purely verbal, they have already received some notice
+in the chapter preceding the last. But their fuller treatment was at
+that time postponed, because definition is so closely connected with
+classification, that, until the nature of the latter process is in some
+measure understood, the former cannot be discussed to much purpose.
+
+The simplest and most correct notion of a Definition is, a proposition
+declaratory of the meaning of a word; namely, either the meaning which
+it bears in common acceptation, or that which the speaker or writer, for
+the particular purposes of his discourse, intends to annex to it.
+
+The definition of a word being the proposition which enunciates its
+meaning, words which have no meaning are unsusceptible of definition.
+Proper names, therefore, cannot be defined. A proper name being a mere
+mark put upon an individual, and of which it is the characteristic
+property to be destitute of meaning, its meaning cannot of course be
+declared; though we may indicate by language, as we might indicate still
+more conveniently by pointing with the finger, upon what individual that
+particular mark has been, or is intended to be, put. It is no definition
+of "John Thomson" to say he is "the son of General Thomson;" for the
+name John Thomson does not express this. Neither is it any definition of
+"John Thomson" to say he is "the man now crossing the street." These
+propositions may serve to make known who is the particular man to whom
+the name belongs, but that may be done still more unambiguously by
+pointing to him, which, however, has not been esteemed one of the modes
+of definition.
+
+In the case of connotative names, the meaning, as has been so often
+observed, is the connotation; and the definition of a connotative name,
+is the proposition which declares its connotation. This might be done
+either directly or indirectly. The direct mode would be by a proposition
+in this form: "Man" (or whatsoever the word may be) "is a name connoting
+such and such attributes," or "is a name which, when predicated of
+anything, signifies the possession of such and such attributes by that
+thing." Or thus: Man is everything which possesses such and such
+attributes: Man is everything which possesses corporeity, organization,
+life, rationality, and certain peculiarities of external form.
+
+This form of definition is the most precise and least equivocal of any;
+but it is not brief enough, and is besides too technical for common
+discourse. The more usual mode of declaring the connotation of a name,
+is to predicate of it another name or names of known signification,
+which connote the same aggregation of attributes. This may be done
+either by predicating of the name intended to be defined, another
+connotative name exactly synonymous, as, "Man is a human being," which
+is not commonly accounted a definition at all; or by predicating two or
+more connotative names, which make up among them the whole connotation
+of the name to be defined. In this last case, again, we may either
+compose our definition of as many connotative names as there are
+attributes, each attribute being connoted by one, as, Man is a
+corporeal, organized, animated, rational being, shaped so and so; or we
+may employ names which connote several of the attributes at once, as,
+Man is a rational _animal_, shaped so and so.
+
+The definition of a name, according to this view of it, is the sum total
+of all the _essential_ propositions which can be framed with that name
+for their subject. All propositions the truth of which is implied in the
+name, all those which we are made aware of by merely hearing the name,
+are included in the definition, if complete, and may be evolved from it
+without the aid of any other premises; whether the definition expresses
+them in two or three words, or in a larger number. It is, therefore, not
+without reason that Condillac and other writers have affirmed a
+definition to be an _analysis_. To resolve any complex whole into the
+elements of which it is compounded, is the meaning of analysis: and this
+we do when we replace one word which connotes a set of attributes
+collectively, by two or more which connote the same attributes singly,
+or in smaller groups.
+
+
+� 2. From this, however, the question naturally arises, in what manner
+are we to define a name which connotes only a single attribute: for
+instance, "white," which connotes nothing but whiteness; "rational,"
+which connotes nothing but the possession of reason. It might seem that
+the meaning of such names could only be declared in two ways; by a
+synonymous term, if any such can be found; or in the direct way already
+alluded to: "White is a name connoting the attribute whiteness." Let us
+see, however, whether the analysis of the meaning of the name, that is,
+the breaking down of that meaning into several parts, admits of being
+carried farther. Without at present deciding this question as to the
+word _white_, it is obvious that in the case of _rational_ some further
+explanation may be given of its meaning than is contained in the
+proposition, "Rational is that which possesses the attribute of reason;"
+since the attribute reason itself admits of being defined. And here we
+must turn our attention to the definitions of attributes, or rather of
+the names of attributes, that is, of abstract names.
+
+In regard to such names of attributes as are connotative, and express
+attributes of those attributes, there is no difficulty: like other
+connotative names they are defined by declaring their connotation. Thus,
+the word _fault_ may be defined, "a quality productive of evil or
+inconvenience." Sometimes, again, the attribute to be defined is not one
+attribute, but an union of several: we have only, therefore, to put
+together the names of all the attributes taken separately, and we obtain
+the definition of the name which belongs to them all taken together; a
+definition which will correspond exactly to that of the corresponding
+concrete name. For, as we define a concrete name by enumerating the
+attributes which it connotes, and as the attributes connoted by a
+concrete name form the entire signification of the corresponding
+abstract name, the same enumeration will serve for the definition of
+both. Thus, if the definition of _a human being_ be this, "a being,
+corporeal, animated, rational, shaped so and so," the definition of
+_humanity_ will be corporeity and animal life, combined with
+rationality, and with such and such a shape.
+
+When, on the other hand, the abstract name does not express a
+complication of attributes, but a single attribute, we must remember
+that every attribute is grounded on some fact or phenomenon, from which,
+and which alone, it derives its meaning. To that fact or phenomenon,
+called in a former chapter the foundation of the attribute, we must,
+therefore, have recourse for its definition. Now, the foundation of the
+attribute may be a phenomenon of any degree of complexity, consisting of
+many different parts, either coexistent or in succession. To obtain a
+definition of the attribute, we must analyse the phenomenon into these
+parts. Eloquence, for example, is the name of one attribute only; but
+this attribute is grounded on external effects of a complicated nature,
+flowing from acts of the person to whom we ascribed the attribute; and
+by resolving this phenomenon of causation into its two parts, the cause
+and the effect, we obtain a definition of eloquence, viz. the power of
+influencing the feelings by speech or writing.
+
+A name, therefore, whether concrete or abstract, admits of definition,
+provided we are able to analyse, that is, to distinguish into parts, the
+attribute or set of attributes which constitute the meaning both of the
+concrete name and of the corresponding abstract: if a set of attributes,
+by enumerating them; if a single attribute, by dissecting the fact or
+phenomenon (whether of perception or of internal consciousness) which is
+the foundation of the attribute. But, further, even when the fact is one
+of our simple feelings or states of consciousness, and therefore
+unsusceptible of analysis, the names both of the object and of the
+attribute still admit of definition: or rather, would do so if all our
+simple feelings had names. Whiteness may be defined, the property or
+power of exciting the sensation of white. A white object may be defined,
+an object which excites the sensation of white. The only names which are
+unsusceptible of definition, because their meaning is unsusceptible of
+analysis, are the names of the simple feelings themselves. These are in
+the same condition as proper names. They are not indeed, like proper
+names, unmeaning; for the words _sensation of white_ signify, that the
+sensation which I so denominate resembles other sensations which I
+remember to have had before, and to have called by that name. But as we
+have no words by which to recal those former sensations, except the very
+word which we seek to define, or some other which, being exactly
+synonymous with it, requires definition as much, words cannot unfold the
+signification of this class of names; and we are obliged to make a
+direct appeal to the personal experience of the individual whom we
+address.
+
+
+� 3. Having stated what seems to be the true idea of a Definition, we
+proceed to examine some opinions of philosophers, and some popular
+conceptions on the subject, which conflict more or less with that idea.
+
+The only adequate definition of a name is, as already remarked, one
+which declares the facts, and the whole of the facts, which the name
+involves in its signification. But with most persons the object of a
+definition does not embrace so much; they look for nothing more, in a
+definition, than a guide to the correct use of the term--a protection
+against applying it in a manner inconsistent with custom and convention.
+Anything, therefore, is to them a sufficient definition of a term, which
+will serve as a correct index to what the term denotes; though not
+embracing the whole, and sometimes, perhaps, not even any part, of what
+it connotes. This gives rise to two sorts of imperfect, or unscientific
+definition; Essential but incomplete Definitions, and Accidental
+Definitions, or Descriptions. In the former, a connotative name is
+defined by a part only of its connotation; in the latter, by something
+which forms no part of the connotation at all.
+
+An example of the first kind of imperfect definitions is the
+following:--Man is a rational animal. It is impossible to consider this
+as a complete definition of the word Man, since (as before remarked) if
+we adhered to it we should be obliged to call the Houyhnhnms men; but as
+there happen to be no Houyhnhnms, this imperfect definition is
+sufficient to mark out and distinguish from all other things, the
+objects at present denoted by "man;" all the beings actually known to
+exist, of whom the name is predicable. Though the word is defined by
+some only among the attributes which it connotes, not by all, it happens
+that all known objects which possess the enumerated attributes, possess
+also those which are omitted; so that the field of predication which the
+word covers, and the employment of it which is conformable to usage, are
+as well indicated by the inadequate definition as by an adequate one.
+Such definitions, however, are always liable to be overthrown by the
+discovery of new objects in nature.
+
+Definitions of this kind are what logicians have had in view, when they
+laid down the rule, that the definition of a species should be _per
+genus et differentiam_. Differentia being seldom taken to mean the whole
+of the peculiarities constitutive of the species, but some one of those
+peculiarities only, a complete definition would be _per genus et
+differentias_, rather than _differentiam_. It would include, with the
+name of the superior genus, not merely _some_ attribute which
+distinguishes the species intended to be defined from all other species
+of the same genus, but _all_ the attributes implied in the name of the
+species, which the name of the superior genus has not already implied.
+The assertion, however, that a definition must of necessity consist of a
+genus and differenti�, is not tenable. It was early remarked by
+logicians, that the _summum genus_ in any classification, having no
+genus superior to itself, could not be defined in this manner. Yet we
+have seen that all names, except those of our elementary feelings, are
+susceptible of definition in the strictest sense; by setting forth in
+words the constituent parts of the fact or phenomenon, of which the
+connotation of every word is ultimately composed.
+
+
+� 4. Although the first kind of imperfect definition, (which defines a
+connotative term by a part only of what it connotes, but a part
+sufficient to mark out correctly the boundaries of its denotation,) has
+been considered by the ancients, and by logicians in general, as a
+complete definition; it has always been deemed necessary that the
+attributes employed should really form part of the connotation; for the
+rule was that the definition must be drawn from the _essence_ of the
+class; and this would not have been the case if it had been in any
+degree made up of attributes not connoted by the name. The second kind
+of imperfect definition, therefore, in which the name of a class is
+defined by any of its accidents,--that is, by attributes which are not
+included in its connotation,--has been rejected from the rank of genuine
+Definition by all logicians, and has been termed Description.
+
+This kind of imperfect definition, however, takes its rise from the same
+cause as the other, namely, the willingness to accept as a definition
+anything which, whether it expounds the meaning of the name or not,
+enables us to discriminate the things denoted by the name from all other
+things, and consequently to employ the term in predication without
+deviating from established usage. This purpose is duly answered by
+stating any (no matter what) of the attributes which are common to the
+whole of the class, and peculiar to it; or any combination of attributes
+which happens to be peculiar to it, though separately each of those
+attributes may be common to it with some other things. It is only
+necessary that the definition (or description) thus formed, should be
+_convertible_ with the name which it professes to define; that is,
+should be exactly co-extensive with it, being predicable of everything
+of which it is predicable, and of nothing of which it is not predicable;
+though the attributes specified may have no connexion with those which
+mankind had in view when they formed or recognised the class, and gave
+it a name. The following are correct definitions of Man, according to
+this test: Man is a mammiferous animal, having (by nature) two hands
+(for the human species answers to this description, and no other animal
+does): Man is an animal who cooks his food: Man is a featherless biped.
+
+What would otherwise be a mere description, may be raised to the rank of
+a real definition by the peculiar purpose which the speaker or writer
+has in view. As was seen in the preceding chapter, it may, for the ends
+of a particular art or science, or for the more convenient statement of
+an author's particular doctrines, be advisable to give to some general
+name, without altering its denotation, a special connotation, different
+from its ordinary one. When this is done, a definition of the name by
+means of the attributes which make up the special connotation, though in
+general a mere accidental definition or description, becomes on the
+particular occasion and for the particular purpose a complete and
+genuine definition. This actually occurs with respect to one of the
+preceding examples, "Man is a mammiferous animal having two hands,"
+which is the scientific definition of man, considered as one of the
+species in Cuvier's distribution of the animal kingdom.
+
+In cases of this sort, though the definition is still a declaration of
+the meaning which in the particular instance the name is appointed to
+convey, it cannot be said that to state the meaning of the word is the
+purpose of the definition. The purpose is not to expound a name, but a
+classification. The special meaning which Cuvier assigned to the word
+Man, (quite foreign to its ordinary meaning, though involving no change
+in the denotation of the word,) was incidental to a plan of arranging
+animals into classes on a certain principle, that is, according to a
+certain set of distinctions. And since the definition of Man according
+to the ordinary connotation of the word, though it would have answered
+every other purpose of a definition, would not have pointed out the
+place which the species ought to occupy in that particular
+classification; he gave the word a special connotation, that he might be
+able to define it by the kind of attributes on which, for reasons of
+scientific convenience, he had resolved to found his division of
+animated nature.
+
+Scientific definitions, whether they are definitions of scientific
+terms, or of common terms used in a scientific sense, are almost always
+of the kind last spoken of: their main purpose is to serve as the
+landmarks of scientific classification. And since the classifications in
+any science are continually modified as scientific knowledge advances,
+the definitions in the sciences are also constantly varying. A striking
+instance is afforded by the words Acid and Alkali, especially the
+former. As experimental discovery advanced, the substances classed with
+acids have been constantly multiplying, and by a natural consequence the
+attributes connoted by the word have receded and become fewer. At first
+it connoted the attributes, of combining with an alkali to form a
+neutral substance (called a salt); being compounded of a base and
+oxygen; causticity to the taste and touch; fluidity, &c. The true
+analysis of muriatic acid, into chlorine and hydrogen, caused the second
+property, composition from a base and oxygen, to be excluded from the
+connotation. The same discovery fixed the attention of chemists upon
+hydrogen as an important element in acids; and more recent discoveries
+having led to the recognition of its presence in sulphuric, nitric, and
+many other acids, where its existence was not previously suspected,
+there is now a tendency to include the presence of this element in the
+connotation of the word. But carbonic acid, silica, sulphurous acid,
+have no hydrogen in their composition; that property cannot therefore be
+connoted by the term, unless those substances are no longer to be
+considered acids. Causticity and fluidity have long since been excluded
+from the characteristics of the class, by the inclusion of silica and
+many other substances in it; and the formation of neutral bodies by
+combination with alkalis, together with such electro-chemical
+peculiarities as this is supposed to imply, are now the only
+_differenti�_ which form the fixed connotation of the word Acid, as a
+term of chemical science.
+
+What is true of the definition of any term of science, is of course true
+of the definition of a science itself: and accordingly, (as observed in
+the Introductory Chapter of this work,) the definition of a science must
+necessarily be progressive and provisional. Any extension of knowledge
+or alteration in the current opinions respecting the subject matter, may
+lead to a change more or less extensive in the particulars included in
+the science; and its composition being thus altered, it may easily
+happen that a different set of characteristics will be found better
+adapted as differenti� for defining its name.
+
+In the same manner in which a special or technical definition has for
+its object to expound the artificial classification out of which it
+grows; the Aristotelian logicians seem to have imagined that it was also
+the business of ordinary definition to expound the ordinary, and what
+they deemed the natural, classification of things, namely, the division
+of them into Kinds; and to show the place which each Kind occupies, as
+superior, collateral, or subordinate, among other Kinds. This notion
+would account for the rule that all definition must necessarily be _per
+genus et differentiam_, and would also explain why a single differentia
+was deemed sufficient. But to expound, or express in words, a
+distinction of Kind, has already been shown to be an impossibility: the
+very meaning of a Kind is, that the properties which distinguish it do
+not grow out of one another, and cannot therefore be set forth in words,
+even by implication, otherwise than by enumerating them all: and all are
+not known, nor are ever likely to be so. It is idle, therefore, to look
+to this as one of the purposes of a definition: while, if it be only
+required that the definition of a Kind should indicate what Kinds
+include it or are included by it, any definitions which expound the
+connotation of the names will do this: for the name of each class must
+necessarily connote enough of its properties to fix the boundaries of
+the class. If the definition, therefore, be a full statement of the
+connotation, it is all that a definition can be required to be.
+
+
+� 5. Of the two incomplete and popular modes of definition, and in what
+they differ from the complete or philosophical mode, enough has now been
+said. We shall next examine an ancient doctrine, once generally
+prevalent and still by no means exploded, which I regard as the source
+of a great part of the obscurity hanging over some of the most important
+processes of the understanding in the pursuit of truth. According to
+this, the definitions of which we have now treated are only one of two
+sorts into which definitions may be divided, viz. definitions of names,
+and definitions of things. The former are intended to explain the
+meaning of a term; the latter, the nature of a thing; the last being
+incomparably the most important.
+
+This opinion was held by the ancient philosophers, and by their
+followers, with the exception of the Nominalists; but as the spirit of
+modern metaphysics, until a recent period, has been on the whole a
+Nominalist spirit, the notion of definitions of things has been to a
+certain extent in abeyance, still continuing, however, to breed
+confusion in logic, by its consequences indeed rather than by itself.
+Yet the doctrine in its own proper form now and then breaks out, and has
+appeared (among other places) where it was scarcely to be expected, in a
+justly admired work, Archbishop Whately's _Logic_.[27] In a review of
+that work published by me in the _Westminster Review_ for January 1828,
+and containing some opinions which I no longer entertain, I find the
+following observations on the question now before us; observations with
+which my present view of that question is still sufficiently in
+accordance.
+
+"The distinction between nominal and real definitions, between
+definitions of words and what are called definitions of things, though
+conformable to the ideas of most of the Aristotelian logicians, cannot,
+as it appears to us, be maintained. We apprehend that no definition is
+ever intended to 'explain and unfold the nature of a thing.' It is some
+confirmation of our opinion, that none of those writers who have thought
+that there were definitions of things, have ever succeeded in
+discovering any criterion by which the definition of a thing can be
+distinguished from any other proposition relating to the thing. The
+definition, they say, unfolds the nature of the thing: but no definition
+can unfold its whole nature; and every proposition in which any quality
+whatever is predicated of the thing, unfolds some part of its nature.
+The true state of the case we take to be this. All definitions are of
+names, and of names only; but, in some definitions, it is clearly
+apparent, that nothing is intended except to explain the meaning of the
+word; while in others, besides explaining the meaning of the word, it is
+intended to be implied that there exists a thing, corresponding to the
+word. Whether this be or be not implied in any given case, cannot be
+collected from the mere form of the expression. 'A centaur is an animal
+with the upper parts of a man and the lower parts of a horse,' and 'A
+triangle is a rectilineal figure with three sides,' are, in form,
+expressions precisely similar; although in the former it is not implied
+that any _thing_, conformable to the term, really exists, while in the
+latter it is; as may be seen by substituting, in both definitions, the
+word _means_ for _is_. In the first expression, 'A centaur means an
+animal,' &c., the sense would remain unchanged: in the second, 'A
+triangle means,' &c., the meaning would be altered, since it would be
+obviously impossible to deduce any of the truths of geometry from a
+proposition expressive only of the manner in which we intend to employ a
+particular sign.
+
+"There are, therefore, expressions, commonly passing for definitions,
+which include in themselves more than the mere explanation of the
+meaning of a term. But it is not correct to call an expression of this
+sort a peculiar kind of definition. Its difference from the other kind
+consists in this, that it is not a definition, but a definition and
+something more. The definition above given of a triangle, obviously
+comprises not one, but two propositions, perfectly distinguishable. The
+one is, 'There may exist a figure, bounded by three straight lines;' the
+other, 'And this figure may be termed a triangle.' The former of these
+propositions is not a definition at all: the latter is a mere nominal
+definition, or explanation of the use and application of a term. The
+first is susceptible of truth or falsehood, and may therefore be made
+the foundation of a train of reasoning. The latter can neither be true
+nor false; the only character it is susceptible of is that of conformity
+or disconformity to the ordinary usage of language."
+
+There is a real distinction, then, between definitions of names, and
+what are erroneously called definitions of things; but it is, that the
+latter, along with the meaning of a name, covertly asserts a matter of
+fact. This covert assertion is not a definition, but a postulate. The
+definition is a mere identical proposition, which gives information only
+about the use of language, and from which no conclusions affecting
+matters of fact can possibly be drawn. The accompanying postulate, on
+the other hand, affirms a fact, which may lead to consequences of every
+degree of importance. It affirms the actual or possible existence of
+Things possessing the combination of attributes set forth in the
+definition; and this, if true, may be foundation sufficient on which to
+build a whole fabric of scientific truth.
+
+We have already made, and shall often have to repeat, the remark, that
+the philosophers who overthrew Realism by no means got rid of the
+consequences of Realism, but retained long afterwards, in their own
+philosophy, numerous propositions which could only have a rational
+meaning as part of a Realistic system. It had been handed down from
+Aristotle, and probably from earlier times, as an obvious truth, that
+the science of Geometry is deduced from definitions. This, so long as a
+definition was considered to be a proposition "unfolding the nature of
+the thing," did well enough. But Hobbes followed, and rejected utterly
+the notion that a definition declares the nature of the thing, or does
+anything but state the meaning of a name; yet he continued to affirm as
+broadly as any of his predecessors, that the [Greek: archai],
+_principia_, or original premises of mathematics, and even of all
+science, are definitions; producing the singular paradox, that systems
+of scientific truth, nay, all truths whatever at which we arrive by
+reasoning, are deduced from the arbitrary conventions of mankind
+concerning the signification of words.
+
+To save the credit of the doctrine that definitions are the premises of
+scientific knowledge, the proviso is sometimes added, that they are so
+only under a certain condition, namely, that they be framed conformably
+to the phenomena of nature; that is, that they ascribe such meanings to
+terms as shall suit objects actually existing. But this is only an
+instance of the attempt so often made, to escape from the necessity of
+abandoning old language after the ideas which it expresses have been
+exchanged for contrary ones. From the meaning of a name (we are told) it
+is possible to infer physical facts, provided the name has corresponding
+to it an existing thing. But if this proviso be necessary, from which of
+the two is the inference really drawn? From the existence of a thing
+having the properties, or from the existence of a name meaning them?
+
+Take, for instance, any of the definitions laid down as premises in
+Euclid's Elements; the definition, let us say, of a circle. This, being
+analysed, consists of two propositions; the one an assumption with
+respect to a matter of fact, the other a genuine definition. "A figure
+may exist, having all the points in the line which bounds it equally
+distant from a single point within it:" "Any figure possessing this
+property is called a circle." Let us look at one of the demonstrations
+which are said to depend on this definition, and observe to which of the
+two propositions contained in it the demonstration really appeals.
+"About the centre A, describe the circle B C D." Here is an assumption
+that a figure, such as the definition expresses, _may_ be described;
+which is no other than the postulate, or covert assumption, involved in
+the so-called definition. But whether that figure be called a circle or
+not is quite immaterial. The purpose would be as well answered, in all
+respects except brevity, were we to say, "Through the point B, draw a
+line returning into itself, of which every point shall be at an equal
+distance from the point A." By this the definition of a circle would be
+got rid of, and rendered needless; but not the postulate implied in it;
+without that the demonstration could not stand. The circle being now
+described, let us proceed to the consequence. "Since B C D is a circle,
+the radius B A is equal to the radius C A." B A is equal to C A, not
+because B C D is a circle, but because B C D is a figure with the radii
+equal. Our warrant for assuming that such a figure about the centre A,
+with the radius B A, may be made to exist, is the postulate. Whether the
+admissibility of these postulates rests on intuition, or on proof, may
+be a matter of dispute; but in either case they are the premises on
+which the theorems depend; and while these are retained it would make no
+difference in the certainty of geometrical truths, though every
+definition in Euclid, and every technical term therein defined, were
+laid aside.
+
+It is, perhaps, superfluous to dwell at so much length on what is so
+nearly self-evident; but when a distinction, obvious as it may appear,
+has been confounded, and by powerful intellects, it is better to say too
+much than too little for the purpose of rendering such mistakes
+impossible in future. I will, therefore, detain the reader while I point
+out one of the absurd consequences flowing from the supposition that
+definitions, as such, are the premises in any of our reasonings, except
+such as relate to words only. If this supposition were true, we might
+argue correctly from true premises, and arrive at a false conclusion. We
+should only have to assume as a premise the definition of a nonentity;
+or rather of a name which has no entity corresponding to it. Let this,
+for instance, be our definition:
+
+  A dragon is a serpent breathing flame.
+
+This proposition, considered only as a definition, is indisputably
+correct. A dragon _is_ a serpent breathing flame: the word _means_ that.
+The tacit assumption, indeed, (if there were any such understood
+assertion), of the existence of an object with properties corresponding
+to the definition, would, in the present instance, be false. Out of this
+definition we may carve the premises of the following syllogism:
+
+  A dragon is a thing which breathes flame:
+  A dragon is a serpent:
+
+From which the conclusion is,
+
+  Therefore some serpent or serpents breathe flame:--
+
+an unexceptionable syllogism in the first mode of the third figure, in
+which both premises are true and yet the conclusion false; which every
+logician knows to be an absurdity. The conclusion being false and the
+syllogism correct, the premises cannot be true. But the premises,
+considered as parts of a definition, are true. Therefore, the premises
+considered as parts of a definition cannot be the real ones. The real
+premises must be--
+
+  A dragon is a _really existing_ thing which breathes flame:
+  A dragon is a _really existing_ serpent:
+
+which implied premises being false, the falsity of the conclusion
+presents no absurdity.
+
+If we would determine what conclusion follows from the same ostensible
+premises when the tacit assumption of real existence is left out, let
+us, according to the recommendation in a previous page, substitute
+_means_ for _is_. We then have--
+
+  Dragon is _a word meaning_ a thing which breathes flame:
+  Dragon is _a word meaning_ a serpent:
+
+From which the conclusion is,
+
+  Some _word or words which mean_ a serpent, also mean a thing which
+  breathes flame:
+
+where the conclusion (as well as the premises) is true, and is the only
+kind of conclusion which can ever follow from a definition, namely, a
+proposition relating to the meaning of words.
+
+There is still another shape into which we may transform this syllogism.
+We may suppose the middle term to be the designation neither of a thing
+nor of a name, but of an idea. We then have--
+
+  The _idea of_ a dragon is _an idea of_ a thing which breathes
+    flame:
+  The _idea of_ a dragon is _an idea of_ a serpent:
+  Therefore, there is _an idea of_ a serpent, which is _an idea of_
+    a thing breathing flame.
+
+Here the conclusion is true, and also the premises; but the premises are
+not definitions. They are propositions affirming that an idea existing
+in the mind, includes certain ideal elements. The truth of the
+conclusion follows from the existence of the psychological phenomenon
+called the idea of a dragon; and therefore still from the tacit
+assumption of a matter of fact.[28]
+
+When, as in this last syllogism, the conclusion is a proposition
+respecting an idea, the assumption on which it depends may be merely
+that of the existence of an idea. But when the conclusion is a
+proposition concerning a Thing, the postulate involved in the definition
+which stands as the apparent premise, is the existence of a thing
+conformable to the definition, and not merely of an idea conformable to
+it. This assumption of real existence will always convey the impression
+that we intend to make, when we profess to define any name which is
+already known to be a name of really existing objects. On this account
+it is, that the assumption was not necessarily implied in the definition
+of a dragon, while there was no doubt of its being included in the
+definition of a circle.
+
+
+� 6. One of the circumstances which have contributed to keep up the
+notion, that demonstrative truths follow from definitions rather than
+from the postulates implied in those definitions, is, that the
+postulates, even in those sciences which are considered to surpass all
+others in demonstrative certainty, are not always exactly true. It is
+not true that a circle exists, or can be described, which has all its
+radii _exactly_ equal. Such accuracy is ideal only; it is not found in
+nature, still less can it be realized by art. People had a difficulty,
+therefore, in conceiving that the most certain of all conclusions could
+rest on premises which, instead of being certainly true, are certainly
+not true to the full extent asserted. This apparent paradox will be
+examined when we come to treat of Demonstration; where we shall be able
+to show that as much of the postulate is true, as is required to support
+as much as is true of the conclusion. Philosophers, however, to whom
+this view had not occurred, or whom it did not satisfy, have thought it
+indispensable that there should be found in definitions something _more_
+certain, or at least more accurately true, than the implied postulate of
+the real existence of a corresponding object. And this something they
+flattered themselves they had found, when they laid it down that a
+definition is a statement and analysis not of the mere meaning of a
+word, nor yet of the nature of a thing, but of an idea. Thus, the
+proposition, "A circle is a plane figure bounded by a line all the
+points of which are at an equal distance from a given point within it,"
+was considered by them, not as an assertion that any real circle has
+that property, (which would not be exactly true,) but that we _conceive_
+a circle as having it; that our abstract idea of a circle is an idea of
+a figure with its radii exactly equal.
+
+Conformably to this it is said, that the subject-matter of mathematics,
+and of every other demonstrative science, is not things as they really
+exist, but abstractions of the mind. A geometrical line is a line
+without breadth; but no such line exists in nature; it is a notion
+merely suggested to the mind by its experience of nature. The definition
+(it is said) is a definition of this mental line, not of any actual
+line: and it is only of the mental line, not of any line existing in
+nature, that the theorems of geometry are accurately true.
+
+Allowing this doctrine respecting the nature of demonstrative truth to
+be correct (which, in a subsequent place, I shall endeavour to prove
+that it is not;) even on that supposition, the conclusions which seem to
+follow from a definition, do not follow from the definition as such, but
+from an implied postulate. Even if it be true that there is no object in
+nature answering to the definition of a line, and that the geometrical
+properties of lines are not true of any lines in nature, but only of the
+idea of a line; the definition, at all events, postulates the real
+existence of such an idea: it assumes that the mind can frame, or rather
+has framed, the notion of length without breadth, and without any other
+sensible property whatever. To me, indeed, it appears that the mind
+cannot form any such notion; it cannot conceive length without breadth;
+it can only, in contemplating objects, attend to their length,
+exclusively of their other sensible qualities, and so determine what
+properties may be predicated of them in virtue of their length alone. If
+this be true, the postulate involved in the geometrical definition of a
+line, is the real existence, not of length without breadth, but merely
+of length, that is, of long objects. This is quite enough to support all
+the truths of geometry, since every property of a geometrical line is
+really a property of all physical objects in so far as possessing
+length. But even what I hold to be the false doctrine on the subject,
+leaves the conclusion that our reasonings are grounded on the matters of
+fact postulated in definitions, and not on the definitions themselves,
+entirely unaffected; and accordingly this conclusion is one which I have
+in common with Dr. Whewell, in his _Philosophy of the Inductive
+Sciences_: though, on the nature of demonstrative truth, Dr. Whewell's
+opinions are greatly at variance with mine. And here, as in many other
+instances, I gladly acknowledge that his writings are eminently
+serviceable in clearing from confusion the initial steps in the analysis
+of the mental processes, even where his views respecting the ultimate
+analysis are such as (though with unfeigned respect) I cannot but regard
+as fundamentally erroneous.
+
+
+� 7. Although, according to the opinion here presented, Definitions are
+properly of names only, and not of things, it does not follow from this
+that definitions are arbitrary. How to define a name, may not only be an
+inquiry of considerable difficulty and intricacy, but may involve
+considerations going deep into the nature of the things which are
+denoted by the name. Such, for instance, are the inquiries which form
+the subjects of the most important of Plato's Dialogues; as, "What is
+rhetoric?" the topic of the Gorgias, or "What is justice?" that of the
+Republic. Such, also, is the question scornfully asked by Pilate, "What
+is truth?" and the fundamental question with speculative moralists in
+all ages, "What is virtue?"
+
+It would be a mistake to represent these difficult and noble inquiries
+as having nothing in view beyond ascertaining the conventional meaning
+of a name. They are inquiries not so much to determine what is, as what
+should be, the meaning of a name; which, like other practical questions
+of terminology, requires for its solution that we should enter, and
+sometimes enter very deeply, into the properties not merely of names but
+of the things named.
+
+Although the meaning of every concrete general name resides in the
+attributes which it connotes, the objects were named before the
+attributes; as appears from the fact that in all languages, abstract
+names are mostly compounds or other derivatives of the concrete names
+which correspond to them. Connotative names, therefore, were, after
+proper names, the first which were used: and in the simpler cases, no
+doubt, a distinct connotation was present to the minds of those who
+first used the name, and was distinctly intended by them to be conveyed
+by it. The first person who used the word white, as applied to snow or
+to any other object, knew, no doubt, very well what quality he intended
+to predicate, and had a perfectly distinct conception in his mind of the
+attribute signified by the name.
+
+But where the resemblances and differences on which our classifications
+are founded are not of this palpable and easily determinable kind;
+especially where they consist not in any one quality but in a number of
+qualities, the effects of which being blended together are not very
+easily discriminated, and referred each to its true source; it often
+happens that names are applied to nameable objects, with no distinct
+connotation present to the minds of those who apply them. They are only
+influenced by a general resemblance between the new object and all or
+some of the old familiar objects which they have been accustomed to call
+by that name. This, as we have seen, is the law which even the mind of
+the philosopher must follow, in giving names to the simple elementary
+feelings of our nature: but, where the things to be named are complex
+wholes, a philosopher is not content with noticing a general
+resemblance; he examines what the resemblance consists in: and he only
+gives the same name to things which resemble one another in the same
+definite particulars. The philosopher, therefore, habitually employs his
+general names with a definite connotation. But language was not made,
+and can only in some small degree be mended, by philosophers. In the
+minds of the real arbiters of language, general names, especially where
+the classes they denote cannot be brought before the tribunal of the
+outward senses to be identified and discriminated, connote little more
+than a vague gross resemblance to the things which they were earliest,
+or have been most, accustomed to call by those names. When, for
+instance, ordinary persons predicate the words _just_ or _unjust_ of any
+action, _noble_ or _mean_ of any sentiment, expression, or demeanour,
+_statesman_ or _charlatan_ of any personage figuring in politics, do
+they mean to affirm of those various subjects any determinate
+attributes, of whatever kind? No: they merely recognise, as they think,
+some likeness, more or less vague and loose, between these and some
+other things which they have been accustomed to denominate or to hear
+denominated by those appellations.
+
+Language, as Sir James Mackintosh used to say of governments, "is not
+made, but grows." A name is not imposed at once and by previous purpose
+upon a _class_ of objects, but is first applied to one thing, and then
+extended by a series of transitions to another and another. By this
+process (as has been remarked by several writers, and illustrated with
+great force and clearness by Dugald Stewart in his Philosophical Essays)
+a name not unfrequently passes by successive links of resemblance from
+one object to another, until it becomes applied to things having nothing
+in common with the first things to which the name was given; which,
+however, do not, for that reason, drop the name; so that it at last
+denotes a confused huddle of objects, having nothing whatever in common;
+and connotes nothing, not even a vague and general resemblance. When a
+name has fallen into this state, in which by predicating it of any
+object we assert literally nothing about the object, it has become unfit
+for the purposes either of thought or of the communication of thought;
+and can only be made serviceable by stripping it of some part of its
+multifarious denotation, and confining it to objects possessed of some
+attributes in common, which it may be made to connote. Such are the
+inconveniences of a language which "is not made, but grows." Like the
+governments which are in a similar case, it may be compared to a road
+which is not made but has made itself: it requires continual mending in
+order to be passable.
+
+From this it is already evident, why the question respecting the
+definition of an abstract name is often one of so much difficulty. The
+question, What is justice? is, in other words, What is the attribute
+which mankind mean to predicate when they call an action just? To which
+the first answer is, that having come to no precise agreement on the
+point, they do not mean to predicate distinctly any attribute at all.
+Nevertheless, all believe that there is some common attribute belonging
+to all the actions which they are in the habit of calling just. The
+question then must be, whether there is any such common attribute? and,
+in the first place, whether mankind agree sufficiently with one another
+as to the particular actions which they do or do not call just, to
+render the inquiry, what quality those actions have in common, a
+possible one: if so, whether the actions really have any quality in
+common; and if they have, what it is. Of these three, the first alone is
+an inquiry into usage and convention; the other two are inquiries into
+matters of fact. And if the second question (whether the actions form a
+class at all) has been answered negatively, there remains a fourth,
+often more arduous than all the rest, namely, how best to form a class
+artificially, which the name may denote.
+
+And here it is fitting to remark, that the study of the spontaneous
+growth of languages is of the utmost importance to those who would
+logically remodel them. The classifications rudely made by established
+language, when retouched, as they almost all require to be, by the hands
+of the logician, are often in themselves excellently suited to his
+purposes. As compared with the classifications of a philosopher, they
+are like the customary law of a country, which has grown up as it were
+spontaneously, compared with laws methodized and digested into a code:
+the former are a far less perfect instrument than the latter; but being
+the result of a long, though unscientific, course of experience, they
+contain a mass of materials which may be made very usefully available in
+the formation of the systematic body of written law. In like manner, the
+established grouping of objects under a common name, even when founded
+only on a gross and general resemblance, is evidence, in the first
+place, that the resemblance is obvious, and therefore considerable;
+and, in the next place, that it is a resemblance which has struck great
+numbers of persons during a series of years and ages. Even when a name,
+by successive extensions, has come to be applied to things among which
+there does not exist this gross resemblance common to them all, still at
+every step in its progress we shall find such a resemblance. And these
+transitions of the meaning of words are often an index to real
+connexions between the things denoted by them, which might otherwise
+escape the notice of thinkers; of those at least who, from using a
+different language, or from any difference in their habitual
+associations, have fixed their attention in preference on some other
+aspect of the things. The history of philosophy abounds in examples of
+such oversights, committed for want of perceiving the hidden link that
+connected together the seemingly disparate meanings of some ambiguous
+word.[29]
+
+Whenever the inquiry into the definition of the name of any real object
+consists of anything else than a mere comparison of authorities, we
+tacitly assume that a meaning must be found for the name, compatible
+with its continuing to denote, if possible all, but at any rate the
+greater or the more important part, of the things of which it is
+commonly predicated. The inquiry, therefore, into the definition, is an
+inquiry into the resemblances and differences among those things:
+whether there be any resemblance running through them all; if not,
+through what portion of them such a general resemblance can be traced:
+and finally, what are the common attributes, the possession of which
+gives to them all, or to that portion of them, the character of
+resemblance which has led to their being classed together. When these
+common attributes have been ascertained and specified, the name which
+belongs in common to the resembling objects acquires a distinct instead
+of a vague connotation; and by possessing this distinct connotation,
+becomes susceptible of definition.
+
+In giving a distinct connotation to the general name, the philosopher
+will endeavour to fix upon such attributes as, while they are common to
+all the things usually denoted by the name, are also of greatest
+importance in themselves; either directly, or from the number, the
+conspicuousness, or the interesting character, of the consequences to
+which they lead. He will select, as far as possible, such _differenti�_
+as lead to the greatest number of interesting _propria_. For these,
+rather than the more obscure and recondite qualities on which they often
+depend, give that general character and aspect to a set of objects,
+which determine the groups into which they naturally fall. But to
+penetrate to the more hidden agreement on which these obvious and
+superficial agreements depend, is often one of the most difficult of
+scientific problems. As it is among the most difficult, so it seldom
+fails to be among the most important. And since upon the result of this
+inquiry respecting the causes of the properties of a class of things,
+there incidentally depends the question what shall be the meaning of a
+word; some of the most profound and most valuable investigations which
+philosophy presents to us, have been introduced by, and have offered
+themselves under the guise of, inquiries into the definition of a name.
+
+FOOTNOTES:
+
+[1] _Computation or Logic_, chap. ii.
+
+[2] In the original "had, _or had not_." These last words, as involving
+a subtlety foreign to our present purpose, I have forborne to quote.
+
+[3] Vide infra, note at the end of � 3, book ii. ch. ii.
+
+[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one
+thing _with_ or _in addition to_ another.
+
+[5] Archbishop Whately, who, in the later editions of his _Elements of
+Logic_, aided in reviving the important distinction treated of in the
+text, proposes the term "Attributive" as a substitute for "Connotative"
+(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it
+has not the advantage of being connected with any verb, of so markedly
+distinctive a character as "to connote," it is not, I think, fitted to
+supply the place of the word Connotative in scientific use.
+
+[6] A writer who entitles his book _Philosophy; or, the Science of
+Truth_, charges me in his very first page (referring at the foot of it
+to this passage) with asserting that _general_ names have properly no
+signification. And he repeats this statement many times in the course of
+his volume, with comments, not at all flattering, thereon. It is well to
+be now and then reminded to how great a length perverse misquotation
+(for, strange as it appears, I do not believe that the writer is
+dishonest) can sometimes go. It is a warning to readers, when they see
+an author accused, with volume and page referred to, and the apparent
+guarantee of inverted commas, of maintaining something more than
+commonly absurd, not to give implicit credence to the assertion without
+verifying the reference.
+
+[7] Before quitting the subject of connotative names, it is proper to
+observe, that the first writer who, in our times, has adopted from the
+schoolmen the word _to connote_, Mr. James Mill, in his _Analysis of the
+Phenomena of the Human Mind_, employs it in a signification different
+from that in which it is here used. He uses the word in a sense
+coextensive with its etymology, applying it to every case in which a
+name, while pointing directly to one thing, (which is consequently
+termed its signification,) includes also a tacit reference to some other
+thing. In the case considered in the text, that of concrete general
+names, his language and mine are the converse of one another.
+Considering (very justly) the signification of the name to lie in the
+attribute, he speaks of the word as _noting_ the attribute, and
+_connoting_ the things possessing the attribute. And he describes
+abstract names as being properly concrete names with their connotation
+dropped: whereas, in my view, it is the _de_notation which would be said
+to be dropped, what was previously connoted becoming the whole
+signification.
+
+In adopting a phraseology at variance with that which so high an
+authority, and one which I am less likely than any other person to
+undervalue, has deliberately sanctioned, I have been influenced by the
+urgent necessity for a term exclusively appropriated to express the
+manner in which a concrete general name serves to mark the attributes
+which are involved in its signification. This necessity can scarcely be
+felt in its full force by any one who has not found by experience how
+vain is the attempt to communicate clear ideas on the philosophy of
+language without such a word. It is hardly an exaggeration to say, that
+some of the most prevalent of the errors with which logic has been
+infected, and a large part of the cloudiness and confusion of ideas
+which have enveloped it, would, in all probability, have been avoided,
+if a term had been in common use to express exactly what I have
+signified by the term to connote. And the schoolmen, to whom we are
+indebted for the greater part of our logical language, gave us this
+also, and in this very sense. For though some of their general
+expressions countenance the use of the word in the more extensive and
+vague acceptation in which it is taken by Mr. Mill, yet when they had to
+define it specifically as a technical term, and to fix its meaning as
+such, with that admirable precision which always characterizes their
+definitions, they clearly explained that nothing was said to be connoted
+except _forms_, which word may generally, in their writings, be
+understood as synonymous with _attributes_.
+
+Now, if the word _to connote_, so well suited to the purpose to which
+they applied it, be diverted from that purpose by being taken to fulfil
+another, for which it does not seem to me to be at all required; I am
+unable to find any expression to replace it, but such as are commonly
+employed in a sense so much more general, that it would be useless
+attempting to associate them peculiarly with this precise idea. Such are
+the words, to involve, to imply, &c. By employing these, I should fail
+of attaining the object for which alone the name is needed, namely, to
+distinguish this particular kind of involving and implying from all
+other kinds, and to assure to it the degree of habitual attention which
+its importance demands.
+
+[8] Or rather, all objects except itself and the percipient mind; for,
+as we shall see hereafter, to ascribe any attribute to an object,
+necessarily implies a mind to perceive it.
+
+The simple and clear explanation given in the text, of relation and
+relative names, a subject so long the opprobrium of metaphysics, was
+given (as far as I know) for the first time, by Mr. James Mill, in his
+Analysis of the Phenomena of the Human Mind.
+
+[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.
+
+[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.
+
+[11] It is to be regretted that Sir William Hamilton, though he often
+strenuously insists on this doctrine, and though, in the passage quoted,
+he states it with a comprehensiveness and force which leave nothing to
+be desired, did not consistently adhere to his own doctrine, but
+maintained along with it opinions with which it is utterly
+irreconcileable. See the third and other chapters of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous
+ne pouvons expliquer nos perceptions sans les rattacher � des causes
+distinctes de nous-m�mes; nous savons de plus que ces causes, dont nous
+ne connaissons pas d'ailleurs l'essence, produisent les effets les plus
+variables, les plus divers, et m�me les plus contraires, selon qu'elles
+rencontrent telle nature ou telle disposition du sujet. Mais savons-nous
+quelque chose de plus? et m�me, vu le caract�re ind�termin� des causes
+que nous concevons dans les corps, y a-t-il quelque chose de plus �
+savoir? Y a-t-il lieu de nous enqu�rir si nous percevons les choses
+telles qu'elles sont? Non �videmment.... Je ne dis pas que le probl�me
+est insoluble, _je dis qu'il est absurde et enferme une contradiction_.
+Nous _ne savons pas ce que ces causes sont en elles-m�mes_, et la raison
+nous d�fend de chercher � le conna�tre: mais il est bien �vident _�
+priori_, qu'_elles ne sont pas en elles-m�mes ce qu'elles sont par
+rapport � nous_, puisque la pr�sence du sujet modifie n�cessairement
+leur action. Supprimez tout sujet sentant, il est certain que ces causes
+agiraient encore puisqu'elles continueraient d'exister; mais elles
+agiraient autrement; elles seraient encore des qualit�s et des
+propri�t�s, mais qui ne ressembleraient � rien de ce que nous
+connaissons. Le feu ne manifesterait plus aucune des propri�t�s que nous
+lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.
+_C'est d'ailleurs peut-�tre un probl�me qui ne r�pugne pas seulement �
+la nature de notre esprit, mais � l'essence m�me des choses._ Quand m�me
+en effet on supprimerait par la pens�e tous les sujets sentants, il
+faudrait encore admettre que nul corps ne manifesterait ses propri�t�s
+autrement qu'en relation avec un sujet quelconque, et dans ce cas _ses
+propri�t�s ne seraient encore que relatives_: en sorte qu'il me para�t
+fort raisonnable d'admettre que les propri�t�s d�termin�es des corps
+n'existent pas ind�pendamment d'un sujet quelconque, et que quand on
+demande si les propri�t�s de la mati�re sont telles que nous les
+percevons, il faudrait voir auparavant si elles sont en tant que
+d�termin�es, et dans quel sens il est vrai de dire qu'elles
+sont."--_Cours d'Histoire de la Philosophie Morale au 18me si�cle_, 8me
+le�on.
+
+[13] An attempt, indeed, has been made by Reid and others, to establish
+that although some of the properties we ascribe to objects exist only in
+our sensations, others exist in the things themselves, being such as
+cannot possibly be copies of any impression upon the senses; and they
+ask, from what sensations our notions of extension and figure have been
+derived? The gauntlet thrown down by Reid was taken up by Brown, who,
+applying greater powers of analysis than had previously been applied to
+the notions of extension and figure, pointed out that the sensations
+from which those notions are derived, are sensations of touch, combined
+with sensations of a class previously too little adverted to by
+metaphysicians, those which have their seat in our muscular frame. His
+analysis, which was adopted and followed up by James Mill, has been
+further and greatly improved upon in Professor Bain's profound work,
+_The Senses and the Intellect_, and in the chapters on "Perception" of a
+work of eminent analytic power, Mr. Herbert Spencer's _Principles of
+Psychology_.
+
+On this point M. Cousin may again be cited in favour of the better
+doctrine. M. Cousin recognises, in opposition to Reid, the essential
+subjectivity of our conceptions of what are called the primary qualities
+of matter, as extension, solidity, &c., equally with those of colour,
+heat, and the remainder of the so-called secondary qualities.--_Cours_,
+ut supra, 9me le�on.
+
+[14] This doctrine, which is the most complete form of the philosophical
+theory known as the Relativity of Human Knowledge, has, since the recent
+revival in this country of an active interest in metaphysical
+speculation, been the subject of a greatly increased amount of
+discussion and controversy; and dissentients have manifested themselves
+in considerably greater number than I had any knowledge of when the
+passage in the text was written. The doctrine has been attacked from two
+sides. Some thinkers, among whom are the late Professor Ferrier, in his
+_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio
+Philosophica_, appear to deny altogether the reality of Noumena, or
+Things in themselves--of an unknowable substratum or support for the
+sensations which we experience, and which, according to the theory,
+constitute all our knowledge of an external world. It seems to me,
+however, that in Professor Grote's case at least, the denial of Noumena
+is only apparent, and that he does not essentially differ from the other
+class of objectors, including Mr. Bailey in his valuable _Letters on the
+Philosophy of the Human Mind_, and (in spite of the striking passage
+quoted in the text) also Sir William Hamilton, who contend for a direct
+knowledge by the human mind of more than the sensations--of certain
+attributes or properties as they exist not in us, but in the Things
+themselves.
+
+With the first of these opinions, that which denies Noumena, I have, as
+a metaphysician, no quarrel; but, whether it be true or false, it is
+irrelevant to Logic. And since all the forms of language are in
+contradiction to it, nothing but confusion could result from its
+unnecessary introduction into a treatise, every essential doctrine of
+which could stand equally well with the opposite and accredited opinion.
+The other and rival doctrine, that of a direct perception or intuitive
+knowledge of the outward object as it is in itself, considered as
+distinct from the sensations we receive from it, is of far greater
+practical moment. But even this question, depending on the nature and
+laws of Intuitive Knowledge, is not within the province of Logic. For
+the grounds of my own opinion concerning it, I must content myself with
+referring to a work already mentioned--_An Examination of Sir William
+Hamilton's Philosophy_; several chapters of which are devoted to a full
+discussion of the questions and theories relating to the supposed direct
+perception of external objects.
+
+[15] _Analysis of the Human Mind_, i. 126 et seq.
+
+[16] It may, however, be considered as equivalent to an universal
+proposition with a different predicate, viz. "All wine is good _qu�_
+wine," or "is good in respect of the qualities which constitute it
+wine."
+
+[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
+statement, and asks, "Are we to say that a mole cannot dig the ground,
+except he has an idea of the ground, and of the snout and paws with
+which he digs it?" I do not know what passes in a mole's mind, nor what
+amount of mental apprehension may or may not accompany his instinctive
+actions. But a human being does not use a spade by instinct; and he
+certainly could not use it unless he had knowledge of a spade, and of
+the earth which he uses it upon.
+
+[18] "From hence also this may be deduced, that the first truths were
+arbitrarily made by those that first of all imposed names upon things,
+or received them from the imposition of others. For it is true (for
+example) that _man is a living creature_, but it is for this reason,
+that it pleased men to impose both these names on the same
+thing."--_Computation or Logic_, ch. iii. sect. 8.
+
+[19] "Men are subject to err not only in affirming and denying, but also
+in perception, and in silent cogitation.... Tacit errors, or the errors
+of sense and cogitation, are made by passing from one imagination to the
+imagination of another different thing; or by feigning that to be past,
+or future, which never was, nor ever shall be; as when by seeing the
+image of the sun in water, we imagine the sun itself to be there; or by
+seeing swords, that there has been, or shall be, fighting, because it
+uses to be so for the most part; or when from promises we feign the mind
+of the promiser to be such and such; or, lastly, when from any sign we
+vainly imagine something to be signified which is not. And errors of
+this sort are common to all things that have sense."--_Computation or
+Logic_, ch. v. sect. 1.
+
+[20] Ch. iii. sect. 3.
+
+[21] To the preceding statement it has been objected, that "we naturally
+construe the subject of a proposition in its extension, and the
+predicate (which therefore may be an adjective) in its intension,
+(connotation): and that consequently coexistence of attributes does not,
+any more than the opposite theory of equation of groups, correspond with
+the living processes of thought and language." I acknowledge the
+distinction here drawn, which, indeed, I had myself laid down and
+exemplified a few pages back (p. 104). But though it is true that we
+naturally "construe the subject of a proposition in its extension," this
+extension, or in other words, the extent of the class denoted by the
+name, is not apprehended or indicated directly. It is both apprehended
+and indicated solely through the attributes. In the "living processes of
+thought and language" the extension, though in this case really thought
+of (which in the case of the predicate it is not), is thought of only
+through the medium of what my acute and courteous critic terms the
+"intension."
+
+For further illustrations of this subject, see _Examination of Sir
+William Hamilton's Philosophy_, ch. xxii.
+
+[22] Book iv. ch. vii.
+
+[23] The doctrines which prevented the real meaning of Essences from
+being understood, had not assumed so settled a shape in the time of
+Aristotle and his immediate followers, as was afterwards given to them
+by the Realists of the middle ages. Aristotle himself (in his Treatise
+on the Categories) expressly denies that the [Greek: deuterai ousiai],
+or Substanti� Secund�, inhere in a subject. They are only, he says,
+predicated of it.
+
+[24] The always acute and often profound author of _An Outline of
+Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more
+intelligible if, in the majority of places, we substitute 'the knowledge
+of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms
+on Locke's use of the word Idea, this is the one which, as it appears to
+me, most nearly hits the mark; and I quote it for the additional reason
+that it precisely expresses the point of difference respecting the
+import of Propositions, between my view and what I have spoken of as the
+Conceptualist view of them. Where a Conceptualist says that a name or a
+proposition expresses our Idea of a thing, I should generally say
+(instead of our Idea) our Knowledge, or Belief, concerning the thing
+itself.
+
+[25] This distinction corresponds to that which is drawn by Kant and
+other metaphysicians between what they term _analytic_, and _synthetic_,
+judgments; the former being those which can be evolved from the meaning
+of the terms used.
+
+[26] If we allow a differentia to what is not really a species. For the
+distinction of Kinds, in the sense explained by us, not being in any way
+applicable to attributes, it of course follows that although attributes
+may be put into classes, those classes can be admitted to be genera or
+species only by courtesy.
+
+[27] In the fuller discussion which Archbishop Whately has given to this
+subject in his later editions, he almost ceases to regard the
+definitions of names and those of things as, in any important sense,
+distinct. He seems (9th ed. p. 145) to limit the notion of a Real
+Definition to one which "explains anything _more_ of the nature of the
+thing than is implied in the name;" (including under the word "implied,"
+not only what the name connotes, but everything which can be deduced by
+reasoning from the attributes connoted). Even this, as he adds, is
+usually called, not a Definition, but a Description; and (as it seems to
+me) rightly so called. A Description, I conceive, can only be ranked
+among Definitions, when taken (as in the case of the zoological
+definition of man) to fulfil the true office of a Definition, by
+declaring the connotation given to a word in some special use, as a term
+of science or art: which special connotation of course would not be
+expressed by the proper definition of the word in its ordinary
+employment.
+
+Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
+understands by a Real Definition one which contains _less_ than the
+Nominal Definition, provided only that what it contains is sufficient
+for distinction. "By _real_ definition I mean such an explanation of the
+word, be it the whole of the meaning or only part, as will be sufficient
+to separate the things contained under that word from all others. Thus
+the following, I believe, is a complete definition of an elephant: An
+animal which naturally drinks by drawing the water into its nose, and
+then spurting it into its mouth."--_Formal Logic_, p. 36. Mr. De
+Morgan's general proposition and his example are at variance; for the
+peculiar mode of drinking of the elephant certainly forms no part of the
+meaning of the word elephant. It could not be said, because a person
+happened to be ignorant of this property, that he did not know what an
+elephant means.
+
+[28] In the only attempt which, so far as I know, has been made to
+refute the preceding argumentation, it is maintained that in the first
+form of the syllogism,
+
+  A dragon is a thing which breathes flame,
+  A dragon is a serpent,
+  Therefore some serpent or serpents breathe flame,
+
+"there is just as much truth in the conclusion as there is in the
+premises, or rather, no more in the latter than in the former. If the
+general name serpent includes both real and imaginary serpents, there is
+no falsity in the conclusion; if not, there is falsity in the minor
+premise."
+
+Let us, then, try to set out the syllogism on the hypothesis that the
+name serpent includes imaginary serpents. We shall find that it is now
+necessary to alter the predicates; for it cannot be asserted that an
+imaginary creature breathes flame: in predicating of it such a fact, we
+assert by the most positive implication that it is real and not
+imaginary. The conclusion must run thus, "Some serpent or serpents
+either do or are _imagined_ to breathe flame." And to prove this
+conclusion by the instance of dragons, the premises must be, A dragon is
+_imagined_ as breathing flame, A dragon is a (real or imaginary)
+serpent: from which it undoubtedly follows, that there are serpents
+which are imagined to breathe flame; but the major premise is not a
+definition, nor part of a definition; which is all that I am concerned
+to prove.
+
+Let us now examine the other assertion--that if the word serpent stands
+for none but real serpents, the minor premise (a dragon is a serpent) is
+false. This is exactly what I have myself said of the premise,
+considered as a statement of fact: but it is not false as part of the
+definition of a dragon; and since the premises, or one of them, must be
+false, (the conclusion being so,) the real premise cannot be the
+definition, which is true, but the statement of fact, which is false.
+
+[29] "Few people" (I have said in another place) "have reflected how
+great a knowledge of Things is required to enable a man to affirm that
+any given argument turns wholly upon words. There is, perhaps, not one
+of the leading terms of philosophy which is not used in almost
+innumerable shades of meaning, to express ideas more or less widely
+different from one another. Between two of these ideas a sagacious and
+penetrating mind will discern, as it were intuitively, an unobvious link
+of connexion, upon which, though perhaps unable to give a logical
+account of it, he will found a perfectly valid argument, which his
+critic, not having so keen an insight into the Things, will mistake for
+a fallacy turning on the double meaning of a term. And the greater the
+genius of him who thus safely leaps over the chasm, the greater will
+probably be the crowing and vain-glory of the mere logician, who,
+hobbling after him, evinces his own superior wisdom by pausing on its
+brink, and giving up as desperate his proper business of bridging it
+over."
+
+
+
+
+BOOK II.
+
+OF REASONING.
+
+
+[Greek: Di�rismen�n de tout�n leg�men �d�, dia tin�n, kai pote, kai p�s
+ginetai pas syllogismos hysteron de lekteon peri apodeixe�s. Proteron
+gar peri syllogismou lekteon, � peri apodeixe�s, dia to katholou mallon
+einai ton syllogismon. H� men gar apodeixis, syllogismos tis; ho
+syllogismos de ou pas, apodeixis.]
+
+                    ARIST. _Analyt. Prior._ l. i. cap. 4.
+
+
+
+
+CHAPTER I.
+
+OF INFERENCE, OR REASONING, IN GENERAL.
+
+
+� 1. In the preceding Book, we have been occupied not with the nature of
+Proof, but with the nature of Assertion: the import conveyed by a
+Proposition, whether that Proposition be true or false; not the means by
+which to discriminate true from false Propositions. The proper subject,
+however, of Logic is Proof. Before we could understand what Proof is, it
+was necessary to understand what that is to which proof is applicable;
+what that is which can be a subject of belief or disbelief, of
+affirmation or denial; what, in short, the different kinds of
+Propositions assert.
+
+This preliminary inquiry we have prosecuted to a definite result.
+Assertion, in the first place, relates either to the meaning of words,
+or to some property of the things which words signify. Assertions
+respecting the meaning of words, among which definitions are the most
+important, hold a place, and an indispensable one, in philosophy; but as
+the meaning of words is essentially arbitrary, this class of assertions
+are not susceptible of truth or falsity, nor therefore of proof or
+disproof. Assertions respecting Things, or what may be called Real
+Propositions, in contradistinction to verbal ones, are of various sorts.
+We have analysed the import of each sort, and have ascertained the
+nature of the things they relate to, and the nature of what they
+severally assert respecting those things. We found that whatever be the
+form of the proposition, and whatever its nominal subject or predicate,
+the real subject of every proposition is some one or more facts or
+phenomena of consciousness, or some one or more of the hidden causes or
+powers to which we ascribe those facts; and that what is predicated or
+asserted, either in the affirmative or negative, of those phenomena or
+those powers, is always either Existence, Order in Place, Order in Time,
+Causation, or Resemblance. This, then, is the theory of the Import of
+Propositions, reduced to its ultimate elements: but there is another and
+a less abstruse expression for it, which, though stopping short in an
+earlier stage of the analysis, is sufficiently scientific for many of
+the purposes for which such a general expression is required. This
+expression recognises the commonly received distinction between Subject
+and Attribute, and gives the following as the analysis of the meaning of
+propositions:--Every Proposition asserts, that some given subject does
+or does not possess some attribute; or that some attribute is or is not
+(either in all or in some portion of the subjects in which it is met
+with) conjoined with some other attribute.
+
+We shall now for the present take our leave of this portion of our
+inquiry, and proceed to the peculiar problem of the Science of Logic,
+namely, how the assertions, of which we have analysed the import, are
+proved or disproved; such of them, at least, as, not being amenable to
+direct consciousness or intuition, are appropriate subjects of proof.
+
+We say of a fact or statement, that it is proved, when we believe its
+truth by reason of some other fact or statement from which it is said to
+_follow_. Most of the propositions, whether affirmative or negative,
+universal, particular, or singular, which we believe, are not believed
+on their own evidence, but on the ground of something previously
+assented to, from which they are said to be _inferred_. To infer a
+proposition from a previous proposition or propositions; to give
+credence to it, or claim credence for it, as a conclusion from something
+else; is to _reason_, in the most extensive sense of the term. There is
+a narrower sense, in which the name reasoning is confined to the form of
+inference which is termed ratiocination, and of which the syllogism is
+the general type. The reasons for not conforming to this restricted use
+of the term were stated in an earlier stage of our inquiry, and
+additional motives will be suggested by the considerations on which we
+are now about to enter.
+
+
+� 2. In proceeding to take into consideration the cases in which
+inferences can legitimately be drawn, we shall first mention some cases
+in which the inference is apparent, not real; and which require notice
+chiefly that they may not be confounded with cases of inference properly
+so called. This occurs when the proposition ostensibly inferred from
+another, appears on analysis to be merely a repetition of the same, or
+part of the same, assertion, which was contained in the first. All the
+cases mentioned in books of Logic as examples of �quipollency or
+equivalence of propositions, are of this nature. Thus, if we were to
+argue, No man is incapable of reason, for every man is rational; or, All
+men are mortal, for no man is exempt from death; it would be plain that
+we were not proving the proposition, but only appealing to another mode
+of wording it, which may or may not be more readily comprehensible by
+the hearer, or better adapted to suggest the real proof, but which
+contains in itself no shadow of proof.
+
+Another case is where, from an universal proposition, we affect to infer
+another which differs from it only in being particular: as All A is B,
+therefore Some A is B: No A is B, therefore Some A is not B. This, too,
+is not to conclude one proposition from another, but to repeat a second
+time something which had been asserted at first; with the difference,
+that we do not here repeat the whole of the previous assertion, but only
+an indefinite part of it.
+
+A third case is where, the antecedent having affirmed a predicate of a
+given subject, the consequent affirms of the same subject something
+already connoted by the former predicate: as, Socrates is a man,
+therefore Socrates is a living creature; where all that is connoted by
+living creature was affirmed of Socrates when he was asserted to be a
+man. If the propositions are negative, we must invert their order, thus:
+Socrates is not a living creature, therefore he is not a man; for if we
+deny the less, the greater, which includes it, is already denied by
+implication. These, therefore, are not really cases of inference; and
+yet the trivial examples by which, in manuals of Logic, the rules of the
+syllogism are illustrated, are often of this ill-chosen kind; formal
+demonstrations of conclusions to which whoever understands the terms
+used in the statement of the data, has already, and consciously,
+assented.
+
+The most complex case of this sort of apparent inference is what is
+called the Conversion of propositions; which consists in turning the
+predicate into a subject, and the subject into a predicate, and framing
+out of the same terms thus reversed, another proposition, which must be
+true if the former is true. Thus, from the particular affirmative
+proposition, Some A is B, we may infer that Some B is A. From the
+universal negative, No A is B, we may conclude that No B is A. From the
+universal affirmative proposition, All A is B, it cannot be inferred
+that all B is A; though all water is liquid, it is not implied that all
+liquid is water; but it is implied that some liquid is so; and hence the
+proposition, All A is B, is legitimately convertible into Some B is A.
+This process, which converts an universal proposition into a particular,
+is termed conversion _per accidens_. From the proposition, Some A is not
+B, we cannot even infer that some B is not A; though some men are not
+Englishmen, it does not follow that some Englishmen are not men. The
+only mode usually recognised of converting a particular negative
+proposition, is in the form, Some A is not B, therefore, something which
+is not B is A; and this is termed conversion by contraposition. In this
+case, however, the predicate and subject are not merely reversed, but
+one of them is changed. Instead of [A] and [B], the terms of the new
+proposition are [a thing which is not B], and [A]. The original
+proposition, Some A _is not_ B, is first changed into a proposition
+�quipollent with it, Some A _is_ "a thing which is not B;" and the
+proposition, being now no longer a particular negative, but a particular
+affirmative, _admits_ of conversion in the first mode, or as it is
+called, _simple_ conversion.[1]
+
+In all these cases there is not really any inference; there is in the
+conclusion no new truth, nothing but what was already asserted in the
+premises, and obvious to whoever apprehends them. The fact asserted in
+the conclusion is either the very same fact, or part of the fact
+asserted in the original proposition. This follows from our previous
+analysis of the Import of Propositions. When we say, for example, that
+some lawful sovereigns are tyrants, what is the meaning of the
+assertion? That the attributes connoted by the term "lawful sovereign,"
+and the attributes connoted by the term "tyrant," sometimes coexist in
+the same individual. Now this is also precisely what we mean, when we
+say that some tyrants are lawful sovereigns; which, therefore, is not a
+second proposition inferred from the first, any more than the English
+translation of Euclid's Elements is a collection of theorems different
+from, and consequences of, those contained in the Greek original. Again,
+if we assert that no great general is a rash man, we mean that the
+attributes connoted by "great general," and those connoted by "rash,"
+never coexist in the same subject; which is also the exact meaning which
+would be expressed by saying, that no rash man is a great general. When
+we say that all quadrupeds are warm-blooded, we assert, not only that
+the attributes connoted by "quadruped" and those connoted by
+"warm-blooded" sometimes coexist, but that the former never exist
+without the latter: now the proposition, Some warm-blooded creatures are
+quadrupeds, expresses the first half of this meaning, dropping the
+latter half; and therefore has been already affirmed in the antecedent
+proposition, All quadrupeds are warm-blooded. But that _all_
+warm-blooded creatures are quadrupeds, or, in other words, that the
+attributes connoted by "warm-blooded" never exist without those connoted
+by "quadruped," has not been asserted, and cannot be inferred. In order
+to reassert, in an inverted form, the whole of what was affirmed in the
+proposition, All quadrupeds are warm-blooded, we must convert it by
+contraposition, thus, Nothing which is not warm-blooded is a quadruped.
+This proposition, and the one from which it is derived, are exactly
+equivalent, and either of them may be substituted for the other; for,
+to say that when the attributes of a quadruped are present, those of a
+warm-blooded creature are present, is to say that when the latter are
+absent the former are absent.
+
+In a manual for young students, it would be proper to dwell at greater
+length on the conversion and �quipollency of propositions. For, though
+that cannot be called reasoning or inference which is a mere reassertion
+in different words of what had been asserted before, there is no more
+important intellectual habit, nor any the cultivation of which falls
+more strictly within the province of the art of logic, than that of
+discerning rapidly and surely the identity of an assertion when
+disguised under diversity of language. That important chapter in logical
+treatises which relates to the Opposition of Propositions, and the
+excellent technical language which logic provides for distinguishing the
+different kinds or modes of opposition, are of use chiefly for this
+purpose. Such considerations as these, that contrary propositions may
+both be false, but cannot both be true; that subcontrary propositions
+may both be true, but cannot both be false; that of two contradictory
+propositions one must be true and the other false; that of two
+subalternate propositions the truth of the universal proves the truth of
+the particular, and the falsity of the particular proves the falsity of
+the universal, but not _vice vers�_;[2] are apt to appear, at first
+sight, very technical and mysterious, but when explained, seem almost
+too obvious to require so formal a statement, since the same amount of
+explanation which is necessary to make the principles intelligible,
+would enable the truths which they convey to be apprehended in any
+particular case which can occur. In this respect, however, these axioms
+of logic are on a level with those of mathematics. That things which are
+equal to the same thing are equal to one another, is as obvious in any
+particular case as it is in the general statement: and if no such
+general maxim had ever been laid down, the demonstrations in Euclid
+would never have halted for any difficulty in stepping across the gap
+which this axiom at present serves to bridge over. Yet no one has ever
+censured writers on geometry, for placing a list of these elementary
+generalizations at the head of their treatises, as a first exercise to
+the learner of the faculty which will be required in him at every step,
+that of apprehending a _general_ truth. And the student of logic, in the
+discussion even of such truths as we have cited above, acquires habits
+of circumspect interpretation of words, and of exactly measuring the
+length and breadth of his assertions, which are among the most
+indispensable conditions of any considerable mental attainment, and
+which it is one of the primary objects of logical discipline to
+cultivate.
+
+
+� 3. Having noticed, in order to exclude from the province of Reasoning
+or Inference properly so called, the cases in which the progression from
+one truth to another is only apparent, the logical consequent being a
+mere repetition of the logical antecedent; we now pass to those which
+are cases of inference in the proper acceptation of the term, those in
+which we set out from known truths, to arrive at others really distinct
+from them.
+
+Reasoning, in the extended sense in which I use the term, and in which
+it is synonymous with Inference, is popularly said to be of two kinds:
+reasoning from particulars to generals, and reasoning from generals to
+particulars; the former being called Induction, the latter Ratiocination
+or Syllogism. It will presently be shown that there is a third species
+of reasoning, which falls under neither of these descriptions, and
+which, nevertheless, is not only valid, but is the foundation of both
+the others.
+
+It is necessary to observe, that the expressions, reasoning from
+particulars to generals, and reasoning from generals to particulars, are
+recommended by brevity rather than by precision, and do not adequately
+mark, without the aid of a commentary, the distinction between Induction
+(in the sense now adverted to) and Ratiocination. The meaning intended
+by these expressions is, that Induction is inferring a proposition from
+propositions _less general_ than itself, and Ratiocination is inferring
+a proposition from propositions _equally_ or _more_ general. When, from
+the observation of a number of individual instances, we ascend to a
+general proposition, or when, by combining a number of general
+propositions, we conclude from them another proposition still more
+general, the process, which is substantially the same in both instances,
+is called Induction. When from a general proposition, not alone (for
+from a single proposition nothing can be concluded which is not involved
+in the terms), but by combining it with other propositions, we infer a
+proposition of the same degree of generality with itself, or a less
+general proposition, or a proposition merely individual, the process is
+Ratiocination. When, in short, the conclusion is more general than the
+largest of the premises, the argument is commonly called Induction; when
+less general, or equally general, it is Ratiocination.
+
+As all experience begins with individual cases, and proceeds from them
+to generals, it might seem most conformable to the natural order of
+thought that Induction should be treated of before we touch upon
+Ratiocination. It will, however, be advantageous, in a science which
+aims at tracing our acquired knowledge to its sources, that the inquirer
+should commence with the latter rather than with the earlier stages of
+the process of constructing our knowledge; and should trace derivative
+truths backward to the truths from which they are deduced, and on which
+they depend for their evidence, before attempting to point out the
+original spring from which both ultimately take their rise. The
+advantages of this order of proceeding in the present instance will
+manifest themselves as we advance, in a manner superseding the necessity
+of any further justification or explanation.
+
+Of Induction, therefore, we shall say no more at present, than that it
+at least is, without doubt, a process of real inference. The conclusion
+in an induction embraces more than is contained in the premises. The
+principle or law collected from particular instances, the general
+proposition in which we embody the result of our experience, covers a
+much larger extent of ground than the individual experiments which form
+its basis. A principle ascertained by experience, is more than a mere
+summing up of what has been specifically observed in the individual
+cases which have been examined; it is a generalization grounded on those
+cases, and expressive of our belief, that what we there found true is
+true in an indefinite number of cases which we have not examined, and
+are never likely to examine. The nature and grounds of this inference,
+and the conditions necessary to make it legitimate, will be the subject
+of discussion in the Third Book: but that such inference really takes
+place is not susceptible of question. In every induction we proceed from
+truths which we knew, to truths which we did not know; from facts
+certified by observation, to facts which we have not observed, and even
+to facts not capable of being now observed; future facts, for example;
+but which we do not hesitate to believe on the sole evidence of the
+induction itself.
+
+Induction, then, is a real process of Reasoning or Inference. Whether,
+and in what sense, as much can be said of the Syllogism, remains to be
+determined by the examination into which we are about to enter.
+
+
+
+
+CHAPTER II.
+
+OF RATIOCINATION, OR SYLLOGISM.
+
+
+� 1. The analysis of the Syllogism has been so accurately and fully
+performed in the common manuals of Logic, that in the present work,
+which is not designed as a manual, it is sufficient to recapitulate,
+_memori� caus�_, the leading results of that analysis, as a foundation
+for the remarks to be afterwards made on the functions of the syllogism,
+and the place which it holds in science.
+
+To a legitimate syllogism it is essential that there should be three,
+and no more than three, propositions, namely, the conclusion, or
+proposition to be proved, and two other propositions which together
+prove it, and which are called the premises. It is essential that there
+should be three, and no more than three, terms, namely, the subject and
+predicate of the conclusion, and another called the middleterm, which
+must be found in both premises, since it is by means of it that the
+other two terms are to be connected together. The predicate of the
+conclusion is called the major term of the syllogism; the subject of the
+conclusion is called the minor term. As there can be but three terms,
+the major and minor terms must each be found in one, and only one, of
+the premises, together with the middleterm which is in them both. The
+premise which contains the middleterm and the major term is called the
+major premise; that which contains the middleterm and the minor term is
+called the minor premise.
+
+Syllogisms are divided by some logicians into three _figures_, by others
+into four, according to the position of the middleterm, which may either
+be the subject in both premises, the predicate in both, or the subject
+in one and the predicate in the other. The most common case is that in
+which the middleterm is the subject of the major premise and the
+predicate of the minor. This is reckoned as the first figure. When the
+middleterm is the predicate in both premises, the syllogism belongs to
+the second figure; when it is the subject in both, to the third. In the
+fourth figure the middleterm is the subject of the minor premise and the
+predicate of the major. Those writers who reckon no more than three
+figures, include this case in the first.
+
+Each figure is divided into _moods_, according to what are called the
+_quantity_ and _quality_ of the propositions, that is, according as they
+are universal or particular, affirmative or negative. The following are
+examples of all the legitimate moods, that is, all those in which the
+conclusion correctly follows from the premises. A is the minor term, C
+the major, B the middleterm.
+
+FIRST FIGURE.
+
+  All B is C    No B is C     All B is C     No B is C
+  All A is B    All A is B    Some A is B    Some A is B
+    therefore     therefore     therefore      therefore
+  All A is C    No A is C     Some A is C    Some A is not C
+
+SECOND FIGURE.
+
+  No C is B     All C is B    No C is B         All C is B
+  All A is B    No A is B     Some A is B       Some A is not B
+    therefore     therefore     therefore         therefore
+  No A is C     No A is C     Some A is not C   Some A is not C
+
+THIRD FIGURE.
+
+  All B is C   No B is C    Some B is C  All B is C   Some B      No B is C
+                                                        is not C
+  All B is A   All B is A   All B is A   Some B is A  All B is A  Some B is A
+    therefore    therefore    therefore    therefore    therefore   therefore
+  Some A is C  Some A       Some A is C  Some A is C  Some A      Some A
+                 is not C                               is not C    is not C
+
+FOURTH FIGURE.
+
+  All C is B   All C is B       Some C is B  No C is B        No C is B
+  All B is A   No B is A        All B is A   All B is A       Some B is A
+    therefore    therefore        therefore    therefore        therefore
+  Some A is C  Some A is not C  Some A is C  Some A is not C  Some A is not C
+
+In these exemplars, or blank forms for making syllogisms, no place is
+assigned to _singular_ propositions; not, of course, because such
+propositions are not used in ratiocination, but because, their predicate
+being affirmed or denied of the whole of the subject, they are ranked,
+for the purposes of the syllogism, with universal propositions. Thus,
+these two syllogisms--
+
+  All men are mortal,      All men are mortal,
+  All kings are men,       Socrates is a man,
+    therefore                therefore
+  All kings are mortal,    Socrates is mortal,
+
+are arguments precisely similar, and are both ranked in the first mood
+of the first figure.
+
+The reasons why syllogisms in any of the above forms are legitimate,
+that is, why, if the premises are true, the conclusion must inevitably
+be so, and why this is not the case in any other possible mood, (that
+is, in any other combination of universal and particular, affirmative
+and negative propositions,) any person taking interest in these
+inquiries may be presumed to have either learned from the common school
+books of the syllogistic logic, or to be capable of discovering for
+himself. The reader may, however, be referred, for every needful
+explanation, to Archbishop Whately's _Elements of Logic_, where he will
+find stated with philosophical precision, and explained with remarkable
+perspicuity, the whole of the common doctrine of the syllogism.
+
+All valid ratiocination; all reasoning by which, from general
+propositions previously admitted, other propositions equally or less
+general are inferred; may be exhibited in some of the above forms. The
+whole of Euclid, for example, might be thrown without difficulty into a
+series of syllogisms, regular in mood and figure.
+
+Though a syllogism framed according to any of these formul� is a valid
+argument, all correct ratiocination admits of being stated in syllogisms
+of the first figure alone. The rules for throwing an argument in any of
+the other figures into the first figure, are called rules for the
+_reduction_ of syllogisms. It is done by the _conversion_ of one or
+other, or both, of the premises. Thus an argument in the first mood of
+the second figure, as--
+
+  No C is B
+  All A is B
+    therefore
+  No A is C,
+
+may be reduced as follows. The proposition, No C is B, being an
+universal negative, admits of simple conversion, and may be changed into
+No B is C, which, as we showed, is the very same assertion in other
+words--the same fact differently expressed. This transformation having
+been effected, the argument assumes the following form:--
+
+  No B is C
+  All A is B
+    therefore
+  No A is C,
+
+which is a good syllogism in the second mood of the first figure. Again,
+an argument in the first mood of the third figure must resemble the
+following:--
+
+  All B is C
+  All B is A
+    therefore
+  Some A is C,
+
+where the minor premise, All B is A, conformably to what was laid down
+in the last chapter respecting universal affirmatives, does not admit of
+simple conversion, but may be converted _per accidens_, thus, Some A is
+B; which, though it does not express the whole of what is asserted in
+the proposition All B is A, expresses, as was formerly shown, part of
+it, and must therefore be true if the whole is true. We have, then, as
+the result of the reduction, the following syllogism in the third mood
+of the first figure:--
+
+  All B is C
+  Some A is B,
+
+from which it obviously follows, that
+
+  Some A is C.
+
+In the same manner, or in a manner on which after these examples it is
+not necessary to enlarge, every mood of the second, third, and fourth
+figures may be reduced to some one of the four moods of the first. In
+other words, every conclusion which can be proved in any of the last
+three figures, may be proved in the first figure from the same premises,
+with a slight alteration in the mere manner of expressing them. Every
+valid ratiocination, therefore, may be stated in the first figure, that
+is, in one of the following forms:--
+
+  Every B is C            No B is C
+  All A   }  is B,        All A   } is B,
+  Some A  }               Some A  }
+      therefore               therefore
+  All A   }  is C.        No A is        }  C.
+  Some A  }               Some A is not  }
+
+Or if more significant symbols are preferred:--
+
+To prove an affirmative, the argument must admit of being stated in this
+form:--
+
+  All animals are mortal;
+  All men   }
+  Some men  }  are animals;
+  Socrates  }
+        therefore
+  All men   }
+  Some men  }  are mortal.
+  Socrates  }
+
+To prove a negative, the argument must be capable of being expressed in
+this form:--
+
+  No one who is capable of self-control is necessarily vicious;
+  All negroes   }
+  Some negroes  }  are capable of self-control;
+  Mr. A's negro }
+        therefore
+  No negroes are        }
+  Some negroes are not  }  necessarily vicious.
+  Mr. A's negro is not  }
+
+Though all ratiocination admits of being thrown into one or the other of
+these forms, and sometimes gains considerably by the transformation,
+both in clearness and in the obviousness of its consequence; there are,
+no doubt, cases in which the argument falls more naturally into one of
+the other three figures, and in which its conclusiveness is more
+apparent at the first glance in those figures, than when reduced to the
+first. Thus, if the proposition were that pagans may be virtuous, and
+the evidence to prove it were the example of Aristides; a syllogism in
+the third figure,
+
+  Aristides was virtuous,
+  Aristides was a pagan,
+       therefore
+  Some pagan was virtuous,
+
+would be a more natural mode of stating the argument, and would carry
+conviction more instantly home, than the same ratiocination strained
+into the first figure, thus--
+
+  Aristides was virtuous,
+  Some pagan was Aristides,
+       therefore
+  Some pagan was virtuous.
+
+A German philosopher, Lambert, whose _Neues Organon_ (published in the
+year 1764) contains among other things one of the most elaborate and
+complete expositions which had ever been made of the syllogistic
+doctrine, has expressly examined what sort of arguments fall most
+naturally and suitably into each of the four figures; and his
+investigation is characterized by great ingenuity and clearness of
+thought.[3] The argument, however, is one and the same, in whichever
+figure it is expressed; since, as we have already seen, the premises of
+a syllogism in the second, third, or fourth figure, and those of the
+syllogism in the first figure to which it may be reduced, are the same
+premises in everything except language, or, at least, as much of them as
+contributes to the proof of the conclusion is the same. We are
+therefore at liberty, in conformity with the general opinion of
+logicians, to consider the two elementary forms of the first figure as
+the universal types of all correct ratiocination; the one, when the
+conclusion to be proved is affirmative, the other, when it is negative;
+even though certain arguments may have a tendency to clothe themselves
+in the forms of the second, third, and fourth figures; which, however,
+cannot possibly happen with the only class of arguments which are of
+first-rate scientific importance, those in which the conclusion is an
+universal affirmative, such conclusions being susceptible of proof in
+the first figure alone.[4]
+
+
+� 2. On examining, then, these two general formul�, we find that in
+both of them, one premise, the major, is an universal proposition; and
+according as this is affirmative or negative, the conclusion is so too.
+All ratiocination, therefore, starts from a _general_ proposition,
+principle, or assumption: a proposition in which a predicate is
+affirmed or denied of an entire class; that is, in which some attribute,
+or the negation of some attribute, is asserted of an indefinite number
+of objects distinguished by a common characteristic, and designated in
+consequence, by a common name.
+
+The other premise is always affirmative, and asserts that something
+(which may be either an individual, a class, or part of a class)
+belongs to, or is included in, the class respecting which something was
+affirmed or denied in the major premise. It follows that the attribute
+affirmed or denied of the entire class may (if that affirmation or
+denial was correct) be affirmed or denied of the object or objects
+alleged to be included in the class: and this is precisely the assertion
+made in the conclusion.
+
+Whether or not the foregoing is an adequate account of the constituent
+parts of the syllogism, will be presently considered; but as far as it
+goes it is a true account. It has accordingly been generalized, and
+erected into a logical maxim, on which all ratiocination is said to be
+founded, insomuch that to reason, and to apply the maxim, are supposed
+to be one and the same thing. The maxim is, That whatever can be
+affirmed (or denied) of a class, may be affirmed (or denied) of
+everything included in the class. This axiom, supposed to be the basis
+of the syllogistic theory, is termed by logicians the _dictum de omni et
+nullo_.
+
+This maxim, however, when considered as a principle of reasoning,
+appears suited to a system of metaphysics once indeed generally
+received, but which for the last two centuries has been considered as
+finally abandoned, though there have not been wanting in our own day
+attempts at its revival. So long as what are termed Universals were
+regarded as a peculiar kind of substances, having an objective existence
+distinct from the individual objects classed under them, the _dictum de
+omni_ conveyed an important meaning; because it expressed the
+intercommunity of nature, which it was necessary on that theory that we
+should suppose to exist between those general substances and the
+particular substances which were subordinated to them. That everything
+predicable of the universal was predicable of the various individuals
+contained under it, was then no identical proposition, but a statement
+of what was conceived as a fundamental law of the universe. The
+assertion that the entire nature and properties of the _substantia
+secunda_ formed part of the nature and properties of each of the
+individual substances called by the same name; that the properties of
+Man, for example, were properties of all men; was a proposition of real
+significance when man did not _mean_ all men, but something inherent in
+men, and vastly superior to them in dignity. Now, however, when it is
+known that a class, an universal, a genus or species, is not an entity
+_per se_, but neither more nor less than the individual substances
+themselves which are placed in the class, and that there is nothing real
+in the matter except those objects, a common name given to them, and
+common attributes indicated by the name; what, I should be glad to know,
+do we learn by being told, that whatever can be affirmed of a class, may
+be affirmed of every object contained in the class? The class is nothing
+but the objects contained in it: and the _dictum de omni_ merely amounts
+to the identical proposition, that whatever is true of certain objects,
+is true of each of those objects. If all ratiocination were no more than
+the application of this maxim to particular cases, the syllogism would
+indeed be, what it has so often been declared to be, solemn trifling.
+The _dictum de omni_ is on a par with another truth, which in its time
+was also reckoned of great importance, "Whatever is, is." To give any
+real meaning to the _dictum de omni_, we must consider it not as an
+axiom, but as a definition; we must look upon it as intended to explain,
+in a circuitous and paraphrastic manner, the meaning of the word,
+_class_.
+
+An error which seemed finally refuted and dislodged from thought, often
+needs only put on a new suit of phrases, to be welcomed back to its old
+quarters, and allowed to repose unquestioned for another cycle of ages.
+Modern philosophers have not been sparing in their contempt for the
+scholastic dogma that genera and species are a peculiar kind of
+substances, which general substances being the only permanent things,
+while the individual substances comprehended under them are in a
+perpetual flux, knowledge, which necessarily imports stability, can only
+have relation to those general substances or universals, and not to the
+facts or particulars included under them. Yet, though nominally
+rejected, this very doctrine, whether disguised under the Abstract Ideas
+of Locke (whose speculations, however, it has less vitiated than those
+of perhaps any other writer who has been infected with it), under the
+ultra-nominalism of Hobbes and Condillac, or the ontology of the later
+Kantians, has never ceased to poison philosophy. Once accustomed to
+consider scientific investigation as essentially consisting in the study
+of universals, men did not drop this habit of thought when they ceased
+to regard universals as possessing an independent existence: and even
+those who went the length of considering them as mere names, could not
+free themselves from the notion that the investigation of truth
+consisted entirely or partly in some kind of conjuration or juggle with
+those names. When a philosopher adopted fully the Nominalist view of the
+signification of general language, retaining along with it the _dictum
+de omni_ as the foundation of all reasoning, two such premises fairly
+put together were likely, if he was a consistent thinker, to land him in
+rather startling conclusions. Accordingly it has been seriously held, by
+writers of deserved celebrity, that the process of arriving at new
+truths by reasoning consists in the mere substitution of one set of
+arbitrary signs for another; a doctrine which they suppose to derive
+irresistible confirmation from the example of algebra. If there were any
+process in sorcery or necromancy more preternatural than this, I should
+be much surprised. The culminating point of this philosophy is the noted
+aphorism of Condillac, that a science is nothing, or scarcely anything,
+but _une langue bien faite_; in other words, that the one sufficient
+rule for discovering the nature and properties of objects is to name
+them properly: as if the reverse were not the truth, that it is
+impossible to name them properly except in proportion as we are already
+acquainted with their nature and properties. Can it be necessary to say,
+that none, not even the most trivial knowledge with respect to Things,
+ever was or could be originally got at by any conceivable manipulation
+of mere names, as such; and that what can be learned from names, is only
+what somebody who used the names knew before? Philosophical analysis
+confirms the indication of common sense, that the function of names is
+but that of enabling us to _remember_ and to _communicate_ our thoughts.
+That they also strengthen, even to an incalculable extent, the power of
+thought itself, is most true: but they do this by no intrinsic and
+peculiar virtue; they do it by the power inherent in an artificial
+memory, an instrument of which few have adequately considered the
+immense potency. As an artificial memory, language truly is, what it has
+so often been called, an instrument of thought; but it is one thing to
+be the instrument, and another to be the exclusive subject upon which
+the instrument is exercised. We think, indeed, to a considerable extent,
+by means of names, but what we think of, are the things called by those
+names; and there cannot be a greater error than to imagine that thought
+can be carried on with nothing in our mind but names, or that we can
+make the names think for us.
+
+
+� 3. Those who considered the _dictum de omni_ as the foundation of the
+syllogism, looked upon arguments in a manner corresponding to the
+erroneous view which Hobbes took of propositions. Because there are some
+propositions which are merely verbal, Hobbes, in order apparently that
+his definition might be rigorously universal, defined a proposition as
+if no propositions declared anything except the meaning of words. If
+Hobbes was right; if no further account than this could be given of the
+import of propositions; no theory could be given but the commonly
+received one, of the combination of propositions in a syllogism. If the
+minor premise asserted nothing more than that something belongs to a
+class, and if the major premise asserted nothing of that class except
+that it is included in another class, the conclusion would only be that
+what was included in the lower class is included in the higher, and the
+result, therefore, nothing except that the classification is consistent
+with itself. But we have seen that it is no sufficient account of the
+meaning of a proposition, to say that it refers something to, or
+excludes something from, a class. Every proposition which conveys real
+information asserts a matter of fact, dependent on the laws of nature,
+and not on classification. It asserts that a given object does or does
+not possess a given attribute; or it asserts that two attributes, or
+sets of attributes, do or do not (constantly or occasionally) coexist.
+Since such is the purport of all propositions which convey any real
+knowledge, and since ratiocination is a mode of acquiring real
+knowledge, any theory of ratiocination which does not recognise this
+import of propositions, cannot, we may be sure, be the true one.
+
+Applying this view of propositions to the two premises of a syllogism,
+we obtain the following results. The major premise, which, as already
+remarked, is always universal, asserts, that all things which have a
+certain attribute (or attributes) have or have not along with it, a
+certain other attribute (or attributes). The minor premise asserts that
+the thing or set of things which are the subject of that premise, have
+the first-mentioned attribute; and the conclusion is, that they have (or
+that they have not) the second. Thus in our former example,
+
+  All men are mortal,
+  Socrates is a man,
+        therefore
+  Socrates is mortal,
+
+the subject and predicate of the major premise are connotative terms,
+denoting objects and connoting attributes. The assertion in the major
+premise is, that along with one of the two sets of attributes, we always
+find the other: that the attributes connoted by "man" never exist unless
+conjoined with the attribute called mortality. The assertion in the
+minor premise is that the individual named Socrates possesses the former
+attributes; and it is concluded that he possesses also the attribute
+mortality. Or if both the premises are general propositions, as
+
+  All men are mortal,
+  All kings are men,
+        therefore
+  All kings are mortal,
+
+the minor premise asserts that the attributes denoted by kingship only
+exist in conjunction with those signified by the word man. The major
+asserts as before, that the last-mentioned attributes are never found
+without the attribute of mortality. The conclusion is, that wherever the
+attributes of kingship are found, that of mortality is found also.
+
+If the major premise were negative, as, No men are omnipotent, it would
+assert, not that the attributes connoted by "man" never exist without,
+but that they never exist with, those connoted by "omnipotent:" from
+which, together with the minor premise, it is concluded, that the same
+incompatibility exists between the attribute omnipotence and those
+constituting a king. In a similar manner we might analyse any other
+example of the syllogism.
+
+If we generalize this process, and look out for the principle or law
+involved in every such inference, and presupposed in every syllogism,
+the propositions of which are anything more than merely verbal; we find,
+not the unmeaning _dictum de omni et nullo_, but a fundamental
+principle, or rather two principles, strikingly resembling the axioms of
+mathematics. The first, which is the principle of affirmative
+syllogisms, is, that things which coexist with the same thing, coexist
+with one another. The second is the principle of negative syllogisms,
+and is to this effect: that a thing which coexists with another thing,
+with which other a third thing does not coexist, is not coexistent with
+that third thing. These axioms manifestly relate to facts, and not to
+conventions; and one or other of them is the ground of the legitimacy of
+every argument in which facts and not conventions are the matter treated
+of.[5]
+
+
+� 4. It remains to translate this exposition of the syllogism from the
+one into the other of the two languages in which we formerly
+remarked[6] that all propositions, and of course therefore all
+combinations of propositions, might be expressed. We observed that a
+proposition might be considered in two different lights; as a portion of
+our knowledge of nature, or as a memorandum for our guidance. Under the
+former, or speculative aspect, an affirmative general proposition is an
+assertion of a speculative truth, viz. that whatever has a certain
+attribute has a certain other attribute. Under the other aspect, it is
+to be regarded not as a part of our knowledge, but as an aid for our
+practical exigencies, by enabling us, when we see or learn that an
+object possesses one of the two attributes, to infer that it possesses
+the other; thus employing the first attribute as a mark or evidence of
+the second. Thus regarded, every syllogism comes within the following
+general formula:--
+
+  Attribute A is a mark of attribute B,
+  The given object has the mark A,
+              therefore
+  The given object has the attribute B.
+
+Referred to this type, the arguments which we have lately cited as
+specimens of the syllogism, will express themselves in the following
+manner:--
+
+  The attributes of man are a mark of the attribute mortality,
+  Socrates has the attributes of man,
+              therefore
+  Socrates has the attribute mortality.
+
+And again,
+
+  The attributes of man are a mark of the attribute mortality,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the attribute mortality.
+
+And, lastly,
+
+  The attributes of man are a mark of the absence of
+    the attribute omnipotence,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the absence of
+    the attribute signified by the word omnipotent
+    (or, are evidence of the absence of that attribute).
+
+To correspond with this alteration in the form of the syllogisms, the
+axioms on which the syllogistic process is founded must undergo a
+corresponding transformation. In this altered phraseology, both those
+axioms may be brought under one general expression; namely, that
+whatever has any mark, has that which it is a mark of. Or, when the
+minor premise as well as the major is universal, we may state it thus:
+Whatever is a mark of any mark, is a mark of that which this last is a
+mark of. To trace the identity of these axioms with those previously
+laid down, may be left to the intelligent reader. We shall find, as we
+proceed, the great convenience of the phraseology into which we have
+last thrown them, and which is better adapted than any I am acquainted
+with, to express with precision and force what is aimed at, and actually
+accomplished, in every case of the ascertainment of a truth by
+ratiocination.
+
+
+
+
+CHAPTER III.
+
+OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.
+
+
+� 1. We have shown what is the real nature of the truths with which the
+Syllogism is conversant, in contradistinction to the more superficial
+manner in which their import is conceived in the common theory; and what
+are the fundamental axioms on which its probative force or
+conclusiveness depends. We have now to inquire, whether the syllogistic
+process, that of reasoning from generals to particulars, is, or is not,
+a process of inference; a progress from the known to the unknown: a
+means of coming to a knowledge of something which we did not know
+before.
+
+Logicians have been remarkably unanimous in their mode of answering this
+question. It is universally allowed that a syllogism is vicious if there
+be anything more in the conclusion than was assumed in the premises. But
+this is, in fact, to say, that nothing ever was, or can be, proved by
+syllogism, which was not known, or assumed to be known, before. Is
+ratiocination, then, not a process of inference? And is the syllogism,
+to which the word reasoning has so often been represented to be
+exclusively appropriate, not really entitled to be called reasoning at
+all? This seems an inevitable consequence of the doctrine, admitted by
+all writers on the subject, that a syllogism can prove no more than is
+involved in the premises. Yet the acknowledgment so explicitly made, has
+not prevented one set of writers from continuing to represent the
+syllogism as the correct analysis of what the mind actually performs in
+discovering and proving the larger half of the truths, whether of
+science or of daily life, which we believe; while those who have avoided
+this inconsistency, and followed out the general theorem respecting the
+logical value of the syllogism to its legitimate corollary, have been
+led to impute uselessness and frivolity to the syllogistic theory
+itself, on the ground of the _petitio principii_ which they allege to be
+inherent in every syllogism. As I believe both these opinions to be
+fundamentally erroneous, I must request the attention of the reader to
+certain considerations, without which any just appreciation of the true
+character of the syllogism, and the functions it performs in philosophy,
+appears to me impossible; but which seem to have been either overlooked,
+or insufficiently adverted to, both by the defenders of the syllogistic
+theory and by its assailants.
+
+
+� 2. It must be granted that in every syllogism, considered as an
+argument to prove the conclusion, there is a _petitio principii_. When
+we say,
+
+  All men are mortal,
+  Socrates is a man,
+      therefore
+  Socrates is mortal;
+
+it is unanswerably urged by the adversaries of the syllogistic theory,
+that the proposition, Socrates is mortal, is presupposed in the more
+general assumption, All men are mortal: that we cannot be assured of the
+mortality of all men, unless we are already certain of the mortality of
+every individual man: that if it be still doubtful whether Socrates, or
+any other individual we choose to name, be mortal or not, the same
+degree of uncertainty must hang over the assertion, All men are mortal:
+that the general principle, instead of being given as evidence of the
+particular case, cannot itself be taken for true without exception,
+until every shadow of doubt which could affect any case comprised with
+it, is dispelled by evidence _aliund�_; and then what remains for the
+syllogism to prove? That, in short, no reasoning from generals to
+particulars can, as such, prove anything: since from a general principle
+we cannot infer any particulars, but those which the principle itself
+assumes as known.
+
+This doctrine appears to me irrefragable; and if logicians, though
+unable to dispute it, have usually exhibited a strong disposition to
+explain it away, this was not because they could discover any flaw in
+the argument itself, but because the contrary opinion seemed to rest on
+arguments equally indisputable. In the syllogism last referred to, for
+example, or in any of those which we previously constructed, is it not
+evident that the conclusion may, to the person to whom the syllogism is
+presented, be actually and _bon� fide_ a new truth? Is it not matter of
+daily experience that truths previously unthought of, facts which have
+not been, and cannot be, directly observed, are arrived at by way of
+general reasoning? We believe that the Duke of Wellington is mortal. We
+do not know this by direct observation, so long as he is not yet dead.
+If we were asked how, this being the case, we know the duke to be
+mortal, we should probably answer, Because all men are so. Here,
+therefore, we arrive at the knowledge of a truth not (as yet)
+susceptible of observation, by a reasoning which admits of being
+exhibited in the following syllogism:--
+
+  All men are mortal,
+  The Duke of Wellington is a man,
+              therefore
+  The Duke of Wellington is mortal.
+
+And since a large portion of our knowledge is thus acquired, logicians
+have persisted in representing the syllogism as a process of inference
+or proof; though none of them has cleared up the difficulty which arises
+from the inconsistency between that assertion, and the principle, that
+if there be anything in the conclusion which was not already asserted in
+the premises, the argument is vicious. For it is impossible to attach
+any serious scientific value to such a mere salvo, as the distinction
+drawn between being involved _by implication_ in the premises, and being
+directly asserted in them. When Archbishop Whately says[7] that the
+object of reasoning is "merely to expand and unfold the assertions wrapt
+up, as it were, and implied in those with which we set out, and to bring
+a person to perceive and acknowledge the full force of that which he
+has admitted," he does not, I think, meet the real difficulty requiring
+to be explained, namely, how it happens that a science, like geometry,
+_can_ be all "wrapt up" in a few definitions and axioms. Nor does this
+defence of the syllogism differ much from what its assailants urge
+against it as an accusation, when they charge it with being of no use
+except to those who seek to press the consequences of an admission into
+which a person has been entrapped without having considered and
+understood its full force. When you admitted the major premise, you
+asserted the conclusion; but, says Archbishop Whately, you asserted it
+by implication merely: this, however, can here only mean that you
+asserted it unconsciously; that you did not know you were asserting it;
+but, if so, the difficulty revives in this shape--Ought you not to have
+known? Were you warranted in asserting the general proposition without
+having satisfied yourself of the truth of everything which it fairly
+includes? And if not, is not the syllogistic art _prim� facie_ what its
+assailants affirm it to be, a contrivance for catching you in a trap,
+and holding you fast in it?[8]
+
+
+� 3. From this difficulty there appears to be but one issue. The
+proposition that the Duke of Wellington is mortal, is evidently an
+inference; it is got at as a conclusion from something else; but do we,
+in reality, conclude it from the proposition, All men are mortal? I
+answer, no.
+
+The error committed is, I conceive, that of overlooking the distinction
+between two parts of the process of philosophizing, the inferring part,
+and the registering part; and ascribing to the latter the functions of
+the former. The mistake is that of referring a person to his own notes
+for the origin of his knowledge. If a person is asked a question, and is
+at the moment unable to answer it, he may refresh his memory by turning
+to a memorandum which he carries about with him. But if he were asked,
+how the fact came to his knowledge, he would scarcely answer, because it
+was set down in his note-book: unless the book was written, like the
+Koran, with a quill from the wing of the angel Gabriel.
+
+Assuming that the proposition, The Duke of Wellington is mortal, is
+immediately an inference from the proposition, All men are mortal;
+whence do we derive our knowledge of that general truth? Of course from
+observation. Now, all which man can observe are individual cases. From
+these all general truths must be drawn, and into these they may be again
+resolved; for a general truth is but an aggregate of particular truths;
+a comprehensive expression, by which an indefinite number of individual
+facts are affirmed or denied at once. But a general proposition is not
+merely a compendious form for recording and preserving in the memory a
+number of particular facts, all of which have been observed.
+Generalization is not a process of mere naming, it is also a process of
+inference. From instances which we have observed, we feel warranted in
+concluding, that what we found true in those instances, holds in all
+similar ones, past, present, and future, however numerous they may be.
+We then, by that valuable contrivance of language which enables us to
+speak of many as if they were one, record all that we have observed,
+together with all that we infer from our observations, in one concise
+expression; and have thus only one proposition, instead of an endless
+number, to remember or to communicate. The results of many observations
+and inferences, and instructions for making innumerable inferences in
+unforeseen cases, are compressed into one short sentence.
+
+When, therefore, we conclude from the death of John and Thomas, and
+every other person we ever heard of in whose case the experiment had
+been fairly tried, that the Duke of Wellington is mortal like the rest;
+we may, indeed, pass through the generalization, All men are mortal, as
+an intermediate stage; but it is not in the latter half of the process,
+the descent from all men to the Duke of Wellington, that the _inference_
+resides. The inference is finished when we have asserted that all men
+are mortal. What remains to be performed afterwards is merely
+decyphering our own notes.
+
+Archbishop Whately has contended that syllogizing, or reasoning from
+generals to particulars, is not, agreeably to the vulgar idea, a
+peculiar _mode_ of reasoning, but the philosophical analysis of _the_
+mode in which all men reason, and must do so if they reason at all. With
+the deference due to so high an authority, I cannot help thinking that
+the vulgar notion is, in this case, the more correct. If, from our
+experience of John, Thomas, &c., who once were living, but are now dead,
+we are entitled to conclude that all human beings are mortal, we might
+surely without any logical inconsequence have concluded at once from
+those instances, that the Duke of Wellington is mortal. The mortality of
+John, Thomas, and company is, after all, the whole evidence we have for
+the mortality of the Duke of Wellington. Not one iota is added to the
+proof by interpolating a general proposition. Since the individual cases
+are all the evidence we can possess, evidence which no logical form into
+which we choose to throw it can make greater than it is; and since that
+evidence is either sufficient in itself, or, if insufficient for the one
+purpose, cannot be sufficient for the other; I am unable to see why we
+should be forbidden to take the shortest cut from these sufficient
+premises to the conclusion, and constrained to travel the "high priori
+road," by the arbitrary fiat of logicians. I cannot perceive why it
+should be impossible to journey from one place to another unless we
+"march up a hill, and then march down again." It may be the safest road,
+and there may be a resting-place at the top of the hill, affording a
+commanding view of the surrounding country; but for the mere purpose of
+arriving at our journey's end, our taking that road is perfectly
+optional; it is a question of time, trouble, and danger.
+
+Not only _may_ we reason from particulars to particulars without passing
+through generals, but we perpetually do so reason. All our earliest
+inferences are of this nature. From the first dawn of intelligence we
+draw inferences, but years elapse before we learn the use of general
+language. The child, who, having burnt his fingers, avoids to thrust
+them again into the fire, has reasoned or inferred, though he has never
+thought of the general maxim, Fire burns. He knows from memory that he
+has been burnt, and on this evidence believes, when he sees a candle,
+that if he puts his finger into the flame of it, he will be burnt again.
+He believes this in every case which happens to arise; but without
+looking, in each instance, beyond the present case. He is not
+generalizing; he is inferring a particular from particulars. In the same
+way, also, brutes reason. There is no ground for attributing to any of
+the lower animals the use of signs, of such a nature as to render
+general propositions possible. But those animals profit by experience,
+and avoid what they have found to cause them pain, in the same manner,
+though not always with the same skill, as a human creature. Not only the
+burnt child, but the burnt dog, dreads the fire.
+
+I believe that, in point of fact, when drawing inferences from our
+personal experience, and not from maxims handed down to us by books or
+tradition, we much oftener conclude from particulars to particulars
+directly, than through the intermediate agency of any general
+proposition. We are constantly reasoning from ourselves to other people,
+or from one person to another, without giving ourselves the trouble to
+erect our observations into general maxims of human or external nature.
+When we conclude that some person will, on some given occasion, feel or
+act so and so, we sometimes judge from an enlarged consideration of the
+manner in which human beings in general, or persons of some particular
+character, are accustomed to feel and act: but much oftener from merely
+recollecting the feelings and conduct of the same person in some
+previous instance, or from considering how we should feel or act
+ourselves. It is not only the village matron, who, when called to a
+consultation upon the case of a neighbour's child, pronounces on the
+evil and its remedy simply on the recollection and authority of what she
+accounts the similar case of her Lucy. We all, where we have no definite
+maxims to steer by, guide ourselves in the same way: and if we have an
+extensive experience, and retain its impressions strongly, we may
+acquire in this manner a very considerable power of accurate judgment,
+which we may be utterly incapable of justifying or of communicating to
+others. Among the higher order of practical intellects there have been
+many of whom it was remarked how admirably they suited their means to
+their ends, without being able to give any sufficient reasons for what
+they did; and applied, or seemed to apply, recondite principles which
+they were wholly unable to state. This is a natural consequence of
+having a mind stored with appropriate particulars, and having been long
+accustomed to reason at once from these to fresh particulars, without
+practising the habit of stating to oneself or to others the
+corresponding general propositions. An old warrior, on a rapid glance at
+the outlines of the ground, is able at once to give the necessary orders
+for a skilful arrangement of his troops; though if he has received
+little theoretical instruction, and has seldom been called upon to
+answer to other people for his conduct, he may never have had in his
+mind a single general theorem respecting the relation between ground and
+array. But his experience of encampments, in circumstances more or less
+similar, has left a number of vivid, unexpressed, ungeneralized
+analogies in his mind, the most appropriate of which, instantly
+suggesting itself, determines him to a judicious arrangement.
+
+The skill of an uneducated person in the use of weapons, or of tools,
+is of a precisely similar nature. The savage who executes unerringly the
+exact throw which brings down his game, or his enemy, in the manner most
+suited to his purpose, under the operation of all the conditions
+necessarily involved, the weight and form of the weapon, the direction
+and distance of the object, the action of the wind, &c., owes this power
+to a long series of previous experiments, the results of which he
+certainly never framed into any verbal theorems or rules. The same thing
+may generally be said of any other extraordinary manual dexterity. Not
+long ago a Scotch manufacturer procured from England, at a high rate of
+wages, a working dyer, famous for producing very fine colours, with the
+view of teaching to his other workmen the same skill. The workman came;
+but his mode of proportioning the ingredients, in which lay the secret
+of the effects he produced, was by taking them up in handfuls, while the
+common method was to weigh them. The manufacturer sought to make him
+turn his handling system into an equivalent weighing system, that the
+general principle of his peculiar mode of proceeding might be
+ascertained. This, however, the man found himself quite unable to do,
+and therefore could impart his skill to nobody. He had, from the
+individual cases of his own experience, established a connexion in his
+mind between fine effects of colour, and tactual perceptions in handling
+his dyeing materials; and from these perceptions he could, in any
+particular case, infer the means to be employed, and the effects which
+would be produced, but could not put others in possession of the grounds
+on which he proceeded, from having never generalized them in his own
+mind, or expressed them in language.
+
+Almost every one knows Lord Mansfield's advice to a man of practical
+good sense, who, being appointed governor of a colony, had to preside in
+its court of justice, without previous judicial practice or legal
+education. The advice was to give his decision boldly, for it would
+probably be right; but never to venture on assigning reasons, for they
+would almost infallibly be wrong. In cases like this, which are of no
+uncommon occurrence, it would be absurd to suppose that the bad reason
+was the source of the good decision. Lord Mansfield knew that if any
+reason were assigned it would be necessarily an afterthought, the judge
+being _in fact_ guided by impressions from past experience, without the
+circuitous process of framing general principles from them, and that if
+he attempted to frame any such he would assuredly fail. Lord Mansfield,
+however, would not have doubted that a man of equal experience who had
+also a mind stored with general propositions derived by legitimate
+induction from that experience, would have been greatly preferable as a
+judge, to one, however sagacious, who could not be trusted with the
+explanation and justification of his own judgments. The cases of men of
+talent performing wonderful things they know not how, are examples of
+the rudest and most spontaneous form of the operations of superior
+minds. It is a defect in them, and often a source of errors, not to have
+generalized as they went on; but generalization, though a help, the most
+important indeed of all helps, is not an essential.
+
+Even the scientifically instructed, who possess, in the form of general
+propositions, a systematic record of the results of the experience of
+mankind, need not always revert to those general propositions in order
+to apply that experience to a new case. It is justly remarked by Dugald
+Stewart, that though the reasonings in mathematics depend entirely on
+the axioms, it is by no means necessary to our seeing the conclusiveness
+of the proof, that the axioms should be expressly adverted to. When it
+is inferred that AB is equal to CD because each of them is equal to EF,
+the most uncultivated understanding, as soon as the propositions were
+understood, would assent to the inference, without having ever heard of
+the general truth that "things which are equal to the same thing are
+equal to one another." This remark of Stewart, consistently followed
+out, goes to the root, as I conceive, of the philosophy of
+ratiocination; and it is to be regretted that he himself stopt short at
+a much more limited application of it. He saw that the general
+propositions on which a reasoning is said to depend, may, in certain
+cases, be altogether omitted, without impairing its probative force.
+But he imagined this to be a peculiarity belonging to axioms; and argued
+from it, that axioms are not the foundations or first principles of
+geometry, from which all the other truths of the science are
+synthetically deduced (as the laws of motion and of the composition of
+forces in dynamics, the equal mobility of fluids in hydrostatics, the
+laws of reflection and refraction in optics, are the first principles of
+those sciences); but are merely necessary assumptions, self-evident
+indeed, and the denial of which would annihilate all demonstration, but
+from which, as premises, nothing can be demonstrated. In the present, as
+in many other instances, this thoughtful and elegant writer has
+perceived an important truth, but only by halves. Finding, in the case
+of geometrical axioms, that general names have not any talismanic virtue
+for conjuring new truths out of the well where they lie hid, and not
+seeing that this is equally true in every other case of generalization,
+he contended that axioms are in their nature barren of consequences, and
+that the really fruitful truths, the real first principles of geometry,
+are the definitions; that the definition, for example, of the circle is
+to the properties of the circle, what the laws of equilibrium and of the
+pressure of the atmosphere are to the rise of the mercury in the
+Torricellian tube. Yet all that he had asserted respecting the function
+to which the axioms are confined in the demonstrations of geometry,
+holds equally true of the definitions. Every demonstration in Euclid
+might be carried on without them. This is apparent from the ordinary
+process of proving a proposition of geometry by means of a diagram. What
+assumption, in fact, do we set out from, to demonstrate by a diagram any
+of the properties of the circle? Not that in all circles the radii are
+equal, but only that they are so in the circle ABC. As our warrant for
+assuming this, we appeal, it is true, to the definition of a circle in
+general; but it is only necessary that the assumption be granted in the
+case of the particular circle supposed. From this, which is not a
+general but a singular proposition, combined with other propositions of
+a similar kind, some of which _when generalized_ are called definitions,
+and others axioms, we prove that a certain conclusion is true, not of
+all circles, but of the particular circle ABC; or at least would be so,
+if the facts precisely accorded with our assumptions. The enunciation,
+as it is called, that is, the general theorem which stands at the head
+of the demonstration, is not the proposition actually demonstrated. One
+instance only is demonstrated: but the process by which this is done, is
+a process which, when we consider its nature, we perceive might be
+exactly copied in an indefinite number of other instances; in every
+instance which conforms to certain conditions. The contrivance of
+general language furnishing us with terms which connote these
+conditions, we are able to assert this indefinite multitude of truths in
+a single expression, and this expression is the general theorem. By
+dropping the use of diagrams, and substituting, in the demonstrations,
+general phrases for the letters of the alphabet, we might prove the
+general theorem directly, that is, we might demonstrate all the cases at
+once; and to do this we must, of course, employ as our premises, the
+axioms and definitions in their general form. But this only means, that
+if we can prove an individual conclusion by assuming an individual fact,
+then in whatever case we are warranted in making an exactly similar
+assumption, we may draw an exactly similar conclusion. The definition is
+a sort of notice to ourselves and others, what assumptions we think
+ourselves entitled to make. And so in all cases, the general
+propositions, whether called definitions, axioms, or laws of nature,
+which we lay down at the beginning of our reasonings, are merely
+abridged statements, in a kind of short-hand, of the particular facts,
+which, as occasion arises, we either think we may proceed on as proved,
+or intend to assume. In any one demonstration it is enough if we assume
+for a particular case suitably selected, what by the statement of the
+definition or principle we announce that we intend to assume in all
+cases which may arise. The definition of the circle, therefore, is to
+one of Euclid's demonstrations, exactly what, according to Stewart, the
+axioms are; that is, the demonstration does not depend on it, but yet if
+we deny it the demonstration fails. The proof does not rest on the
+general assumption, but on a similar assumption confined to the
+particular case: that case, however, being chosen as a specimen or
+paradigm of the whole class of cases included in the theorem, there can
+be no ground for making the assumption in that case which does not exist
+in every other; and to deny the assumption as a general truth, is to
+deny the right of making it in the particular instance.
+
+There are, undoubtedly, the most ample reasons for stating both the
+principles and the theorems in their general form, and these will be
+explained presently, so far as explanation is requisite. But, that
+unpractised learners, even in making use of one theorem to demonstrate
+another, reason rather from particular to particular than from the
+general proposition, is manifest from the difficulty they find in
+applying a theorem to a case in which the configuration of the diagram
+is extremely unlike that of the diagram by which the original theorem
+was demonstrated. A difficulty which, except in cases of unusual mental
+power, long practice can alone remove, and removes chiefly by rendering
+us familiar with all the configurations consistent with the general
+conditions of the theorem.
+
+
+� 4. From the considerations now adduced, the following conclusions seem
+to be established. All inference is from particulars to particulars:
+General propositions are merely registers of such inferences already
+made, and short formul� for making more: The major premise of a
+syllogism, consequently, is a formula of this description: and the
+conclusion is not an inference drawn _from_ the formula, but an
+inference drawn _according_ to the formula: the real logical antecedent,
+or premise, being the particular facts from which the general
+proposition was collected by induction. Those facts, and the individual
+instances which supplied them, may have been forgotten: but a record
+remains, not indeed descriptive of the facts themselves, but showing how
+those cases may be distinguished, respecting which the facts, when
+known, were considered to warrant a given inference. According to the
+indications of this record we draw our conclusion; which is, to all
+intents and purposes, a conclusion from the forgotten facts. For this
+it is essential that we should read the record correctly: and the rules
+of the syllogism are a set of precautions to ensure our doing so.
+
+This view of the functions of the syllogism is confirmed by the
+consideration of precisely those cases which might be expected to be
+least favourable to it, namely, those in which ratiocination is
+independent of any previous induction. We have already observed that the
+syllogism, in the ordinary course of our reasoning, is only the latter
+half of the process of travelling from premises to a conclusion. There
+are, however, some peculiar cases in which it is the whole process.
+Particulars alone are capable of being subjected to observation; and all
+knowledge which is derived from observation, begins, therefore, of
+necessity, in particulars; but our knowledge may, in cases of certain
+descriptions, be conceived as coming to us from other sources than
+observation. It may present itself as coming from testimony, which, on
+the occasion and for the purpose in hand, is accepted as of an
+authoritative character: and the information thus communicated, may be
+conceived to comprise not only particular facts but general
+propositions, as when a scientific doctrine is accepted without
+examination on the authority of writers, or a theological doctrine on
+that of Scripture. Or the generalization may not be, in the ordinary
+sense, an assertion at all, but a command; a law, not in the
+philosophical, but in the moral and political sense of the term: an
+expression of the desire of a superior, that we, or any number of other
+persons, shall conform our conduct to certain general instructions. So
+far as this asserts a fact, namely, a volition of the legislator, that
+fact is an individual fact, and the proposition, therefore, is not a
+general proposition. But the description therein contained of the
+conduct which it is the will of the legislator that his subjects should
+observe, is general. The proposition asserts, not that all men _are_
+anything, but that all men _shall_ do something.
+
+In both these cases the generalities are the original data, and the
+particulars are elicited from them by a process which correctly resolves
+itself into a series of syllogisms. The real nature, however, of the
+supposed deductive process, is evident enough. The only point to be
+determined is, whether the authority which declared the general
+proposition, intended to include this case in it; and whether the
+legislator intended his command to apply to the present case among
+others, or not. This is ascertained by examining whether the case
+possesses the marks by which, as those authorities have signified, the
+cases which they meant to certify or to influence may be known. The
+object of the inquiry is to make out the witness's or the legislator's
+intention, through the indication given by their words. This is a
+question, as the Germans express it, of hermeneutics. The operation is
+not a process of inference, but a process of interpretation.
+
+In this last phrase we have obtained an expression which appears to me
+to characterize, more aptly than any other, the functions of the
+syllogism in all cases. When the premises are given by authority, the
+function of Reasoning is to ascertain the testimony of a witness, or the
+will of a legislator, by interpreting the signs in which the one has
+intimated his assertion and the other his command. In like manner, when
+the premises are derived from observation, the function of Reasoning is
+to ascertain what we (or our predecessors) formerly thought might be
+inferred from the observed facts, and to do this by interpreting a
+memorandum of ours, or of theirs. The memorandum reminds us, that from
+evidence, more or less carefully weighed, it formerly appeared that a
+certain attribute might be inferred wherever we perceive a certain mark.
+The proposition, All men are mortal (for instance) shows that we have
+had experience from which we thought it followed that the attributes
+connoted by the term man, are a mark of mortality. But when we conclude
+that the Duke of Wellington is mortal, we do not infer this from the
+memorandum, but from the former experience. All that we infer from the
+memorandum is our own previous belief, (or that of those who transmitted
+to us the proposition), concerning the inferences which that former
+experience would warrant.
+
+This view of the nature of the syllogism renders consistent and
+intelligible what otherwise remains obscure and confused in the theory
+of Archbishop Whately and other enlightened defenders of the syllogistic
+doctrine, respecting the limits to which its functions are confined.
+They affirm in as explicit terms as can be used, that the sole office of
+general reasoning is to prevent inconsistency in our opinions; to
+prevent us from assenting to anything, the truth of which would
+contradict something to which we had previously on good grounds given
+our assent. And they tell us, that the sole ground which a syllogism
+affords for assenting to the conclusion, is that the supposition of its
+being false, combined with the supposition that the premises are true,
+would lead to a contradiction in terms. Now this would be but a lame
+account of the real grounds which we have for believing the facts which
+we learn from reasoning, in contradistinction to observation. The true
+reason why we believe that the Duke of Wellington will die, is that his
+fathers, and our fathers, and all other persons who were cotemporary
+with them, have died. Those facts are the real premises of the
+reasoning. But we are not led to infer the conclusion from those
+premises, by the necessity of avoiding any verbal inconsistency. There
+is no contradiction in supposing that all those persons have died, and
+that the Duke of Wellington may, notwithstanding, live for ever. But
+there would be a contradiction if we first, on the ground of those same
+premises, made a general assertion including and covering the case of
+the Duke of Wellington, and then refused to stand to it in the
+individual case. There is an inconsistency to be avoided between the
+memorandum we make of the inferences which may be justly drawn in future
+cases, and the inferences we actually draw in those cases when they
+arise. With this view we interpret our own formula, precisely as a judge
+interprets a law: in order that we may avoid drawing any inferences not
+conformable to our former intention, as a judge avoids giving any
+decision not conformable to the legislator's intention. The rules for
+this interpretation are the rules of the syllogism: and its sole purpose
+is to maintain consistency between the conclusions we draw in every
+particular case, and the previous general directions for drawing them;
+whether those general directions were framed by ourselves as the result
+of induction, or were received by us from an authority competent to give
+them.
+
+
+� 5. In the above observations it has, I think, been shown, that, though
+there is always a process of reasoning or inference where a syllogism is
+used, the syllogism is not a correct analysis of that process of
+reasoning or inference; which is, on the contrary, (when not a mere
+inference from testimony) an inference from particulars to particulars;
+authorized by a previous inference from particulars to generals, and
+substantially the same with it; of the nature, therefore, of Induction.
+But while these conclusions appear to me undeniable, I must yet enter a
+protest, as strong as that of Archbishop Whately himself, against the
+doctrine that the syllogistic art is useless for the purposes of
+reasoning. The reasoning lies in the act of generalization, not in
+interpreting the record of that act; but the syllogistic form is an
+indispensable collateral security for the correctness of the
+generalization itself.
+
+It has already been seen, that if we have a collection of particulars
+sufficient for grounding an induction, we need not frame a general
+proposition; we may reason at once from those particulars to other
+particulars. But it is to be remarked withal, that whenever, from a set
+of particular cases, we can legitimately draw any inference, we may
+legitimately make our inference a general one. If, from observation and
+experiment, we can conclude to one new case, so may we to an indefinite
+number. If that which has held true in our past experience will
+therefore hold in time to come, it will hold not merely in some
+individual case, but in all cases of some given description. Every
+induction, therefore, which suffices to prove one fact, proves an
+indefinite multitude of facts: the experience which justifies a single
+prediction must be such as will suffice to bear out a general theorem.
+This theorem it is extremely important to ascertain and declare, in its
+broadest form of generality; and thus to place before our minds, in its
+full extent, the whole of what our evidence must prove if it proves
+anything.
+
+This throwing of the whole body of possible inferences from a given set
+of particulars, into one general expression, operates as a security for
+their being just inferences, in more ways than one. First, the general
+principle presents a larger object to the imagination than any of the
+singular propositions which it contains. A process of thought which
+leads to a comprehensive generality, is felt as of greater importance
+than one which terminates in an insulated fact; and the mind is, even
+unconsciously, led to bestow greater attention upon the process, and to
+weigh more carefully the sufficiency of the experience appealed to, for
+supporting the inference grounded upon it. There is another, and a more
+important, advantage. In reasoning from a course of individual
+observations to some new and unobserved case, which we are but
+imperfectly acquainted with (or we should not be inquiring into it), and
+in which, since we are inquiring into it, we probably feel a peculiar
+interest; there is very little to prevent us from giving way to
+negligence, or to any bias which may affect our wishes or our
+imagination, and, under that influence, accepting insufficient evidence
+as sufficient. But if, instead of concluding straight to the particular
+case, we place before ourselves an entire class of facts--the whole
+contents of a general proposition, every tittle of which is legitimately
+inferrible from our premises, if that one particular conclusion is so;
+there is then a considerable likelihood that if the premises are
+insufficient, and the general inference, therefore, groundless, it will
+comprise within it some fact or facts the reverse of which we already
+know to be true; and we shall thus discover the error in our
+generalization by a _reductio ad impossibile_.
+
+Thus if, during the reign of Marcus Aurelius, a subject of the Roman
+empire, under the bias naturally given to the imagination and
+expectations by the lives and characters of the Antonines, had been
+disposed to expect that Commodus would be a just ruler; supposing him to
+stop there, he might only have been undeceived by sad experience. But if
+he reflected that this expectation could not be justifiable unless from
+the same evidence he was warranted in concluding some general
+proposition, as, for instance, that all Roman emperors are just rulers;
+he would immediately have thought of Nero, Domitian, and other
+instances, which, showing the falsity of the general conclusion, and
+therefore the insufficiency of the premises, would have warned him that
+those premises could not prove in the instance of Commodus, what they
+were inadequate to prove in any collection of cases in which his was
+included.
+
+The advantage, in judging whether any controverted inference is
+legitimate, of referring to a parallel case, is universally
+acknowledged. But by ascending to the general proposition, we bring
+under our view not one parallel case only, but all possible parallel
+cases at once; all cases to which the same set of evidentiary
+considerations are applicable.
+
+When, therefore, we argue from a number of known cases to another case
+supposed to be analogous, it is always possible, and generally
+advantageous, to divert our argument into the circuitous channel of an
+induction from those known cases to a general proposition, and a
+subsequent application of that general proposition to the unknown case.
+This second part of the operation, which, as before observed, is
+essentially a process of interpretation, will be resolvable into a
+syllogism or a series of syllogisms, the majors of which will be general
+propositions embracing whole classes of cases; every one of which
+propositions must be true in all its extent, if the argument is
+maintainable. If, therefore, any fact fairly coming within the range of
+one of these general propositions, and consequently asserted by it, is
+known or suspected to be other than the proposition asserts it to be,
+this mode of stating the argument causes us to know or to suspect that
+the original observations, which are the real grounds of our conclusion,
+are not sufficient to support it. And in proportion to the greater
+chance of our detecting the inconclusiveness of our evidence, will be
+the increased reliance we are entitled to place in it if no such
+evidence of defect shall appear.
+
+The value, therefore, of the syllogistic form, and of the rules for
+using it correctly, does not consist in their being the form and the
+rules according to which our reasonings are necessarily, or even
+usually, made; but in their furnishing us with a mode in which those
+reasonings may always be represented, and which is admirably calculated,
+if they are inconclusive, to bring their inconclusiveness to light. An
+induction from particulars to generals, followed by a syllogistic
+process from those generals to other particulars, is a form in which we
+may always state our reasonings if we please. It is not a form in which
+we _must_ reason, but it is a form in which we _may_ reason, and into
+which it is indispensable to throw our reasoning, when there is any
+doubt of its validity: though when the case is familiar and little
+complicated, and there is no suspicion of error, we may, and do, reason
+at once from the known particular cases to unknown ones.[9]
+
+These are the uses of syllogism, as a mode of verifying any given
+argument. Its ulterior uses, as respects the general course of our
+intellectual operations, hardly require illustration, being in fact the
+acknowledged uses of general language. They amount substantially to
+this, that the inductions may be made once for all: a single careful
+interrogation of experience may suffice, and the result may be
+registered in the form of a general proposition, which is committed to
+memory or to writing, and from which afterwards we have only to
+syllogize. The particulars of our experiments may then be dismissed from
+the memory, in which it would be impossible to retain so great a
+multitude of details; while the knowledge which those details afforded
+for future use, and which would otherwise be lost as soon as the
+observations were forgotten, or as their record became too bulky for
+reference, is retained in a commodious and immediately available shape
+by means of general language.
+
+Against this advantage is to be set the countervailing inconvenience,
+that inferences originally made on insufficient evidence, become
+consecrated, and, as it were, hardened into general maxims; and the mind
+cleaves to them from habit, after it has outgrown any liability to be
+misled by similar fallacious appearances if they were now for the first
+time presented; but having forgotten the particulars, it does not think
+of revising its own former decision. An inevitable drawback, which,
+however considerable in itself, forms evidently but a small set-off
+against the immense benefits of general language.
+
+The use of the syllogism is in truth no other than the use of general
+propositions in reasoning. We _can_ reason without them; in simple and
+obvious cases we habitually do so; minds of great sagacity can do it in
+cases not simple and obvious, provided their experience supplies them
+with instances essentially similar to every combination of circumstances
+likely to arise. But other minds, and the same minds where they have not
+the same pre-eminent advantages of personal experience, are quite
+helpless without the aid of general propositions, wherever the case
+presents the smallest complication; and if we made no general
+propositions, few persons would get much beyond those simple inferences
+which are drawn by the more intelligent of the brutes. Though not
+necessary to reasoning, general propositions are necessary to any
+considerable progress in reasoning. It is, therefore, natural and
+indispensable to separate the process of investigation into two parts;
+and obtain general formul� for determining what inferences may be drawn,
+before the occasion arises for drawing the inferences. The work of
+drawing them is then that of applying the formul�; and the rules of
+syllogism are a system of securities for the correctness of the
+application.
+
+
+� 6. To complete the series of considerations connected with the
+philosophical character of the syllogism, it is requisite to consider,
+since the syllogism is not the universal type of the reasoning process,
+what is the real type. This resolves itself into the question, what is
+the nature of the minor premise, and in what manner it contributes to
+establish the conclusion: for as to the major, we now fully understand,
+that the place which it nominally occupies in our reasonings, properly
+belongs to the individual facts or observations of which it expresses
+the general result; the major itself being no real part of the argument,
+but an intermediate halting-place for the mind, interposed by an
+artifice of language between the real premises and the conclusion, by
+way of a security, which it is in a most material degree, for the
+correctness of the process. The minor, however, being an indispensable
+part of the syllogistic expression of an argument, without doubt either
+is, or corresponds to, an equally indispensable part of the argument
+itself, and we have only to inquire what part.
+
+It is perhaps worth while to notice here a speculation of a philosopher
+to whom mental science is much indebted, but who, though a very
+penetrating, was a very hasty thinker, and whose want of due
+circumspection rendered him fully as remarkable for what he did not see,
+as for what he saw. I allude to Dr. Thomas Brown, whose theory of
+ratiocination is peculiar. He saw the _petitio principii_ which is
+inherent in every syllogism, if we consider the major to be itself the
+evidence by which the conclusion is proved, instead of being, what in
+fact it is, an assertion of the existence of evidence sufficient to
+prove any conclusion of a given description. Seeing this, Dr. Brown not
+only failed to see the immense advantage, in point of security for
+correctness, which is gained by interposing this step between the real
+evidence and the conclusion; but he thought it incumbent on him to
+strike out the major altogether from the reasoning process, without
+substituting anything else, and maintained that our reasonings consist
+only of the minor premise and the conclusion, Socrates is a man,
+therefore Socrates is mortal: thus actually suppressing, as an
+unnecessary step in the argument, the appeal to former experience. The
+absurdity of this was disguised from him by the opinion he adopted, that
+reasoning is merely analysing our own general notions, or abstract
+ideas; and that the proposition, Socrates is mortal, is evolved from the
+proposition, Socrates is a man, simply by recognising the notion of
+mortality as already contained in the notion we form of a man.
+
+After the explanations so fully entered into on the subject of
+propositions, much further discussion cannot be necessary to make the
+radical error of this view of ratiocination apparent. If the word man
+connoted mortality; if the meaning of "mortal" were involved in the
+meaning of "man;" we might, undoubtedly, evolve the conclusion from the
+minor alone, because the minor would have already asserted it. But if,
+as is in fact the case, the word man does not connote mortality, how
+does it appear that in the mind of every person who admits Socrates to
+be a man, the idea of man must include the idea of mortality? Dr. Brown
+could not help seeing this difficulty, and in order to avoid it, was
+led, contrary to his intention, to re-establish, under another name,
+that step in the argument which corresponds to the major, by affirming
+the necessity of _previously perceiving_ the relation between the idea
+of man and the idea of mortal. If the reasoner has not previously
+perceived this relation, he will not, says Dr. Brown, infer because
+Socrates is a man, that Socrates is mortal. But even this admission,
+though amounting to a surrender of the doctrine that an argument
+consists of the minor and the conclusion alone, will not save the
+remainder of Dr. Brown's theory. The failure of assent to the argument
+does not take place merely because the reasoner, for want of due
+analysis, does not perceive that his idea of man includes the idea of
+mortality; it takes place, much more commonly, because in his mind that
+relation between the two ideas has never existed. And in truth it never
+does exist, except as the result of experience. Consenting, for the sake
+of the argument, to discuss the question on a supposition of which we
+have recognised the radical incorrectness, namely, that the meaning of a
+proposition relates to the ideas of the things spoken of, and not to
+the things themselves; I must yet observe, that the idea of man, as an
+universal idea, the common property of all rational creatures, cannot
+involve anything but what is strictly implied in the name. If any one
+includes in his own private idea of man, as no doubt is always the case,
+some other attributes, such for instance as mortality, he does so only
+as the consequence of experience, after having satisfied himself that
+all men possess that attribute: so that whatever the idea contains, in
+any person's mind, beyond what is included in the conventional
+signification of the word, has been added to it as the result of assent
+to a proposition; while Dr. Brown's theory requires us to suppose, on
+the contrary, that assent to the proposition is produced by evolving,
+through an analytic process, this very element out of the idea. This
+theory, therefore, may be considered as sufficiently refuted; and the
+minor premise must be regarded as totally insufficient to prove the
+conclusion, except with the assistance of the major, or of that which
+the major represents, namely, the various singular propositions
+expressive of the series of observations, of which the generalization
+called the major premise is the result.
+
+In the argument, then, which proves that Socrates is mortal, one
+indispensable part of the premises will be as follows: "My father, and
+my father's father, A, B, C, and an indefinite number of other persons,
+were mortal;" which is only an expression in different words of the
+observed fact that they have died. This is the major premise divested of
+the _petitio principii_, and cut down to as much as is really known by
+direct evidence.
+
+In order to connect this proposition with the conclusion Socrates is
+mortal, the additional link necessary is such a proposition as the
+following: "Socrates resembles my father, and my father's father, and
+the other individuals specified." This proposition we assert when we say
+that Socrates is a man. By saying so we likewise assert in what respect
+he resembles them, namely, in the attributes connoted by the word man.
+And we conclude that he further resembles them in the attribute
+mortality.
+
+
+� 7. We have thus obtained what we were seeking, an universal type of
+the reasoning process. We find it resolvable in all cases into the
+following elements: Certain individuals have a given attribute; an
+individual or individuals resemble the former in certain other
+attributes; therefore they resemble them also in the given attribute.
+This type of ratiocination does not claim, like the syllogism, to be
+conclusive, from the mere form of the expression; nor can it possibly be
+so. That one proposition does or does not assert the very fact which was
+already asserted in another, may appear from the form of the expression,
+that is, from a comparison of the language; but when the two
+propositions assert facts which are _bon� fide_ different, whether the
+one fact proves the other or not can never appear from the language, but
+must depend on other considerations. Whether, from the attributes in
+which Socrates resembles those men who have heretofore died, it is
+allowable to infer that he resembles them also in being mortal, is a
+question of Induction; and is to be decided by the principles or canons
+which we shall hereafter recognise as tests of the correct performance
+of that great mental operation.
+
+Meanwhile, however, it is certain, as before remarked, that if this
+inference can be drawn as to Socrates, it can be drawn as to all others
+who resemble the observed individuals in the same attributes in which he
+resembles them; that is (to express the thing concisely) of all mankind.
+If, therefore, the argument be admissible in the case of Socrates, we
+are at liberty, once for all, to treat the possession of the attributes
+of man as a mark, or satisfactory evidence, of the attribute of
+mortality. This we do by laying down the universal proposition, All men
+are mortal, and interpreting this, as occasion arises, in its
+application to Socrates and others. By this means we establish a very
+convenient division of the entire logical operation into two steps;
+first, that of ascertaining what attributes are marks of mortality; and,
+secondly, whether any given individuals possess those marks. And it will
+generally be advisable, in our speculations on the reasoning process, to
+consider this double operation as in fact taking place, and all
+reasoning as carried on in the form into which it must necessarily be
+thrown to enable us to apply to it any test of its correct performance.
+
+Although, therefore, all processes of thought in which the ultimate
+premises are particulars, whether we conclude from particulars to a
+general formula, or from particulars to other particulars according to
+that formula, are equally Induction: we shall yet, conformably to usage,
+consider the name Induction as more peculiarly belonging to the process
+of establishing the general proposition, and the remaining operation,
+which is substantially that of interpreting the general proposition, we
+shall call by its usual name, Deduction. And we shall consider every
+process by which anything is inferred respecting an unobserved case, as
+consisting of an Induction followed by a Deduction; because, although
+the process needs not necessarily be carried on in this form, it is
+always susceptible of the form, and must be thrown into it when
+assurance of scientific accuracy is needed and desired.
+
+
+� 8. The theory of the syllogism, laid down in the preceding pages, has
+obtained, among other important adhesions, three of peculiar value;
+those of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir
+John Herschel considering the doctrine, though not strictly "a
+discovery,"[13] to be "one of the greatest steps which have yet been
+made in the philosophy of Logic." "When we consider" (to quote the
+further words of the same authority) "the inveteracy of the habits and
+prejudices which it has cast to the winds," there is no cause for
+misgiving in the fact that other thinkers, no less entitled to
+consideration, have formed a very different estimate of it. Their
+principal objection cannot be better or more succinctly stated than by
+borrowing a sentence from Archbishop Whately.[14] "In every case where
+an inference is drawn from Induction (unless that name is to be given to
+a mere random guess without any grounds at all) we must form a judgment
+that the instance or instances adduced are _sufficient_ to authorize the
+conclusion; that it is _allowable_ to take these instances as a sample
+warranting an inference respecting the whole class;" and the expression
+of this judgment in words (it has been said by several of my critics)
+_is_ the major premise.
+
+I quite admit that the major is an affirmation of the sufficiency of the
+evidence on which the conclusion rests. That it is so, is the very
+essence of my own theory. And whoever admits that the major premise is
+_only_ this, adopts the theory in its essentials.
+
+But I cannot concede that this recognition of the sufficiency of the
+evidence--that is, of the correctness of the induction--is a part of the
+induction itself; unless we ought to say that it is a part of everything
+we do, to satisfy ourselves that it has been done rightly. We conclude
+from known instances to unknown by the impulse of the generalizing
+propensity; and (until after a considerable amount of practice and
+mental discipline) the question of the sufficiency of the evidence is
+only raised by a retrospective act, turning back upon our own footsteps,
+and examining whether we were warranted in doing what we have already
+done. To speak of this reflex operation as part of the original one,
+requiring to be expressed in words in order that the verbal formula may
+correctly represent the psychological process, appears to me false
+psychology.[15] We review our syllogistic as well as our inductive
+processes, and recognise that they have been correctly performed; but
+logicians do not add a third premise to the syllogism, to express this
+act of recognition. A careful copyist verifies his transcript by
+collating it with the original; and if no error appears, he recognises
+that the transcript has been correctly made. But we do not call the
+examination of the copy a part of the act of copying.
+
+The conclusion in an induction is inferred from the evidence itself, and
+not from a recognition of the sufficiency of the evidence; as I infer
+that my friend is walking towards me because I see him, and not because
+I recognise that my eyes are open, and that eyesight is a means of
+knowledge. In all operations which require care, it is good to assure
+ourselves that the process has been performed accurately; but the
+testing of the process is not the process itself; and, besides, may have
+been omitted altogether, and yet the process be correct. It is precisely
+because that operation is omitted in ordinary unscientific reasoning,
+that there is anything gained in certainty by throwing reasoning into
+the syllogistic form. To make sure, as far as possible, that it shall
+not be omitted, we make the testing operation a part of the reasoning
+process itself. We insist that the inference from particulars to
+particulars shall pass through a general proposition. But this is a
+security for good reasoning, not a condition of all reasoning; and in
+some cases not even a security. Our most familiar inferences are all
+made before we learn the use of general propositions; and a person of
+untutored sagacity will skilfully apply his acquired experience to
+adjacent cases, though he would bungle grievously in fixing the limits
+of the appropriate general theorem. But though he may conclude rightly,
+he never, properly speaking, knows whether he has done so or not; he has
+not tested his reasoning. Now, this is precisely what forms of reasoning
+do for us. We do not need them to enable us to reason, but to enable us
+to know whether we reason correctly.
+
+In still further answer to the objection, it may be added that, even
+when the test has been applied, and the sufficiency of the evidence
+recognised,--if it is sufficient to support the general proposition, it
+is sufficient also to support an inference from particulars to
+particulars without passing through the general proposition. The
+inquirer who has logically satisfied himself that the conditions of
+legitimate induction were realized in the cases A, B, C, would be as
+much justified in concluding directly to the Duke of Wellington as in
+concluding to all men. The general conclusion is never legitimate,
+unless the particular one would be so too; and in no sense, intelligible
+to me, can the particular conclusion be said to be drawn from the
+general one. Whenever there is ground for drawing any conclusion at all
+from particular instances, there is ground for a general conclusion; but
+that this general conclusion should be actually drawn, however useful,
+cannot be an indispensable condition of the validity of the inference in
+the particular case. A man gives away sixpence by the same power by
+which he disposes of his whole fortune; but it is not necessary to the
+legality of the smaller act, that he should make a formal assertion of
+his right to the greater one.
+
+Some additional remarks, in reply to minor objections, are appended.[16]
+
+
+� 9. The preceding considerations enable us to understand the true
+nature of what is termed, by recent writers, Formal Logic, and the
+relation between it and Logic in the widest sense. Logic, as I conceive
+it, is the entire theory of the ascertainment of reasoned or inferred
+truth. Formal Logic, therefore, which Sir William Hamilton from his own
+point of view, and Archbishop Whately from his, have represented as the
+whole of Logic properly so called, is really a very subordinate part of
+it, not being directly concerned with the process of Reasoning or
+Inference in the sense in which that process is a part of the
+Investigation of Truth. What, then, is Formal Logic? The name seems to
+be properly applied to all that portion of doctrine which relates to the
+equivalence of different modes of expression; the rules for determining
+when assertions in a given form imply or suppose the truth or falsity of
+other assertions. This includes the theory of the Import of
+Propositions, and of their Conversion, �quipollence, and Opposition; of
+those falsely called Inductions (to be hereafter spoken of[17]), in
+which the apparent generalization is a mere abridged statement of cases
+known individually; and finally, of the syllogism: while the theory of
+Naming, and of (what is inseparably connected with it) Definition,
+though belonging still more to the other and larger kind of logic than
+to this, is a necessary preliminary to this. The end aimed at by Formal
+Logic, and attained by the observance of its precepts, is not truth, but
+consistency. It has been seen that this is the only direct purpose of
+the rules of the syllogism; the intention and effect of which is simply
+to keep our inferences or conclusions in complete consistency with our
+general formul� or directions for drawing them. The Logic of Consistency
+is a necessary auxiliary to the logic of truth, not only because what is
+inconsistent with itself or with other truths cannot be true, but also
+because truth can only be successfully pursued by drawing inferences
+from experience, which, if warrantable at all, admit of being
+generalized, and, to test their warrantableness, require to be exhibited
+in a generalized form; after which the correctness of their application
+to particular cases is a question which specially concerns the Logic of
+Consistency. This Logic, not requiring any preliminary knowledge of the
+processes or conclusions of the various sciences, may be studied with
+benefit in a much earlier stage of education than the Logic of Truth:
+and the practice which has empirically obtained of teaching it apart,
+through elementary treatises which do not attempt to include anything
+else, though the reasons assigned for the practice are in general very
+far from philosophical, admits of a philosophical justification.
+
+
+
+
+CHAPTER IV.
+
+OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
+
+
+� 1. In our analysis of the syllogism, it appeared that the minor
+premise always affirms a resemblance between a new case and some cases
+previously known; while the major premise asserts something which,
+having been found true of those known cases, we consider ourselves
+warranted in holding true of any other case resembling the former in
+certain given particulars.
+
+If all ratiocinations resembled, as to the minor premise, the examples
+which were exclusively employed in the preceding chapter; if the
+resemblance, which that premise asserts, were obvious to the senses, as
+in the proposition "Socrates is a man," or were at once ascertainable by
+direct observation; there would be no necessity for trains of reasoning,
+and Deductive or Ratiocinative Sciences would not exist. Trains of
+reasoning exist only for the sake of extending an induction founded, as
+all inductions must be, on observed cases, to other cases in which we
+not only cannot directly observe what is to be proved, but cannot
+directly observe even the mark which is to prove it.
+
+
+� 2. Suppose the syllogism to be, All cows ruminate, the animal which is
+before me is a cow, therefore it ruminates. The minor, if true at all,
+is obviously so: the only premise the establishment of which requires
+any anterior process of inquiry, is the major; and provided the
+induction of which that premise is the expression was correctly
+performed, the conclusion respecting the animal now present will be
+instantly drawn; because, as soon as she is compared with the formula,
+she will be identified as being included in it. But suppose the
+syllogism to be the following:--All arsenic is poisonous, the substance
+which is before me is arsenic, therefore it is poisonous. The truth of
+the minor may not here be obvious at first sight; it may not be
+intuitively evident, but may itself be known only by inference. It may
+be the conclusion of another argument, which, thrown into the
+syllogistic form, would stand thus:--Whatever when lighted produces a
+dark spot on a piece of white porcelain held in the flame, which spot is
+soluble in hypochlorite of calcium, is arsenic; the substance before me
+conforms to this condition; therefore it is arsenic. To establish,
+therefore, the ultimate conclusion, The substance before me is
+poisonous, requires a process, which, in order to be syllogistically
+expressed, stands in need of two syllogisms; and we have a Train of
+Reasoning.
+
+When, however, we thus add syllogism to syllogism, we are really adding
+induction to induction. Two separate inductions must have taken place to
+render this chain of inference possible; inductions founded, probably,
+on different sets of individual instances, but which converge in their
+results, so that the instance which is the subject of inquiry comes
+within the range of them both. The record of these inductions is
+contained in the majors of the two syllogisms. First, we, or others for
+us, have examined various objects which yielded under the given
+circumstances a dark spot with the given property, and found that they
+possessed the properties connoted by the word arsenic; they were
+metallic, volatile, their vapour had a smell of garlic, and so forth.
+Next, we, or others for us, have examined various specimens which
+possessed this metallic and volatile character, whose vapour had this
+smell, &c., and have invariably found that they were poisonous. The
+first observation we judge that we may extend to all substances whatever
+which yield that particular kind of dark spot; the second, to all
+metallic and volatile substances resembling those we examined; and
+consequently, not to those only which are seen to be such, but to those
+which are concluded to be such by the prior induction. The substance
+before us is only seen to come within one of these inductions; but by
+means of this one, it is brought within the other. We are still, as
+before, concluding from particulars to particulars; but we are now
+concluding from particulars observed, to other particulars which are
+not, as in the simple case, _seen_ to resemble them in the material
+points, but _inferred_ to do so, because resembling them in something
+else, which we have been led by quite a different set of instances to
+consider as a mark of the former resemblance.
+
+This first example of a train of reasoning is still extremely simple,
+the series consisting of only two syllogisms. The following is somewhat
+more complicated:--No government, which earnestly seeks the good of its
+subjects, is likely to be overthrown; some particular government
+earnestly seeks the good of its subjects, therefore it is not likely to
+be overthrown. The major premise in this argument we shall suppose not
+to be derived from considerations _� priori_, but to be a generalization
+from history, which, whether correct or erroneous, must have been
+founded on observation of governments concerning whose desire of the
+good of their subjects there was no doubt. It has been found, or thought
+to be found, that these were not easily overthrown, and it has been
+deemed that those instances warranted an extension of the same predicate
+to any and every government which resembles them in the attribute of
+desiring earnestly the good of its subjects. But _does_ the government
+in question thus resemble them? This may be debated _pro_ and _con_ by
+many arguments, and must, in any case, be proved by another induction;
+for we cannot directly observe the sentiments and desires of the persons
+who carry on the government. To prove the minor, therefore, we require
+an argument in this form: Every government which acts in a certain
+manner, desires the good of its subjects; the supposed government acts
+in that particular manner, therefore it desires the good of its
+subjects. But is it true that the government acts in the manner
+supposed? This minor also may require proof; still another induction, as
+thus:--What is asserted by intelligent and disinterested witnesses, may
+be believed to be true; that the government acts in this manner, is
+asserted by such witnesses, therefore it may be believed to be true. The
+argument hence consists of three steps. Having the evidence of our
+senses that the case of the government under consideration resembles a
+number of former cases, in the circumstance of having something asserted
+respecting it by intelligent and disinterested witnesses, we infer,
+first, that, as in those former instances, so in this instance, the
+assertion is true. Secondly, what was asserted of the government being
+that it acts in a particular manner, and other governments or persons
+having been observed to act in the same manner, the government in
+question is brought into known resemblance with those other governments
+or persons; and since they were known to desire the good of the people,
+it is thereupon, by a second induction, inferred that the particular
+government spoken of, desires the good of the people. This brings that
+government into known resemblance with the other governments which were
+thought likely to escape revolution, and thence, by a third induction,
+it is concluded that this particular government is also likely to
+escape. This is still reasoning from particulars to particulars, but we
+now reason to the new instance from three distinct sets of former
+instances: to one only of those sets of instances do we directly
+perceive the new one to be similar; but from that similarity we
+inductively infer that it has the attribute by which it is assimilated
+to the next set, and brought within the corresponding induction; after
+which by a repetition of the same operation we infer it to be similar to
+the third set, and hence a third induction conducts us to the ultimate
+conclusion.
+
+
+� 3. Notwithstanding the superior complication of these examples,
+compared with those by which in the preceding chapter we illustrated the
+general theory of reasoning, every doctrine which we then laid down
+holds equally true in these more intricate cases. The successive general
+propositions are not steps in the reasoning, are not intermediate links
+in the chain of inference, between the particulars observed and those to
+which we apply the observation. If we had sufficiently capacious
+memories, and a sufficient power of maintaining order among a huge mass
+of details, the reasoning could go on without any general propositions;
+they are mere formul� for inferring particulars from particulars. The
+principle of general reasoning is (as before explained), that if from
+observation of certain known particulars, what was seen to be true of
+them can be inferred to be true of any others, it may be inferred of all
+others which are of a certain description. And in order that we may
+never fail to draw this conclusion in a new case when it can be drawn
+correctly, and may avoid drawing it when it cannot, we determine once
+for all what are the distinguishing marks by which such cases may be
+recognised. The subsequent process is merely that of identifying an
+object, and ascertaining it to have those marks; whether we identify it
+by the very marks themselves, or by others which we have ascertained
+(through another and a similar process) to be marks of those marks. The
+real inference is always from particulars to particulars, from the
+observed instances to an unobserved one: but in drawing this inference,
+we conform to a formula which we have adopted for our guidance in such
+operations, and which is a record of the criteria by which we thought we
+had ascertained that we might distinguish when the inference could, and
+when it could not, be drawn. The real premises are the individual
+observations, even though they may have been forgotten, or, being the
+observations of others and not of ourselves, may, to us, never have been
+known: but we have before us proof that we or others once thought them
+sufficient for an induction, and we have marks to show whether any new
+case is one of those to which, if then known, the induction would have
+been deemed to extend. These marks we either recognise at once, or by
+the aid of other marks, which by another previous induction we collected
+to be marks of the first. Even these marks of marks may only be
+recognised through a third set of marks; and we may have a train of
+reasoning, of any length, to bring a new case within the scope of an
+induction grounded on particulars its similarity to which is only
+ascertained in this indirect manner.
+
+Thus, in the preceding example, the ultimate inductive inference was,
+that a certain government was not likely to be overthrown; this
+inference was drawn according to a formula in which desire of the public
+good was set down as a mark of not being likely to be overthrown; a mark
+of this mark was, acting in a particular manner; and a mark of acting in
+that manner was, being asserted to do so by intelligent and
+disinterested witnesses: this mark, the government under discussion was
+recognised by the senses as possessing. Hence that government fell
+within the last induction, and by it was brought within all the others.
+The perceived resemblance of the case to one set of observed particular
+cases, brought it into known resemblance with another set, and that with
+a third.
+
+In the more complex branches of knowledge, the deductions seldom
+consist, as in the examples hitherto exhibited, of a single chain, _a_ a
+mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They
+consist (to carry on the same metaphor) of several chains united at the
+extremity, as thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_
+of _n_, therefore _a b c_ a mark of _n_. Suppose, for example, the
+following combination of circumstances; 1st, rays of light impinging on
+a reflecting surface; 2nd, that surface parabolic; 3rd, those rays
+parallel to each other and to the axis of the surface. It is to be
+proved that the concourse of these three circumstances is a mark that
+the reflected rays will pass through the focus of the parabolic surface.
+Now, each of the three circumstances is singly a mark of something
+material to the case. Rays of light impinging on a reflecting surface,
+are a mark that those rays will be reflected at an angle equal to the
+angle of incidence. The parabolic form of the surface is a mark that,
+from any point of it, a line drawn to the focus and a line parallel to
+the axis will make equal angles with the surface. And finally, the
+parallelism of the rays to the axis is a mark that their angle of
+incidence coincides with one of these equal angles. The three marks
+taken together are therefore a mark of all these three things united.
+But the three united are evidently a mark that the angle of reflection
+must coincide with the other of the two equal angles, that formed by a
+line drawn to the focus; and this again, by the fundamental axiom
+concerning straight lines, is a mark that the reflected rays pass
+through the focus. Most chains of physical deduction are of this more
+complicated type; and even in mathematics such are abundant, as in all
+propositions where the hypothesis includes numerous conditions: "_If_ a
+circle be taken, and _if_ within that circle a point be taken, not the
+centre, and _if_ straight lines be drawn from that point to the
+circumference, then," &c.
+
+
+� 4. The considerations now stated remove a serious difficulty from the
+view we have taken of reasoning; which view might otherwise have seemed
+not easily reconcileable with the fact that there are Deductive or
+Ratiocinative Sciences. It might seem to follow, if all reasoning be
+induction, that the difficulties of philosophical investigation must lie
+in the inductions exclusively, and that when these were easy, and
+susceptible of no doubt or hesitation, there could be no science, or, at
+least, no difficulties in science. The existence, for example, of an
+extensive Science of Mathematics, requiring the highest scientific
+genius in those who contributed to its creation, and calling for a most
+continued and vigorous exertion of intellect in order to appropriate it
+when created, may seem hard to be accounted for on the foregoing theory.
+But the considerations more recently adduced remove the mystery, by
+showing, that even when the inductions themselves are obvious, there may
+be much difficulty in finding whether the particular case which is the
+subject of inquiry comes within them; and ample room for scientific
+ingenuity in so combining various inductions, as, by means of one within
+which the case evidently falls, to bring it within others in which it
+cannot be directly seen to be included.
+
+When the more obvious of the inductions which can be made in any science
+from direct observations, have been made, and general formulas have been
+framed, determining the limits within which these inductions are
+applicable; as often as a new case can be at once seen to come within
+one of the formulas, the induction is applied to the new case, and the
+business is ended. But new cases are continually arising, which do not
+obviously come within any formula whereby the question we want solved in
+respect of them could be answered. Let us take an instance from
+geometry: and as it is taken only for illustration, let the reader
+concede to us for the present, what we shall endeavour to prove in the
+next chapter, that the first principles of geometry are results of
+induction. Our example shall be the fifth proposition of the first book
+of Euclid. The inquiry is, Are the angles at the base of an isosceles
+triangle equal or unequal? The first thing to be considered is, what
+inductions we have, from which we can infer equality or inequality. For
+inferring equality we have the following formul�:--Things which being
+applied to each other coincide, are equals. Things which are equal to
+the same thing are equals. A whole and the sum of its parts are equals.
+The sums of equal things are equals. The differences of equal things are
+equals. There are no other original formul� to prove equality. For
+inferring inequality we have the following:--A whole and its parts are
+unequals. The sums of equal things and unequal things are unequals. The
+differences of equal things and unequal things are unequals. In all,
+eight formul�. The angles at the base of an isosceles triangle do not
+obviously come within any of these. The formul� specify certain marks of
+equality and of inequality, but the angles cannot be perceived
+intuitively to have any of those marks. On examination it appears that
+they have; and we ultimately succeed in bringing them within the
+formula, "The differences of equal things are equal." Whence comes the
+difficulty of recognising these angles as the differences of equal
+things? Because each of them is the difference not of one pair only, but
+of innumerable pairs of angles; and out of these we had to imagine and
+select two, which could either be intuitively perceived to be equals, or
+possessed some of the marks of equality set down in the various formul�.
+By an exercise of ingenuity, which, on the part of the first inventor,
+deserves to be regarded as considerable, two pairs of angles were hit
+upon, which united these requisites. First, it could be perceived
+intuitively that their differences were the angles at the base; and,
+secondly, they possessed one of the marks of equality, namely,
+coincidence when applied to one another. This coincidence, however, was
+not perceived intuitively, but inferred, in conformity to another
+formula.
+
+For greater clearness, I subjoin an analysis of the demonstration.
+Euclid, it will be remembered, demonstrates his fifth proposition by
+means of the fourth. This it is not allowable for us to do, because we
+are undertaking to trace deductive truths not to prior deductions, but
+to their original inductive foundation. We must therefore use the
+premises of the fourth proposition instead of its conclusion, and prove
+the fifth directly from first principles. To do so requires six
+formulas. (We must begin, as in Euclid, by prolonging the equal sides
+AB, AC, to equal distances, and joining the extremities BE, DC.)
+
+[Illustration]
+
+FIRST FORMULA. _The sums of equals are equal._
+
+AD and AE are sums of equals by the supposition. Having that mark of
+equality, they are concluded by this formula to be equal.
+
+SECOND FORMULA. _Equal straight lines being applied to one another
+coincide._
+
+AC, AB, are within this formula by supposition; AD, AE, have been
+brought within it by the preceding step. Both these pairs of straight
+lines have the property of equality; which, according to the second
+formula, is a mark that, if applied to each other, they will coincide.
+Coinciding altogether means coinciding in every part, and of course at
+their extremities, D, E, and B, C.
+
+THIRD FORMULA. _Straight lines, having their extremities coincident,
+coincide._
+
+BE and CD have been brought within this formula by the preceding
+induction; they will, therefore, coincide.
+
+FOURTH FORMULA. _Angles, having their sides coincident, coincide._
+
+The third induction having shown that BE and CD coincide, and the second
+that AB, AC, coincide, the angles ABE and ACD are thereby brought within
+the fourth formula, and accordingly coincide.
+
+FIFTH FORMULA. _Things which coincide are equal._
+
+The angles ABE and ACD are brought within this formula by the induction
+immediately preceding. This train of reasoning being also applicable,
+_mutatis mutandis_, to the angles EBC, DCB, these also are brought
+within the fifth formula. And, finally,
+
+SIXTH FORMULA. _The differences of equals are equal._
+
+The angle ABC being the difference of ABE, CBE, and the angle ACB being
+the difference of ACD, DCB; which have been proved to be equals; ABC and
+ACB are brought within the last formula by the whole of the previous
+process.
+
+The difficulty here encountered is chiefly that of figuring to ourselves
+the two angles at the base of the triangle ABC as remainders made by
+cutting one pair of angles out of another, while each pair shall be
+corresponding angles of triangles which have two sides and the
+intervening angle equal. It is by this happy contrivance that so many
+different inductions are brought to bear upon the same particular case.
+And this not being at all an obvious thought, it may be seen from an
+example so near the threshold of mathematics, how much scope there may
+well be for scientific dexterity in the higher branches of that and
+other sciences, in order so to combine a few simple inductions, as to
+bring within each of them innumerable cases which are not obviously
+included in it; and how long, and numerous, and complicated may be the
+processes necessary for bringing the inductions together, even when each
+induction may itself be very easy and simple. All the inductions
+involved in all geometry are comprised in those simple ones, the formul�
+of which are the Axioms, and a few of the so-called Definitions. The
+remainder of the science is made up of the processes employed for
+bringing unforeseen cases within these inductions; or (in syllogistic
+language) for proving the minors necessary to complete the syllogisms;
+the majors being the definitions and axioms. In those definitions and
+axioms are laid down the whole of the marks, by an artful combination of
+which it has been found possible to discover and prove all that is
+proved in geometry. The marks being so few, and the inductions which
+furnish them being so obvious and familiar; the connecting of several of
+them together, which constitutes Deductions, or Trains of Reasoning,
+forms the whole difficulty of the science, and with a trifling
+exception, its whole bulk; and hence Geometry is a Deductive Science.
+
+
+� 5. It will be seen hereafter[18] that there are weighty scientific
+reasons for giving to every science as much of the character of a
+Deductive Science as possible; for endeavouring to construct the science
+from the fewest and the simplest possible inductions, and to make these,
+by any combinations however complicated, suffice for proving even such
+truths, relating to complex cases, as could be proved, if we chose, by
+inductions from specific experience. Every branch of natural philosophy
+was originally experimental; each generalization rested on a special
+induction, and was derived from its own distinct set of observations and
+experiments. From being sciences of pure experiment, as the phrase is,
+or, to speak more correctly, sciences in which the reasonings mostly
+consist of no more than one step, and are expressed by single
+syllogisms, all these sciences have become to some extent, and some of
+them in nearly the whole of their extent, sciences of pure reasoning;
+whereby multitudes of truths, already known by induction from as many
+different sets of experiments, have come to be exhibited as deductions
+or corollaries from inductive propositions of a simpler and more
+universal character. Thus mechanics, hydrostatics, optics, acoustics,
+thermology, have successively been rendered mathematical; and astronomy
+was brought by Newton within the laws of general mechanics. Why it is
+that the substitution of this circuitous mode of proceeding for a
+process apparently much easier and more natural, is held, and justly, to
+be the greatest triumph of the investigation of nature, we are not, in
+this stage of our inquiry, prepared to examine. But it is necessary to
+remark, that although, by this progressive transformation, all sciences
+tend to become more and more Deductive, they are not, therefore, the
+less Inductive; every step in the Deduction is still an Induction. The
+opposition is not between the terms Deductive and Inductive, but between
+Deductive and Experimental. A science is experimental, in proportion as
+every new case, which presents any peculiar features, stands in need of
+a new set of observations and experiments--a fresh induction. It is
+deductive, in proportion as it can draw conclusions, respecting cases of
+a new kind, by processes which bring those cases under old inductions;
+by ascertaining that cases which cannot be observed to have the
+requisite marks, have, however, marks of those marks.
+
+We can now, therefore, perceive what is the generic distinction between
+sciences which can be made Deductive, and those which must as yet remain
+Experimental. The difference consists in our having been able, or not
+yet able, to discover marks of marks. If by our various inductions we
+have been able to proceed no further than to such propositions as these,
+_a_ a mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of
+_d_, or _c_ and _d_ marks of one another, without anything to connect
+_a_ or _b_ with _c_ or _d_; we have a science of detached and mutually
+independent generalizations, such as these, that acids redden vegetable
+blues, and that alkalies colour them green; from neither of which
+propositions could we, directly or indirectly, infer the other: and a
+science, so far as it is composed of such propositions, is purely
+experimental. Chemistry, in the present state of our knowledge, has not
+yet thrown off this character. There are other sciences, however, of
+which the propositions are of this kind: _a_ a mark of _b_, _b_ a mark
+of _c_, _c_ of _d_, _d_ of _e_, &c. In these sciences we can mount the
+ladder from _a_ to _e_ by a process of ratiocination; we can conclude
+that _a_ is a mark of _e_, and that every object which has the mark _a_
+has the property _e_, although, perhaps, we never were able to observe
+_a_ and _e_ together, and although even _d_, our only direct mark of
+_e_, may not be perceptible in those objects, but only inferrible. Or,
+varying the first metaphor, we may be said to get from _a_ to _e_
+underground: the marks _b_, _c_, _d_, which indicate the route, must all
+be possessed somewhere by the objects concerning which we are inquiring;
+but they are below the surface: _a_ is the only mark that is visible,
+and by it we are able to trace in succession all the rest.
+
+
+� 6. We can now understand how an experimental may transform itself into
+a deductive science by the mere progress of experiment. In an
+experimental science, the inductions, as we have said, lie detached, as,
+_a_ a mark of _b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now,
+a new set of instances, and a consequent new induction, may at any time
+bridge over the interval between two of these unconnected arches; _b_,
+for example, may be ascertained to be a mark of _c_, which enables us
+thenceforth to prove deductively that _a_ is a mark of _c_. Or, as
+sometimes happens, some comprehensive induction may raise an arch high
+in the air, which bridges over hosts of them at once: _b_, _d_, _f_, and
+all the rest, turning out to be marks of some one thing, or of things
+between which a connexion has already been traced. As when Newton
+discovered that the motions, whether regular or apparently anomalous, of
+all the bodies of the solar system, (each of which motions had been
+inferred by a separate logical operation, from separate marks,) were all
+marks of moving round a common centre, with a centripetal force varying
+directly as the mass, and inversely as the square of the distance from
+that centre. This is the greatest example which has yet occurred of the
+transformation, at one stroke, of a science which was still to a great
+degree merely experimental, into a deductive science.
+
+Transformations of the same nature, but on a smaller scale, continually
+take place in the less advanced branches of physical knowledge, without
+enabling them to throw off the character of experimental sciences. Thus
+with regard to the two unconnected propositions before cited, namely,
+Acids redden vegetable blues, Alkalies make them green; it is remarked
+by Liebig, that all blue colouring matters which are reddened by acids
+(as well as, reciprocally, all red colouring matters which are rendered
+blue by alkalies) contain nitrogen: and it is quite possible that this
+circumstance may one day furnish a bond of connexion between the two
+propositions in question, by showing that the antagonistic action of
+acids and alkalies in producing or destroying the colour blue, is the
+result of some one, more general, law. Although this connecting of
+detached generalizations is so much gain, it tends but little to give a
+deductive character to any science as a whole; because the new courses
+of observation and experiment, which thus enable us to connect together
+a few general truths, usually make known to us a still greater number of
+unconnected new ones. Hence chemistry, though similar extensions and
+simplifications of its generalizations are continually taking place, is
+still in the main an experimental science; and is likely so to continue
+unless some comprehensive induction should be hereafter arrived at,
+which, like Newton's, shall connect a vast number of the smaller known
+inductions together, and change the whole method of the science at once.
+Chemistry has already one great generalization, which, though relating
+to one of the subordinate aspects of chemical phenomena, possesses
+within its limited sphere this comprehensive character; the principle of
+Dalton, called the atomic theory, or the doctrine of chemical
+equivalents: which by enabling us to a certain extent to foresee the
+proportions in which two substances will combine, before the experiment
+has been tried, constitutes undoubtedly a source of new chemical truths
+obtainable by deduction, as well as a connecting principle for all
+truths of the same description previously obtained by experiment.
+
+
+� 7. The discoveries which change the method of a science from
+experimental to deductive, mostly consist in establishing, either by
+deduction or by direct experiment, that the varieties of a particular
+phenomenon uniformly accompany the varieties of some other phenomenon
+better known. Thus the science of sound, which previously stood in the
+lowest rank of merely experimental science, became deductive when it was
+proved by experiment that every variety of sound was consequent on, and
+therefore a mark of, a distinct and definable variety of oscillatory
+motion among the particles of the transmitting medium. When this was
+ascertained, it followed that every relation of succession or
+coexistence which obtained between phenomena of the more known class,
+obtained also between the phenomena which corresponded to them in the
+other class. Every sound, being a mark of a particular oscillatory
+motion, became a mark of everything which, by the laws of dynamics, was
+known to be inferrible from that motion; and everything which by those
+same laws was a mark of any oscillatory motion among the particles of an
+elastic medium, became a mark of the corresponding sound. And thus many
+truths, not before suspected, concerning sound, become deducible from
+the known laws of the propagation of motion through an elastic medium;
+while facts already empirically known respecting sound, become an
+indication of corresponding properties of vibrating bodies, previously
+undiscovered.
+
+But the grand agent for transforming experimental into deductive
+sciences, is the science of number. The properties of numbers, alone
+among all known phenomena, are, in the most rigorous sense, properties
+of all things whatever. All things are not coloured, or ponderable, or
+even extended; but all things are numerable. And if we consider this
+science in its whole extent, from common arithmetic up to the calculus
+of variations, the truths already ascertained seem all but infinite, and
+admit of indefinite extension.
+
+These truths, though affirmable of all things whatever, of course apply
+to them only in respect of their quantity. But if it comes to be
+discovered that variations of quality in any class of phenomena,
+correspond regularly to variations of quantity either in those same or
+in some other phenomena; every formula of mathematics applicable to
+quantities which vary in that particular manner, becomes a mark of a
+corresponding general truth respecting the variations in quality which
+accompany them: and the science of quantity being (as far as any science
+can be) altogether deductive, the theory of that particular kind of
+qualities becomes, to this extent, deductive likewise.
+
+The most striking instance in point which history affords (though not an
+example of an experimental science rendered deductive, but of an
+unparalleled extension given to the deductive process in a science which
+was deductive already), is the revolution in geometry which originated
+with Descartes, and was completed by Clairaut. These great
+mathematicians pointed out the importance of the fact, that to every
+variety of position in points, direction in lines, or form in curves or
+surfaces (all of which are Qualities), there corresponds a peculiar
+relation of quantity between either two or three rectilineal
+co-ordinates; insomuch that if the law were known according to which
+those co-ordinates vary relatively to one another, every other
+geometrical property of the line or surface in question, whether
+relating to quantity or quality, would be capable of being inferred.
+Hence it followed that every geometrical question could be solved, if
+the corresponding algebraical one could; and geometry received an
+accession (actual or potential) of new truths, corresponding to every
+property of numbers which the progress of the calculus had brought, or
+might in future bring, to light. In the same general manner, mechanics,
+astronomy, and in a less degree, every branch of natural philosophy
+commonly so called, have been made algebraical. The varieties of
+physical phenomena with which those sciences are conversant, have been
+found to answer to determinable varieties in the quantity of some
+circumstance or other; or at least to varieties of form or position, for
+which corresponding equations of quantity had already been, or were
+susceptible of being, discovered by geometers.
+
+In these various transformations, the propositions of the science of
+number do but fulfil the function proper to all propositions forming a
+train of reasoning, viz. that of enabling us to arrive in an indirect
+method, by marks of marks, at such of the properties of objects as we
+cannot directly ascertain (or not so conveniently) by experiment. We
+travel from a given visible or tangible fact, through the truths of
+numbers, to the facts sought. The given fact is a mark that a certain
+relation subsists between the quantities of some of the elements
+concerned; while the fact sought presupposes a certain relation between
+the quantities of some other elements: now, if these last quantities are
+dependent in some known manner upon the former, or _vice vers�_, we can
+argue from the numerical relation between the one set of quantities, to
+determine that which subsists between the other set; the theorems of the
+calculus affording the intermediate links. And thus one of the two
+physical facts becomes a mark of the other, by being a mark of a mark of
+a mark of it.
+
+
+
+
+CHAPTER V.
+
+OF DEMONSTRATION, AND NECESSARY TRUTHS.
+
+
+� 1. If, as laid down in the two preceding chapters, the foundation of
+all sciences, even deductive or demonstrative sciences, is Induction; if
+every step in the ratiocinations even of geometry is an act of
+induction; and if a train of reasoning is but bringing many inductions
+to bear upon the same subject of inquiry, and drawing a case within one
+induction by means of another; wherein lies the peculiar certainty
+always ascribed to the sciences which are entirely, or almost entirely,
+deductive? Why are they called the Exact Sciences? Why are mathematical
+certainty, and the evidence of demonstration, common phrases to express
+the very highest degree of assurance attainable by reason? Why are
+mathematics by almost all philosophers, and (by some) even those
+branches of natural philosophy which, through the medium of mathematics,
+have been converted into deductive sciences, considered to be
+independent of the evidence of experience and observation, and
+characterized as systems of Necessary Truth?
+
+The answer I conceive to be, that this character of necessity, ascribed
+to the truths of mathematics, and even (with some reservations to be
+hereafter made) the peculiar certainty attributed to them, is an
+illusion; in order to sustain which, it is necessary to suppose that
+those truths relate to, and express the properties of, purely imaginary
+objects. It is acknowledged that the conclusions of geometry are
+deduced, partly at least, from the so-called Definitions, and that those
+definitions are assumed to be correct representations, as far as they
+go, of the objects with which geometry is conversant. Now we have
+pointed out that, from a definition as such, no proposition, unless it
+be one concerning the meaning of a word, can ever follow; and that what
+apparently follows from a definition, follows in reality from an
+implied assumption that there exists a real thing conformable thereto.
+This assumption, in the case of the definitions of geometry, is false:
+there exist no real things exactly conformable to the definitions. There
+exist no points without magnitude; no lines without breadth, nor
+perfectly straight; no circles with all their radii exactly equal, nor
+squares with all their angles perfectly right. It will perhaps be said
+that the assumption does not extend to the actual, but only to the
+possible, existence of such things. I answer that, according to any test
+we have of possibility, they are not even possible. Their existence, so
+far as we can form any judgment, would seem to be inconsistent with the
+physical constitution of our planet at least, if not of the universe. To
+get rid of this difficulty, and at the same time to save the credit of
+the supposed system of necessary truth, it is customary to say that the
+points, lines, circles, and squares which are the subject of geometry,
+exist in our conceptions merely, and are part of our minds; which minds,
+by working on their own materials, construct an _� priori_ science, the
+evidence of which is purely mental, and has nothing whatever to do with
+outward experience. By howsoever high authorities this doctrine may have
+been sanctioned, it appears to me psychologically incorrect. The points,
+lines, circles, and squares, which any one has in his mind, are (I
+apprehend) simply copies of the points, lines, circles, and squares
+which he has known in his experience. Our idea of a point, I apprehend
+to be simply our idea of the _minimum visibile_, the smallest portion of
+surface which we can see. A line, as defined by geometers, is wholly
+inconceivable. We can reason about a line as if it had no breadth;
+because we have a power, which is the foundation of all the control we
+can exercise over the operations of our minds; the power, when a
+perception is present to our senses, or a conception to our intellects,
+of _attending_ to a part only of that perception or conception, instead
+of the whole. But we cannot _conceive_ a line without breadth; we can
+form no mental picture of such a line: all the lines which we have in
+our minds are lines possessing breadth. If any one doubts this, we may
+refer him to his own experience. I much question if any one who fancies
+that he can conceive what is called a mathematical line, thinks so from
+the evidence of his consciousness: I suspect it is rather because he
+supposes that unless such a conception were possible, mathematics could
+not exist as a science: a supposition which there will be no difficulty
+in showing to be entirely groundless.
+
+Since, then, neither in nature, nor in the human mind, do there exist
+any objects exactly corresponding to the definitions of geometry, while
+yet that science cannot be supposed to be conversant about non-entities;
+nothing remains but to consider geometry as conversant with such lines,
+angles, and figures, as really exist; and the definitions, as they are
+called, must be regarded as some of our first and most obvious
+generalizations concerning those natural objects. The correctness of
+those generalizations, as generalizations, is without a flaw: the
+equality of all the radii of a circle is true of all circles, so far as
+it is true of any one: but it is not exactly true of any circle; it is
+only nearly true; so nearly that no error of any importance in practice
+will be incurred by feigning it to be exactly true. When we have
+occasion to extend these inductions, or their consequences, to cases in
+which the error would be appreciable--to lines of perceptible breadth or
+thickness, parallels which deviate sensibly from equidistance, and the
+like--we correct our conclusions, by combining with them a fresh set of
+propositions relating to the aberration; just as we also take in
+propositions relating to the physical or chemical properties of the
+material, if those properties happen to introduce any modification into
+the result; which they easily may, even with respect to figure and
+magnitude, as in the case, for instance, of expansion by heat. So long,
+however, as there exists no practical necessity for attending to any of
+the properties of the object except its geometrical properties, or to
+any of the natural irregularities in those, it is convenient to neglect
+the consideration of the other properties and of the irregularities, and
+to reason as if these did not exist: accordingly, we formally announce
+in the definitions, that we intend to proceed on this plan. But it is
+an error to suppose, because we resolve to confine our attention to a
+certain number of the properties of an object, that we therefore
+conceive, or have an idea of, the object, denuded of its other
+properties. We are thinking, all the time, of precisely such objects as
+we have seen and touched, and with all the properties which naturally
+belong to them; but, for scientific convenience, we feign them to be
+divested of all properties, except those which are material to our
+purpose, and in regard to which we design to consider them.
+
+The peculiar accuracy, supposed to be characteristic of the first
+principles of geometry, thus appears to be fictitious. The assertions on
+which the reasonings of the science are founded, do not, any more than
+in other sciences, exactly correspond with the fact; but we suppose that
+they do so, for the sake of tracing the consequences which follow from
+the supposition. The opinion of Dugald Stewart respecting the
+foundations of geometry, is, I conceive, substantially correct; that it
+is built on hypotheses; that it owes to this alone the peculiar
+certainty supposed to distinguish it; and that in any science whatever,
+by reasoning from a set of hypotheses, we may obtain a body of
+conclusions as certain as those of geometry, that is, as strictly in
+accordance with the hypotheses, and as irresistibly compelling assent,
+_on condition_ that those hypotheses are true.
+
+When, therefore, it is affirmed that the conclusions of geometry are
+necessary truths, the necessity consists in reality only in this, that
+they correctly follow from the suppositions from which they are deduced.
+Those suppositions are so far from being necessary, that they are not
+even true; they purposely depart, more or less widely, from the truth.
+The only sense in which necessity can be ascribed to the conclusions of
+any scientific investigation, is that of legitimately following from
+some assumption, which, by the conditions of the inquiry, is not to be
+questioned. In this relation, of course, the derivative truths of every
+deductive science must stand to the inductions, or assumptions, on which
+the science is founded, and which, whether true or untrue, certain or
+doubtful in themselves, are always supposed certain for the purposes of
+the particular science. And therefore the conclusions of all deductive
+sciences were said by the ancients to be necessary propositions. We have
+observed already that to be predicated necessarily was characteristic of
+the predicable Proprium, and that a proprium was any property of a thing
+which could be deduced from its essence, that is, from the properties
+included in its definition.
+
+
+� 2. The important doctrine of Dugald Stewart, which I have endeavoured
+to enforce, has been contested by Dr. Whewell, both in the dissertation
+appended to his excellent _Mechanical Euclid_, and in his elaborate work
+on the _Philosophy of the Inductive Sciences_; in which last he also
+replies to an article in the Edinburgh Review, (ascribed to a writer of
+great scientific eminence), in which Stewart's opinion was defended
+against his former strictures. The supposed refutation of Stewart
+consists in proving against him (as has also been done in this work)
+that the premises of geometry are not definitions, but assumptions of
+the real existence of things corresponding to those definitions. This,
+however, is doing little for Dr. Whewell's purpose; for it is these very
+assumptions which are asserted to be hypotheses, and which he, if he
+denies that geometry is founded on hypotheses, must show to be absolute
+truths. All he does, however, is to observe, that they at any rate, are
+not _arbitrary_ hypotheses; that we should not be at liberty to
+substitute other hypotheses for them; that not only "a definition, to be
+admissible, must necessarily refer to and agree with some conception
+which we can distinctly frame in our thoughts," but that the straight
+lines, for instance, which we define, must be "those by which angles are
+contained, those by which triangles are bounded, those of which
+parallelism may be predicated, and the like."[19] And this is true; but
+this has never been contradicted. Those who say that the premises of
+geometry are hypotheses, are not bound to maintain them to be hypotheses
+which have no relation whatever to fact. Since an hypothesis framed for
+the purpose of scientific inquiry must relate to something which has
+real existence, (for there can be no science respecting non-entities,)
+it follows that any hypothesis we make respecting an object, to
+facilitate our study of it, must not involve anything which is
+distinctly false, and repugnant to its real nature: we must not ascribe
+to the thing any property which it has not; our liberty extends only to
+slightly exaggerating some of those which it has, (by assuming it to be
+completely what it really is very nearly,) and suppressing others, under
+the indispensable obligation of restoring them whenever, and in as far
+as, their presence or absence would make any material difference in the
+truth of our conclusions. Of this nature, accordingly, are the first
+principles involved in the definitions of geometry. That the hypotheses
+should be of this particular character, is however no further necessary,
+than inasmuch as no others could enable us to deduce conclusions which,
+with due corrections, would be true of real objects: and in fact, when
+our aim is only to illustrate truths, and not to investigate them, we
+are not under any such restriction. We might suppose an imaginary
+animal, and work out by deduction, from the known laws of physiology,
+its natural history; or an imaginary commonwealth, and from the elements
+composing it, might argue what would be its fate. And the conclusions
+which we might thus draw from purely arbitrary hypotheses, might form a
+highly useful intellectual exercise: but as they could only teach us
+what _would_ be the properties of objects which do not really exist,
+they would not constitute any addition to our knowledge of nature: while
+on the contrary, if the hypothesis merely divests a real object of some
+portion of its properties, without clothing it in false ones, the
+conclusions will always express, under known liability to correction,
+actual truth.
+
+
+� 3. But though Dr. Whewell has not shaken Stewart's doctrine as to the
+hypothetical character of that portion of the first principles of
+geometry which are involved in the so-called definitions, he has, I
+conceive, greatly the advantage of Stewart on another important point in
+the theory of geometrical reasoning; the necessity of admitting, among
+those first principles, axioms as well as definitions. Some of the
+axioms of Euclid might, no doubt, be exhibited in the form of
+definitions, or might be deduced, by reasoning, from propositions
+similar to what are so called. Thus, if instead of the axiom, Magnitudes
+which can be made to coincide are equal, we introduce a definition,
+"Equal magnitudes are those which may be so applied to one another as to
+coincide;" the three axioms which follow (Magnitudes which are equal to
+the same are equal to one another--If equals are added to equals the
+sums are equal--If equals are taken from equals the remainders are
+equal,) may be proved by an imaginary superposition, resembling that by
+which the fourth proposition of the first book of Euclid is
+demonstrated. But though these and several others may be struck out of
+the list of first principles, because, though not requiring
+demonstration, they are susceptible of it; there will be found in the
+list of axioms two or three fundamental truths, not capable of being
+demonstrated: among which must be reckoned the proposition that two
+straight lines cannot inclose a space, (or its equivalent, Straight
+lines which coincide in two points coincide altogether,) and some
+property of parallel lines, other than that which constitutes their
+definition: one of the most suitable for the purpose being that selected
+by Professor Playfair: "Two straight lines which intersect each other
+cannot both of them be parallel to a third straight line."[20]
+
+The axioms, as well those which are indemonstrable as those which admit
+of being demonstrated, differ from that other class of fundamental
+principles which are involved in the definitions, in this, that they
+are true without any mixture of hypothesis. That things which are equal
+to the same thing are equal to one another, is as true of the lines and
+figures in nature, as it would be of the imaginary ones assumed in the
+definitions. In this respect, however, mathematics are only on a par
+with most other sciences. In almost all sciences there are some general
+propositions which are exactly true, while the greater part are only
+more or less distant approximations to the truth. Thus in mechanics, the
+first law of motion (the continuance of a movement once impressed, until
+stopped or slackened by some resisting force) is true without
+qualification or error. The rotation of the earth in twenty-four hours,
+of the same length as in our time, has gone on since the first accurate
+observations, without the increase or diminution of one second in all
+that period. These are inductions which require no fiction to make them
+be received as accurately true: but along with them there are others, as
+for instance the propositions respecting the figure of the earth, which
+are but approximations to the truth; and in order to use them for the
+further advancement of our knowledge, we must feign that they are
+exactly true, though they really want something of being so.
+
+
+� 4. It remains to inquire, what is the ground of our belief in
+axioms--what is the evidence on which they rest? I answer, they are
+experimental truths; generalizations from observation. The proposition,
+Two straight lines cannot inclose a space--or in other words, Two
+straight lines which have once met, do not meet again, but continue to
+diverge--is an induction from the evidence of our senses.
+
+This opinion runs counter to a scientific prejudice of long standing and
+great strength, and there is probably no proposition enunciated in this
+work for which a more unfavourable reception is to be expected. It is,
+however, no new opinion; and even if it were so, would be entitled to be
+judged, not by its novelty, but by the strength of the arguments by
+which it can be supported. I consider it very fortunate that so eminent
+a champion of the contrary opinion as Dr. Whewell, has found occasion
+for a most elaborate treatment of the whole theory of axioms, in
+attempting to construct the philosophy of the mathematical and physical
+sciences on the basis of the doctrine against which I now contend.
+Whoever is anxious that a discussion should go to the bottom of the
+subject, must rejoice to see the opposite side of the question worthily
+represented. If what is said by Dr. Whewell, in support of an opinion
+which he has made the foundation of a systematic work, can be shown not
+to be conclusive, enough will have been done, without going further in
+quest of stronger arguments and a more powerful adversary.
+
+It is not necessary to show that the truths which we call axioms are
+originally _suggested_ by observation, and that we should never have
+known that two straight lines cannot inclose a space if we had never
+seen a straight line: thus much being admitted by Dr. Whewell, and by
+all, in recent times, who have taken his view of the subject. But they
+contend, that it is not experience which _proves_ the axiom; but that
+its truth is perceived _� priori_, by the constitution of the mind
+itself, from the first moment when the meaning of the proposition is
+apprehended; and without any necessity for verifying it by repeated
+trials, as is requisite in the case of truths really ascertained by
+observation.
+
+They cannot, however, but allow that the truth of the axiom, Two
+straight lines cannot inclose a space, even if evident independently of
+experience, is also evident from experience. Whether the axiom needs
+confirmation or not, it receives confirmation in almost every instant of
+our lives; since we cannot look at any two straight lines which
+intersect one another, without seeing that from that point they continue
+to diverge more and more. Experimental proof crowds in upon us in such
+endless profusion, and without one instance in which there can be even a
+suspicion of an exception to the rule, that we should soon have stronger
+ground for believing the axiom, even as an experimental truth, than we
+have for almost any of the general truths which we confessedly learn
+from the evidence of our senses. Independently of _� priori_ evidence,
+we should certainly believe it with an intensity of conviction far
+greater than we accord to any ordinary physical truth: and this too at a
+time of life much earlier than that from which we date almost any part
+of our acquired knowledge, and much too early to admit of our retaining
+any recollection of the history of our intellectual operations at that
+period. Where then is the necessity for assuming that our recognition of
+these truths has a different origin from the rest of our knowledge, when
+its existence is perfectly accounted for by supposing its origin to be
+the same? when the causes which produce belief in all other instances,
+exist in this instance, and in a degree of strength as much superior to
+what exists in other cases, as the intensity of the belief itself is
+superior? The burden of proof lies on the advocates of the contrary
+opinion: it is for them to point out some fact, inconsistent with the
+supposition that this part of our knowledge of nature is derived from
+the same sources as every other part.[21]
+
+This, for instance, they would be able to do, if they could prove
+chronologically that we had the conviction (at least practically) so
+early in infancy as to be anterior to those impressions on the senses,
+upon which, on the other theory, the conviction is founded. This,
+however, cannot be proved: the point being too far back to be within the
+reach of memory, and too obscure for external observation. The advocates
+of the _� priori_ theory are obliged to have recourse to other
+arguments. These are reducible to two, which I shall endeavour to state
+as clearly and as forcibly as possible.
+
+
+� 5. In the first place it is said that if our assent to the proposition
+that two straight lines cannot inclose a space, were derived from the
+senses, we could only be convinced of its truth by actual trial, that
+is, by seeing or feeling the straight lines; whereas in fact it is seen
+to be true by merely thinking of them. That a stone thrown into water
+goes to the bottom, may be perceived by our senses, but mere thinking of
+a stone thrown into the water would never have led us to that
+conclusion: not so, however, with the axioms relating to straight lines:
+if I could be made to conceive what a straight line is, without having
+seen one, I should at once recognise that two such lines cannot inclose
+a space. Intuition is "imaginary looking;"[22] but experience must be
+real looking: if we see a property of straight lines to be true by
+merely fancying ourselves to be looking at them, the ground of our
+belief cannot be the senses, or experience; it must be something mental.
+
+To this argument it might be added in the case of this particular axiom,
+(for the assertion would not be true of all axioms,) that the evidence
+of it from actual ocular inspection is not only unnecessary, but
+unattainable. What says the axiom? That two straight lines _cannot_
+inclose a space; that after having once intersected, if they are
+prolonged to infinity they do not meet, but continue to diverge from one
+another. How can this, in any single case, be proved by actual
+observation? We may follow the lines to any distance we please; but we
+cannot follow them to infinity: for aught our senses can testify, they
+may, immediately beyond the farthest point to which we have traced them,
+begin to approach, and at last meet. Unless, therefore, we had some
+other proof of the impossibility than observation affords us, we should
+have no ground for believing the axiom at all.
+
+To these arguments, which I trust I cannot be accused of understating, a
+satisfactory answer will, I conceive, be found, if we advert to one of
+the characteristic properties of geometrical forms--their capacity of
+being painted in the imagination with a distinctness equal to reality:
+in other words, the exact resemblance of our ideas of form to the
+sensations which suggest them. This, in the first place, enables us to
+make (at least with a little practice) mental pictures of all possible
+combinations of lines and angles, which resemble the realities quite as
+well as any which we could make on paper; and in the next place, make
+those pictures just as fit subjects of geometrical experimentation as
+the realities themselves; inasmuch as pictures, if sufficiently
+accurate, exhibit of course all the properties which would be manifested
+by the realities at one given instant, and on simple inspection: and in
+geometry we are concerned only with such properties, and not with that
+which pictures could not exhibit, the mutual action of bodies one upon
+another. The foundations of geometry would therefore be laid in direct
+experience, even if the experiments (which in this case consist merely
+in attentive contemplation) were practised solely upon what we call our
+ideas, that is, upon the diagrams in our minds, and not upon outward
+objects. For in all systems of experimentation we take some objects to
+serve as representatives of all which resemble them; and in the present
+case the conditions which qualify a real object to be the representative
+of its class, are completely fulfilled by an object existing only in our
+fancy. Without denying, therefore, the possibility of satisfying
+ourselves that two straight lines cannot inclose a space, by merely
+thinking of straight lines without actually looking at them; I contend,
+that we do not believe this truth on the ground of the imaginary
+intuition simply, but because we know that the imaginary lines exactly
+resemble real ones, and that we may conclude from them to real ones with
+quite as much certainty as we could conclude from one real line to
+another. The conclusion, therefore, is still an induction from
+observation. And we should not be authorized to substitute observation
+of the image in our mind, for observation of the reality, if we had not
+learnt by long-continued experience that the properties of the reality
+are faithfully represented in the image; just as we should be
+scientifically warranted in describing an animal which we have never
+seen, from a picture made of it with a daguerreotype; but not until we
+had learnt by ample experience, that observation of such a picture is
+precisely equivalent to observation of the original.
+
+These considerations also remove the objection arising from the
+impossibility of ocularly following the lines in their prolongation to
+infinity. For though, in order actually to see that two given lines
+never meet, it would be necessary to follow them to infinity; yet
+without doing so we may know that if they ever do meet, or if, after
+diverging from one another, they begin again to approach, this must take
+place not at an infinite, but at a finite distance. Supposing,
+therefore, such to be the case, we can transport ourselves thither in
+imagination, and can frame a mental image of the appearance which one or
+both of the lines must present at that point, which we may rely on as
+being precisely similar to the reality. Now, whether we fix our
+contemplation upon this imaginary picture, or call to mind the
+generalizations we have had occasion to make from former ocular
+observation, we learn by the evidence of experience, that a line which,
+after diverging from another straight line, begins to approach to it,
+produces the impression on our senses which we describe by the
+expression, "a bent line," not by the expression, "a straight line."[23]
+
+
+� 6. The first of the two arguments in support of the theory that
+axioms are _� priori_ truths, having, I think, been sufficiently
+answered; I proceed to the second, which is usually the most relied on.
+Axioms (it is asserted) are conceived by us not only as true, but as
+universally and necessarily true. Now, experience cannot possibly give
+to any proposition this character. I may have seen snow a hundred
+times, and may have seen that it was white, but this cannot give me
+entire assurance even that all snow is white; much less that snow _must_
+be white. "However many instances we may have observed of the truth of a
+proposition, there is nothing to assure us that the next case shall not
+be an exception to the rule. If it be strictly true that every ruminant
+animal yet known has cloven hoofs, we still cannot be sure that some
+creature will not hereafter be discovered which has the first of these
+attributes, without having the other.... Experience must always consist
+of a limited number of observations; and, however numerous these may be,
+they can show nothing with regard to the infinite number of cases in
+which the experiment has not been made." Besides, Axioms are not only
+universal, they are also necessary. Now "experience cannot offer the
+smallest ground for the necessity of a proposition. She can observe and
+record what has happened; but she cannot find, in any case, or in any
+accumulation of cases, any reason for what _must_ happen. She may see
+objects side by side; but she cannot see a reason why they must ever be
+side by side. She finds certain events to occur in succession; but the
+succession supplies, in its occurrence, no reason for its recurrence.
+She contemplates external objects; but she cannot detect any internal
+bond, which indissolubly connects the future with the past, the possible
+with the real. To learn a proposition by experience, and to see it to be
+necessarily true, are two altogether different processes of
+thought."[24] And Dr. Whewell adds, "If any one does not clearly
+comprehend this distinction of necessary and contingent truths, he will
+not be able to go along with us in our researches into the foundations
+of human knowledge; nor, indeed, to pursue with success any speculation
+on the subject."[25]
+
+In the following passage, we are told what the distinction is, the
+non-recognition of which incurs this denunciation. "Necessary truths are
+those in which we not only learn that the proposition is true, but see
+that it _must_ be true; in which the negation of the truth is not only
+false, but impossible; in which we cannot, even by an effort of
+imagination, or in a supposition, conceive the reverse of that which is
+asserted. That there are such truths cannot be doubted. We may take, for
+example, all relations of number. Three and Two added together make
+Five. We cannot conceive it to be otherwise. We cannot, by any freak of
+thought, imagine Three and Two to make Seven."[26]
+
+Although Dr. Whewell has naturally and properly employed a variety of
+phrases to bring his meaning more forcibly home, he would, I presume,
+allow that they are all equivalent; and that what he means by a
+necessary truth, would be sufficiently defined, a proposition the
+negation of which is not only false but inconceivable. I am unable to
+find in any of his expressions, turn them what way you will, a meaning
+beyond this, and I do not believe he would contend that they mean
+anything more.
+
+This, therefore, is the principle asserted: that propositions, the
+negation of which is inconceivable, or in other words, which we cannot
+figure to ourselves as being false, must rest on evidence of a higher
+and more cogent description than any which experience can afford.
+
+Now I cannot but wonder that so much stress should be laid on the
+circumstance of inconceivableness, when there is such ample experience
+to show, that our capacity or incapacity of conceiving a thing has very
+little to do with the possibility of the thing in itself; but is in
+truth very much an affair of accident, and depends on the past history
+and habits of our own minds. There is no more generally acknowledged
+fact in human nature, than the extreme difficulty at first felt in
+conceiving anything as possible, which is in contradiction to long
+established and familiar experience; or even to old familiar habits of
+thought. And this difficulty is a necessary result of the fundamental
+laws of the human mind. When we have often seen and thought of two
+things together, and have never in any one instance either seen or
+thought of them separately, there is by the primary law of association
+an increasing difficulty, which may in the end become insuperable, of
+conceiving the two things apart. This is most of all conspicuous in
+uneducated persons, who are in general utterly unable to separate any
+two ideas which have once become firmly associated in their minds; and
+if persons of cultivated intellect have any advantage on the point, it
+is only because, having seen and heard and read more, and being more
+accustomed to exercise their imagination, they have experienced their
+sensations and thoughts in more varied combinations, and have been
+prevented from forming many of these inseparable associations. But this
+advantage has necessarily its limits. The most practised intellect is
+not exempt from the universal laws of our conceptive faculty. If daily
+habit presents to any one for a long period two facts in combination,
+and if he is not led during that period either by accident or by his
+voluntary mental operations to think of them apart, he will probably in
+time become incapable of doing so even by the strongest effort; and the
+supposition that the two facts can be separated in nature, will at last
+present itself to his mind with all the characters of an inconceivable
+phenomenon.[27] There are remarkable instances of this in the history of
+science: instances in which the most instructed men rejected as
+impossible, because inconceivable, things which their posterity, by
+earlier practice and longer perseverance in the attempt, found it quite
+easy to conceive, and which everybody now knows to be true. There was a
+time when men of the most cultivated intellects, and the most
+emancipated from the dominion of early prejudice, could not credit the
+existence of antipodes; were unable to conceive, in opposition to old
+association, the force of gravity acting upwards instead of downwards.
+The Cartesians long rejected the Newtonian doctrine of the
+gravitation of all bodies towards one another, on the faith of
+a general proposition, the reverse of which seemed to them to be
+inconceivable--the proposition that a body cannot act where it is not.
+All the cumbrous machinery of imaginary vortices, assumed without the
+smallest particle of evidence, appeared to these philosophers a more
+rational mode of explaining the heavenly motions, than one which
+involved what seemed to them so great an absurdity.[28] And they no
+doubt found it as impossible to conceive that a body should act upon the
+earth at the distance of the sun or moon, as we find it to conceive an
+end to space or time, or two straight lines inclosing a space. Newton
+himself had not been able to realize the conception, or we should not
+have had his hypothesis of a subtle ether, the occult cause of
+gravitation; and his writings prove, that though he deemed the
+particular nature of the intermediate agency a matter of conjecture, the
+necessity of _some_ such agency appeared to him indubitable. It would
+seem that even now the majority of scientific men have not completely
+got over this very difficulty; for though they have at last learnt to
+conceive the sun _attracting_ the earth without any intervening fluid,
+they cannot yet conceive the sun _illuminating_ the earth without some
+such medium.
+
+If, then, it be so natural to the human mind, even in a high state of
+culture, to be incapable of conceiving, and on that ground to believe
+impossible, what is afterwards not only found to be conceivable but
+proved to be true; what wonder if in cases where the association is
+still older, more confirmed, and more familiar, and in which nothing
+ever occurs to shake our conviction, or even suggest to us any
+conception at variance with the association, the acquired incapacity
+should continue, and be mistaken for a natural incapacity? It is true,
+our experience of the varieties in nature enables us, within certain
+limits, to conceive other varieties analogous to them. We can conceive
+the sun or moon falling; for though we never saw them fall, nor ever
+perhaps imagined them falling, we have seen so many other things fall,
+that we have innumerable familiar analogies to assist the conception;
+which, after all, we should probably have some difficulty in framing,
+were we not well accustomed to see the sun and moon move (or appear to
+move,) so that we are only called upon to conceive a slight change in
+the direction of motion, a circumstance familiar to our experience. But
+when experience affords no model on which to shape the new conception,
+how is it possible for us to form it? How, for example, can we imagine
+an end to space or time? We never saw any object without something
+beyond it, nor experienced any feeling without something following it.
+When, therefore, we attempt to conceive the last point of space, we have
+the idea irresistibly raised of other points beyond it. When we try to
+imagine the last instant of time, we cannot help conceiving another
+instant after it. Nor is there any necessity to assume, as is done by a
+modern school of metaphysicians, a peculiar fundamental law of the mind
+to account for the feeling of infinity inherent in our conceptions of
+space and time; that apparent infinity is sufficiently accounted for by
+simpler and universally acknowledged laws.
+
+Now, in the case of a geometrical axiom, such, for example, as that two
+straight lines cannot inclose a space,--a truth which is testified to us
+by our very earliest impressions of the external world,--how is it
+possible (whether those external impressions be or be not the ground of
+our belief) that the reverse of the proposition _could_ be otherwise
+than inconceivable to us? What analogy have we, what similar order of
+facts in any other branch of our experience, to facilitate to us the
+conception of two straight lines inclosing a space? Nor is even this
+all. I have already called attention to the peculiar property of our
+impressions of form, that the ideas or mental images exactly resemble
+their prototypes, and adequately represent them for the purposes of
+scientific observation. From this, and from the intuitive character of
+the observation, which in this case reduces itself to simple inspection,
+we cannot so much as call up in our imagination two straight lines, in
+order to attempt to conceive them inclosing a space, without by that
+very act repeating the scientific experiment which establishes the
+contrary. Will it really be contended that the inconceivableness of the
+thing, in such circumstances, proves anything against the experimental
+origin of the conviction? Is it not clear that in whichever mode our
+belief in the proposition may have originated, the impossibility of our
+conceiving the negative of it must, on either hypothesis, be the same?
+As, then, Dr. Whewell exhorts those who have any difficulty in
+recognising the distinction held by him between necessary and contingent
+truths, to study geometry,--a condition which I can assure him I have
+conscientiously fulfilled,--I, in return, with equal confidence, exhort
+those who agree with him, to study the general laws of association;
+being convinced that nothing more is requisite than a moderate
+familiarity with those laws, to dispel the illusion which ascribes a
+peculiar necessity to our earliest inductions from experience, and
+measures the possibility of things in themselves, by the human capacity
+of conceiving them.
+
+I hope to be pardoned for adding, that Dr. Whewell himself has both
+confirmed by his testimony the effect of habitual association in giving
+to an experimental truth the appearance of a necessary one, and afforded
+a striking instance of that remarkable law in his own person. In his
+_Philosophy of the Inductive Sciences_ he continually asserts, that
+propositions which not only are not self-evident, but which we know to
+have been discovered gradually, and by great efforts of genius and
+patience, have, when once established, appeared so self-evident that,
+but for historical proof, it would have been impossible to conceive that
+they had not been recognised from the first by all persons in a sound
+state of their faculties. "We now despise those who, in the Copernican
+controversy, could not conceive the apparent motion of the sun on the
+heliocentric hypothesis; or those who, in opposition to Galileo, thought
+that a uniform force might be that which generated a velocity
+proportional to the space; or those who held there was something absurd
+in Newton's doctrine of the different refrangibility of differently
+coloured rays; or those who imagined that when elements combine, their
+sensible qualities must be manifest in the compound; or those who were
+reluctant to give up the distinction of vegetables into herbs, shrubs,
+and trees. We cannot help thinking that men must have been singularly
+dull of comprehension, to find a difficulty in admitting what is to us
+so plain and simple. We have a latent persuasion that we in their place
+should have been wiser and more clear-sighted; that we should have taken
+the right side, and given our assent at once to the truth. Yet in
+reality such a persuasion is a mere delusion. The persons who, in such
+instances as the above, were on the losing side, were very far, in most
+cases, from being persons more prejudiced, or stupid, or narrow-minded,
+than the greater part of mankind now are; and the cause for which they
+fought was far from being a manifestly bad one, till it had been so
+decided by the result of the war.... So complete has been the victory of
+truth in most of these instances, that at present we can hardly imagine
+the struggle to have been necessary. _The very essence of these triumphs
+is, that they lead us to regard the views we reject as not only false
+but inconceivable._"[29]
+
+This last proposition is precisely what I contend for; and I ask no
+more, in order to overthrow the whole theory of its author on the nature
+of the evidence of axioms. For what is that theory? That the truth of
+axioms cannot have been learnt from experience, because their falsity is
+inconceivable. But Dr. Whewell himself says, that we are continually
+led, by the natural progress of thought, to regard as inconceivable what
+our forefathers not only conceived but believed, nay even (he might
+have added) were unable to conceive the reverse of. He cannot intend to
+justify this mode of thought: he cannot mean to say, that we can be
+right in regarding as inconceivable what others have conceived, and as
+self-evident what to others did not appear evident at all. After so
+complete an admission that inconceivableness is an accidental thing, not
+inherent in the phenomenon itself, but dependent on the mental history
+of the person who tries to conceive it, how can he ever call upon us to
+reject a proposition as impossible on no other ground than its
+inconceivableness? Yet he not only does so, but has unintentionally
+afforded some of the most remarkable examples which can be cited of the
+very illusion which he has himself so clearly pointed out. I select as
+specimens, his remarks on the evidence of the three laws of motion, and
+of the atomic theory.
+
+With respect to the laws of motion, Dr. Whewell says: "No one can doubt
+that, in historical fact, these laws were collected from experience.
+That such is the case, is no matter of conjecture. We know the time, the
+persons, the circumstances, belonging to each step of each
+discovery."[30] After this testimony, to adduce evidence of the fact
+would be superfluous. And not only were these laws by no means
+intuitively evident, but some of them were originally paradoxes. The
+first law was especially so. That a body, once in motion, would continue
+for ever to move in the same direction with undiminished velocity unless
+acted upon by some new force, was a proposition which mankind found for
+a long time the greatest difficulty in crediting. It stood opposed to
+apparent experience of the most familiar kind, which taught that it was
+the nature of motion to abate gradually, and at last terminate of
+itself. Yet when once the contrary doctrine was firmly established,
+mathematicians, as Dr. Whewell observes, speedily began to believe that
+laws, thus contradictory to first appearances, and which, even after
+full proof had been obtained, it had required generations to render
+familiar to the minds of the scientific world, were under "a
+demonstrable necessity, compelling them to be such as they are and no
+other;" and he himself, though not venturing "absolutely to pronounce"
+that _all_ these laws "can be rigorously traced to an absolute necessity
+in the nature of things,"[31] does actually so think of the law just
+mentioned; of which he says: "Though the discovery of the first law of
+motion was made, historically speaking, by means of experiment, we have
+now attained a point of view in which we see that it might have been
+certainly known to be true, independently of experience."[32] Can there
+be a more striking exemplification than is here afforded, of the effect
+of association which we have described? Philosophers, for generations,
+have the most extraordinary difficulty in putting certain ideas
+together; they at last succeed in doing so; and after a sufficient
+repetition of the process, they first fancy a natural bond between the
+ideas, then experience a growing difficulty, which at last, by the
+continuation of the same progress, becomes an impossibility, of severing
+them from one another. If such be the progress of an experimental
+conviction of which the date is of yesterday, and which is in opposition
+to first appearances, how must it fare with those which are conformable
+to appearances familiar from the first dawn of intelligence, and of the
+conclusiveness of which, from the earliest records of human thought, no
+sceptic has suggested even a momentary doubt?
+
+The other instance which I shall quote is a truly astonishing one, and
+may be called the _reductio ad absurdum_ of the theory of
+inconceivableness. Speaking of the laws of chemical composition, Dr.
+Whewell says:[33] "That they could never have been clearly understood,
+and therefore never firmly established, without laborious and exact
+experiments, is certain; but yet we may venture to say, that being once
+known, they possess an evidence beyond that of mere experiment. _For how
+in fact can we conceive combinations, otherwise than as definite in kind
+and quality?_ If we were to suppose each element ready to combine with
+any other indifferently, and indifferently in any quantity, we should
+have a world in which all would be confusion and indefiniteness. There
+would be no fixed kinds of bodies. Salts, and stones, and ores, would
+approach to and graduate into each other by insensible degrees. Instead
+of this, we know that the world consists of bodies distinguishable from
+each other by definite differences, capable of being classified and
+named, and of having general propositions asserted concerning them. And
+as _we cannot conceive a world in which this should not be the case_, it
+would appear that we cannot conceive a state of things in which the laws
+of the combination of elements should not be of that definite and
+measured kind which we have above asserted."
+
+That a philosopher of Dr. Whewell's eminence should gravely assert that
+we cannot conceive a world in which the simple elements should combine
+in other than definite proportions; that by dint of meditating on a
+scientific truth, the original discoverer of which was still living, he
+should have rendered the association in his own mind between the idea of
+combination and that of constant proportions so familiar and intimate as
+to be unable to conceive the one fact without the other; is so signal an
+instance of the mental law for which I am contending, that one word more
+in illustration must be superfluous.
+
+In the latest and most complete elaboration of his metaphysical system
+(the _Philosophy of Discovery_), as well as in the earlier discourse on
+the _Fundamental Antithesis of Philosophy_, reprinted as an appendix to
+that work, Dr. Whewell, while very candidly admitting that his language
+was open to misconception, disclaims having intended to say that mankind
+in general can _now_ perceive the law of definite proportions in
+chemical combination to be a necessary truth. All he meant was that
+philosophical chemists in a future generation may possibly see this.
+"Some truths may be seen by intuition, but yet the intuition of them may
+be a rare and a difficult attainment."[34] And he explains that the
+inconceivableness which, according to his theory, is the test of
+axioms, "depends entirely upon the clearness of the Ideas which the
+axioms involve. So long as those Ideas are vague and indistinct, the
+contrary of an Axiom may be assented to, though it cannot be distinctly
+conceived. It may be assented to, not because it is possible, but
+because we do not see clearly what is possible. To a person who is only
+beginning to think geometrically, there may appear nothing absurd in the
+assertion, that two straight lines may inclose a space. And in the same
+manner, to a person who is only beginning to think of mechanical truths,
+it may not appear to be absurd, that in mechanical processes, Reaction
+should be greater or less than Action; and so, again, to a person who
+has not thought steadily about Substance, it may not appear
+inconceivable, that by chemical operations, we should generate new
+matter, or destroy matter which already exists."[35] Necessary truths,
+therefore, are not those of which we cannot conceive, but "those of
+which we cannot _distinctly_ conceive, the contrary."[36] So long as our
+ideas are indistinct altogether, we do not know what is or is not
+capable of being distinctly conceived; but, by the ever increasing
+distinctness with which scientific men apprehend the general conceptions
+of science, they in time come to perceive that there are certain laws of
+nature, which, though historically and as a matter of fact they were
+learnt from experience, we cannot, now that we know them, distinctly
+conceive to be other than they are.
+
+The account which I should give of this progress of the scientific mind
+is somewhat different. After a general law of nature has been
+ascertained, men's minds do not at first acquire a complete facility of
+familiarly representing to themselves the phenomena of nature in the
+character which that law assigns to them. The habit which constitutes
+the scientific cast of mind, that of conceiving facts of all
+descriptions conformably to the laws which regulate them--phenomena of
+all descriptions according to the relations which have been ascertained
+really to exist between them; this habit, in the case of newly
+discovered relations, comes only by degrees. So long as it is not
+thoroughly formed, no necessary character is ascribed to the new truth.
+But in time, the philosopher attains a state of mind in which his mental
+picture of nature spontaneously represents to him all the phenomena with
+which the new theory is concerned, in the exact light in which the
+theory regards them: all images or conceptions derived from any other
+theory, or from the confused view of the facts which is anterior to any
+theory, having entirely disappeared from his mind. The mode of
+representing facts which results from the theory, has now become, to his
+faculties, the only natural mode of conceiving them. It is a known
+truth, that a prolonged habit of arranging phenomena in certain groups,
+and explaining them by means of certain principles, makes any other
+arrangement or explanation of these facts be felt as unnatural: and it
+may at last become as difficult to him to represent the facts to himself
+in any other mode, as it often was, originally, to represent them in
+that mode.
+
+But, further, if the theory is true, as we are supposing it to be, any
+other mode in which he tries, or in which he was formerly accustomed, to
+represent the phenomena, will be seen by him to be inconsistent with the
+facts that suggested the new theory--facts which now form a part of his
+mental picture of nature. And since a contradiction is always
+inconceivable, his imagination rejects these false theories, and
+declares itself incapable of conceiving them. Their inconceivableness to
+him does not, however, result from anything in the theories themselves,
+intrinsically and _� priori_ repugnant to the human faculties; it
+results from the repugnance between them and a portion of the facts;
+which facts as long as he did not know, or did not distinctly realize in
+his mental representations, the false theory did not appear other than
+conceivable; it becomes inconceivable, merely from the fact that
+contradictory elements cannot be combined in the same conception.
+Although, then, his real reason for rejecting theories at variance with
+the true one, is no other than that they clash with his experience, he
+easily falls into the belief, that he rejects them because they are
+inconceivable, and that he adopts the true theory because it is
+self-evident, and does not need the evidence of experience at all.
+
+This I take to be the real and sufficient explanation of the paradoxical
+truth, on which so much stress is laid by Dr. Whewell, that a
+scientifically cultivated mind is actually, in virtue of that
+cultivation, unable to conceive suppositions which a common man
+conceives without the smallest difficulty. For there is nothing
+inconceivable in the suppositions themselves; the impossibility is in
+combining them with facts inconsistent with them, as part of the same
+mental picture; an obstacle of course only felt by those who know the
+facts, and are able to perceive the inconsistency. As far as the
+suppositions themselves are concerned, in the case of many of Dr.
+Whewell's necessary truths the negative of the axiom is, and probably
+will be as long as the human race lasts, as easily conceivable as the
+affirmative. There is no axiom (for example) to which Dr. Whewell
+ascribes a more thorough character of necessity and self-evidence, than
+that of the indestructibility of matter. That this is a true law of
+nature I fully admit; but I imagine there is no human being to whom the
+opposite supposition is inconceivable--who has any difficulty in
+imagining a portion of matter annihilated: inasmuch as its apparent
+annihilation, in no respect distinguishable from real by our unassisted
+senses, takes place every time that water dries up, or fuel is consumed.
+Again, the law that bodies combine chemically in definite proportions is
+undeniably true; but few besides Dr. Whewell have reached the point
+which he seems personally to have arrived at, (though he only dares
+prophesy similar success to the multitude after the lapse of
+generations,) that of being unable to conceive a world in which the
+elements are ready to combine with one another "indifferently in any
+quantity;" nor is it likely that we shall ever rise to this sublime
+height of inability, so long as all the mechanical mixtures in our
+planet, whether solid, liquid, or a�riform, exhibit to our daily
+observation the very phenomenon declared to be inconceivable.
+
+According to Dr. Whewell, these and similar laws of nature cannot be
+drawn from experience, inasmuch as they are, on the contrary, assumed
+in the interpretation of experience. Our inability to "add to or
+diminish the quantity of matter in the world," is a truth which "neither
+is nor can be derived from experience; for the experiments which we make
+to verify it presuppose its truth.... When men began to use the balance
+in chemical analysis, they did not prove by trial, but took for granted,
+as self-evident, that the weight of the whole must be found in the
+aggregate weight of the elements."[37] True, it is assumed; but, I
+apprehend, no otherwise than as all experimental inquiry assumes
+provisionally some theory or hypothesis, which is to be finally held
+true or not, according as the experiments decide. The hypothesis chosen
+for this purpose will naturally be one which groups together some
+considerable number of facts already known. The proposition that the
+material of the world, as estimated by weight, is neither increased nor
+diminished by any of the processes of nature or art, had many
+appearances in its favour to begin with. It expressed truly a great
+number of familiar facts. There were other facts which it had the
+appearance of conflicting with, and which made its truth, as an
+universal law of nature, at first doubtful. Because it was doubtful,
+experiments were devised to verify it. Men assumed its truth
+hypothetically, and proceeded to try whether, on more careful
+examination, the phenomena which apparently pointed to a different
+conclusion, would not be found to be consistent with it. This turned out
+to be the case; and from that time the doctrine took its place as an
+universal truth, but as one proved to be such by experience. That the
+theory itself preceded the proof of its truth--that it had to be
+conceived before it could be proved, and in order that it might be
+proved--does not imply that it was self-evident, and did not need proof.
+Otherwise all the true theories in the sciences are necessary and
+self-evident; for no one knows better than Dr. Whewell that they all
+began by being assumed, for the purpose of connecting them by deductions
+with those facts of experience on which, as evidence, they now
+confessedly rest.[38]
+
+
+
+
+CHAPTER VI.
+
+THE SAME SUBJECT CONTINUED.
+
+
+� 1. In the examination which formed the subject of the last chapter,
+into the nature of the evidence of those deductive sciences which are
+commonly represented to be systems of necessary truth, we have been led
+to the following conclusions. The results of those sciences are indeed
+necessary, in the sense of necessarily following from certain first
+principles, commonly called axioms and definitions; that is, of being
+certainly true if those axioms and definitions are so; for the word
+necessity, even in this acceptation of it, means no more than certainty.
+But their claim to the character of necessity in any sense beyond this,
+as implying an evidence independent of and superior to observation and
+experience, must depend on the previous establishment of such a claim in
+favour of the definitions and axioms themselves. With regard to axioms,
+we found that, considered as experimental truths, they rest on
+superabundant and obvious evidence. We inquired, whether, since this is
+the case, it be imperative to suppose any other evidence of those truths
+than experimental evidence, any other origin for our belief of them than
+an experimental origin. We decided, that the burden of proof lies with
+those who maintain the affirmative, and we examined, at considerable
+length, such arguments as they have produced. The examination having led
+to the rejection of those arguments, we have thought ourselves warranted
+in concluding that axioms are but a class, the most universal class, of
+inductions from experience; the simplest and easiest cases of
+generalization from the facts furnished to us by our senses or by our
+internal consciousness.
+
+While the axioms of demonstrative sciences thus appeared to be
+experimental truths, the definitions, as they are incorrectly called, in
+those sciences, were found by us to be generalizations from experience
+which are not even, accurately speaking, truths; being propositions in
+which, while we assert of some kind of object, some property or
+properties which observation shows to belong to it, we at the same time
+deny that it possesses any other properties, though in truth other
+properties do in every individual instance accompany, and in almost all
+instances modify, the property thus exclusively predicated. The denial,
+therefore, is a mere fiction, or supposition, made for the purpose of
+excluding the consideration of those modifying circumstances, when their
+influence is of too trifling amount to be worth considering, or
+adjourning it, when important, to a more convenient moment.
+
+From these considerations it would appear that Deductive or
+Demonstrative Sciences are all, without exception, Inductive Sciences;
+that their evidence is that of experience; but that they are also, in
+virtue of the peculiar character of one indispensable portion of the
+general formul� according to which their inductions are made,
+Hypothetical Sciences. Their conclusions are only true on certain
+suppositions, which are, or ought to be, approximations to the truth,
+but are seldom, if ever, exactly true; and to this hypothetical
+character is to be ascribed the peculiar certainty, which is supposed to
+be inherent in demonstration.
+
+What we have now asserted, however, cannot be received as universally
+true of Deductive or Demonstrative Sciences, until verified by being
+applied to the most remarkable of all those sciences, that of Numbers;
+the theory of the Calculus; Arithmetic and Algebra. It is harder to
+believe of the doctrines of this science than of any other, either that
+they are not truths _� priori_, but experimental truths, or that their
+peculiar certainty is owing to their being not absolute but only
+conditional truths. This, therefore, is a case which merits examination
+apart; and the more so, because on this subject we have a double set of
+doctrines to contend with; that of the _� priori_ philosophers on one
+side; and on the other, a theory the most opposite to theirs, which was
+at one time very generally received, and is still far from being
+altogether exploded, among metaphysicians.
+
+
+� 2. This theory attempts to solve the difficulty apparently inherent in
+the case, by representing the propositions of the science of numbers as
+merely verbal, and its processes as simple transformations of language,
+substitutions of one expression for another. The proposition, Two and
+one are equal to three, according to these writers, is not a truth, is
+not the assertion of a really existing fact, but a definition of the
+word three; a statement that mankind have agreed to use the name three
+as a sign exactly equivalent to two and one; to call by the former name
+whatever is called by the other more clumsy phrase. According to this
+doctrine, the longest process in algebra is but a succession of changes
+in terminology, by which equivalent expressions are substituted one for
+another; a series of translations of the same fact, from one into
+another language; though how, after such a series of translations, the
+fact itself comes out changed (as when we demonstrate a new geometrical
+theorem by algebra,) they have not explained; and it is a difficulty
+which is fatal to their theory.
+
+It must be acknowledged that there are peculiarities in the processes of
+arithmetic and algebra which render the theory in question very
+plausible, and have not unnaturally made those sciences the stronghold
+of Nominalism. The doctrine that we can discover facts, detect the
+hidden processes of nature, by an artful manipulation of language, is so
+contrary to common sense, that a person must have made some advances in
+philosophy to believe it: men fly to so paradoxical a belief to avoid,
+as they think, some even greater difficulty, which the vulgar do not
+see. What has led many to believe that reasoning is a mere verbal
+process, is, that no other theory seemed reconcileable with the nature
+of the Science of Numbers. For we do not carry any ideas along with us
+when we use the symbols of arithmetic or of algebra. In a geometrical
+demonstration we have a mental diagram, if not one on paper; AB, AC, are
+present to our imagination as lines, intersecting other lines, forming
+an angle with one another, and the like; but not so _a_ and _b_. These
+may represent lines or any other magnitudes, but those magnitudes are
+never thought of; nothing is realized in our imagination but _a_ and
+_b_. The ideas which, on the particular occasion, they happen to
+represent, are banished from the mind during every intermediate part of
+the process, between the beginning, when the premises are translated
+from things into signs, and the end, when the conclusion is translated
+back from signs into things. Nothing, then, being in the reasoner's mind
+but the symbols, what can seem more inadmissible than to contend that
+the reasoning process has to do with anything more? We seem to have come
+to one of Bacon's Prerogative Instances; an _experimentum crucis_ on the
+nature of reasoning itself.
+
+Nevertheless, it will appear on consideration, that this apparently so
+decisive instance is no instance at all; that there is in every step of
+an arithmetical or algebraical calculation a real induction, a real
+inference of facts from facts; and that what disguises the induction is
+simply its comprehensive nature, and the consequent extreme generality
+of the language. All numbers must be numbers of something: there are no
+such things as numbers in the abstract. _Ten_ must mean ten bodies, or
+ten sounds, or ten beatings of the pulse. But though numbers must be
+numbers of something, they may be numbers of anything. Propositions,
+therefore, concerning numbers, have the remarkable peculiarity that they
+are propositions concerning all things whatever; all objects, all
+existences of every kind, known to our experience. All things possess
+quantity; consist of parts which can be numbered; and in that character
+possess all the properties which are called properties of numbers. That
+half of four is two, must be true whatever the word four represents,
+whether four hours, four miles, or four pounds weight. We need only
+conceive a thing divided into four equal parts, (and all things may be
+conceived as so divided,) to be able to predicate of it every property
+of the number four, that is, every arithmetical proposition in which the
+number four stands on one side of the equation. Algebra extends the
+generalization still farther: every number represents that particular
+number of all things without distinction, but every algebraical symbol
+does more, it represents all numbers without distinction. As soon as we
+conceive a thing divided into equal parts, without knowing into what
+number of parts, we may call it _a_ or _x_, and apply to it, without
+danger of error, every algebraical formula in the books. The
+proposition, _2(a + b) = 2a + 2b_, is a truth co-extensive with all
+nature. Since then algebraical truths are true of all things whatever,
+and not, like those of geometry, true of lines only or angles only, it
+is no wonder that the symbols should not excite in our minds ideas of
+any things in particular. When we demonstrate the forty-seventh
+proposition of Euclid, it is not necessary that the words should raise
+in us an image of all right-angled triangles, but only of some one
+right-angled triangle: so in algebra we need not, under the symbol _a_,
+picture to ourselves all things whatever, but only some one thing; why
+not, then, the letter itself? The mere written characters, _a_, _b_,
+_x_, _y_, _z_, serve as well for representatives of Things in general,
+as any more complex and apparently more concrete conception. That we are
+conscious of them however in their character of things, and not of mere
+signs, is evident from the fact that our whole process of reasoning is
+carried on by predicating of them the properties of things. In resolving
+an algebraic equation, by what rules do we proceed? By applying at each
+step to _a_, _b_, and _x_, the proposition that equals added to equals
+make equals; that equals taken from equals leave equals; and other
+propositions founded on these two. These are not properties of language,
+or of signs as such, but of magnitudes, which is as much as to say, of
+all things. The inferences, therefore, which are successively drawn, are
+inferences concerning things, not symbols; though as any Things whatever
+will serve the turn, there is no necessity for keeping the idea of the
+Thing at all distinct, and consequently the process of thought may, in
+this case, be allowed without danger to do what all processes of
+thought, when they have been performed often, will do if permitted,
+namely, to become entirely mechanical. Hence the general language of
+algebra comes to be used familiarly without exciting ideas, as all
+other general language is prone to do from mere habit, though in no
+other case than this can it be done with complete safety. But when we
+look back to see from whence the probative force of the process is
+derived, we find that at every single step, unless we suppose ourselves
+to be thinking and talking of the things, and not the mere symbols, the
+evidence fails.
+
+There is another circumstance, which, still more than that which we have
+now mentioned, gives plausibility to the notion that the propositions of
+arithmetic and algebra are merely verbal. That is, that when considered
+as propositions respecting Things, they all have the appearance of being
+identical propositions. The assertion, Two and one are equal to three,
+considered as an assertion respecting objects, as for instance "Two
+pebbles and one pebble are equal to three pebbles," does not affirm
+equality between two collections of pebbles, but absolute identity. It
+affirms that if we put one pebble to two pebbles, those very pebbles are
+three. The objects, therefore, being the very same, and the mere
+assertion that "objects are themselves" being insignificant, it seems
+but natural to consider the proposition, Two and one are equal to three,
+as asserting mere identity of signification between the two names.
+
+This, however, though it looks so plausible, will not bear examination.
+The expression "two pebbles and one pebble," and the expression, "three
+pebbles," stand indeed for the same aggregation of objects, but they by
+no means stand for the same physical fact. They are names of the same
+objects, but of those objects in two different states: though they
+_de_note the same things, their _con_notation is different. Three
+pebbles in two separate parcels, and three pebbles in one parcel, do not
+make the same impression on our senses; and the assertion that the very
+same pebbles may by an alteration of place and arrangement be made to
+produce either the one set of sensations or the other, though a very
+familiar proposition, is not an identical one. It is a truth known to us
+by early and constant experience: an inductive truth; and such truths
+are the foundation of the science of Number. The fundamental truths of
+that science all rest on the evidence of sense; they are proved by
+showing to our eyes and our fingers that any given number of objects,
+ten balls for example, may by separation and re-arrangement exhibit to
+our senses all the different sets of numbers the sum of which is equal
+to ten. All the improved methods of teaching arithmetic to children
+proceed on a knowledge of this fact. All who wish to carry the child's
+_mind_ along with them in learning arithmetic; all who wish to teach
+numbers, and not mere ciphers--now teach it through the evidence of the
+senses, in the manner we have described.
+
+We may, if we please, call the proposition, "Three is two and one," a
+definition of the number three, and assert that arithmetic, as it has
+been asserted that geometry, is a science founded on definitions. But
+they are definitions in the geometrical sense, not the logical;
+asserting not the meaning of a term only, but along with it an observed
+matter of fact. The proposition, "A circle is a figure bounded by a line
+which has all its points equally distant from a point within it," is
+called the definition of a circle; but the proposition from which so
+many consequences follow, and which is really a first principle in
+geometry, is, that figures answering to this description exist. And thus
+we may call "Three is two and one" a definition of three; but the
+calculations which depend on that proposition do not follow from the
+definition itself, but from an arithmetical theorem presupposed in it,
+namely, that collections of objects exist, which while they impress the
+senses thus,
+
+  o o
+   o,
+
+may be separated into two parts, thus,
+
+  o o     o.
+
+This proposition being granted, we term all such parcels Threes, after
+which the enunciation of the above mentioned physical fact will serve
+also for a definition of the word Three.
+
+The Science of Number is thus no exception to the conclusion we
+previously arrived at, that the processes even of deductive sciences are
+altogether inductive, and that their first principles are
+generalizations from experience. It remains to be examined whether this
+science resembles geometry in the further circumstance, that some of its
+inductions are not exactly true; and that the peculiar certainty
+ascribed to it, on account of which its propositions are called
+Necessary Truths, is fictitious and hypothetical, being true in no other
+sense than that those propositions legitimately follow from the
+hypothesis of the truth of premises which are avowedly mere
+approximations to truth.
+
+
+� 3. The inductions of arithmetic are of two sorts: first, those which
+we have just expounded, such as One and one are two, Two and one are
+three, &c., which may be called the definitions of the various numbers,
+in the improper or geometrical sense of the word Definition; and
+secondly, the two following axioms: The sums of equals are equal, The
+differences of equals are equal. These two are sufficient; for the
+corresponding propositions respecting unequals may be proved from these,
+by a _reductio ad absurdum_.
+
+These axioms, and likewise the so-called definitions, are, as has
+already been said, results of induction; true of all objects whatever,
+and, as it may seem, exactly true, without the hypothetical assumption
+of unqualified truth where an approximation to it is all that exists.
+The conclusions, therefore, it will naturally be inferred, are exactly
+true, and the science of number is an exception to other demonstrative
+sciences in this, that the categorical certainty which is predicable of
+its demonstrations is independent of all hypothesis.
+
+On more accurate investigation, however, it will be found that, even in
+this case, there is one hypothetical element in the ratiocination. In
+all propositions concerning numbers, a condition is implied, without
+which none of them would be true; and that condition is an assumption
+which maybe false. The condition, is that 1 = 1; that all the numbers
+are numbers of the same or of equal units. Let this be doubtful, and not
+one of the propositions of arithmetic will hold true. How can we know
+that one pound and one pound make two pounds, if one of the pounds may
+be troy, and the other avoirdupois? They may not make two pounds of
+either, or of any weight. How can we know that a forty-horse power is
+always equal to itself, unless we assume that all horses are of equal
+strength? It is certain that 1 is always equal in _number_ to 1; and
+where the mere number of objects, or of the parts of an object, without
+supposing them to be equivalent in any other respect, is all that is
+material, the conclusions of arithmetic, so far as they go to that
+alone, are true without mixture of hypothesis. There are a few such
+cases; as, for instance, an inquiry into the amount of the population of
+any country. It is indifferent to that inquiry whether they are grown
+people or children, strong or weak, tall or short; the only thing we
+want to ascertain is their number. But whenever, from equality or
+inequality of number, equality or inequality in any other respect is to
+be inferred, arithmetic carried into such inquiries becomes as
+hypothetical a science as geometry. All units must be assumed to be
+equal in that other respect; and this is never accurately true, for one
+actual pound weight is not exactly equal to another, nor one measured
+mile's length to another; a nicer balance, or more accurate measuring
+instruments, would always detect some difference.
+
+What is commonly called mathematical certainty, therefore, which
+comprises the twofold conception of unconditional truth and perfect
+accuracy, is not an attribute of all mathematical truths, but of those
+only which relate to pure Number, as distinguished from Quantity in the
+more enlarged sense; and only so long as we abstain from supposing that
+the numbers are a precise index to actual quantities. The certainty
+usually ascribed to the conclusions of geometry, and even to those of
+mechanics, is nothing whatever but certainty of inference. We can have
+full assurance of particular results under particular suppositions, but
+we cannot have the same assurance that these suppositions are accurately
+true, nor that they include all the data which may exercise an influence
+over the result in any given instance.
+
+
+� 4. It appears, therefore, that the method of all Deductive Sciences is
+hypothetical. They proceed by tracing the consequences of certain
+assumptions; leaving for separate consideration whether the assumptions
+are true or not, and if not exactly true, whether they are a
+sufficiently near approximation to the truth. The reason is obvious.
+Since it is only in questions of pure number that the assumptions are
+exactly true, and even there, only so long as no conclusions except
+purely numerical ones are to be founded on them; it must, in all other
+cases of deductive investigation, form a part of the inquiry, to
+determine how much the assumptions want of being exactly true in the
+case in hand. This is generally a matter of observation, to be repeated
+in every fresh case; or if it has to be settled by argument instead of
+observation, may require in every different case different evidence, and
+present every degree of difficulty from the lowest to the highest. But
+the other part of the process--namely, to determine what else may be
+concluded if we find, and in proportion as we find, the assumptions to
+be true--may be performed once for all, and the results held ready to be
+employed as the occasions turn up for use. We thus do all beforehand
+that can be so done, and leave the least possible work to be performed
+when cases arise and press for a decision. This inquiry into the
+inferences which can be drawn from assumptions, is what properly
+constitutes Demonstrative Science.
+
+It is of course quite as practicable to arrive at new conclusions from
+facts assumed, as from facts observed; from fictitious, as from real,
+inductions. Deduction, as we have seen, consists of a series of
+inferences in this form--_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_,
+therefore _a_ is a mark of _d_, which last may be a truth inaccessible
+to direct observation. In like manner it is allowable to say, _suppose_
+that _a_ were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a
+mark of _d_, which last conclusion was not thought of by those who laid
+down the premises. A system of propositions as complicated as geometry
+might be deduced from assumptions which are false; as was done by
+Ptolemy, Descartes, and others, in their attempts to explain
+synthetically the phenomena of the solar system on the supposition that
+the apparent motions of the heavenly bodies were the real motions, or
+were produced in some way more or less different from the true one.
+Sometimes the same thing is knowingly done, for the purpose of showing
+the falsity of the assumption; which is called a _reductio ad absurdum_.
+In such cases, the reasoning is as follows: _a_ is a mark of _b_, and
+_b_ of _c_; now if _c_ were also a mark of _d_, _a_ would be a mark of
+_d_; but _d_ is known to be a mark of the absence of _a_; consequently
+_a_ would be a mark of its own absence, which is a contradiction;
+therefore _c_ is not a mark of _d_.
+
+
+� 5. It has even been held by some writers, that all ratiocination rests
+in the last resort on a _reductio ad absurdum_; since the way to enforce
+assent to it, in case of obscurity, would be to show that if the
+conclusion be denied we must deny some one at least of the premises,
+which, as they are all supposed true, would be a contradiction. And in
+accordance with this, many have thought that the peculiar nature of the
+evidence of ratiocination consisted in the impossibility of admitting
+the premises and rejecting the conclusion without a contradiction in
+terms. This theory, however, is inadmissible as an explanation of the
+grounds on which ratiocination itself rests. If any one denies the
+conclusion notwithstanding his admission of the premises, he is not
+involved in any direct and express contradiction until he is compelled
+to deny some premise; and he can only be forced to do this by a
+_reductio ad absurdum_, that is, by another ratiocination: now, if he
+denies the validity of the reasoning process itself, he can no more be
+forced to assent to the second syllogism than to the first. In truth,
+therefore, no one is ever forced to a contradiction in terms: he can
+only be forced to a contradiction (or rather an infringement) of the
+fundamental maxim of ratiocination, namely, that whatever has a mark,
+has what it is a mark of; or, (in the case of universal propositions,)
+that whatever is a mark of anything, is a mark of whatever else that
+thing is a mark of. For in the case of every correct argument, as soon
+as thrown into the syllogistic form, it is evident without the aid of
+any other syllogism, that he who, admitting the premises, fails to draw
+the conclusion, does not conform to the above axiom.
+
+We have now proceeded as far in the theory of Deduction as we can
+advance in the present stage of our inquiry. Any further insight into
+the subject requires that the foundation shall have been laid of the
+philosophic theory of Induction itself; in which theory that of
+deduction, as a mode of induction, which we have now shown it to be,
+will assume spontaneously the place which belongs to it, and will
+receive its share of whatever light may be thrown upon the great
+intellectual operation of which it forms so important a part.
+
+
+
+
+CHAPTER VII.
+
+EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.
+
+
+� 1. Polemical discussion is foreign to the plan of this work. But an
+opinion which stands in need of much illustration, can often receive it
+most effectually, and least tediously, in the form of a defence against
+objections. And on subjects concerning which speculative minds are still
+divided, a writer does but half his duty by stating his own doctrine, if
+he does not also examine, and to the best of his ability judge, those of
+other thinkers.
+
+In the dissertation which Mr. Herbert Spencer has prefixed to his, in
+many respects, highly philosophical treatise on the Mind,[39] he
+criticises some of the doctrines of the two preceding chapters, and
+propounds a theory of his own on the subject of first principles. Mr.
+Spencer agrees with me in considering axioms to be "simply our earliest
+inductions from experience." But he differs from me "widely as to the
+worth of the test of inconceivableness." He thinks that it is the
+ultimate test of all beliefs. He arrives at this conclusion by two
+steps. First, we never can have any stronger ground for believing
+anything, than that the belief of it "invariably exists." Whenever any
+fact or proposition is invariably believed; that is, if I understand Mr.
+Spencer rightly, believed by all persons, and by oneself at all times;
+it is entitled to be received as one of the primitive truths, or
+original premises of our knowledge. Secondly, the criterion by which we
+decide whether anything is invariably believed to be true, is our
+inability to conceive it as false. "The inconceivability of its negation
+is the test by which we ascertain whether a given belief invariably
+exists or not." "For our primary beliefs, the fact of invariable
+existence, tested by an abortive effort to cause their non-existence, is
+the only reason assignable." He thinks this the sole ground of our
+belief in our own sensations. If I believe that I feel cold, I only
+receive this as true because I cannot conceive that I am not feeling
+cold. "While the proposition remains true, the negation of it remains
+inconceivable." There are numerous other beliefs which Mr. Spencer
+considers to rest on the same basis; being chiefly those, or a part of
+those, which the metaphysicians of the Reid and Stewart school consider
+as truths of immediate intuition. That there exists a material world;
+that this is the very world which we directly and immediately perceive,
+and not merely the hidden cause of our perceptions; that Space, Time,
+Force, Extension, Figure, are not modes of our consciousness, but
+objective realities; are regarded by Mr. Spencer as truths known by the
+inconceivableness of their negatives. We cannot, he says, by any effort,
+conceive these objects of thought as mere states of our mind; as not
+having an existence external to us. Their real existence is, therefore,
+as certain as our sensations themselves. The truths which are the
+subject of direct knowledge, being, according to this doctrine, known to
+be truths only by the inconceivability of their negation; and the truths
+which are not the object of direct knowledge, being known as inferences
+from those which are; and those inferences being believed to follow from
+the premises, only because we cannot conceive them not to follow;
+inconceivability is thus the ultimate ground of all assured beliefs.
+
+Thus far, there is no very wide difference between Mr. Spencer's
+doctrine and the ordinary one of philosophers of the intuitive school,
+from Descartes to Dr. Whewell; but at this point Mr. Spencer diverges
+from them. For he does not, like them, set up the test of
+inconceivability as infallible. On the contrary, he holds that it may be
+fallacious, not from any fault in the test itself, but because "men have
+mistaken for inconceivable things, some things which were not
+inconceivable." And he himself, in this very book, denies not a few
+propositions usually regarded as among the most marked examples of
+truths whose negations are inconceivable. But occasional failure, he
+says, is incident to all tests. If such failure vitiates "the test of
+inconceivableness," it "must similarly vitiate all tests whatever. We
+consider an inference logically drawn from established premises to be
+true. Yet in millions of cases men have been wrong in the inferences
+they have thought thus drawn. Do we therefore argue that it is absurd to
+consider an inference true on no other ground than that it is logically
+drawn from established premises? No: we say that though men may have
+taken for logical inferences, inferences that were not logical, there
+nevertheless _are_ logical inferences, and that we are justified in
+assuming the truth of what seem to us such, until better instructed.
+Similarly, though men may have thought some things inconceivable which
+were not so, there may still be inconceivable things; and the inability
+to conceive the negation of a thing, may still be our best warrant for
+believing it.... Though occasionally it may prove an imperfect test,
+yet, as our most certain beliefs are capable of no better, to doubt any
+one belief because we have no higher guarantee for it, is really to
+doubt all beliefs." Mr. Spencer's doctrine, therefore, does not erect
+the curable, but only the incurable limitations of the human conceptive
+faculty, into laws of the outward universe.
+
+
+� 2. The doctrine, that "a belief which is proved by the
+inconceivableness of its negation to invariably exist, is true," Mr.
+Spencer enforces by two arguments, one of which may be distinguished as
+positive, and the other as negative.
+
+The positive argument is, that every such belief represents the
+aggregate of all past experience. "Conceding the entire truth of" the
+"position, that during any phase of human progress, the ability or
+inability to form a specific conception wholly depends on the
+experiences men have had; and that, by a widening of their experiences,
+they may, by and by, be enabled to conceive things before inconceivable
+to them; it may still be argued that as, at any time, the best warrant
+men can have for a belief is the perfect agreement of all pre-existing
+experience in support of it, it follows that, at any time, the
+inconceivableness of its negation is the deepest test any belief admits
+of.... Objective facts are ever impressing themselves upon us; our
+experience is a register of these objective facts; and the
+inconceivableness of a thing implies that it is wholly at variance with
+the register. Even were this all, it is not clear how, if every truth is
+primarily inductive, any better test of truth could exist. But it must
+be remembered that whilst many of these facts, impressing themselves
+upon us, are occasional; whilst others again are very general; some are
+universal and unchanging. These universal and unchanging facts are, by
+the hypothesis, certain to establish beliefs of which the negations are
+inconceivable; whilst the others are not certain to do this; and if they
+do, subsequent facts will reverse their action. Hence if, after an
+immense accumulation of experiences, there remain beliefs of which the
+negations are still inconceivable, most, if not all of them, must
+correspond to universal objective facts. If there be ... certain
+absolute uniformities in nature; if these uniformities produce, as they
+must, absolute uniformities in our experience; and if ... these absolute
+uniformities in our experience disable us from conceiving the negations
+of them; then answering to each absolute uniformity in nature which we
+can cognize, there must exist in us a belief of which the negation is
+inconceivable, and which is absolutely true. In this wide range of cases
+subjective inconceivableness must correspond to objective impossibility.
+Further experience will produce correspondence where it may not yet
+exist; and we may expect the correspondence to become ultimately
+complete. In nearly all cases this test of inconceivableness must be
+valid now;" (I wish I could think we were so nearly arrived at
+omniscience) "and where it is not, it still expresses the net result of
+our experience up to the present time; which is the most that any test
+can do."
+
+To this I answer: Even if it were true that inconceivableness represents
+"the net result" of all past experience, why should we stop at the
+representative when we can get at the thing represented? If our
+incapacity to conceive the negation of a given supposition is proof of
+its truth, because proving that our experience has hitherto been
+uniform in its favour, the real evidence for the supposition is not the
+inconceivableness, but the uniformity of experience. Now this, which is
+the substantial and only proof, is directly accessible. We are not
+obliged to presume it from an incidental consequence. If all past
+experience is in favour of a belief, let this be stated, and the belief
+openly rested on that ground: after which the question arises, what that
+fact may be worth as evidence of its truth? For uniformity of experience
+is evidence in very different degrees: in some cases it is strong
+evidence, in others weak, in others it scarcely amounts to evidence at
+all. That all metals sink in water, was an uniform experience, from the
+origin of the human race to the discovery of potassium in the present
+century by Sir Humphry Davy. That all swans are white, was an uniform
+experience down to the discovery of Australia. In the few cases in which
+uniformity of experience does amount to the strongest possible proof, as
+with such propositions as these, Two straight lines cannot inclose a
+space, Every event has a cause, it is not because their negations are
+inconceivable, which is not always the fact; but because the experience,
+which has been thus uniform, pervades all nature. It will be shown in
+the following Book that none of the conclusions either of induction or
+of deduction can be considered certain, except as far as their truth is
+shown to be inseparably bound up with truths of this class.
+
+I maintain then, first, that uniformity of past experience is very far
+from being universally a criterion of truth. But secondly,
+inconceivableness is still farther from being a test even of that test.
+Uniformity of contrary experience is only one of many causes of
+inconceivability. Tradition handed down from a period of more limited
+knowledge, is one of the commonest. The mere familiarity of one mode of
+production of a phenomenon, often suffices to make every other mode
+appear inconceivable. Whatever connects two ideas by a strong
+association may, and continually does, render their separation in
+thought impossible; as Mr. Spencer, in other parts of his speculations,
+frequently recognises. It was not for want of experience that the
+Cartesians were unable to conceive that one body could produce motion
+in another without contact. They had as much experience of other modes
+of producing motion, as they had of that mode. The planets had revolved,
+and heavy bodies had fallen, every hour of their lives. But they fancied
+these phenomena to be produced by a hidden machinery which they did not
+see, because without it they were unable to conceive what they did see.
+The inconceivableness, instead of representing their experience,
+dominated and overrode their experience. It is needless to dwell farther
+on what I have termed the positive argument of Mr. Spencer in support of
+his criterion of truth. I pass to his negative argument, on which he
+lays more stress.
+
+
+� 3. The negative argument is, that, whether inconceivability be good
+evidence or bad, no stronger evidence is to be obtained. That what is
+inconceivable cannot be true, is postulated in every act of thought. It
+is the foundation of all our original premises. Still more it is assumed
+in all conclusions from those premises. The invariability of belief,
+tested by the inconceivableness of its negation, "is our sole warrant
+for every demonstration. Logic is simply a systematization of the
+process by which we indirectly obtain this warrant for beliefs that do
+not directly possess it. To gain the strongest conviction possible
+respecting any complex fact, we either analytically descend from it by
+successive steps, each of which we unconsciously test by the
+inconceivableness of its negation, until we reach some axiom or truth
+which we have similarly tested; or we synthetically ascend from such
+axiom or truth by such steps. In either case we connect some isolated
+belief, with a belief which invariably exists, by a series of
+intermediate beliefs which invariably exist." The following passage sums
+up the whole theory: "When we perceive that the negation of the belief
+is inconceivable, we have all possible warrant for asserting the
+invariability of its existence: and in asserting this, we express alike
+our logical justification of it, and the inexorable necessity we are
+under of holding it.... We have seen that this is the assumption on
+which every conclusion whatever ultimately rests. We have no other
+guarantee for the reality of consciousness, of sensations, of personal
+existence; we have no other guarantee for any axiom; we have no other
+guarantee for any step in a demonstration. Hence, as being taken for
+granted in every act of the understanding, it must be regarded as the
+Universal Postulate." But as this postulate which we are under an
+"inexorable necessity" of holding true, is sometimes false; as "beliefs
+that once were shown by the inconceivableness of their negations to
+invariably exist, have since been found untrue," and as "beliefs that
+now possess this character may some day share the same fate;" the canon
+of belief laid down by Mr. Spencer is, that "the most certain
+conclusion" is that "which involves the postulate the fewest times."
+Reasoning, therefore, never ought to prevail against one of the
+immediate beliefs (the belief in Matter, in the outward reality of
+Extension, Space, and the like), because each of these involves the
+postulate only once; while an argument, besides involving it in the
+premises, involves it again in every step of the ratiocination, no one
+of the successive acts of inference being recognised as valid except
+because we cannot conceive the conclusion not to follow from the
+premises.
+
+It will be convenient to take the last part of this argument first. In
+every reasoning, according to Mr. Spencer, the assumption of the
+postulate is renewed at every step. At each inference we judge that the
+conclusion follows from the premises, our sole warrant for that judgment
+being that we cannot conceive it not to follow. Consequently if the
+postulate is fallible, the conclusions of reasoning are more vitiated by
+that uncertainty than direct intuitions; and the disproportion is
+greater, the more numerous the steps of the argument.
+
+To test this doctrine, let us first suppose an argument consisting only
+of a single step, which would be represented by one syllogism. This
+argument does rest on an assumption, and we have seen in the preceding
+chapters what the assumption is. It is, that whatever has a mark, has
+what it is a mark of. The evidence of this axiom I shall not consider at
+present;[40] let us suppose it (with Mr. Spencer) to be the
+inconceivableness of its reverse.
+
+Let us now add a second step to the argument: we require, what? Another
+assumption? No: the same assumption a second time; and so on to a third,
+and a fourth. I confess I do not see how, on Mr. Spencer's own
+principles, the repetition of the assumption at all weakens the force of
+the argument. If it were necessary the second time to assume some other
+axiom, the argument would no doubt be weakened, since it would be
+necessary to its validity that both axioms should be true, and it might
+happen that one was true and not the other: making two chances of error
+instead of one. But since it is the _same_ axiom, if it is true once it
+is true every time; and if the argument, being of a hundred links,
+assumed the axiom a hundred times, these hundred assumptions would make
+but one chance of error among them all. It is satisfactory that we are
+not obliged to suppose the deductions of pure mathematics to be among
+the most uncertain of argumentative processes, which on Mr. Spencer's
+theory they could hardly fail to be, since they are the longest. But the
+number of steps in an argument does not subtract from its reliableness,
+if no new _premises_, of an uncertain character, are taken up by the
+way.
+
+To speak next of the premises. Our assurance of their truth, whether
+they be generalities or individual facts, is grounded, in Mr. Spencer's
+opinion, on the inconceivableness of their being false. It is necessary
+to advert to a double meaning of the word inconceivable, which Mr.
+Spencer is aware of, and would sincerely disclaim founding an argument
+upon, but from which his case derives no little advantage
+notwithstanding. By inconceivableness is sometimes meant, inability to
+form or get rid of an _idea_; sometimes, inability to form or get rid of
+a _belief_. The former meaning is the most conformable to the analogy of
+language; for a conception always means an idea, and never a belief.
+The wrong meaning of "inconceivable" is, however, fully as frequent in
+philosophical discussion as the right meaning, and the intuitive school
+of metaphysicians could not well do without either. To illustrate the
+difference, we will take two contrasted examples. The early physical
+speculators considered antipodes incredible, because inconceivable. But
+antipodes were not inconceivable in the primitive sense of the word. An
+idea of them could be formed without difficulty: they could be
+completely pictured to the mental eye. What was difficult, and as it
+then seemed, impossible, was to apprehend them as believable. The idea
+could be put together, of men sticking on by their feet to the under
+side of the earth; but the belief _would_ follow, that they must fall
+off. Antipodes were not unimaginable, but they were unbelievable.
+
+On the other hand, when I endeavour to conceive an end to extension, the
+two ideas refuse to come together. When I attempt to form a conception
+of the last point of space, I cannot help figuring to myself a vast
+space beyond that last point. The combination is, under the conditions
+of our experience, unimaginable. This double meaning of inconceivable it
+is very important to bear in mind, for the argument from
+inconceivableness almost always turns on the alternate substitution of
+each of those meanings for the other.
+
+In which of these two senses does Mr. Spencer employ the term, when he
+makes it a test of the truth of a proposition that its negation is
+inconceivable? Until Mr. Spencer expressly stated the contrary, I
+inferred from the course of his argument, that he meant unbelievable. He
+has, however, in a paper published in the fifth number of the
+_Fortnightly Review_, disclaimed this meaning, and declared that by an
+inconceivable proposition he means, now and always, "one of which the
+terms cannot, by any effort, be brought before consciousness in that
+relation which the proposition asserts between them--a proposition of
+which the subject and predicate offer an insurmountable resistance to
+union in thought." We now, therefore, know positively that Mr. Spencer
+always endeavours to use the word inconceivable in this, its proper,
+sense: but it may yet be questioned whether his endeavour is always
+successful; whether the other, and popular use of the word does not
+sometimes creep in with its associations, and prevent him from
+maintaining a clear separation between the two. When, for example, he
+says, that when I feel cold, I cannot conceive that I am not feeling
+cold, this expression cannot be translated into, "I cannot conceive
+myself not feeling cold," for it is evident that I can: the word
+conceive, therefore, is here used to express the recognition of a matter
+of fact--the perception of truth or falsehood; which I apprehend to be
+exactly the meaning of an act of belief, as distinguished from simple
+conception. Again, Mr. Spencer calls the attempt to conceive something
+which is inconceivable, "an abortive effort to cause the non-existence"
+not of a conception or mental representation, but of a belief. There is
+need, therefore, to revise a considerable part of Mr. Spencer's
+language, if it is to be kept always consistent with his definition of
+inconceivability. But in truth the point is of little importance; since
+inconceivability, in Mr. Spencer's theory, is only a test of truth,
+inasmuch as it is a test of believability. The inconceivableness of a
+supposition is the extreme case of its unbelievability. This is the very
+foundation of Mr. Spencer's doctrine. The invariability of the belief is
+with him the real guarantee. The attempt to conceive the negative, is
+made in order to test the inevitableness of the belief. It should be
+called, an attempt to _believe_ the negative. When Mr. Spencer says that
+while looking at the sun a man cannot conceive that he is looking into
+darkness, he should have said that a man cannot _believe_ that he is
+doing so. For it is surely possible, in broad daylight, to _imagine_
+oneself looking into darkness.[41] As Mr. Spencer himself says, speaking
+of the belief of our own existence: "That he _might_ not exist, he can
+conceive well enough; but that he _does_ not exist, he finds it
+impossible to conceive," _i.e._ to believe. So that the statement
+resolves itself into this: That I exist, and that I have sensations, I
+believe, because I cannot believe otherwise. And in this case every one
+will admit that the necessity is real. Any one's present sensations, or
+other states of subjective consciousness, that one person inevitably
+believes. They are facts known _per se_: it is impossible to ascend
+beyond them. Their negative is really unbelievable, and therefore there
+is never any question about believing it. Mr. Spencer's theory is not
+needed for these truths.
+
+But according to Mr. Spencer there are other beliefs, relating to other
+things than our own subjective feelings, for which we have the same
+guarantee--which are, in a similar manner, invariable and necessary.
+With regard to these other beliefs, they cannot be necessary, since they
+do not always exist. There have been, and are, many persons who do not
+believe the reality of an external world, still less the reality of
+extension and figure as the forms of that external world; who do not
+believe that space and time have an existence independent of the
+mind--nor any other of Mr. Spencer's objective intuitions. The negations
+of these alleged invariable beliefs are not unbelievable, for they are
+believed. It may be maintained, without obvious error, that we cannot
+_imagine_ tangible objects as mere states of our own and other people's
+consciousness; that the perception of them irresistibly suggests to us
+the _idea_ of something external to ourselves: and I am not in a
+condition to say that this is not the fact (though I do not think any
+one is entitled to affirm it of any person besides himself). But many
+thinkers have believed, whether they could conceive it or not, that what
+we represent to ourselves as material objects, are mere modifications of
+consciousness; complex feelings of touch and of muscular action. Mr.
+Spencer may think the inference correct from the unimaginable to the
+unbelievable, because he holds that belief itself is but the persistence
+of an idea, and that what we can succeed in imagining, we cannot at the
+moment help apprehending as believable. But of what consequence is it
+what we apprehend at the moment, if the moment is in contradiction to
+the permanent state of our mind? A person who has been frightened when
+an infant by stories of ghosts, though he disbelieves them in after
+years (and perhaps disbelieved them at first), may be unable all his
+life to be in a dark place, in circumstances stimulating to the
+imagination, without mental discomposure. The idea of ghosts, with all
+its attendant terrors, is irresistibly called up in his mind by the
+outward circumstances. Mr. Spencer may say, that while he is under the
+influence of this terror he does not disbelieve in ghosts, but has a
+temporary and uncontrollable belief in them. Be it so; but allowing it
+to be so, which would it be truest to say of this man on the whole--that
+he believes in ghosts, or that he does not believe in them? Assuredly
+that he does not believe in them. The case is similar with those who
+disbelieve a material world. Though they cannot get rid of the idea;
+though while looking at a solid object they cannot help having the
+conception, and therefore, according to Mr. Spencer's metaphysics, the
+momentary belief, of its externality; even at that moment they would
+sincerely deny holding that belief: and it would be incorrect to call
+them other than disbelievers of the doctrine. The belief therefore is
+not invariable; and the test of inconceivableness fails in the only
+cases to which there could ever be any occasion to apply it.
+
+That a thing may be perfectly believable, and yet may not have become
+conceivable, and that we may habitually believe one side of an
+alternative, and conceive only in the other, is familiarly exemplified
+in the state of mind of educated persons respecting sunrise and sunset.
+All educated persons either know by investigation, or believe on the
+authority of science, that it is the earth and not the sun which moves:
+but there are probably few who habitually _conceive_ the phenomenon
+otherwise than as the ascent or descent of the sun. Assuredly no one can
+do so without a prolonged trial; and it is probably not easier now than
+in the first generation after Copernicus. Mr. Spencer does not say, "In
+looking at sunrise it is impossible not to conceive that it is the sun
+which moves, therefore this is what everybody believes, and we have all
+the evidence for it that we can have for any truth." Yet this would be
+an exact parallel to his doctrine about the belief in matter.
+
+The existence of matter, and other Noumena, as distinguished from the
+phenomenal world, remains a question of argument, as it was before; and
+the very general, but neither necessary nor universal, belief in them,
+stands as a psychological phenomenon to be explained, either on the
+hypothesis of its truth, or on some other. The belief is not a
+conclusive proof of its own truth, unless there are no such things as
+_idola trib�s_; but, being a fact, it calls on antagonists to show, from
+what except the real existence of the thing believed, so general and
+apparently spontaneous a belief can have originated. And its opponents
+have never hesitated to accept this challenge.[42] The amount of their
+success in meeting it will probably determine the ultimate verdict of
+philosophers on the question.
+
+
+� 4. Sir William Hamilton holds as I do, that inconceivability is no
+criterion of impossibility. "There is no ground for inferring a certain
+fact to be impossible, merely from our inability to conceive its
+possibility." "Things there are which _may_, nay _must_, be true, of
+which the understanding is wholly unable to construe to itself the
+possibility."[43] Sir William Hamilton is however a firm believer in the
+_� priori_ character of many axioms, and of the sciences deduced from
+them; and is so far from considering those axioms to rest on the
+evidence of experience, that he declares certain of them to be true even
+of Noumena--of the Unconditioned--of which it is one of the principal
+aims of his philosophy to prove that the nature of our faculties debars
+us from having any knowledge. The axioms to which he attributes this
+exceptional emancipation from the limits which confine all our other
+possibilities of knowledge; the chinks through which, as he represents,
+one ray of light finds its way to us from behind the curtain which veils
+from us the mysterious world of Things in themselves,--are the two
+principles, which he terms, after the schoolmen, the Principle of
+Contradiction, and the Principle of Excluded Middle: the first, that two
+contradictory propositions cannot both be true; the second, that they
+cannot both be false. Armed with these logical weapons, we may boldly
+face Things in themselves, and tender to them the double alternative,
+sure that they must absolutely elect one or the other side, though we
+may be for ever precluded from discovering which. To take his favourite
+example, we cannot conceive the infinite divisibility of matter, and we
+cannot conceive a minimum, or end to divisibility: yet one or the other
+must be true.
+
+As I have hitherto said nothing of the two axioms in question, those of
+Contradiction and of Excluded Middle, it is not unseasonable to consider
+them here. The former asserts that an affirmative proposition and the
+corresponding negative proposition cannot both be true; which has
+generally been held to be intuitively evident. Sir William Hamilton and
+the Germans consider it to be the statement in words of a form or law of
+our thinking faculty. Other philosophers, not less deserving of
+consideration, deem it to be an identical proposition; an assertion
+involved in the meaning of terms; a mode of defining Negation, and the
+word Not.
+
+I am able to go one step with these last. An affirmative assertion and
+its negative are not two independent assertions, connected with each
+other only as mutually incompatible. That if the negative be true, the
+affirmative must be false, really is a mere identical proposition; for
+the negative proposition asserts nothing but the falsity of the
+affirmative, and has no other sense or meaning whatever. The Principium
+Contradictionis should therefore put off the ambitious phraseology which
+gives it the air of a fundamental antithesis pervading nature, and
+should be enunciated in the simpler form, that the same proposition
+cannot at the same time be false and true. But I can go no farther with
+the Nominalists; for I cannot look upon this last as a merely verbal
+proposition. I consider it to be, like other axioms, one of our first
+and most familiar generalizations from experience. The original
+foundation of it I take to be, that Belief and Disbelief are two
+different mental states, excluding one another. This we know by the
+simplest observation of our own minds. And if we carry our observation
+outwards, we also find that light and darkness, sound and silence,
+motion and quiescence, equality and inequality, preceding and following,
+succession and simultaneousness, any positive phenomenon whatever and
+its negative, are distinct phenomena, pointedly contrasted, and the one
+always absent where the other is present. I consider the maxim in
+question to be a generalization from all these facts.
+
+In like manner as the Principle of Contradiction (that one of two
+contradictories must be false) means that an assertion cannot be _both_
+true and false, so the Principle of Excluded Middle, or that one of two
+contradictories must be true, means that an assertion must be _either_
+true or false: either the affirmative is true, or otherwise the negative
+is true, which means that the affirmative is false. I cannot help
+thinking this principle a surprising specimen of a so-called necessity
+of Thought, since it is not even true, unless with a large
+qualification. A proposition must be either true or false, _provided_
+that the predicate be one which can in any intelligible sense be
+attributed to the subject; (and as this is always assumed to be the case
+in treatises on logic, the axiom is always laid down there as of
+absolute truth). "Abracadabra is a second intention" is neither true nor
+false. Between the true and the false there is a third possibility, the
+Unmeaning: and this alternative is fatal to Sir William Hamilton's
+extension of the maxim to Noumena. That Matter must either have a
+minimum of divisibility or be infinitely divisible, is more than we can
+ever know. For in the first place, Matter, in any other than the
+phenomenal sense of the term, may not exist: and it will scarcely be
+said that a non-entity must be either infinitely or finitely
+divisible.[44] In the second place, though matter, considered as the
+occult cause of our sensations, do really exist, yet what we call
+divisibility may be an attribute only of our sensations of sight and
+touch, and not of their uncognizable cause. Divisibility may not be
+predicable at all, in any intelligible sense, of Things in themselves,
+nor therefore of Matter in itself; and the assumed necessity of being
+either infinitely or finitely divisible, may be an inapplicable
+alternative.
+
+On this question I am happy to have the full concurrence of Mr. Herbert
+Spencer, from whose paper in the _Fortnightly Review_ I extract the
+following passage. The germ of an idea identical with that of Mr.
+Spencer may be found in the present chapter, about a page back, but in
+Mr. Spencer it is not an undeveloped thought, but a philosophical
+theory.
+
+"When remembering a certain thing as in a certain place, the place and
+the thing are mentally represented together; while to think of the
+non-existence of the thing in that place, implies a consciousness in
+which the place is represented, but not the thing. Similarly, if instead
+of thinking of an object as colourless, we think of its having colour,
+the change consists in the addition to the concept of an element that
+was before absent from it--the object cannot be thought of first as red
+and then as not red, without one component of the thought being totally
+expelled from the mind by another. The law of the Excluded Middle, then,
+is simply a generalization of the universal experience that some mental
+states are directly destructive of other states. It formulates a certain
+absolutely constant law, that the appearance of any positive mode of
+consciousness cannot occur without excluding a correlative negative
+mode; and that the negative mode cannot occur without excluding the
+correlative positive mode: the antithesis of positive and negative
+being, indeed, merely an expression of this experience. Hence it follows
+that if consciousness is not in one of the two modes it must be in the
+other."[45]
+
+I must here close this supplementary chapter, and with it the Second
+Book. The theory of Induction, in the most comprehensive sense of the
+term, will form the subject of the Third.
+
+FOOTNOTES:
+
+[1] As Sir William Hamilton has pointed out, "Some A is not B" may also
+be converted in the following form: "No B is _some_ A." Some men are not
+negroes; therefore, No negroes are _some_ men (_e.g._ Europeans).
+
+[2]
+  All A is B } contraries.
+  No  A is B }
+
+  Some A is B     } subcontraries.
+  Some A is not B }
+
+  All  A is B     } contradictories.
+  Some A is not B }
+
+  No   A is B } also contradictories.
+  Some A is B }
+
+  All  A is B } and  No   A is B     } respectively subalternate.
+  Some A is B }      Some A is not B }
+
+[3] His conclusions are, "The first figure is suited to the discovery or
+proof of the properties of a thing; the second to the discovery or proof
+of the distinctions between things; the third to the discovery or proof
+of instances and exceptions; the fourth to the discovery, or exclusion,
+of the different species of a genus." The reference of syllogisms in the
+last three figures to the _dictum de omni et nullo_ is, in Lambert's
+opinion, strained and unnatural: to each of the three belongs, according
+to him, a separate axiom, co-ordinate and of equal authority with that
+_dictum_, and to which he gives the names of _dictum de diverso_ for the
+second figure, _dictum de exemplo_ for the third, and _dictum de
+reciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. �
+229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74)
+takes a similar view of the subject.
+
+[4] Since this chapter was written, two treatises have appeared (or
+rather a treatise and a fragment of a treatise), which aim at a further
+improvement in the theory of the forms of ratiocination: Mr. De Morgan's
+"Formal Logic; or, the Calculus of Inference, Necessary and Probable;"
+and the "New Analytic of Logical Forms," attached as an Appendix to Sir
+William Hamilton's _Discussions on Philosophy_, and at greater length,
+to his posthumous _Lectures on Logic_.
+
+In Mr. De Morgan's volume--abounding, in its more popular parts, with
+valuable observations felicitously expressed--the principal feature of
+originality is an attempt to bring within strict technical rules the
+cases in which a conclusion can be drawn from premises of a form usually
+classed as particular. Mr. De Morgan observes, very justly, that from
+the premises Most Bs are Cs, most Bs are As, it may be concluded with
+certainty that some As are Cs, since two portions of the class B, each
+of them comprising more than half, must necessarily in part consist of
+the same individuals. Following out this line of thought, it is equally
+evident that if we knew exactly what proportion the "most" in each of
+the premises bear to the entire class B, we could increase in a
+corresponding degree the definiteness of the conclusion. Thus if 60 per
+cent of B are included in C, and 70 per cent in A, 30 per cent at least
+must be common to both; in other words, the number of As which are Cs,
+and of Cs which are As, must be at least equal to 30 per cent of the
+class B. Proceeding on this conception of "numerically definite
+propositions," and extending it to such forms as these:--"45 Xs (or
+more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
+them to be found among 70 Ys," and examining what inferences admit of
+being drawn from the various combinations which may be made of premises
+of this description, Mr. De Morgan establishes universal formul� for
+such inferences; creating for that purpose not only a new technical
+language, but a formidable array of symbols analogous to those of
+algebra.
+
+Since it is undeniable that inferences, in the cases examined by Mr. De
+Morgan, can legitimately be drawn, and that the ordinary theory takes no
+account of them, I will not say that it was not worth while to show in
+detail how these also could be reduced to formul� as rigorous as those
+of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
+more than once, as a school exercise); but I question if its results are
+worth studying and mastering for any practical purpose. The practical
+use of technical forms of reasoning is to bar out fallacies: but the
+fallacies which require to be guarded against in ratiocination properly
+so called, arise from the incautious use of the common forms of
+language; and the logician must track the fallacy into that territory,
+instead of waiting for it on a territory of his own. While he remains
+among propositions which have acquired the numerical precision of the
+Calculus of Probabilities, the enemy is left in possession of the only
+ground on which he can be formidable. And since the propositions (short
+of universal) on which a thinker has to depend, either for purposes of
+speculation or of practice, do not, except in a few peculiar cases,
+admit of any numerical precision; common reasoning cannot be translated
+into Mr. De Morgan's forms, which therefore cannot serve any purpose as
+a test of it.
+
+Sir William Hamilton's theory of the "quantification of the predicate"
+(concerning the originality of which in his case there can be no doubt,
+however Mr. De Morgan may have also, and independently, originated an
+equivalent doctrine) may be briefly described as follows:--
+
+"Logically" (I quote his own words) "we ought to take into account the
+quantity, always understood in thought, but usually, for manifest
+reasons, elided in its expression, not only of the subject, but also of
+the predicate of a judgment." All A is B, is equivalent to all A is
+_some_ B. No A is B, to No A is _any_ B. Some A is B, is tantamount to
+some A is _some_ B. Some A is not B, to Some A is _not any_ B. As in
+these forms of assertion the predicate is exactly coextensive with the
+subject, they all admit of simple conversion; and by this we obtain two
+additional forms--Some B is _all_ A, and No B is _some_ A. We may also
+make the assertion All A is all B, which will be true if the classes A
+and B are exactly coextensive. The last three forms, though conveying
+real assertions, have no place in the ordinary classification of
+Propositions. All propositions, then, being supposed to be translated
+into this language, and written each in that one of the preceding forms
+which answers to its signification, there emerges a new set of
+syllogistic rules, materially different from the common ones. A general
+view of the points of difference may be given in the words of Sir W.
+Hamilton (_Discussions_, 2nd ed. p. 651):--
+
+"The revocation of the two terms of a Proposition to their true
+relation; a proposition being always an _equation_ of its subject and
+its predicate.
+
+"The consequent reduction of the Conversion of Propositions from three
+species to one--that of Simple Conversion.
+
+"The reduction of all the _General Laws_ of Categorical Syllogisms to a
+single Canon.
+
+"The evolution from that one canon of all the Species and varieties of
+Syllogisms.
+
+"The abrogation of all the _Special Laws_ of Syllogism.
+
+"A demonstration of the exclusive possibility of Three syllogistic
+Figures; and (on new grounds) the scientific and final abolition of the
+Fourth.
+
+"A manifestation that Figure is an unessential variation in syllogistic
+form; and the consequent absurdity of Reducing the syllogisms of the
+other figures to the first.
+
+"An enouncement of _one Organic Principle_ for each Figure.
+
+"A determination of the true number of the Legitimate Moods; with
+
+"Their amplification in number (thirty-six);
+
+"Their numerical equality under all the figures; and
+
+"Their relative equivalence, or virtual identity, throughout every
+schematic difference.
+
+"That, in the second and third figures, the extremes holding both the
+same relation to the middle term, there is not, as in the first, an
+opposition and subordination between a term major and a term minor,
+mutually containing and contained, in the counter wholes of Extension
+and Comprehension.
+
+"Consequently, in the second and third figures, there is no determinate
+major and minor premise, and there are two indifferent conclusions:
+whereas in the first the premises are determinate, and there is a single
+proximate conclusion."
+
+This doctrine, like that of Mr. De Morgan previously noticed, is a real
+addition to the syllogistic theory; and has moreover this advantage over
+Mr. De Morgan's "numerically definite Syllogism," that the forms it
+supplies are really available as a test of the correctness of
+ratiocination; since propositions in the common form may always have
+their predicates quantified, and so be made amenable to Sir W.
+Hamilton's rules. Considered however as a contribution to the _Science_
+of Logic, that is, to the analysis of the mental processes concerned in
+reasoning, the new doctrine appears to me, I confess, not merely
+superfluous, but erroneous; since the form in which it clothes
+propositions does not, like the ordinary form, express what is in the
+mind of the speaker when he enunciates the proposition. I cannot think
+Sir William Hamilton right in maintaining that the quantity of the
+predicate is "always understood in thought." It is implied, but is not
+present to the mind of the person who asserts the proposition. The
+quantification of the predicate, instead of being a means of bringing
+out more clearly the meaning of the proposition, actually leads the mind
+out of the proposition, into another order of ideas. For when we say,
+All men are mortal, we simply mean to affirm the attribute mortality of
+all men; without thinking at all of the _class_ mortal in the concrete,
+or troubling ourselves about whether it contains any other beings or
+not. It is only for some artificial purpose that we ever look at the
+proposition in the aspect in which the predicate also is thought of as a
+class-name, either including the subject only, or the subject and
+something more. (See above, p. 104.)
+
+For a fuller discussion of this subject, see the twenty-second chapter
+of a work already referred to, "An Examination of Sir William Hamilton's
+Philosophy."
+
+[5] Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though
+his theory of the syllogism coincides with all that is essential of
+mine, thinks it a logical fallacy to present the two axioms in the text,
+as the regulating principles of syllogism. He charges me with falling
+into the error pointed out by Archbishop Whately and myself, of
+confounding exact likeness with literal identity; and maintains, that we
+ought not to say that Socrates possesses _the same_ attributes which are
+connoted by the word Man, but only that he possesses attributes _exactly
+like_ them: according to which phraseology, Socrates, and the attribute
+mortality, are not two things coexisting with the same thing, as the
+axiom asserts, but two things coexisting with two different things.
+
+The question between Mr. Spencer and me is merely one of language; for
+neither of us (if I understand Mr. Spencer's opinions rightly) believes
+an attribute to be a real thing, possessed of objective existence; we
+believe it to be a particular mode of naming our sensations, or our
+expectations of sensation, when looked at in their relation to an
+external object which excites them. The question raised by Mr. Spencer
+does not, therefore, concern the properties of any really existing
+thing, but the comparative appropriateness, for philosophical purposes,
+of two different modes of using a name. Considered in this point of
+view, the phraseology I have employed, which is that commonly used by
+philosophers, seems to me to be the best. Mr. Spencer is of opinion that
+because Socrates and Alcibiades are not the same man, the attribute
+which constitutes them men should not be called the same attribute; that
+because the humanity of one man and that of another express themselves
+to our senses not by the same individual sensations but by sensations
+exactly alike, humanity ought to be regarded as a different attribute in
+every different man. But on this showing, the humanity even of any one
+man should be considered as different attributes now and half-an-hour
+hence; for the sensations by which it will then manifest itself to my
+organs will not be a continuation of my present sensations, but a
+repetition of them; fresh sensations, not identical with, but only
+exactly like the present. If every general conception, instead of being
+"the One in the Many," were considered to be as many different
+conceptions as there are things to which it is applicable, there would
+be no such thing as general language. A name would have no general
+meaning if _man_ connoted one thing when predicated of John, and
+another, though closely resembling, thing when predicated of William.
+Accordingly a recent pamphlet asserts the impossibility of general
+knowledge on this precise ground.
+
+The meaning of any general name is some outward or inward phenomenon,
+consisting, in the last resort, of feelings; and these feelings, if
+their continuity is for an instant broken, are no longer the same
+feelings, in the sense of individual identity. What, then, is the common
+something which gives a meaning to the general name? Mr. Spencer can
+only say, it is the similarity of the feelings; and I rejoin, the
+attribute is precisely that similarity. The names of attributes are in
+their ultimate analysis names for the resemblances of our sensations (or
+other feelings). Every general name, whether abstract or concrete,
+denotes or connotes one or more of those resemblances. It will not,
+probably, be denied, that if a hundred sensations are undistinguishably
+alike, their resemblance ought to be spoken of as one resemblance, and
+not a hundred resemblances which merely _resemble_ one another. The
+things compared are many, but the something common to all of them must
+be conceived as one, just as the name is conceived as one, though
+corresponding to numerically different sensations of sound each time it
+is pronounced. The general term _man_ does not connote the sensations
+derived once from one man, which, once gone, can no more occur again
+than the same flash of lightning. It connotes the general type of the
+sensations derived always from all men, and the power (always thought of
+as one) of producing sensations of that type. And the axiom might be
+thus worded: Two _types of sensation_ each of which coexists with a
+third type, coexist with another; or Two _powers_ each of which coexists
+with a third power coexist with one another.
+
+Mr. Spencer has misunderstood me in another particular. He supposes that
+the coexistence spoken of in the axiom, of two things with the same
+third thing, means simultaneousness in time. The coexistence meant is
+that of being jointly attributes of the same subject. The attribute of
+being born without teeth, and the attribute of having thirty-two teeth
+in mature age, are in this sense coexistent, both being attributes of
+man, though _ex vi termini_ never of the same man at the same time.
+
+[6] Supra, p. 128.
+
+[7] _Logic_, p. 239 (9th ed.).
+
+[8] It is hardly necessary to say, that I am not contending for any such
+absurdity as that we _actually_ "ought to have known" and considered the
+case of every individual man, past, present, and future, before
+affirming that all men are mortal: although this interpretation has
+been, strangely enough, put upon the preceding observations. There is no
+difference between me and Archbishop Whately, or any other defender of
+the syllogism, on the practical part of the matter; I am only pointing
+out an inconsistency in the logical theory of it, as conceived by almost
+all writers. I do not say that a person who affirmed, before the Duke of
+Wellington was born, that all men are mortal, _knew_ that the Duke of
+Wellington was mortal; but I do say that he _asserted_ it; and I ask for
+an explanation of the apparent logical fallacy, of adducing in proof of
+the Duke of Wellington's mortality, a general statement which
+presupposes it. Finding no sufficient resolution of this difficulty in
+any of the writers on Logic, I have attempted to supply one.
+
+[9] The language of ratiocination would, I think, be brought into closer
+agreement with the real nature of the process, if the general
+propositions employed in reasoning, instead of being in the form All men
+are mortal, or Every man is mortal, were expressed in the form Any man
+is mortal. This mode of expression, exhibiting as the type of all
+reasoning from experience "The men A, B, C, &c. are so and so, therefore
+_any_ man is so and so," would much better manifest the true idea--that
+inductive reasoning is always, at bottom, inference from particulars to
+particulars, and that the whole function of general propositions in
+reasoning, is to vouch for the legitimacy of such inferences.
+
+[10] Review of Quetelet on Probabilities, _Essays_, p. 367.
+
+[11] _Philosophy of Discovery_, p. 289.
+
+[12] _Theory of Reasoning_, ch. iv. to which I may refer for an able
+statement and enforcement of the grounds of the doctrine.
+
+[13] It is very probable that the doctrine is not new, and that it was,
+as Sir John Herschel thinks, substantially anticipated by Berkeley. But
+I certainly am not aware that it is (as has been affirmed by one of my
+ablest and most candid critics) "among the standing marks of what is
+called the empirical philosophy."
+
+[14] _Logic_, book iv. ch. i. sect. 1.
+
+[15] See the important chapter on Belief, in Professor Bain's great
+treatise, _The Emotions and the Will_, pp. 581-4.
+
+[16] A writer in the "British Quarterly Review" (August 1846), in a
+review of this treatise, endeavours to show that there is no _petitio
+principii_ in the syllogism, by denying that the proposition, All men
+are mortal, asserts or assumes that Socrates is mortal. In support of
+this denial, he argues that we may, and in fact do, admit the general
+proposition that all men are mortal, without having particularly
+examined the case of Socrates, and even without knowing whether the
+individual so named is a man or something else. But this of course was
+never denied. That we can and do draw conclusions concerning cases
+specifically unknown to us, is the datum from which all who discuss this
+subject must set out. The question is, in what terms the evidence, or
+ground, on which we draw these conclusions, may best be
+designated--whether it is most correct to say, that the unknown case is
+proved by known cases, or that it is proved by a general proposition
+including both sets of cases, the unknown and the known? I contend for
+the former mode of expression. I hold it an abuse of language to say,
+that the proof that Socrates is mortal, is that all men are mortal. Turn
+it in what way we will, this seems to me to be asserting that a thing is
+the proof of itself. Whoever pronounces the words, All men are mortal,
+has affirmed that Socrates is mortal, though he may never have heard of
+Socrates; for since Socrates, whether known to be so or not, really is a
+man, he is included in the words, All men, and in every assertion of
+which they are the subject. If the reviewer does not see that there is a
+difficulty here, I can only advise him to reconsider the subject until
+he does: after which he will be a better judge of the success or failure
+of an attempt to remove the difficulty. That he had reflected very
+little on the point when he wrote his remarks, is shown by his oversight
+respecting the _dictum de omni et nullo_. He acknowledges that this
+maxim as commonly expressed,--"Whatever is true of a class, is true of
+everything included in the class," is a mere identical proposition,
+since the class _is_ nothing but the things included in it. But he
+thinks this defect would be cured by wording the maxim thus,--"Whatever
+is true of a class, is true of everything which _can be shown_ to be a
+member of the class:" as if a thing could "be shown" to be a member of
+the class without being one. If a class means the sum of all the things
+included in the class, the things which can "be shown" to be included in
+it are part of the sum, and the _dictum_ is as much an identical
+proposition with respect to them as to the rest. One would almost
+imagine that, in the reviewer's opinion, things are not members of a
+class until they are called up publicly to take their place in it--that
+so long, in fact, as Socrates is not known to be a man, he _is not_ a
+man, and any assertion which can be made concerning men does not at all
+regard him, nor is affected as to its truth or falsity by anything in
+which he is concerned.
+
+The difference between the reviewer's theory and mine may be thus
+stated. Both admit that when we say, All men are mortal, we make an
+assertion reaching beyond the sphere of our knowledge of individual
+cases; and that when a new individual, Socrates, is brought within the
+field of our knowledge by means of the minor premise, we learn that we
+have already made an assertion respecting Socrates without knowing it:
+our own general formula being, to that extent, for the first time
+_interpreted_ to us. But according to the reviewer's theory, the smaller
+assertion is proved by the larger: while I contend, that both assertions
+are proved together, by the same evidence, namely, the grounds of
+experience on which the general assertion was made, and by which it must
+be justified.
+
+The reviewer says, that if the major premise included the conclusion,
+"we should be able to affirm the conclusion without the intervention of
+the minor premise; but every one sees that that is impossible." A
+similar argument is urged by Mr. De Morgan (_Formal Logic_, p. 259):
+"The whole objection tacitly assumes the superfluity of the minor; that
+is, tacitly assumes we know Socrates[46] to be a man as soon as we know
+him to be Socrates." The objection would be well grounded if the
+assertion that the major premise includes the conclusion, meant that it
+individually specifies all it includes. As however the only indication
+it gives is a description by marks, we have still to compare any new
+individual with the marks; and to show that this comparison has been
+made, is the office of the minor. But since, by supposition, the new
+individual has the marks, whether we have ascertained him to have them
+or not; if we have affirmed the major premise, we have asserted him to
+be mortal. Now my position is that this assertion cannot be a necessary
+part of the argument. It cannot be a necessary condition of reasoning
+that we should begin by making an assertion, which is afterwards to be
+employed in proving a part of itself. I can conceive only one way out of
+this difficulty, viz. that what really forms the proof is _the other_
+part of the assertion; the portion of it, the truth of which has been
+ascertained previously: and that the unproved part is bound up in one
+formula with the proved part in mere anticipation, and as a memorandum
+of the nature of the conclusions which we are prepared to prove.
+
+With respect to the minor premise in its formal shape, the minor as it
+stands in the syllogism, predicating of Socrates a definite class name,
+I readily admit that it is no more a necessary part of reasoning than
+the major. When there is a major, doing its work by means of a class
+name, minors are needed to interpret it: but reasoning can be carried on
+without either the one or the other. They are not the conditions of
+reasoning, but a precaution against erroneous reasoning. The only minor
+premise necessary to reasoning in the example under consideration, is,
+Socrates is _like_ A, B, C, and the other individuals who are known to
+have died. And this is the only universal type of that step in the
+reasoning process which is represented by the minor. Experience,
+however, of the uncertainty of this loose mode of inference, teaches the
+expediency of determining beforehand what _kind_ of likeness to the
+cases observed, is necessary to bring an unobserved case within the same
+predicate; and the answer to this question is the major. Thus the
+syllogistic major and the syllogistic minor start into existence
+together, and are called forth by the same exigency. When we conclude
+from personal experience without referring to any record--to any general
+theorems, either written, or traditional, or mentally registered by
+ourselves as conclusions of our own drawing, we do not use, in our
+thoughts, either a major or a minor, such as the syllogism puts into
+words. When, however, we revise this rough inference from particulars to
+particulars, and substitute a careful one, the revision consists in
+selecting two syllogistic premises. But this neither alters nor adds to
+the evidence we had before; it only puts us in a better position for
+judging whether our inference from particulars to particulars is well
+grounded.
+
+[17] Infra, book iii. ch. ii.
+
+[18] Infra, book iii. ch. iv. � 3, and elsewhere.
+
+[19] _Mechanical Euclid_, pp. 149 _et seqq._
+
+[20] We might, it is true, insert this property into the definition of
+parallel lines, framing the definition so as to require, both that when
+produced indefinitely they shall never meet, and also that any straight
+line which intersects one of them shall, if prolonged, meet the other.
+But by doing this we by no means get rid of the assumption; we are still
+obliged to take for granted the geometrical truth, that all straight
+lines in the same plane, which have the former of these properties, have
+also the latter. For if it were possible that they should not, that is,
+if any straight lines other than those which are parallel according to
+the definition, had the property of never meeting although indefinitely
+produced, the demonstrations of the subsequent portions of the theory of
+parallels could not be maintained.
+
+[21] Some persons find themselves prevented from believing that the
+axiom, Two straight lines cannot inclose a space, could ever become
+known to us through experience, by a difficulty which may be stated as
+follows. If the straight lines spoken of are those contemplated in the
+definition--lines absolutely without breadth and absolutely
+straight;--that such are incapable of inclosing a space is not proved by
+experience, for lines such as these do not present themselves in our
+experience. If, on the other hand, the lines meant are such straight
+lines as we do meet with in experience, lines straight enough for
+practical purposes, but in reality slightly zigzag, and with some,
+however trifling, breadth; as applied to these lines the axiom is not
+true, for two of them may, and sometimes do, inclose a small portion of
+space. In neither case, therefore, does experience prove the axiom.
+
+Those who employ this argument to show that geometrical axioms cannot be
+proved by induction, show themselves unfamiliar with a common and
+perfectly valid mode of inductive proof; proof by approximation. Though
+experience furnishes us with no lines so unimpeachably straight that two
+of them are incapable of inclosing the smallest space, it presents us
+with gradations of lines possessing less and less either of breadth or
+of flexure, of which series the straight line of the definition is the
+ideal limit. And observation shows that just as much, and as nearly, as
+the straight lines of experience approximate to having no breadth or
+flexure, so much and so nearly does the space-inclosing power of any two
+of them approach to zero. The inference that if they had no breadth or
+flexure at all, they would inclose no space at all, is a correct
+inductive inference from these facts, conformable to one of the four
+Inductive Methods hereinafter characterized, the Method of Concomitant
+Variations; of which the mathematical Doctrine of Limits presents the
+extreme case.
+
+[22] Whewell's _History of Scientific Ideas_, i. 140.
+
+[23] Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
+unreasonable to contend that we know by experience, that our idea of a
+line exactly resembles a real line. "It does not appear," he says, "how
+we can compare our ideas with the realities, since we know the realities
+only by our ideas." We know the realities (I conceive) by our senses.
+Dr. Whewell surely does not hold the "doctrine of perception by means of
+ideas," which Reid gave himself so much trouble to refute.
+
+If Dr. Whewell doubts whether we compare our ideas with the
+corresponding sensations, and assume that they resemble, let me ask on
+what evidence do we judge that a portrait of a person not present is
+like the original. Surely because it is like our idea, or mental image
+of the person, and because our idea is like the man himself.
+
+Dr. Whewell also says, that it does not appear why this resemblance of
+ideas to the sensations of which they are copies, should be spoken of as
+if it were a peculiarity of one class of ideas, those of space. My reply
+is, that I do not so speak of it. The peculiarity I contend for is only
+one of degree. All our ideas of sensation of course resemble the
+corresponding sensations, but they do so with very different degrees of
+exactness and of reliability. No one, I presume, can recal in
+imagination a colour or an odour with the same distinctness and accuracy
+with which almost every one can mentally reproduce an image of a
+straight line or a triangle. To the extent, however, of their
+capabilities of accuracy, our recollections of colours or of odours may
+serve as subjects of experimentation, as well as those of lines and
+spaces, and may yield conclusions which will be true of their external
+prototypes. A person in whom, either from natural gift or from
+cultivation, the impressions of colour were peculiarly vivid and
+distinct, if asked which of two blue flowers was of the darkest tinge,
+though he might never have compared the two, or even looked at them
+together, might be able to give a confident answer on the faith of his
+distinct recollection of the colours; that is, he might examine his
+mental pictures, and find there a property of the outward objects. But
+in hardly any case except that of simple geometrical forms, could this
+be done by mankind generally, with a degree of assurance equal to that
+which is given by a contemplation of the objects themselves. Persons
+differ most widely in the precision of their recollection, even of
+forms: one person, when he has looked any one in the face for half a
+minute, can draw an accurate likeness of him from memory; another may
+have seen him every day for six months, and hardly know whether his nose
+is long or short. But everybody has a perfectly distinct mental image of
+a straight line, a circle, or a rectangle. And every one concludes
+confidently from these mental images to the corresponding outward
+things. The truth is, that we may, and continually do, study nature in
+our recollections, when the objects themselves are absent; and in the
+case of geometrical forms we can perfectly, but in most other cases only
+imperfectly, trust our recollections.
+
+[24] _History of Scientific Ideas_, i. 65-67.
+
+[25] Ibid. 60.
+
+[26] _History of Scientific Ideas_, i. 58, 59.
+
+[27] "If all mankind had spoken one language, we cannot doubt that there
+would have been a powerful, perhaps a universal, school of philosophers,
+who would have believed in the inherent connexion between names and
+things, who would have taken the sound _man_ to be the mode of agitating
+the air which is essentially communicative of the ideas of reason,
+cookery, bipedality, &c."--De Morgan, _Formal Logic_, p. 246.
+
+[28] It would be difficult to name a man more remarkable at once for the
+greatness and the wide range of his mental accomplishments, than
+Leibnitz. Yet this eminent man gave as a reason for rejecting Newton's
+scheme of the solar system, that God _could not_ make a body revolve
+round a distant centre, unless either by some impelling mechanism, or by
+miracle:--"Tout ce qui n'est pas explicable" says he in a letter to the
+Abb� Conti, "par la nature des cr�atures, est miraculeux. Il ne suffit
+pas de dire: Dieu a fait une telle loi de nature; donc la chose est
+naturelle. Il faut que la loi soit ex�cutable par les natures des
+cr�atures. Si Dieu donnait cette loi, par exemple, � un corps libre, de
+tourner � l'entour d'un certain centre, _il faudrait ou qu'il y joign�t
+d'autres corps qui par leur impulsion l'obligeassent de rester toujours
+dans son orbite circulaire, ou qu'il m�t un ange � ses trousses, ou
+enfin il faudrait qu'il y concour�t extraordinairement_; car
+naturellement il s'�cartera par la tangente."--_Works of Leibnitz_, ed.
+Dutens, iii. 446.
+
+[29] _Novum Organum Renovatum_, pp. 32, 33.
+
+[30] _History of Scientific Ideas_, i. 264.
+
+[31] _Hist. Sc. Id._, i. 263.
+
+[32] Ibid. 240.
+
+[33] _Hist. Sc. Id._, ii. 25, 26.
+
+[34] _Phil. of Disc._, p. 339.
+
+[35] _Phil. of Disc._, p. 338.
+
+[36] Ib. p. 463.
+
+[37] _Phil. of Disc._, pp. 472, 473.
+
+[38] The _Quarterly Review_ for June 1841, contained an article of great
+ability on Dr. Whewell's two great works (since acknowledged and
+reprinted in Sir John Herschel's Essays) which maintains, on the subject
+of axioms, the doctrine advanced in the text, that they are
+generalizations from experience, and supports that opinion by a line of
+argument strikingly coinciding with mine. When I state that the whole of
+the present chapter (except the last four pages, added in the fifth
+edition) was written before I had seen the article, (the greater part,
+indeed, before it was published,) it is not my object to occupy the
+reader's attention with a matter so unimportant as the degree of
+originality which may or may not belong to any portion of my own
+speculations, but to obtain for an opinion which is opposed to reigning
+doctrines, the recommendation derived from a striking concurrence of
+sentiment between two inquirers entirely independent of one another. I
+embrace the opportunity of citing from a writer of the extensive
+acquirements in physical and metaphysical knowledge and the capacity of
+systematic thought which the article evinces, passages so remarkably in
+unison with my own views as the following:--
+
+"The truths of geometry are summed up and embodied in its definitions
+and axioms.... Let us turn to the axioms, and what do we find? A string
+of propositions concerning magnitude in the abstract, which are equally
+true of space, time, force, number, and every other magnitude
+susceptible of aggregation and subdivision. Such propositions, where
+they are not mere definitions, as some of them are, carry their
+inductive origin on the face of their enunciation.... Those which
+declare that two straight lines cannot inclose a space, and that two
+straight lines which cut one another cannot both be parallel to a third,
+are in reality the only ones which express characteristic properties of
+space, and these it will be worth while to consider more nearly. Now the
+only clear notion we can form of straightness is uniformity of
+direction, for space in its ultimate analysis is nothing but an
+assemblage of distances and directions. And (not to dwell on the notion
+of continued contemplation, _i.e._, mental experience, as included in
+the very idea of uniformity; nor on that of transfer of the
+contemplating being from point to point, and of experience, during such
+transfer, of the homogeneity of the interval passed over) we cannot even
+propose the proposition in an intelligible form to any one whose
+experience ever since he was born has not assured him of the fact. The
+unity of direction, or that we cannot march from a given point by more
+than one path direct to the same object, is matter of practical
+experience long before it can by possibility become matter of abstract
+thought. _We cannot attempt mentally to exemplify the conditions of the
+assertion in an imaginary case opposed to it, without violating our
+habitual recollection of this experience, and defacing our mental
+picture of space as grounded on it._ What but experience, we may ask,
+can possibly assure us of the homogeneity of the parts of distance,
+time, force, and measurable aggregates in general, on which the truth of
+the other axioms depends? As regards the latter axiom, after what has
+been said it must be clear that the very same course of remarks equally
+applies to its case, and that its truth is quite as much forced on the
+mind as that of the former by daily and hourly experience, ...
+_including always, be it observed, in our notion of experience, that
+which is gained by contemplation of the inward picture which the mind
+forms to itself in any proposed case, or which it arbitrarily selects as
+an example--such picture, in virtue of the extreme simplicity of these
+primary relations, being called up by the imagination with as much
+vividness and clearness as could be done by any external impression,
+which is the only meaning we can attach to the word intuition, as
+applied to such relations_."
+
+And again, of the axioms of mechanics:--"As we admit no such
+propositions, other than as truths inductively collected from
+observation, even in geometry itself, it can hardly be expected that, in
+a science of obviously contingent relations, we should acquiesce in a
+contrary view. Let us take one of these axioms and examine its evidence:
+for instance, that equal forces perpendicularly applied at the opposite
+ends of equal arms of a straight lever will balance each other. What but
+experience, we may ask, in the first place, can possibly inform us that
+a force so applied will have any tendency to turn the lever on its
+centre at all? or that force can be so transmitted along a rigid line
+perpendicular to its direction, as to act elsewhere in space than along
+its own line of action? Surely this is so far from being self-evident
+that it has even a paradoxical appearance, which is only to be removed
+by giving our lever thickness, material composition, and molecular
+powers. Again, we conclude, that the two forces, being equal and applied
+under precisely similar circumstances, must, if they exert any effort at
+all to turn the lever, exert equal and opposite efforts: but what _�
+priori_ reasoning can possibly assure us that they _do_ act under
+precisely similar circumstances? that points which differ in place _are_
+similarly circumstanced as regards the exertion of force? that universal
+space may not have relations to universal force--or, at all events, that
+the organization of the material universe may not be such as to place
+that portion of space occupied by it in such relations to the forces
+exerted in it, as may invalidate the absolute similarity of
+circumstances assumed? Or we may argue, what have we to do with the
+notion of angular movement in the lever at all? The case is one of rest,
+and of quiescent destruction of force by force. Now how is this
+destruction effected? Assuredly by the counter-pressure which supports
+the fulcrum. But would not this destruction equally arise, and by the
+same amount of counter-acting force, if each force simply pressed its
+own half of the lever against the fulcrum? And what can assure us that
+it is not so, except removal of one or other force, and consequent
+tilting of the lever? The other fundamental axiom of statics, that the
+pressure on the point of support is the sum of the weights ... is merely
+a scientific transformation and more refined mode of stating a coarse
+and obvious result of universal experience, viz. that the weight of a
+rigid body is the same, handle it or suspend it in what position or by
+what point we will, and that whatever sustains it sustains its total
+weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever
+made a trial for the purpose of showing that the pressure on the support
+is equal to the sum of the weights.' ... But it is precisely because in
+every action of his life from earliest infancy he has been continually
+making the trial, and seeing it made by every other living being about
+him, that he never dreams of staking its result on one additional
+attempt made with scientific accuracy. This would be as if a man should
+resolve to decide by experiment whether his eyes were useful for the
+purpose of seeing, by hermetically sealing himself up for half an hour
+in a metal case."
+
+On the "paradox of universal propositions obtained by experience," the
+same writer says: "If there be necessary and universal truths
+expressible in propositions of axiomatic simplicity and obviousness, and
+having for their subject-matter the elements of all our experience and
+all our knowledge, surely these are the truths which, if experience
+suggest to us any truths at all, it ought to suggest most readily,
+clearly, and unceasingly. If it were a truth, universal and necessary,
+that a net is spread over the whole surface of every planetary globe, we
+should not travel far on our own without getting entangled in its
+meshes, and making the necessity of some means of extrication an axiom
+of locomotion.... There is, therefore, nothing paradoxical, but the
+reverse, in our being led by observation to a recognition of such
+truths, as _general_ propositions, coextensive at least with all human
+experience. That they pervade all the objects of experience, must ensure
+their continual suggestion _by_ experience; that they are true, must
+ensure that consistency of suggestion, that iteration of uncontradicted
+assertion, which commands implicit assent, and removes all occasion of
+exception; that they are simple, and admit of no misunderstanding, must
+secure their admission by every mind."
+
+"A truth, necessary and universal, relative to any object of our
+knowledge, must verify itself in every instance where that object is
+before our contemplation, and if at the same time it be simple and
+intelligible, its verification must be obvious. _The sentiment of such a
+truth cannot, therefore, but be present to our minds whenever that
+object is contemplated, and must therefore make a part of the mental
+picture or idea of that object which we may on any occasion summon
+before our imagination.... All propositions, therefore, become not only
+untrue but inconceivable_, if ... axioms be violated in their
+enunciation."
+
+Another eminent mathematician had previously sanctioned by his authority
+the doctrine of the origin of geometrical axioms in experience.
+"Geometry is thus founded likewise on observation; but of a kind so
+familiar and obvious, that the primary notions which it furnishes might
+seem intuitive."--_Sir John Leslie_, quoted by Sir William Hamilton,
+_Discourses_, &c. p. 272.
+
+[39] _Principles of Psychology._
+
+[40] Mr. Spencer is mistaken in supposing me to claim any peculiar
+"necessity" for this axiom as compared with others. I have corrected the
+expressions which led him into that misapprehension of my meaning.
+
+[41] Mr. Spencer makes a distinction between conceiving myself looking
+into darkness, and conceiving _that I am_ then and there looking into
+darkness. To me it seems that this change of the expression to the form
+_I am_, just marks the transition from conception to belief, and that
+the phrase "to conceive that _I am_," or "that anything _is_," is not
+consistent with using the word conceive in its rigorous sense.
+
+[42] I have myself accepted the contest, and fought it out on this
+battleground, in the eleventh chapter of _An Examination of Sir William
+Hamilton's Philosophy_.
+
+[43] _Discussions_, &c., 2nd ed. p. 624.
+
+[44] If it be said that the _existence_ of matter is among the things
+proved by the principle of Excluded Middle, that principle must prove
+also the existence of dragons and hippogriffs, because they must be
+either scaly or not scaly, creeping or not creeping, and so forth.
+
+[45] For further considerations respecting the axioms of Contradiction
+and Excluded Middle, see the twenty-first chapter of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[46] Mr. De Morgan says "Plato," but to prevent confusion I have kept to
+my own _exemplum_.
+
+
+
+
+BOOK III.
+
+OF INDUCTION.
+
+
+"According to the doctrine now stated, the highest, or rather the only
+proper object of physics, is to ascertain those established conjunctions
+of successive events, which constitute the order of the universe; to
+record the phenomena which it exhibits to our observations, or which it
+discloses to our experiments; and to refer these phenomena to their
+general laws."--D. STEWART, _Elements of the Philosophy of the Human
+Mind_, vol. ii. chap. iv. sect. 1.
+
+
+
+
+CHAPTER I.
+
+PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.
+
+
+� 1. The portion of the present inquiry upon which we are now about to
+enter, may be considered as the principal, both from its surpassing in
+intricacy all the other branches, and because it relates to a process
+which has been shown in the preceding Book to be that in which the
+investigation of nature essentially consists. We have found that all
+Inference, consequently all Proof, and all discovery of truths not
+self-evident, consists of inductions, and the interpretation of
+inductions: that all our knowledge, not intuitive, comes to us
+exclusively from that source. What Induction is, therefore, and what
+conditions render it legitimate, cannot but be deemed the main question
+of the science of logic--the question which includes all others. It is,
+however, one which professed writers on logic have almost entirely
+passed over. The generalities of the subject have not been altogether
+neglected by metaphysicians; but, for want of sufficient acquaintance
+with the processes by which science has actually succeeded in
+establishing general truths, their analysis of the inductive operation,
+even when unexceptionable as to correctness, has not been specific
+enough to be made the foundation of practical rules, which might be for
+induction itself what the rules of the syllogism are for the
+interpretation of induction: while those by whom physical science has
+been carried to its present state of improvement--and who, to arrive at
+a complete theory of the process, needed only to generalize, and adapt
+to all varieties of problems, the methods which they themselves employed
+in their habitual pursuits--never until very lately made any serious
+attempt to philosophize on the subject, nor regarded the mode in which
+they arrived at their conclusions as deserving of study, independently
+of the conclusions themselves.
+
+
+� 2. For the purposes of the present inquiry, Induction may be defined,
+the operation of discovering and proving general propositions. It is
+true that (as already shown) the process of indirectly ascertaining
+individual facts, is as truly inductive as that by which we establish
+general truths. But it is not a different kind of induction; it is a
+form of the very same process: since, on the one hand, generals are but
+collections of particulars, definite in kind but indefinite in number;
+and on the other hand, whenever the evidence which we derive from
+observation of known cases justifies us in drawing an inference
+respecting even one unknown case, we should on the same evidence be
+justified in drawing a similar inference with respect to a whole class
+of cases. The inference either does not hold at all, or it holds in all
+cases of a certain description; in all cases which, in certain definable
+respects, resemble those we have observed.
+
+If these remarks are just; if the principles and rules of inference are
+the same whether we infer general propositions or individual facts; it
+follows that a complete logic of the sciences would be also a complete
+logic of practical business and common life. Since there is no case of
+legitimate inference from experience, in which the conclusion may not
+legitimately be a general proposition; an analysis of the process by
+which general truths are arrived at, is virtually an analysis of all
+induction whatever. Whether we are inquiring into a scientific principle
+or into an individual fact, and whether we proceed by experiment or by
+ratiocination, every step in the train of inferences is essentially
+inductive, and the legitimacy of the induction depends in both cases on
+the same conditions.
+
+True it is that in the case of the practical inquirer, who is
+endeavouring to ascertain facts not for the purposes of science but for
+those of business, such for instance as the advocate or the judge, the
+chief difficulty is one in which the principles of induction will afford
+him no assistance. It lies not in making his inductions, but in the
+selection of them; in choosing from among all general propositions
+ascertained to be true, those which furnish marks by which he may trace
+whether the given subject possesses or not the predicate in question. In
+arguing a doubtful question of fact before a jury, the general
+propositions or principles to which the advocate appeals are mostly, in
+themselves, sufficiently trite, and assented to as soon as stated: his
+skill lies in bringing his case under those propositions or principles;
+in calling to mind such of the known or received maxims of probability
+as admit of application to the case in hand, and selecting from among
+them those best adapted to his object. Success is here dependent on
+natural or acquired sagacity, aided by knowledge of the particular
+subject, and of subjects allied with it. Invention, though it can be
+cultivated, cannot be reduced to rule; there is no science which will
+enable a man to bethink himself of that which will suit his purpose.
+
+But when he _has_ thought of something, science can tell him whether
+that which he has thought of will suit his purpose or not. The inquirer
+or arguer must be guided by his own knowledge and sagacity in the choice
+of the inductions out of which he will construct his argument. But the
+validity of the argument when constructed, depends on principles and
+must be tried by tests which are the same for all descriptions of
+inquiries, whether the result be to give A an estate, or to enrich
+science with a new general truth. In the one case and in the other, the
+senses, or testimony, must decide on the individual facts; the rules of
+the syllogism will determine whether, those facts being supposed
+correct, the case really falls within the formul� of the different
+inductions under which it has been successively brought; and finally,
+the legitimacy of the inductions themselves must be decided by other
+rules, and these it is now our purpose to investigate. If this third
+part of the operation be, in many of the questions of practical life,
+not the most, but the least arduous portion of it, we have seen that
+this is also the case in some great departments of the field of science;
+in all those which are principally deductive, and most of all in
+mathematics; where the inductions themselves are few in number, and so
+obvious and elementary that they seem to stand in no need of the
+evidence of experience, while to combine them so as to prove a given
+theorem or solve a problem, may call for the utmost powers of invention
+and contrivance with which our species is gifted.
+
+If the identity of the logical processes which prove particular facts
+and those which establish general scientific truths, required any
+additional confirmation, it would be sufficient to consider that in many
+branches of science, single facts have to be proved, as well as
+principles; facts as completely individual as any that are debated in a
+court of justice; but which are proved in the same manner as the other
+truths of the science, and without disturbing in any degree the
+homogeneity of its method. A remarkable example of this is afforded by
+astronomy. The individual facts on which that science grounds its most
+important deductions, such facts as the magnitudes of the bodies of the
+solar system, their distances from one another, the figure of the earth,
+and its rotation, are scarcely any of them accessible to our means of
+direct observation: they are proved indirectly, by the aid of inductions
+founded on other facts which we can more easily reach. For example, the
+distance of the moon from the earth was determined by a very circuitous
+process. The share which direct observation had in the work consisted in
+ascertaining, at one and the same instant, the zenith distances of the
+moon, as seen from two points very remote from one another on the
+earth's surface. The ascertainment of these angular distances
+ascertained their supplements; and since the angle at the earth's centre
+subtended by the distance between the two places of observation was
+deducible by spherical trigonometry from the latitude and longitude of
+those places, the angle at the moon subtended by the same line became
+the fourth angle of a quadrilateral of which the other three angles were
+known. The four angles being thus ascertained, and two sides of the
+quadrilateral being radii of the earth; the two remaining sides and the
+diagonal, or in other words, the moon's distance from the two places of
+observation and from the centre of the earth, could be ascertained, at
+least in terms of the earth's radius, from elementary theorems of
+geometry. At each step in this demonstration we take in a new
+induction, represented, in the aggregate of its results, by a general
+proposition.
+
+Not only is the process by which an individual astronomical fact was
+thus ascertained, exactly similar to those by which the same science
+establishes its general truths, but also (as we have shown to be the
+case in all legitimate reasoning) a general proposition might have been
+concluded instead of a single fact. In strictness, indeed, the result of
+the reasoning _is_ a general proposition; a theorem respecting the
+distance, not of the moon in particular, but of any inaccessible object:
+showing in what relation that distance stands to certain other
+quantities. And although the moon is almost the only heavenly body the
+distance of which from the earth can really be thus ascertained, this is
+merely owing to the accidental circumstances of the other heavenly
+bodies, which render them incapable of affording such data as the
+application of the theorem requires; for the theorem itself is as true
+of them as it is of the moon.[1]
+
+We shall fall into no error, then, if in treating of Induction, we
+limit our attention to the establishment of general propositions. The
+principles and rules of Induction as directed to this end, are the
+principles and rules of all Induction; and the logic of Science is the
+universal Logic, applicable to all inquiries in which man can engage.
+
+
+
+
+CHAPTER II.
+
+OF INDUCTIONS IMPROPERLY SO CALLED.
+
+
+� 1. Induction, then, is that operation of the mind, by which we infer
+that what we know to be true in a particular case or cases, will be true
+in all cases which resemble the former in certain assignable respects.
+In other words, Induction is the process by which we conclude that what
+is true of certain individuals of a class is true of the whole class, or
+that what is true at certain times will be true in similar circumstances
+at all times.
+
+This definition excludes from the meaning of the term Induction, various
+logical operations, to which it is not unusual to apply that name.
+
+Induction, as above defined, is a process of inference; it proceeds from
+the known to the unknown; and any operation involving no inference, any
+process in which what seems the conclusion is no wider than the premises
+from which it is drawn, does not fall within the meaning of the term.
+Yet in the common books of Logic we find this laid down as the most
+perfect, indeed the only quite perfect, form of induction. In those
+books, every process which sets out from a less general and terminates
+in a more general expression,--which admits of being stated in the form,
+"This and that A are B, therefore every A is B,"--is called an
+induction, whether anything be really concluded or not: and the
+induction is asserted not to be perfect, unless every single individual
+of the class A is included in the antecedent, or premise: that is,
+unless what we affirm of the class has already been ascertained to be
+true of every individual in it, so that the nominal conclusion is not
+really a conclusion, but a mere reassertion of the premises. If we were
+to say, All the planets shine by the sun's light, from observation of
+each separate planet, or All the Apostles were Jews, because this is
+true of Peter, Paul, John, and every other apostle,--these, and such as
+these, would, in the phraseology in question, be called perfect, and the
+only perfect, Inductions. This, however, is a totally different kind of
+induction from ours; it is not an inference from facts known to facts
+unknown, but a mere short-hand registration of facts known. The two
+simulated arguments which we have quoted, are not generalizations; the
+propositions purporting to be conclusions from them, are not really
+general propositions. A general proposition is one in which the
+predicate is affirmed or denied of an unlimited number of individuals;
+namely, all, whether few or many, existing or capable of existing, which
+possess the properties connoted by the subject of the proposition. "All
+men are mortal" does not mean all now living, but all men past, present,
+and to come. When the signification of the term is limited so as to
+render it a name not for any and every individual falling under a
+certain general description, but only for each of a number of
+individuals designated as such, and as it were counted off individually,
+the proposition, though it may be general in its language, is no general
+proposition, but merely that number of singular propositions, written in
+an abridged character. The operation may be very useful, as most forms
+of abridged notation are; but it is no part of the investigation of
+truth, though often bearing an important part in the preparation of the
+materials for that investigation.
+
+As we may sum up a definite number of singular propositions in one
+proposition, which will be apparently, but not really, general, so we
+may sum up a definite number of general propositions in one proposition,
+which will be apparently, but not really, more general. If by a separate
+induction applied to every distinct species of animals, it has been
+established that each possesses a nervous system, and we affirm
+thereupon that all animals have a nervous system; this looks like a
+generalization, though as the conclusion merely affirms of all what has
+already been affirmed of each, it seems to tell us nothing but what we
+knew before. A distinction however must be made. If in concluding that
+all animals have a nervous system, we mean the same thing and no more as
+if we had said "all known animals," the proposition is not general, and
+the process by which it is arrived at is not induction. But if our
+meaning is that the observations made of the various species of animals
+have discovered to us a law of animal nature, and that we are in a
+condition to say that a nervous system will be found even in animals yet
+undiscovered, this indeed is an induction; but in this case the general
+proposition contains more than the sum of the special propositions from
+which it is inferred. The distinction is still more forcibly brought out
+when we consider, that if this real generalization be legitimate at all,
+its legitimacy probably does not require that we should have examined
+without exception every known species. It is the number and nature of
+the instances, and not their being the whole of those which happen to be
+known, that makes them sufficient evidence to prove a general law: while
+the more limited assertion, which stops at all known animals, cannot be
+made unless we have rigorously verified it in every species. In like
+manner (to return to a former example) we might have inferred, not that
+all _the_ planets, but that all _planets_, shine by reflected light: the
+former is no induction; the latter is an induction, and a bad one, being
+disproved by the case of double stars--self-luminous bodies which are
+properly planets, since they revolve round a centre.
+
+
+� 2. There are several processes used in mathematics which require to be
+distinguished from Induction, being not unfrequently called by that
+name, and being so far similar to Induction properly so called, that the
+propositions they lead to are really general propositions. For example,
+when we have proved with respect to the circle, that a straight line
+cannot meet it in more than two points, and when the same thing has been
+successively proved of the ellipse, the parabola, and the hyperbola, it
+may be laid down as an universal property of the sections of the cone.
+The distinction drawn in the two previous examples can have no place
+here, there being no difference between all _known_ sections of the
+cone and _all_ sections, since a cone demonstrably cannot be intersected
+by a plane except in one of these four lines. It would be difficult,
+therefore, to refuse to the proposition arrived at, the name of a
+generalization, since there is no room for any generalization beyond it.
+But there is no induction, because there is no inference: the conclusion
+is a mere summing up of what was asserted in the various propositions
+from which it is drawn. A case somewhat, though not altogether, similar,
+is the proof of a geometrical theorem by means of a diagram. Whether the
+diagram be on paper or only in the imagination, the demonstration (as
+formerly observed[2]) does not prove directly the general theorem; it
+proves only that the conclusion, which the theorem asserts generally, is
+true of the particular triangle or circle exhibited in the diagram; but
+since we perceive that in the same way in which we have proved it of
+that circle, it might also be proved of any other circle, we gather up
+into one general expression all the singular propositions susceptible of
+being thus proved, and embody them in an universal proposition. Having
+shown that the three angles of the triangle ABC are together equal to
+two right angles, we conclude that this is true of every other triangle,
+not because it is true of ABC, but for the same reason which proved it
+to be true of ABC. If this were to be called Induction, an appropriate
+name for it would be, induction by parity of reasoning. But the term
+cannot properly belong to it; the characteristic quality of Induction is
+wanting, since the truth obtained, though really general, is not
+believed on the evidence of particular instances. We do not conclude
+that all triangles have the property because some triangles have, but
+from the ulterior demonstrative evidence which was the ground of our
+conviction in the particular instances.
+
+There are nevertheless, in mathematics, some examples of so-called
+Induction, in which the conclusion does bear the appearance of a
+generalization grounded on some of the particular cases included in it.
+A mathematician, when he has calculated a sufficient number of the
+terms of an algebraical or arithmetical series to have ascertained what
+is called the _law_ of the series, does not hesitate to fill up any
+number of the succeeding terms without repeating the calculations. But I
+apprehend he only does so when it is apparent from _� priori_
+considerations (which might be exhibited in the form of demonstration)
+that the mode of formation of the subsequent terms, each from that which
+preceded it, must be similar to the formation of the terms which have
+been already calculated. And when the attempt has been hazarded without
+the sanction of such general considerations, there are instances on
+record in which it has led to false results.
+
+It is said that Newton discovered the binomial theorem by induction; by
+raising a binomial successively to a certain number of powers, and
+comparing those powers with one another until he detected the relation
+in which the algebraic formula of each power stands to the exponent of
+that power, and to the two terms of the binomial. The fact is not
+improbable: but a mathematician like Newton, who seemed to arrive _per
+saltum_ at principles and conclusions that ordinary mathematicians only
+reached by a succession of steps, certainly could not have performed the
+comparison in question without being led by it to the _� priori_ ground
+of the law; since any one who understands sufficiently the nature of
+multiplication to venture upon multiplying several lines of symbols at
+one operation, cannot but perceive that in raising a binomial to a
+power, the coefficients must depend on the laws of permutation and
+combination: and as soon as this is recognised, the theorem is
+demonstrated. Indeed, when once it was seen that the law prevailed in a
+few of the lower powers, its identity with the law of permutation would
+at once suggest the considerations which prove it to obtain universally.
+Even, therefore, such cases as these, are but examples of what I have
+called Induction by parity of reasoning, that is, not really Induction,
+because not involving inference of a general proposition from particular
+instances.
+
+
+� 3. There remains a third improper use of the term Induction, which it
+is of real importance to clear up, because the theory of Induction has
+been, in no ordinary degree, confused by it, and because the confusion
+is exemplified in the most recent and elaborate treatise on the
+inductive philosophy which exists in our language. The error in question
+is that of confounding a mere description, by general terms, of a set of
+observed phenomena, with an induction from them.
+
+Suppose that a phenomenon consists of parts, and that these parts are
+only capable of being observed separately, and as it were piecemeal.
+When the observations have been made, there is a convenience (amounting
+for many purposes to a necessity) in obtaining a representation of the
+phenomenon as a whole, by combining, or as we may say, piecing these
+detached fragments together. A navigator sailing in the midst of the
+ocean discovers land: he cannot at first, or by any one observation,
+determine whether it is a continent or an island; but he coasts along
+it, and after a few days finds himself to have sailed completely round
+it: he then pronounces it an island. Now there was no particular time or
+place of observation at which he could perceive that this land was
+entirely surrounded by water: he ascertained the fact by a succession of
+partial observations, and then selected a general expression which
+summed up in two or three words the whole of what he so observed. But is
+there anything of the nature of an induction in this process? Did he
+infer anything that had not been observed, from something else which
+had? Certainly not. He had observed the whole of what the proposition
+asserts. That the land in question is an island, is not an inference
+from the partial facts which the navigator saw in the course of his
+circumnavigation; it is the facts themselves; it is a summary of those
+facts; the description of a complex fact, to which those simpler ones
+are as the parts of a whole.
+
+Now there is, I conceive, no difference in kind between this simple
+operation, and that by which Kepler ascertained the nature of the
+planetary orbits: and Kepler's operation, all at least that was
+characteristic in it, was not more an inductive act than that of our
+supposed navigator.
+
+The object of Kepler was to determine the real path described by each
+of the planets, or let us say by the planet Mars (since it was of that
+body that he first established the two of his three laws which did not
+require a comparison of planets). To do this there was no other mode
+than that of direct observation: and all which observation could do was
+to ascertain a great number of the successive places of the planet; or
+rather, of its apparent places. That the planet occupied successively
+all these positions, or at all events, positions which produced the same
+impressions on the eye, and that it passed from one of these to another
+insensibly, and without any apparent breach of continuity; thus much the
+senses, with the aid of the proper instruments, could ascertain. What
+Kepler did more than this, was to find what sort of a curve these
+different points would make, supposing them to be all joined together.
+He expressed the whole series of the observed places of Mars by what Dr.
+Whewell calls the general conception of an ellipse. This operation was
+far from being as easy as that of the navigator who expressed the series
+of his observations on successive points of the coast by the general
+conception of an island. But it is the very same sort of operation; and
+if the one is not an induction but a description, this must also be true
+of the other.
+
+The only real induction concerned in the case, consisted in inferring
+that because the observed places of Mars were correctly represented by
+points in an imaginary ellipse, therefore Mars would continue to revolve
+in that same ellipse; and in concluding (before the gap had been filled
+up by further observations) that the positions of the planet during the
+time which intervened between two observations, must have coincided with
+the intermediate points of the curve. For these were facts which had not
+been directly observed. They were inferences from the observations;
+facts inferred, as distinguished from facts seen. But these inferences
+were so far from being a part of Kepler's philosophical operation, that
+they had been drawn long before he was born. Astronomers had long known
+that the planets periodically returned to the same places. When this had
+been ascertained, there was no induction left for Kepler to make, nor
+did he make any further induction. He merely applied his new conception
+to the facts inferred, as he did to the facts observed. Knowing already
+that the planets continued to move in the same paths; when he found that
+an ellipse correctly represented the past path, he knew that it would
+represent the future path. In finding a compendious expression for the
+one set of facts, he found one for the other: but he found the
+expression only, not the inference; nor did he (which is the true test
+of a general truth) add anything to the power of prediction already
+possessed.
+
+
+� 4. The descriptive operation which enables a number of details to be
+summed up in a single proposition, Dr. Whewell, by an aptly chosen
+expression, has termed the Colligation of Facts. In most of his
+observations concerning that mental process I fully agree, and would
+gladly transfer all that portion of his book into my own pages. I only
+think him mistaken in setting up this kind of operation, which according
+to the old and received meaning of the term, is not induction at all, as
+the type of induction generally; and laying down, throughout his work,
+as principles of induction, the principles of mere colligation.
+
+Dr. Whewell maintains that the general proposition which binds together
+the particular facts, and makes them, as it were, one fact, is not the
+mere sum of those facts, but something more, since there is introduced a
+conception of the mind, which did not exist in the facts themselves.
+"The particular facts," says he,[3] "are not merely brought together,
+but there is a new element added to the combination by the very act of
+thought by which they are combined.... When the Greeks, after long
+observing the motions of the planets, saw that these motions might be
+rightly considered as produced by the motion of one wheel revolving in
+the inside of another wheel, these wheels were creations of their minds,
+added to the facts which they perceived by sense. And even if the
+wheels were no longer supposed to be material, but were reduced to mere
+geometrical spheres or circles, they were not the less products of the
+mind alone,--something additional to the facts observed. The same is the
+case in all other discoveries. The facts are known, but they are
+insulated and unconnected, till the discoverer supplies from his own
+store a principle of connexion. The pearls are there, but they will not
+hang together till some one provides the string."
+
+Let me first remark that Dr. Whewell, in this passage, blends together,
+indiscriminately, examples of both the processes which I am endeavouring
+to distinguish from one another. When the Greeks abandoned the
+supposition that the planetary motions were produced by the revolution
+of material wheels, and fell back upon the idea of "mere geometrical
+spheres or circles," there was more in this change of opinion than the
+mere substitution of an ideal curve for a physical one. There was the
+abandonment of a theory, and the replacement of it by a mere
+description. No one would think of calling the doctrine of material
+wheels a mere description. That doctrine was an attempt to point out the
+force by which the planets were acted upon, and compelled to move in
+their orbits. But when, by a great step in philosophy, the materiality
+of the wheels was discarded, and the geometrical forms alone retained,
+the attempt to account for the motions was given up, and what was left
+of the theory was a mere description of the orbits. The assertion that
+the planets were carried round by wheels revolving in the inside of
+other wheels, gave place to the proposition, that they moved in the same
+lines which would be traced by bodies so carried: which was a mere mode
+of representing the sum of the observed facts; as Kepler's was another
+and a better mode of representing the same observations.
+
+It is true that for these simply descriptive operations, as well as for
+the erroneous inductive one, a conception of the mind was required. The
+conception of an ellipse must have presented itself to Kepler's mind,
+before he could identify the planetary orbits with it. According to Dr.
+Whewell, the conception was something added to the facts. He expresses
+himself as if Kepler had put something into the facts by his mode of
+conceiving them. But Kepler did no such thing. The ellipse was in the
+facts before Kepler recognised it; just as the island was an island
+before it had been sailed round. Kepler did not _put_ what he had
+conceived into the facts, but _saw_ it in them. A conception implies,
+and corresponds to, something conceived: and though the conception
+itself is not in the facts, but in our mind, yet if it is to convey any
+knowledge relating to them, it must be a conception _of_ something which
+really is in the facts, some property which they actually possess, and
+which they would manifest to our senses, if our senses were able to take
+cognizance of it. If, for instance, the planet left behind it in space a
+visible track, and if the observer were in a fixed position at such a
+distance from the plane of the orbit as would enable him to see the
+whole of it at once, he would see it to be an ellipse; and if gifted
+with appropriate instruments and powers of locomotion, he could prove it
+to be such by measuring its different dimensions. Nay, further: if the
+track were visible, and he were so placed that he could see all parts of
+it in succession, but not all of them at once, he might be able, by
+piecing together his successive observations, to discover both that it
+was an ellipse and that the planet moved in it. The case would then
+exactly resemble that of the navigator who discovers the land to be an
+island by sailing round it. If the path was visible, no one I think
+would dispute that to identify it with an ellipse is to describe it: and
+I cannot see why any difference should be made by its not being directly
+an object of sense, when every point in it is as exactly ascertained as
+if it were so.
+
+Subject to the indispensable condition which has just been stated, I
+cannot conceive that the part which conceptions have in the operation of
+studying facts, has ever been overlooked or undervalued. No one ever
+disputed that in order to reason about anything we must have a
+conception of it; or that when we include a multitude of things under a
+general expression, there is implied in the expression a conception of
+something common to those things. But it by no means follows that the
+conception is necessarily pre-existent, or constructed by the mind out
+of its own materials. If the facts are rightly classed under the
+conception, it is because there is in the facts themselves something of
+which the conception is itself a copy; and which if we cannot directly
+perceive, it is because of the limited power of our organs, and not
+because the thing itself is not there. The conception itself is often
+obtained by abstraction from the very facts which, in Dr. Whewell's
+language, it is afterwards called in to connect. This he himself admits,
+when he observes, (which he does on several occasions,) how great a
+service would be rendered to the science of physiology by the
+philosopher "who should establish a precise, tenable, and consistent
+conception of life."[4] Such a conception can only be abstracted from
+the phenomena of life itself; from the very facts which it is put in
+requisition to connect. In other cases, no doubt, instead of collecting
+the conception from the very phenomena which we are attempting to
+colligate, we select it from among those which have been previously
+collected by abstraction from other facts. In the instance of Kepler's
+laws, the latter was the case. The facts being out of the reach of being
+observed, in any such manner as would have enabled the senses to
+identify directly the path of the planet, the conception requisite for
+framing a general description of that path could not be collected by
+abstraction from the observations themselves; the mind had to supply
+hypothetically, from among the conceptions it had obtained from other
+portions of its experience, some one which would correctly represent the
+series of the observed facts. It had to frame a supposition respecting
+the general course of the phenomenon, and ask itself, If this be the
+general description, what will the details be? and then compare these
+with the details actually observed. If they agreed, the hypothesis would
+serve for a description of the phenomenon: if not, it was necessarily
+abandoned, and another tried. It is such a case as this which gives rise
+to the doctrine that the mind, in framing the descriptions, adds
+something of its own which it does not find in the facts.
+
+Yet it is a fact surely, that the planet does describe an ellipse; and a
+fact which we could see, if we had adequate visual organs and a suitable
+position. Not having these advantages, but possessing the conception of
+an ellipse, or (to express the meaning in less technical language)
+knowing what an ellipse was, Kepler tried whether the observed places of
+the planet were consistent with such a path. He found they were so; and
+he, consequently, asserted as a fact that the planet moved in an
+ellipse. But this fact, which Kepler did not add to, but found in, the
+motions of the planet, namely, that it occupied in succession the
+various points in the circumference of a given ellipse, was the very
+fact, the separate parts of which had been separately observed; it was
+the sum of the different observations.
+
+Having stated this fundamental difference between my opinion and that of
+Dr. Whewell, I must add, that his account of the manner in which a
+conception is selected, suitable to express the facts, appears to me
+perfectly just. The experience of all thinkers will, I believe, testify
+that the process is tentative; that it consists of a succession of
+guesses; many being rejected, until one at last occurs fit to be chosen.
+We know from Kepler himself that before hitting upon the "conception" of
+an ellipse, he tried nineteen other imaginary paths, which, finding them
+inconsistent with the observations, he was obliged to reject. But as Dr.
+Whewell truly says, the successful hypothesis, though a guess, ought
+generally to be called, not a lucky, but a skilful guess. The guesses
+which serve to give mental unity and wholeness to a chaos of scattered
+particulars, are accidents which rarely occur to any minds but those
+abounding in knowledge and disciplined in intellectual combinations.
+
+How far this tentative method, so indispensable as a means to the
+colligation of facts for purposes of description, admits of application
+to Induction itself, and what functions belong to it in that department,
+will be considered in the chapter of the present Book which relates to
+Hypotheses. On the present occasion we have chiefly to distinguish this
+process of Colligation from Induction properly so called; and that the
+distinction may be made clearer, it is well to advert to a curious and
+interesting remark, which is as strikingly true of the former operation,
+as it appears to me unequivocally false of the latter.
+
+In different stages of the progress of knowledge, philosophers have
+employed, for the colligation of the same order of facts, different
+conceptions. The early rude observations of the heavenly bodies, in
+which minute precision was neither attained nor sought, presented
+nothing inconsistent with the representation of the path of a planet as
+an exact circle, having the earth for its centre. As observations
+increased in accuracy, and facts were disclosed which were not
+reconcileable with this simple supposition; for the colligation of those
+additional facts, the supposition was varied; and varied again and again
+as facts became more numerous and precise. The earth was removed from
+the centre to some other point within the circle; the planet was
+supposed to revolve in a smaller circle called an epicycle, round an
+imaginary point which revolved in a circle round the earth: in
+proportion as observation elicited fresh facts contradictory to these
+representations, other epicycles and other excentrics were added,
+producing additional complication; until at last Kepler swept all these
+circles away, and substituted the conception of an exact ellipse. Even
+this is found not to represent with complete correctness the accurate
+observations of the present day, which disclose many slight deviations
+from an orbit exactly elliptical. Now Dr. Whewell has remarked that
+these successive general expressions, though apparently so conflicting,
+were all correct: they all answered the purpose of colligation; they all
+enabled the mind to represent to itself with facility, and by a
+simultaneous glance, the whole body of facts at the time ascertained:
+each in its turn served as a correct description of the phenomena, so
+far as the senses had up to that time taken cognizance of them. If a
+necessity afterwards arose for discarding one of these general
+descriptions of the planet's orbit, and framing a different imaginary
+line, by which to express the series of observed positions, it was
+because a number of new facts had now been added, which it was necessary
+to combine with the old facts into one general description. But this did
+not affect the correctness of the former expression, considered as a
+general statement of the only facts which it was intended to represent.
+And so true is this, that, as is well remarked by M. Comte, these
+ancient generalizations, even the rudest and most imperfect of them,
+that of uniform movement in a circle, are so far from being entirely
+false, that they are even now habitually employed by astronomers when
+only a rough approximation to correctness is required. "L'astronomie
+moderne, en d�truisant sans retour les hypoth�ses primitives, envisag�es
+comme lois r�elles du monde, a soigneusement maintenu leur valeur
+positive et permanente, la propri�t� de repr�senter commod�ment les
+ph�nom�nes quand il s'agit d'une premi�re �bauche. Nos ressources � cet
+�gard sont m�me bien plus �tendues, pr�cis�ment � cause que nous ne nous
+faisons aucune illusion sur la r�alit� des hypoth�ses; ce qui nous
+permet d'employer sans scrupule, en chaque cas, celle que nous jugeons
+la plus avantageuse."[5]
+
+Dr. Whewell's remark, therefore, is philosophically correct. Successive
+expressions for the colligation of observed facts, or in other words,
+successive descriptions of a phenomenon as a whole, which has been
+observed only in parts, may, though conflicting, be all correct as far
+as they go. But it would surely be absurd to assert this of conflicting
+inductions.
+
+The scientific study of facts may be undertaken for three different
+purposes: the simple description of the facts; their explanation; or
+their prediction: meaning by prediction, the determination of the
+conditions under which similar facts may be expected again to occur. To
+the first of these three operations the name of Induction does not
+properly belong: to the other two it does. Now, Dr. Whewell's
+observation is true of the first alone. Considered as a mere
+description, the circular theory of the heavenly motions represents
+perfectly well their general features: and by adding epicycles without
+limit, those motions, even as now known to us, might be expressed with
+any degree of accuracy that might be required. The elliptical theory, as
+a mere description, would have a great advantage in point of simplicity,
+and in the consequent facility of conceiving it and reasoning about it;
+but it would not really be more true than the other. Different
+descriptions, therefore, may be all true: but not, surely, different
+explanations. The doctrine that the heavenly bodies moved by a virtue
+inherent in their celestial nature; the doctrine that they were moved by
+impact, (which led to the hypothesis of vortices as the only impelling
+force capable of whirling bodies in circles,) and the Newtonian
+doctrine, that they are moved by the composition of a centripetal with
+an original projectile force; all these are explanations, collected by
+real induction from supposed parallel cases; and they were all
+successively received by philosophers, as scientific truths on the
+subject of the heavenly bodies. Can it be said of these, as was said of
+the different descriptions, that they are all true as far as they go? Is
+it not clear that only one can be true in any degree, and the other two
+must be altogether false? So much for explanations: let us now compare
+different predictions: the first, that eclipses will occur when one
+planet or satellite is so situated as to cast its shadow upon another;
+the second, that they will occur when some great calamity is impending
+over mankind. Do these two doctrines only differ in the degree of their
+truth, as expressing real facts with unequal degrees of accuracy?
+Assuredly the one is true, and the other absolutely false.[6]
+
+In every way, therefore, it is evident that to explain induction as the
+colligation of facts by means of appropriate conceptions, that is,
+conceptions which will really express them, is to confound mere
+description of the observed facts with inference from those facts, and
+ascribe to the latter what is a characteristic property of the former.
+
+There is, however, between Colligation and Induction, a real
+correlation, which it is important to conceive correctly. Colligation is
+not always induction; but induction is always colligation. The assertion
+that the planets move in ellipses, was but a mode of representing
+observed facts; it was but a colligation; while the assertion that they
+are drawn, or tend, towards the sun, was the statement of a new fact,
+inferred by induction. But the induction, once made, accomplishes the
+purposes of colligation likewise. It brings the same facts, which Kepler
+had connected by his conception of an ellipse, under the additional
+conception of bodies acted upon by a central force, and serves therefore
+as a new bond of connexion for those facts; a new principle for their
+classification.
+
+Further, the descriptions which are improperly confounded with
+induction, are nevertheless a necessary preparation for induction; no
+less necessary than correct observation of the facts themselves. Without
+the previous colligation of detached observations by means of one
+general conception, we could never have obtained any basis for an
+induction, except in the case of phenomena of very limited compass. We
+should not be able to affirm any predicates at all, of a subject
+incapable of being observed otherwise than piecemeal: much less could we
+extend those predicates by induction to other similar subjects.
+Induction, therefore, always presupposes, not only that the necessary
+observations are made with the necessary accuracy, but also that the
+results of these observations are, so far as practicable, connected
+together by general descriptions, enabling the mind to represent to
+itself as wholes whatever phenomena are capable of being so represented.
+
+
+� 5. Dr. Whewell has replied at some length to the preceding
+observations, re-stating his opinions, but without (as far as I can
+perceive) adding anything material to his former arguments. Since,
+however, mine have not had the good fortune to make any impression upon
+him, I will subjoin a few remarks, tending to show more clearly in what
+our difference of opinion consists, as well as, in some measure, to
+account for it.
+
+Nearly all the definitions of induction, by writers of authority, make
+it consist in drawing inferences from known cases to unknown; affirming
+of a class, a predicate which has been found true of some cases
+belonging to the class; concluding, because some things have a certain
+property, that other things which resemble them have the same
+property--or because a thing has manifested a property at a certain
+time, that it has and will have that property at other times.
+
+It will scarcely be contended that Kepler's operation was an Induction
+in this sense of the term. The statement, that Mars moves in an
+elliptical orbit, was no generalization from individual cases to a class
+of cases. Neither was it an extension to all time, of what had been
+found true at some particular time. The whole amount of generalization
+which the case admitted of, was already completed, or might have been
+so. Long before the elliptic theory was thought of, it had been
+ascertained that the planets returned periodically to the same apparent
+places; the series of these places was, or might have been, completely
+determined, and the apparent course of each planet marked out on the
+celestial globe in an uninterrupted line. Kepler did not extend an
+observed truth to other cases than those in which it had been observed:
+he did not widen the _subject_ of the proposition which expressed the
+observed facts. The alteration he made was in the predicate. Instead of
+saying, the successive places of Mars are so and so, he summed them up
+in the statement, that the successive places of Mars are points in an
+ellipse. It is true, this statement, as Dr. Whewell says, was not the
+sum of the observations _merely_; it was the sum of the observations
+_seen under a new point of view_.[7] But it was not the sum of _more_
+than the observations, as a real induction is. It took in no cases but
+those which had been actually observed, or which could have been
+inferred from the observations before the new point of view presented
+itself. There was not that transition from known cases to unknown,
+which constitutes Induction in the original and acknowledged meaning of
+the term.
+
+Old definitions, it is true, cannot prevail against new knowledge: and
+if the Keplerian operation, as a logical process, be really identical
+with what takes place in acknowledged induction, the definition of
+induction ought to be so widened as to take it in; since scientific
+language ought to adapt itself to the true relations which subsist
+between the things it is employed to designate. Here then it is that I
+am at issue with Dr. Whewell. He does think the operations identical. He
+allows of no logical process in any case of induction, other than what
+there was in Kepler's case, namely, guessing until a guess is found
+which tallies with the facts; and accordingly, as we shall see
+hereafter, he rejects all canons of induction, because it is not by
+means of them that we guess. Dr. Whewell's theory of the logic of
+science would be very perfect if it did not pass over altogether the
+question of Proof. But in my apprehension there is such a thing as
+proof, and inductions differ altogether from descriptions in their
+relation to that element. Induction is proof; it is inferring something
+unobserved from something observed: it requires, therefore, an
+appropriate test of proof; and to provide that test, is the special
+purpose of inductive logic. When, on the contrary, we merely collate
+known observations, and, in Dr. Whewell's phraseology, connect them by
+means of a new conception; if the conception does serve to connect the
+observations, we have all we want. As the proposition in which it is
+embodied pretends to no other truth than what it may share with many
+other modes of representing the same facts, to be consistent with the
+facts is all it requires: it neither needs nor admits of proof; though
+it may serve to prove other things, inasmuch as, by placing the facts in
+mental connexion with other facts, not previously seen to resemble them,
+it assimilates the case to another class of phenomena, concerning which
+real Inductions have already been made. Thus Kepler's so-called law
+brought the orbit of Mars into the class ellipse, and by doing so,
+proved all the properties of an ellipse to be true of the orbit: but in
+this proof Kepler's law supplied the minor premise, and not (as is the
+case with real Inductions) the major.
+
+Dr. Whewell calls nothing Induction where there is not a new mental
+conception introduced, and everything induction where there is. But this
+is to confound two very different things, Invention and Proof. The
+introduction of a new conception belongs to Invention: and invention may
+be required in any operation, but is the essence of none. A new
+conception may be introduced for descriptive purposes, and so it may for
+inductive purposes. But it is so far from constituting induction, that
+induction does not necessarily stand in need of it. Most inductions
+require no conception but what was present in every one of the
+particular instances on which the induction is grounded. That all men
+are mortal is surely an inductive conclusion; yet no new conception is
+introduced by it. Whoever knows that any man has died, has all the
+conceptions involved in the inductive generalization. But Dr. Whewell
+considers the process of invention which consists in framing a new
+conception consistent with the facts, to be not merely a necessary part
+of all induction, but the whole of it.
+
+The mental operation which extracts from a number of detached
+observations certain general characters in which the observed phenomena
+resemble one another, or resemble other known facts, is what Bacon,
+Locke, and most subsequent metaphysicians, have understood by the word
+Abstraction. A general expression obtained by abstraction, connecting
+known facts by means of common characters, but without concluding from
+them to unknown, may, I think, with strict logical correctness, be
+termed a Description; nor do I know in what other way things can ever be
+described. My position, however, does not depend on the employment of
+that particular word; I am quite content to use Dr. Whewell's term
+Colligation, or the more general phrases, "mode of representing, or of
+expressing, phenomena:" provided it be clearly seen that the process is
+not Induction, but something radically different.
+
+What more may usefully be said on the subject of Colligation, or of the
+correlative expression invented by Dr. Whewell, the Explication of
+Conceptions, and generally on the subject of ideas and mental
+representations as connected with the study of facts, will find a more
+appropriate place in the Fourth Book, on the Operations Subsidiary to
+Induction: to which I must refer the reader for the removal of any
+difficulty which the present discussion may have left.
+
+
+
+
+CHAPTER III.
+
+OF THE GROUND OF INDUCTION.
+
+
+� 1. Induction properly so called, as distinguished from those mental
+operations, sometimes though improperly designated by the name, which I
+have attempted in the preceding chapter to characterize, may, then, be
+summarily defined as Generalization from Experience. It consists in
+inferring from some individual instances in which a phenomenon is
+observed to occur, that it occurs in all instances of a certain class;
+namely, in all which _resemble_ the former, in what are regarded as the
+material circumstances.
+
+In what way the material circumstances are to be distinguished from
+those which are immaterial, or why some of the circumstances are
+material and others not so, we are not yet ready to point out. We must
+first observe, that there is a principle implied in the very statement
+of what Induction is; an assumption with regard to the course of nature
+and the order of the universe; namely, that there are such things in
+nature as parallel cases; that what happens once, will, under a
+sufficient degree of similarity of circumstances, happen again, and not
+only again, but as often as the same circumstances recur. This, I say,
+is an assumption, involved in every case of induction. And, if we
+consult the actual course of nature, we find that the assumption is
+warranted. The universe, so far as known to us, is so constituted, that
+whatever is true in any one case, is true in all cases of a certain
+description; the only difficulty is, to find what description.
+
+This universal fact, which is our warrant for all inferences from
+experience, has been described by different philosophers in different
+forms of language: that the course of nature is uniform; that the
+universe is governed by general laws; and the like. One of the most
+usual of these modes of expression, but also one of the most inadequate,
+is that which has been brought into familiar use by the metaphysicians
+of the school of Reid and Stewart. The disposition of the human mind to
+generalize from experience,--a propensity considered by these
+philosophers as an instinct of our nature,--they usually describe under
+some such name as "our intuitive conviction that the future will
+resemble the past." Now it has been well pointed out by Mr. Bailey,[8]
+that (whether the tendency be or not an original and ultimate element of
+our nature), Time, in its modifications of past, present, and future,
+has no concern either with the belief itself, or with the grounds of it.
+We believe that fire will burn to-morrow, because it burned to-day and
+yesterday; but we believe, on precisely the same grounds, that it burned
+before we were born, and that it burns this very day in Cochin-China. It
+is not from the past to the future, as past and future, that we infer,
+but from the known to the unknown; from facts observed to facts
+unobserved; from what we have perceived, or been directly conscious of,
+to what has not come within our experience. In this last predicament is
+the whole region of the future; but also the vastly greater portion of
+the present and of the past.
+
+Whatever be the most proper mode of expressing it, the proposition that
+the course of nature is uniform, is the fundamental principle, or
+general axiom, of Induction. It would yet be a great error to offer this
+large generalization as any explanation of the inductive process. On the
+contrary, I hold it to be itself an instance of induction, and induction
+by no means of the most obvious kind. Far from being the first induction
+we make, it is one of the last, or at all events one of those which are
+latest in attaining strict philosophical accuracy. As a general maxim,
+indeed, it has scarcely entered into the minds of any but philosophers;
+nor even by them, as we shall have many opportunities of remarking, have
+its extent and limits been always very justly conceived. The truth is,
+that this great generalization is itself founded on prior
+generalizations. The obscurer laws of nature were discovered by means
+of it, but the more obvious ones must have been understood and assented
+to as general truths before it was ever heard of. We should never have
+thought of affirming that all phenomena take place according to general
+laws, if we had not first arrived, in the case of a great multitude of
+phenomena, at some knowledge of the laws themselves; which could be done
+no otherwise than by induction. In what sense, then, can a principle,
+which is so far from being our earliest induction, be regarded as our
+warrant for all the others? In the only sense, in which (as we have
+already seen) the general propositions which we place at the head of our
+reasonings when we throw them into syllogisms, ever really contribute to
+their validity. As Archbishop Whately remarks, every induction is a
+syllogism with the major premise suppressed; or (as I prefer expressing
+it) every induction may be thrown into the form of a syllogism, by
+supplying a major premise. If this be actually done, the principle which
+we are now considering, that of the uniformity of the course of nature,
+will appear as the ultimate major premise of all inductions, and will,
+therefore, stand to all inductions in the relation in which, as has been
+shown at so much length, the major proposition of a syllogism always
+stands to the conclusion; not contributing at all to prove it, but being
+a necessary condition of its being proved; since no conclusion is
+proved, for which there cannot be found a true major premise.[9]
+
+The statement, that the uniformity of the course of nature is the
+ultimate major premise in all cases of induction, may be thought to
+require some explanation. The immediate major premise in every inductive
+argument, it certainly is not. Of that, Archbishop Whately's must be
+held to be the correct account. The induction, "John, Peter, &c. are
+mortal, therefore all mankind are mortal," may, as he justly says, be
+thrown into a syllogism by prefixing as a major premise (what is at any
+rate a necessary condition of the validity of the argument) namely, that
+what is true of John, Peter, &c. is true of all mankind. But how came we
+by this major premise? It is not self-evident; nay, in all cases of
+unwarranted generalization, it is not true. How, then, is it arrived at?
+Necessarily either by induction or ratiocination; and if by induction,
+the process, like all other inductive arguments, may be thrown into the
+form of a syllogism. This previous syllogism it is, therefore, necessary
+to construct. There is, in the long run, only one possible construction.
+The real proof that what is true of John, Peter, &c. is true of all
+mankind, can only be, that a different supposition would be inconsistent
+with the uniformity which we know to exist in the course of nature.
+Whether there would be this inconsistency or not, may be a matter of
+long and delicate inquiry; but unless there would, we have no sufficient
+ground for the major of the inductive syllogism. It hence appears, that
+if we throw the whole course of any inductive argument into a series of
+syllogisms, we shall arrive by more or fewer steps at an ultimate
+syllogism, which will have for its major premise the principle, or
+axiom, of the uniformity of the course of nature.[10]
+
+It was not to be expected that in the case of this axiom, any more than
+of other axioms, there should be unanimity among thinkers with respect
+to the grounds on which it is to be received as true. I have already
+stated that I regard it as itself a generalization from experience.
+Others hold it to be a principle which, antecedently to any verification
+by experience, we are compelled by the constitution of our thinking
+faculty to assume as true. Having so recently, and at so much length,
+combated a similar doctrine as applied to the axioms of mathematics, by
+arguments which are in a great measure applicable to the present case, I
+shall defer the more particular discussion of this controverted point in
+regard to the fundamental axiom of induction, until a more advanced
+period of our inquiry.[11] At present it is of more importance to
+understand thoroughly the import of the axiom itself. For the
+proposition, that the course of nature is uniform, possesses rather the
+brevity suitable to popular, than the precision requisite in
+philosophical language: its terms require to be explained, and a
+stricter than their ordinary signification given to them, before the
+truth of the assertion can be admitted.
+
+
+� 2. Every person's consciousness assures him that he does not always
+expect uniformity in the course of events; he does not always believe
+that the unknown will be similar to the known, that the future will
+resemble the past. Nobody believes that the succession of rain and fine
+weather will be the same in every future year as in the present. Nobody
+expects to have the same dreams repeated every night. On the contrary,
+everybody mentions it as something extraordinary, if the course of
+nature is constant, and resembles itself, in these particulars. To look
+for constancy where constancy is not to be expected, as for instance
+that a day which has once brought good fortune will always be a
+fortunate day, is justly accounted superstition.
+
+The course of nature, in truth, is not only uniform, it is also
+infinitely various. Some phenomena are always seen to recur in the very
+same combinations in which we met with them at first; others seem
+altogether capricious; while some, which we had been accustomed to
+regard as bound down exclusively to a particular set of combinations, we
+unexpectedly find detached from some of the elements with which we had
+hitherto found them conjoined, and united to others of quite a contrary
+description. To an inhabitant of Central Africa, fifty years ago, no
+fact probably appeared to rest on more uniform experience than this,
+that all human beings are black. To Europeans, not many years ago, the
+proposition, All swans are white, appeared an equally unequivocal
+instance of uniformity in the course of nature. Further experience has
+proved to both that they were mistaken; but they had to wait fifty
+centuries for this experience. During that long time, mankind believed
+in an uniformity of the course of nature where no such uniformity really
+existed.
+
+According to the notion which the ancients entertained of induction, the
+foregoing were cases of as legitimate inference as any inductions
+whatever. In these two instances, in which, the conclusion being false,
+the ground of inference must have been insufficient, there was,
+nevertheless, as much ground for it as this conception of induction
+admitted of. The induction of the ancients has been well described by
+Bacon, under the name of "Inductio per enumerationem simplicem, ubi non
+reperitur instantia contradictoria." It consists in ascribing the
+character of general truths to all propositions which are true in every
+instance that we happen to know of. This is the kind of induction which
+is natural to the mind when unaccustomed to scientific methods. The
+tendency, which some call an instinct, and which others account for by
+association, to infer the future from the past, the known from the
+unknown, is simply a habit of expecting that what has been found true
+once or several times, and never yet found false, will be found true
+again. Whether the instances are few or many, conclusive or
+inconclusive, does not much affect the matter: these are considerations
+which occur only on reflection; the unprompted tendency of the mind is
+to generalize its experience, provided this points all in one direction;
+provided no other experience of a conflicting character comes unsought.
+The notion of seeking it, of experimenting for it, of _interrogating_
+nature (to use Bacon's expression) is of much later growth. The
+observation of nature, by uncultivated intellects, is purely passive:
+they accept the facts which present themselves, without taking the
+trouble of searching for more: it is a superior mind only which asks
+itself what facts are needed to enable it to come to a safe conclusion,
+and then looks out for these.
+
+But though we have always a propensity to generalize from unvarying
+experience, we are not always warranted in doing so. Before we can be at
+liberty to conclude that something is universally true because we have
+never known an instance to the contrary, we must have reason to believe
+that if there were in nature any instances to the contrary, we should
+have known of them. This assurance, in the great majority of cases, we
+cannot have, or can have only in a very moderate degree. The possibility
+of having it, is the foundation on which we shall see hereafter that
+induction by simple enumeration may in some remarkable cases amount
+practically to proof.[12] No such assurance, however, can be had, on any
+of the ordinary subjects of scientific inquiry. Popular notions are
+usually founded on induction by simple enumeration; in science it
+carries us but a little way. We are forced to begin with it; we must
+often rely on it provisionally, in the absence of means of more
+searching investigation. But, for the accurate study of nature, we
+require a surer and a more potent instrument.
+
+It was, above all, by pointing out the insufficiency of this rude and
+loose conception of Induction, that Bacon merited the title so generally
+awarded to him, of Founder of the Inductive Philosophy. The value of his
+own contributions to a more philosophical theory of the subject has
+certainly been exaggerated. Although (along with some fundamental
+errors) his writings contain, more or less fully developed, several of
+the most important principles of the Inductive Method, physical
+investigation has now far outgrown the Baconian conception of Induction.
+Moral and political inquiry, indeed, are as yet far behind that
+conception. The current and approved modes of reasoning on these
+subjects are still of the same vicious description against which Bacon
+protested; the method almost exclusively employed by those professing to
+treat such matters inductively, is the very _inductio per enumerationem
+simplicem_ which he condemns; and the experience which we hear so
+confidently appealed to by all sects, parties, and interests, is still,
+in his own emphatic words, _mera palpatio_.
+
+
+� 3. In order to a better understanding of the problem which the
+logician must solve if he would establish a scientific theory of
+Induction, let us compare a few cases of incorrect inductions with
+others which are acknowledged to be legitimate. Some, we know, which
+were believed for centuries to be correct, were nevertheless incorrect.
+That all swans are white, cannot have been a good induction, since the
+conclusion has turned out erroneous. The experience, however, on which
+the conclusion rested, was genuine. From the earliest records, the
+testimony of the inhabitants of the known world was unanimous on the
+point. The uniform experience, therefore, of the inhabitants of the
+known world, agreeing in a common result, without one known instance of
+deviation from that result, is not always sufficient to establish a
+general conclusion.
+
+But let us now turn to an instance apparently not very dissimilar to
+this. Mankind were wrong, it seems, in concluding that all swans were
+white: are we also wrong, when we conclude that all men's heads grow
+above their shoulders, and never below, in spite of the conflicting
+testimony of the naturalist Pliny? As there were black swans, though
+civilized people had existed for three thousand years on the earth
+without meeting with them, may there not also be "men whose heads do
+grow beneath their shoulders," notwithstanding a rather less perfect
+unanimity of negative testimony from observers? Most persons would
+answer No; it was more credible that a bird should vary in its colour,
+than that men should vary in the relative position of their principal
+organs. And there is no doubt that in so saying they would be right: but
+to say why they are right, would be impossible, without entering more
+deeply than is usually done, into the true theory of Induction.
+
+Again, there are cases in which we reckon with the most unfailing
+confidence upon uniformity, and other cases in which we do not count
+upon it at all. In some we feel complete assurance that the future will
+resemble the past, the unknown be precisely similar to the known. In
+others, however invariable may be the result obtained from the instances
+which have been observed, we draw from them no more than a very feeble
+presumption that the like result will hold in all other cases. That a
+straight line is the shortest distance between two points, we do not
+doubt to be true even in the region of the fixed stars. When a chemist
+announces the existence and properties of a newly-discovered substance,
+if we confide in his accuracy, we feel assured that the conclusions he
+has arrived at will hold universally, though the induction be founded
+but on a single instance. We do not withhold our assent, waiting for a
+repetition of the experiment; or if we do, it is from a doubt whether
+the one experiment was properly made, not whether if properly made it
+would be conclusive. Here, then, is a general law of nature, inferred
+without hesitation from a single instance; an universal proposition from
+a singular one. Now mark another case, and contrast it with this. Not
+all the instances which have been observed since the beginning of the
+world, in support of the general proposition that all crows are black,
+would be deemed a sufficient presumption of the truth of the
+proposition, to outweigh the testimony of one unexceptionable witness
+who should affirm that in some region of the earth not fully explored,
+he had caught and examined a crow, and had found it to be grey.
+
+Why is a single instance, in some cases, sufficient for a complete
+induction, while in others, myriads of concurring instances, without a
+single exception known or presumed, go such a very little way towards
+establishing an universal proposition? Whoever can answer this question
+knows more of the philosophy of logic than the wisest of the ancients,
+and has solved the problem of induction.
+
+
+
+
+CHAPTER IV.
+
+OF LAWS OF NATURE.
+
+
+� 1. In the contemplation of that uniformity in the course of nature,
+which is assumed in every inference from experience, one of the first
+observations that present themselves is, that the uniformity in question
+is not properly uniformity, but uniformities. The general regularity
+results from the coexistence of partial regularities. The course of
+nature in general is constant, because the course of each of the various
+phenomena that compose it is so. A certain fact invariably occurs
+whenever certain circumstances are present, and does not occur when they
+are absent; the like is true of another fact; and so on. From these
+separate threads of connexion between parts of the great whole which we
+term nature, a general tissue of connexion unavoidably weaves itself, by
+which the whole is held together. If A is always accompanied by D, B by
+E, and C by F, it follows that A B is accompanied by D E, A C by D F, B
+C by E F, and finally A B C by D E F; and thus the general character of
+regularity is produced, which, along with and in the midst of infinite
+diversity, pervades all nature.
+
+The first point, therefore, to be noted in regard to what is called the
+uniformity of the course of nature, is, that it is itself a complex
+fact, compounded of all the separate uniformities which exist in respect
+to single phenomena. These various uniformities, when ascertained by
+what is regarded as a sufficient induction, we call in common parlance,
+Laws of Nature. Scientifically speaking, that title is employed in a
+more restricted sense, to designate the uniformities when reduced to
+their most simple expression. Thus in the illustration already employed,
+there were seven uniformities; all of which, if considered sufficiently
+certain, would in the more lax application of the term, be called laws
+of nature. But of the seven, three alone are properly distinct and
+independent: these being presupposed, the others follow of course. The
+three first, therefore, according to the stricter acceptation, are
+called laws of nature; the remainder not; because they are in truth mere
+_cases_ of the three first; virtually included in them; said, therefore,
+to _result_ from them: whoever affirms those three has already affirmed
+all the rest.
+
+To substitute real examples for symbolical ones, the following are three
+uniformities, or call them laws of nature: the law that air has weight,
+the law that pressure on a fluid is propagated equally in all
+directions, and the law that pressure in one direction, not opposed by
+equal pressure in the contrary direction, produces motion, which does
+not cease until equilibrium is restored. From these three uniformities
+we should be able to predict another uniformity, namely, the rise of the
+mercury in the Torricellian tube. This, in the stricter use of the
+phrase, is not a law of nature. It is the result of laws of nature. It
+is a _case_ of each and every one of the three laws: and is the only
+occurrence by which they could all be fulfilled. If the mercury were not
+sustained in the barometer, and sustained at such a height that the
+column of mercury were equal in weight to a column of the atmosphere of
+the same diameter; here would be a case, either of the air not pressing
+upon the surface of the mercury with the force which is called its
+weight, or of the downward pressure on the mercury not being propagated
+equally in an upward direction, or of a body pressed in one direction
+and not in the direction opposite, either not moving in the direction in
+which it is pressed, or stopping before it had attained equilibrium. If
+we knew, therefore, the three simple laws, but had never tried the
+Torricellian experiment, we might _deduce_ its result from those laws.
+The known weight of the air, combined with the position of the
+apparatus, would bring the mercury within the first of the three
+inductions; the first induction would bring it within the second, and
+the second within the third, in the manner which we characterized in
+treating of Ratiocination. We should thus come to know the more complex
+uniformity, independently of specific experience, through our knowledge
+of the simpler ones from which it results; though, for reasons which
+will appear hereafter, _verification_ by specific experience would still
+be desirable, and might possibly be indispensable.
+
+Complex uniformities which, like this, are mere cases of simpler ones,
+and have, therefore, been virtually affirmed in affirming those, may
+with propriety be called _laws_, but can scarcely, in the strictness of
+scientific speech, be termed Laws of Nature. It is the custom in
+science, wherever regularity of any kind can be traced, to call the
+general proposition which expresses the nature of that regularity, a
+law; as when, in mathematics, we speak of the law of decrease of the
+successive terms of a converging series. But the expression _law of
+nature_ has generally been employed with a sort of tacit reference to
+the original sense of the word law, namely, the expression of the will
+of a superior. When, therefore, it appeared that any of the uniformities
+which were observed in nature, would result spontaneously from certain
+other uniformities, no separate act of creative will being supposed
+necessary for the production of the derivative uniformities, these have
+not usually been spoken of as laws of nature. According to one mode of
+expression, the question, What are the laws of nature? may be stated
+thus:--What are the fewest and simplest assumptions, which being
+granted, the whole existing order of nature would result? Another mode
+of stating it would be thus: What are the fewest general propositions
+from which all the uniformities which exist in the universe might be
+deductively inferred?
+
+Every great advance which marks an epoch in the progress of science, has
+consisted in a step made towards the solution of this problem. Even a
+simple colligation of inductions already made, without any fresh
+extension of the inductive inference, is already an advance in that
+direction. When Kepler expressed the regularity which exists in the
+observed motions of the heavenly bodies, by the three general
+propositions called his laws, he, in so doing, pointed out three simple
+suppositions which, instead of a much greater number, would suffice to
+construct the whole scheme of the heavenly motions, so far as it was
+known up to that time. A similar and still greater step was made when
+these laws, which at first did not seem to be included in any more
+general truths, were discovered to be cases of the three laws of motion,
+as obtaining among bodies which mutually tend towards one another with a
+certain force, and have had a certain instantaneous impulse originally
+impressed upon them. After this great discovery, Kepler's three
+propositions, though still called laws, would hardly, by any person
+accustomed to use language with precision, be termed laws of nature:
+that phrase would be reserved for the simpler and more general laws into
+which Newton is said to have resolved them.
+
+According to this language, every well-grounded inductive generalization
+is either a law of nature, or a result of laws of nature, capable, if
+those laws are known, of being predicted from them. And the problem of
+Inductive Logic may be summed up in two questions: how to ascertain the
+laws of nature; and how, after having ascertained them, to follow them
+into their results. On the other hand, we must not suffer ourselves to
+imagine that this mode of statement amounts to a real analysis, or to
+anything but a mere verbal transformation of the problem; for the
+expression, Laws of Nature, _means_ nothing but the uniformities which
+exist among natural phenomena (or, in other words, the results of
+induction), when reduced to their simplest expression. It is, however,
+something to have advanced so far, as to see that the study of nature is
+the study of laws, not _a_ law; of uniformities, in the plural number:
+that the different natural phenomena have their separate rules or modes
+of taking place, which, though much intermixed and entangled with one
+another, may, to a certain extent, be studied apart: that (to resume our
+former metaphor) the regularity which exists in nature is a web composed
+of distinct threads, and only to be understood by tracing each of the
+threads separately; for which purpose it is often necessary to unravel
+some portion of the web, and exhibit the fibres apart. The rules of
+experimental inquiry are the contrivances for unravelling the web.
+
+
+� 2. In thus attempting to ascertain the general order of nature by
+ascertaining the particular order of the occurrence of each one of the
+phenomena of nature, the most scientific proceeding can be no more than
+an improved form of that which was primitively pursued by the human
+understanding, while undirected by science. When mankind first formed
+the idea of studying phenomena according to a stricter and surer method
+than that which they had in the first instance spontaneously adopted,
+they did not, conformably to the well-meant but impracticable precept of
+Descartes, set out from the supposition that nothing had been already
+ascertained. Many of the uniformities existing among phenomena are so
+constant, and so open to observation, as to force themselves upon
+involuntary recognition. Some facts are so perpetually and familiarly
+accompanied by certain others, that mankind learnt, as children learn,
+to expect the one where they found the other, long before they knew how
+to put their expectation into words by asserting, in a proposition, the
+existence of a connexion between those phenomena. No science was needed
+to teach that food nourishes, that water drowns, or quenches thirst,
+that the sun gives light and heat, that bodies fall to the ground. The
+first scientific inquirers assumed these and the like as known truths,
+and set out from them to discover others which were unknown: nor were
+they wrong in so doing, subject, however, as they afterwards began to
+see, to an ulterior revision of these spontaneous generalizations
+themselves, when the progress of knowledge pointed out limits to them,
+or showed their truth to be contingent on some circumstance not
+originally attended to. It will appear, I think, from the subsequent
+part of our inquiry, that there is no logical fallacy in this mode of
+proceeding; but we may see already that any other mode is rigorously
+impracticable: since it is impossible to frame any scientific method of
+induction, or test of the correctness of inductions, unless on the
+hypothesis that some inductions deserving of reliance have been already
+made.
+
+Let us revert, for instance, to one of our former illustrations, and
+consider why it is that, with exactly the same amount of evidence, both
+negative and positive, we did not reject the assertion that there are
+black swans, while we should refuse credence to any testimony which
+asserted that there were men wearing their heads underneath their
+shoulders. The first assertion was more credible than the latter. But
+why more credible? So long as neither phenomenon had been actually
+witnessed, what reason was there for finding the one harder to be
+believed than the other? Apparently because there is less constancy in
+the colours of animals, than in the general structure of their anatomy.
+But how do we know this? Doubtless, from experience. It appears, then,
+that we need experience to inform us, in what degree, and in what cases,
+or sort of cases, experience is to be relied on. Experience must be
+consulted in order to learn from it under what circumstances arguments
+from it will be valid. We have no ulterior test to which we subject
+experience in general; but we make experience its own test. Experience
+testifies, that among the uniformities which it exhibits or seems to
+exhibit, some are more to be relied on than others; and uniformity,
+therefore, may be presumed, from any given number of instances, with a
+greater degree of assurance, in proportion as the case belongs to a
+class in which the uniformities have hitherto been found more uniform.
+
+This mode of correcting one generalization by means of another, a
+narrower generalization by a wider, which common sense suggests and
+adopts in practice, is the real type of scientific Induction. All that
+art can do is but to give accuracy and precision to this process, and
+adapt it to all varieties of cases, without any essential alteration in
+its principle.
+
+There are of course no means of applying such a test as that above
+described, unless we already possess a general knowledge of the
+prevalent character of the uniformities existing throughout nature. The
+indispensable foundation, therefore, of a scientific formula of
+induction, must be a survey of the inductions to which mankind have been
+conducted in unscientific practice; with the special purpose of
+ascertaining what kinds of uniformities have been found perfectly
+invariable, pervading all nature, and what are those which have been
+found to vary with difference of time, place, or other changeable
+circumstances.
+
+
+� 3. The necessity of such a survey is confirmed by the consideration,
+that the stronger inductions are the touchstone to which we always
+endeavour to bring the weaker. If we find any means of deducing one of
+the less strong inductions from stronger ones, it acquires, at once, all
+the strength of those from which it is deduced; and even adds to that
+strength; since the independent experience on which the weaker induction
+previously rested, becomes additional evidence of the truth of the
+better established law in which it is now found to be included. We may
+have inferred, from historical evidence, that the uncontrolled power of
+a monarch, of an aristocracy, or of the majority, will often be abused:
+but we are entitled to rely on this generalization with much greater
+assurance when it is shown to be a corollary from still better
+established facts; the very low degree of elevation of character ever
+yet attained by the average of mankind, and the little efficacy, for the
+most part, of the modes of education hitherto practised, in maintaining
+the predominance of reason and conscience over the selfish propensities.
+It is at the same time obvious that even these more general facts derive
+an accession of evidence from the testimony which history bears to the
+effects of despotism. The strong induction becomes still stronger when a
+weaker one has been bound up with it.
+
+On the other hand, if an induction conflicts with stronger inductions,
+or with conclusions capable of being correctly deduced from them, then,
+unless on reconsideration it should appear that some of the stronger
+inductions have been expressed with greater universality than their
+evidence warrants, the weaker one must give way. The opinion so long
+prevalent that a comet, or any other unusual appearance in the heavenly
+regions, was the precursor of calamities to mankind, or to those at
+least who witnessed it; the belief in the veracity of the oracles
+of Delphi or Dodona; the reliance on astrology, or on the
+weather-prophecies in almanacs, were doubtless inductions supposed to be
+grounded on experience:[13] and faith in such delusions seems quite
+capable of holding out against a great multitude of failures, provided
+it be nourished by a reasonable number of casual coincidences between
+the prediction and the event. What has really put an end to these
+insufficient inductions, is their inconsistency with the stronger
+inductions subsequently obtained by scientific inquiry, respecting the
+causes on which terrestrial events really depend; and where those
+scientific truths have not yet penetrated, the same or similar delusions
+still prevail.
+
+It may be affirmed as a general principle, that all inductions, whether
+strong or weak, which can be connected by ratiocination, are
+confirmatory of one another; while any which lead deductively to
+consequences that are incompatible, become mutually each other's test,
+showing that one or other must be given up, or at least more guardedly
+expressed. In the case of inductions which confirm each other, the one
+which becomes a conclusion from ratiocination rises to at least the
+level of certainty of the weakest of those from which it is deduced;
+while in general all are more or less increased in certainty. Thus the
+Torricellian experiment, though a mere case of three more general laws,
+not only strengthened greatly the evidence on which those laws rested,
+but converted one of them (the weight of the atmosphere) from a doubtful
+generalization into a completely established doctrine.
+
+If, then, a survey of the uniformities which have been ascertained to
+exist in nature, should point out some which, as far as any human
+purpose requires certainty, may be considered quite certain and quite
+universal; then by means of these uniformities we may be able to raise
+multitudes of other inductions to the same point in the scale. For if we
+can show, with respect to any inductive inference, that either it must
+be true, or one of these certain and universal inductions must admit of
+an exception; the former generalization will attain the same certainty,
+and indefeasibleness within the bounds assigned to it, which are the
+attributes of the latter. It will be proved to be a law; and if not a
+result of other and simpler laws, it will be a law of nature.
+
+There are such certain and universal inductions; and it is because there
+are such, that a Logic of Induction is possible.
+
+
+
+
+CHAPTER V.
+
+OF THE LAW OF UNIVERSAL CAUSATION.
+
+
+� 1. The phenomena of nature exist in two distinct relations to one
+another; that of simultaneity, and that of succession. Every phenomenon
+is related, in an uniform manner, to some phenomena that coexist with
+it, and to some that have preceded and will follow it.
+
+Of the uniformities which exist among synchronous phenomena, the most
+important, on every account, are the laws of number; and next to them
+those of space, or, in other words, of extension and figure. The laws of
+number are common to synchronous and successive phenomena. That two and
+two make four, is equally true whether the second two follow the first
+two or accompany them. It is as true of days and years as of feet and
+inches. The laws of extension and figure (in other words, the theorems
+of geometry, from its lowest to its highest branches) are, on the
+contrary, laws of simultaneous phenomena only. The various parts of
+space, and of the objects which are said to fill space, coexist; and the
+unvarying laws which are the subject of the science of geometry, are an
+expression of the mode of their coexistence.
+
+This is a class of laws, or in other words, of uniformities, for the
+comprehension and proof of which it is not necessary to suppose any
+lapse of time, any variety of facts or events succeeding one another. If
+all the objects in the universe were unchangeably fixed, and had
+remained in that condition from eternity, the propositions of geometry
+would still be true of those objects. All things which possess
+extension, or, in other words, which fill space, are subject to
+geometrical laws. Possessing extension, they possess figure; possessing
+figure, they must possess some figure in particular, and have all the
+properties which geometry assigns to that figure. If one body be a
+sphere and another a cylinder, of equal height and diameter, the one
+will be exactly two-thirds of the other, let the nature and quality of
+the material be what it will. Again, each body, and each point of a
+body, must occupy some place or position among other bodies; and the
+position of two bodies relatively to each other, of whatever nature the
+bodies be, may be unerringly inferred from the position of each of them
+relatively to any third body.
+
+In the laws of number, then, and in those of space, we recognise in the
+most unqualified manner, the rigorous universality of which we are in
+quest. Those laws have been in all ages the type of certainty, the
+standard of comparison for all inferior degrees of evidence. Their
+invariability is so perfect, that it renders us unable even to conceive
+any exception to them; and philosophers have been led, though (as I have
+endeavoured to show) erroneously, to consider their evidence as lying
+not in experience, but in the original constitution of the intellect. If
+therefore, from the laws of space and number, we were able to deduce
+uniformities of any other description, this would be conclusive evidence
+to us that those other uniformities possessed the same rigorous
+certainty. But this we cannot do. From laws of space and number alone,
+nothing can be deduced but laws of space and number.
+
+Of all truths relating to phenomena, the most valuable to us are those
+which relate to the order of their succession. On a knowledge of these
+is founded every reasonable anticipation of future facts, and whatever
+power we possess of influencing those facts to our advantage. Even the
+laws of geometry are chiefly of practical importance to us as being a
+portion of the premises from which the order of the succession of
+phenomena may be inferred. Inasmuch as the motion of bodies, the action
+of forces, and the propagation of influences of all sorts, take place in
+certain lines and over definite spaces, the properties of those lines
+and spaces are an important part of the laws to which those phenomena
+are themselves subject. Again, motions, forces or other influences, and
+times, are numerable quantities; and the properties of number are
+applicable to them as to all other things. But though the laws of number
+and space are important elements in the ascertainment of uniformities
+of succession, they can do nothing towards it when taken by themselves.
+They can only be made instrumental to that purpose when we combine with
+them additional premises, expressive of uniformities of succession
+already known. By taking, for instance, as premises these propositions,
+that bodies acted upon by an instantaneous force move with uniform
+velocity in straight lines; that bodies acted upon by a continuous force
+move with accelerated velocity in straight lines; and that bodies acted
+upon by two forces in different directions move in the diagonal of a
+parallelogram, whose sides represent the direction and quantity of those
+forces; we may by combining these truths with propositions relating to
+the properties of straight lines and of parallelograms, (as that a
+triangle is half a parallelogram of the same base and altitude,) deduce
+another important uniformity of succession, viz., that a body moving
+round a centre of force describes areas proportional to the times. But
+unless there had been laws of succession in our premises, there could
+have been no truths of succession in our conclusions. A similar remark
+might be extended to every other class of phenomena really peculiar;
+and, had it been attended to, would have prevented many chimerical
+attempts at demonstrations of the indemonstrable, and explanations which
+do not explain.
+
+It is not, therefore, enough for us that the laws of space, which are
+only laws of simultaneous phenomena, and the laws of number, which
+though true of successive phenomena do not relate to their succession,
+possess the rigorous certainty and universality of which we are in
+search. We must endeavour to find some law of succession which has those
+same attributes, and is therefore fit to be made the foundation of
+processes for discovering, and of a test for verifying, all other
+uniformities of succession. This fundamental law must resemble the
+truths of geometry in their most remarkable peculiarity, that of never
+being, in any instance whatever, defeated or suspended by any change of
+circumstances.
+
+Now among all those uniformities in the succession of phenomena, which
+common observation is sufficient to bring to light, there are very few
+which have any, even apparent, pretension to this rigorous
+indefeasibility: and of those few, one only has been found capable of
+completely sustaining it. In that one, however, we recognise a law which
+is universal also in another sense; it is coextensive with the entire
+field of successive phenomena, all instances whatever of succession
+being examples of it. This law is the Law of Causation. The truth that
+every fact which has a beginning has a cause, is coextensive with human
+experience.
+
+This generalization may appear to some minds not to amount to much,
+since after all it asserts only this: "it is a law; that every event
+depends on some law:" "it is a law, that there is a law for everything."
+We must not, however, conclude that the generality of the principle is
+merely verbal; it will be found on inspection to be no vague or
+unmeaning assertion, but a most important and really fundamental truth.
+
+
+� 2. The notion of Cause being the root of the whole theory of
+Induction, it is indispensable that this idea should, at the very outset
+of our inquiry, be, with the utmost practicable degree of precision,
+fixed and determined. If, indeed, it were necessary for the purpose of
+inductive logic that the strife should be quelled, which has so long
+raged among the different schools of metaphysicians, respecting the
+origin and analysis of our idea of causation; the promulgation, or at
+least the general reception, of a true theory of induction, might be
+considered desperate for a long time to come. But the science of the
+Investigation of Truth by means of Evidence, is happily independent of
+many of the controversies which perplex the science of the ultimate
+constitution of the human mind, and is under no necessity of pushing the
+analysis of mental phenomena to that extreme limit which alone ought to
+satisfy a metaphysician.
+
+I premise, then, that when in the course of this inquiry I speak of the
+cause of any phenomenon, I do not mean a cause which is not itself a
+phenomenon; I make no research into the ultimate or ontological cause of
+anything. To adopt a distinction familiar in the writings of the Scotch
+metaphysicians, and especially of Reid, the causes with which I concern
+myself are not _efficient_, but _physical_ causes. They are causes in
+that sense alone, in which one physical fact is said to be the cause of
+another. Of the efficient causes of phenomena, or whether any such
+causes exist at all, I am not called upon to give an opinion. The notion
+of causation is deemed, by the schools of metaphysics most in vogue at
+the present moment, to imply a mysterious and most powerful tie, such as
+cannot, or at least does not, exist between any physical fact and that
+other physical fact on which it is invariably consequent, and which is
+popularly termed its cause: and thence is deduced the supposed necessity
+of ascending higher, into the essences and inherent constitution of
+things, to find the true cause, the cause which is not only followed by,
+but actually produces, the effect. No such necessity exists for the
+purposes of the present inquiry, nor will any such doctrine be found in
+the following pages. The only notion of a cause, which the theory of
+induction requires, is such a notion as can be gained from experience.
+The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it; independently of all
+consideration respecting the ultimate mode of production of phenomena,
+and of every other question regarding the nature of "Things in
+themselves."
+
+Between the phenomena, then, which exist at any instant, and the
+phenomena which exist at the succeeding instant, there is an invariable
+order of succession; and, as we said in speaking of the general
+uniformity of the course of nature, this web is composed of separate
+fibres; this collective order is made up of particular sequences,
+obtaining invariably among the separate parts. To certain facts, certain
+facts always do, and, as we believe, will continue to, succeed. The
+invariable antecedent is termed the cause; the invariable consequent,
+the effect. And the universality of the law of causation consists in
+this, that every consequent is connected in this manner with some
+particular antecedent, or set of antecedents. Let the fact be what it
+may, if it has begun to exist, it was preceded by some fact or facts,
+with which it is invariably connected. For every event there exists some
+combination of objects or events, some given concurrence of
+circumstances, positive and negative, the occurrence of which is always
+followed by that phenomenon. We may not have found out what this
+concurrence of circumstances may be; but we never doubt that there is
+such a one, and that it never occurs without having the phenomenon in
+question as its effect or consequence. On the universality of this truth
+depends the possibility of reducing the inductive process to rules. The
+undoubted assurance we have that there is a law to be found if we only
+knew how to find it, will be seen presently to be the source from which
+the canons of the Inductive Logic derive their validity.
+
+
+� 3. It is seldom, if ever, between a consequent and a single
+antecedent, that this invariable sequence subsists. It is usually
+between a consequent and the sum of several antecedents; the concurrence
+of all of them being requisite to produce, that is, to be certain of
+being followed by, the consequent. In such cases it is very common to
+single out one only of the antecedents under the denomination of Cause,
+calling the others merely Conditions. Thus, if a person eats of a
+particular dish, and dies in consequence, that is, would not have died
+if he had not eaten of it, people would be apt to say that eating of
+that dish was the cause of his death. There needs not, however, be any
+invariable connexion between eating of the dish and death; but there
+certainly is, among the circumstances which took place, some combination
+or other on which death is invariably consequent: as, for instance, the
+act of eating of the dish, combined with a particular bodily
+constitution, a particular state of present health, and perhaps even a
+certain state of the atmosphere; the whole of which circumstances
+perhaps constituted in this particular case the _conditions_ of the
+phenomenon, or, in other words, the set of antecedents which determined
+it, and but for which it would not have happened. The real Cause, is the
+whole of these antecedents; and we have, philosophically speaking, no
+right to give the name of cause to one of them, exclusively of the
+others. What, in the case we have supposed, disguises the incorrectness
+of the expression, is this: that the various conditions, except the
+single one of eating the food, were not _events_ (that is, instantaneous
+changes, or successions of instantaneous changes) but _states_,
+possessing more or less of permanency; and might therefore have preceded
+the effect by an indefinite length of duration, for want of the event
+which was requisite to complete the required concurrence of conditions:
+while as soon as that event, eating the food, occurs, no other cause is
+waited for, but the effect begins immediately to take place: and hence
+the appearance is presented of a more immediate and close connexion
+between the effect and that one antecedent, than between the effect and
+the remaining conditions. But though we may think proper to give the
+name of cause to that one condition, the fulfilment of which completes
+the tale, and brings about the effect without further delay; this
+condition has really no closer relation to the effect than any of the
+other conditions has. The production of the consequent required that
+they should all _exist_ immediately previous, though not that they
+should all _begin_ to exist immediately previous. The statement of the
+cause is incomplete, unless in some shape or other we introduce all the
+conditions. A man takes mercury, goes out of doors, and catches cold. We
+say, perhaps, that the cause of his taking cold was exposure to the air.
+It is clear, however, that his having taken mercury may have been a
+necessary condition of catching cold; and though it might consist with
+usage to say that the cause of his attack was exposure to the air, to be
+accurate we ought to say that the cause was exposure to the air while
+under the effect of mercury.
+
+If we do not, when aiming at accuracy, enumerate all the conditions, it
+is only because some of them will in most cases be understood without
+being expressed, or because for the purpose in view they may without
+detriment be overlooked. For example, when we say, the cause of a man's
+death was that his foot slipped in climbing a ladder, we omit as a
+thing unnecessary to be stated the circumstance of his weight, though
+quite as indispensable a condition of the effect which took place. When
+we say that the assent of the crown to a bill makes it law, we mean that
+the assent, being never given until all the other conditions are
+fulfilled, makes up the sum of the conditions, though no one now regards
+it as the principal one. When the decision of a legislative assembly has
+been determined by the casting vote of the chairman, we sometimes say
+that this one person was the cause of all the effects which resulted
+from the enactment. Yet we do not really suppose that his single vote
+contributed more to the result than that of any other person who voted
+in the affirmative; but, for the purpose we have in view, which is to
+insist on his individual responsibility, the part which any other person
+had in the transaction is not material.
+
+In all these instances the fact which was dignified with the name of
+cause, was the one condition which came last into existence. But it must
+not be supposed that in the employment of the term this or any other
+rule is always adhered to. Nothing can better show the absence of any
+scientific ground for the distinction between the cause of a phenomenon
+and its conditions, than the capricious manner in which we select from
+among the conditions that which we choose to denominate the cause.
+However numerous the conditions may be, there is hardly any of them
+which may not, according to the purpose of our immediate discourse,
+obtain that nominal pre-eminence. This will be seen by analysing the
+conditions of some one familiar phenomenon. For example, a stone thrown
+into water falls to the bottom. What are the conditions of this event?
+In the first place there must be a stone, and water, and the stone must
+be thrown into the water; but these suppositions forming part of the
+enunciation of the phenomenon itself, to include them also among the
+conditions would be a vicious tautology; and this class of conditions,
+therefore, have never received the name of cause from any but the
+Aristotelians, by whom they were called the _material_ cause, _causa
+materialis_. The next condition is, there must be an earth: and
+accordingly it is often said, that the fall of a stone is caused by the
+earth; or by a power or property of the earth, or a force exerted by the
+earth, all of which are merely roundabout ways of saying that it is
+caused by the earth; or, lastly, the earth's attraction; which also is
+only a technical mode of saying that the earth causes the motion, with
+the additional particularity that the motion is towards the earth, which
+is not a character of the cause, but of the effect. Let us now pass to
+another condition. It is not enough that the earth should exist; the
+body must be within that distance from it, in which the earth's
+attraction preponderates over that of any other body. Accordingly we may
+say, and the expression would be confessedly correct, that the cause of
+the stone's falling is its being _within the sphere_ of the earth's
+attraction. We proceed to a further condition. The stone is immersed in
+water: it is therefore a condition of its reaching the ground, that its
+specific gravity exceed that of the surrounding fluid, or in other words
+that it surpass in weight an equal volume of water. Accordingly any one
+would be acknowledged to speak correctly who said, that the cause of the
+stone's going to the bottom is its exceeding in specific gravity the
+fluid in which it is immersed.
+
+Thus we see that each and every condition of the phenomenon may be taken
+in its turn, and, with equal propriety in common parlance, but with
+equal impropriety in scientific discourse, may be spoken of as if it
+were the entire cause. And in practice, that particular condition is
+usually styled the cause, whose share in the matter is superficially the
+most conspicuous, or whose requisiteness to the production of the effect
+we happen to be insisting on at the moment. So great is the force of
+this last consideration, that it sometimes induces us to give the name
+of cause even to one of the negative conditions. We say, for example,
+The army was surprised because the sentinel was off his post. But since
+the sentinel's absence was not what created the enemy, or put the
+soldiers asleep, how did it cause them to be surprised? All that is
+really meant is, that the event would not have happened if he had been
+at his duty. His being off his post was no producing cause, but the mere
+absence of a preventing cause: it was simply equivalent to his
+non-existence. From nothing, from a mere negation, no consequences can
+proceed. All effects are connected, by the law of causation, with some
+set of _positive_ conditions; negative ones, it is true, being almost
+always required in addition. In other words, every fact or phenomenon
+which has a beginning, invariably arises when some certain combination
+of positive facts exists, provided certain other positive facts do not
+exist.
+
+There is, no doubt, a tendency (which our first example, that of death
+from taking a particular food, sufficiently illustrates) to associate
+the idea of causation with the proximate antecedent _event_, rather than
+with any of the antecedent _states_, or permanent facts, which may
+happen also to be conditions of the phenomenon; the reason being that
+the event not only exists, but begins to exist immediately previous;
+while the other conditions may have pre-existed for an indefinite time.
+And this tendency shows itself very visibly in the different logical
+fictions which are resorted to, even by men of science, to avoid the
+necessity of giving the name of cause to anything which had existed for
+an indeterminate length of time before the effect. Thus, rather than say
+that the earth causes the fall of bodies, they ascribe it to a _force_
+exerted by the earth, or an _attraction_ by the earth, abstractions
+which they can represent to themselves as exhausted by each effort, and
+therefore constituting at each successive instant a fresh fact,
+simultaneous with, or only immediately preceding, the effect. Inasmuch
+as the coming of the circumstance which completes the assemblage of
+conditions, is a change or event, it thence happens that an event is
+always the antecedent in closest apparent proximity to the consequent:
+and this may account for the illusion which disposes us to look upon the
+proximate event as standing more peculiarly in the position of a cause
+than any of the antecedent states. But even this peculiarity, of being
+in closer proximity to the effect than any other of its conditions, is,
+as we have already seen, far from being necessary to the common notion
+of a cause; with which notion, on the contrary, any one of the
+conditions, either positive or negative, is found, on occasion,
+completely to accord.[14]
+
+The cause, then, philosophically speaking, is the sum total of the
+conditions, positive and negative taken together; the whole of the
+contingencies of every description, which being realized, the consequent
+invariably follows. The negative conditions, however, of any
+phenomenon, a special enumeration of which would generally be very
+prolix, may be all summed up under one head, namely, the absence of
+preventing or counteracting causes. The convenience of this mode of
+expression is mainly grounded on the fact, that the effects of any cause
+in counteracting another cause may in most cases be, with strict
+scientific exactness, regarded as a mere extension of its own proper and
+separate effects. If gravity retards the upward motion of a projectile,
+and deflects it into a parabolic trajectory, it produces, in so doing,
+the very same kind of effect, and even (as mathematicians know) the
+same quantity of effect, as it does in its ordinary operation of causing
+the fall of bodies when simply deprived of their support. If an alkaline
+solution mixed with an acid destroys its sourness, and prevents it from
+reddening vegetable blues, it is because the specific effect of the
+alkali is to combine with the acid, and form a compound with totally
+different qualities. This property, which causes of all descriptions
+possess, of preventing the effects of other causes by virtue (for the
+most part) of the same laws according to which they produce their
+own,[15] enables us, by establishing the general axiom that all causes
+are liable to be counteracted in their effects by one another, to
+dispense with the consideration of negative conditions entirely, and
+limit the notion of cause to the assemblage of the positive conditions
+of the phenomenon: one negative condition invariably understood, and the
+same in all instances (namely, the absence of counteracting causes)
+being sufficient, along with the sum of the positive conditions, to make
+up the whole set of circumstances on which the phenomenon is dependent.
+
+
+� 4. Among the positive conditions, as we have seen that there are some
+to which, in common parlance, the term cause is more readily and
+frequently awarded, so there are others to which it is, in ordinary
+circumstances, refused. In most cases of causation a distinction is
+commonly drawn between something which acts, and some other thing which
+is acted upon; between an _agent_ and a _patient_. Both of these, it
+would be universally allowed, are conditions of the phenomenon; but it
+would be thought absurd to call the latter the cause, that title being
+reserved for the former. The distinction, however, vanishes on
+examination, or rather is found to be only verbal; arising from an
+incident of mere expression, namely, that the object said to be acted
+upon, and which is considered as the scene in which the effect takes
+place, is commonly included in the phrase by which the effect is spoken
+of, so that if it were also reckoned as part of the cause, the seeming
+incongruity would arise of its being supposed to cause itself. In the
+instance which we have already had, of falling bodies, the question was
+thus put: What is the cause which makes a stone fall? and if the answer
+had been "the stone itself," the expression would have been in apparent
+contradiction to the meaning of the word cause. The stone, therefore, is
+conceived as the patient, and the earth (or, according to the common and
+most unphilosophical practice, some occult quality of the earth) is
+represented as the agent or cause. But that there is nothing fundamental
+in the distinction may be seen from this, that it is quite possible to
+conceive the stone as causing its own fall, provided the language
+employed be such as to save the mere verbal incongruity. We might say
+that the stone moves towards the earth by the properties of the matter
+composing it; and according to this mode of presenting the phenomenon,
+the stone itself might without impropriety be called the agent; though,
+to save the established doctrine of the inactivity of matter, men
+usually prefer here also to ascribe the effect to an occult quality, and
+say that the cause is not the stone itself, but the _weight_ or
+_gravitation_ of the stone.
+
+Those who have contended for a radical distinction between agent and
+patient, have generally conceived the agent as that which causes some
+state of, or some change in the state of, another object which is called
+the patient. But a little reflection will show that the licence we
+assume of speaking of phenomena as _states_ of the various objects which
+take part in them, (an artifice of which so much use has been made by
+some philosophers, Brown in particular, for the apparent explanation of
+phenomena,) is simply a sort of logical fiction, useful sometimes as one
+among several modes of expression, but which should never be supposed to
+be the enunciation of a scientific truth. Even those attributes of an
+object which might seem with greatest propriety to be called states of
+the object itself, its sensible qualities, its colour, hardness, shape,
+and the like, are in reality (as no one has pointed out more clearly
+than Brown himself) phenomena of causation, in which the substance is
+distinctly the agent, or producing cause, the patient being our own
+organs, and those of other sentient beings. What we call states of
+objects, are always sequences into which the objects enter, generally as
+antecedents or causes; and things are never more active than in the
+production of those phenomena in which they are said to be acted upon.
+Thus, in the example of a stone falling to the earth, according to the
+theory of gravitation the stone is as much an agent as the earth, which
+not only attracts, but is itself attracted by, the stone. In the case of
+a sensation produced in our organs, the laws of our organization, and
+even those of our minds, are as directly operative in determining the
+effect produced, as the laws of the outward object. Though we call
+prussic acid the agent of a person's death, the whole of the vital and
+organic properties of the patient are as actively instrumental as the
+poison, in the chain of effects which so rapidly terminates his sentient
+existence. In the process of education, we may call the teacher the
+agent, and the scholar only the material acted upon; yet in truth all
+the facts which pre-existed in the scholar's mind exert either
+co-operating or counteracting agencies in relation to the teacher's
+efforts. It is not light alone which is the agent in vision, but light
+coupled with the active properties of the eye and brain, and with those
+of the visible object. The distinction between agent and patient is
+merely verbal: patients are always agents; in a great proportion,
+indeed, of all natural phenomena, they are so to such a degree as to
+react forcibly on the causes which acted upon them: and even when this
+is not the case, they contribute, in the same manner as any of the other
+conditions, to the production of the effect of which they are vulgarly
+treated as the mere theatre. All the positive conditions of a phenomenon
+are alike agents, alike active; and in any expression of the cause which
+professes to be complete, none of them can with reason be excluded,
+except such as have already been implied in the words used for
+describing the effect; nor by including even these would there be
+incurred any but a merely verbal impropriety.
+
+
+� 5. It now remains to advert to a distinction which is of first-rate
+importance both for clearing up the notion of cause, and for obviating a
+very specious objection often made against the view which we have taken
+of the subject.
+
+When we define the cause of anything (in the only sense in which the
+present inquiry has any concern with causes) to be "the antecedent which
+it invariably follows," we do not use this phrase as exactly synonymous
+with "the antecedent which it invariably _has_ followed in our past
+experience." Such a mode of conceiving causation would be liable to the
+objection very plausibly urged by Dr. Reid, namely, that according to
+this doctrine night must be the cause of day, and day the cause of
+night; since these phenomena have invariably succeeded one another from
+the beginning of the world. But it is necessary to our using the word
+cause, that we should believe not only that the antecedent always _has_
+been followed by the consequent, but that, as long as the present
+constitution of things[16] endures, it always _will_ be so. And this
+would not be true of day and night. We do not believe that night will be
+followed by day under all imaginable circumstances, but only that it
+will be so _provided_ the sun rises above the horizon. If the sun ceased
+to rise, which, for aught we know, may be perfectly compatible with the
+general laws of matter, night would be, or might be, eternal. On the
+other hand, if the sun is above the horizon, his light not extinct, and
+no opaque body between us and him, we believe firmly that unless a
+change takes place in the properties of matter, this combination of
+antecedents will be followed by the consequent, day; that if the
+combination of antecedents could be indefinitely prolonged, it would be
+always day; and that if the same combination had always existed, it
+would always have been day, quite independently of night as a previous
+condition. Therefore is it that we do not call night the cause, nor even
+a condition, of day. The existence of the sun (or some such luminous
+body), and there being no opaque medium in a straight line[17] between
+that body and the part of the earth where we are situated, are the sole
+conditions; and the union of these, without the addition of any
+superfluous circumstance, constitutes the cause. This is what writers
+mean when they say that the notion of cause involves the idea of
+necessity. If there be any meaning which confessedly belongs to the term
+necessity, it is _unconditionalness_. That which is necessary, that
+which _must_ be, means that which will be, whatever supposition we may
+make in regard to all other things. The succession of day and night
+evidently is not necessary in this sense. It is conditional on the
+occurrence of other antecedents. That which will be followed by a given
+consequent when, and only when, some third circumstance also exists, is
+not the cause, even though no case should ever have occurred in which
+the phenomenon took place without it.
+
+Invariable sequence, therefore, is not synonymous with causation, unless
+the sequence, besides being invariable, is unconditional. There are
+sequences, as uniform in past experience as any others whatever, which
+yet we do not regard as cases of causation, but as conjunctions in some
+sort accidental. Such, to an accurate thinker, is that of day and night.
+The one might have existed for any length of time, and the other not
+have followed the sooner for its existence; it follows only if certain
+other antecedents exist; and where those antecedents existed, it would
+follow in any case. No one, probably, ever called night the cause of
+day; mankind must so soon have arrived at the very obvious
+generalization, that the state of general illumination which we call day
+would follow from the presence of a sufficiently luminous body, whether
+darkness had preceded or not.
+
+We may define, therefore, the cause of a phenomenon, to be the
+antecedent, or the concurrence of antecedents, on which it is invariably
+and _unconditionally_ consequent. Or if we adopt the convenient
+modification of the meaning of the word cause, which confines it to the
+assemblage of positive conditions without the negative, then instead of
+"unconditionally," we must say, "subject to no other than negative
+conditions."
+
+To some it may appear, that the sequence between night and day being
+invariable in our experience, we have as much ground in this case as
+experience can give in any case, for recognising the two phenomena as
+cause and effect; and that to say that more is necessary--to require a
+belief that the succession is unconditional, or in other words that it
+would be invariable under all changes of circumstances, is to
+acknowledge in causation an element of belief not derived from
+experience. The answer to this is, that it is experience itself which
+teaches us that one uniformity of sequence is conditional and another
+unconditional. When we judge that the succession of night and day is a
+derivative sequence, depending on something else, we proceed on grounds
+of experience. It is the evidence of experience which convinces us that
+day could equally exist without being followed by night, and that night
+could equally exist without being followed by day. To say that these
+beliefs are "not generated by our mere observation of sequence,"[18] is
+to forget that twice in every twenty-four hours, when the sky is clear,
+we have an _experimentum crucis_ that the cause of day is the sun. We
+have an experimental knowledge of the sun which justifies us on
+experimental grounds in concluding, that if the sun were always above
+the horizon there would be day, though there had been no night, and that
+if the sun were always below the horizon there would be night, though
+there had been no day. We thus know from experience that the succession
+of night and day is not unconditional. Let me add, that the antecedent
+which is only conditionally invariable, is not the invariable
+antecedent. Though a fact may, in experience, have always been followed
+by another fact, yet if the remainder of our experience teaches us that
+it might not always be so followed, or if the experience itself is such
+as leaves room for a possibility that the known cases may not correctly
+represent all possible cases, the hitherto invariable antecedent is not
+accounted the cause; but why? Because we are not sure that it _is_ the
+invariable antecedent.
+
+Such cases of sequence as that of day and night not only do not
+contradict the doctrine which resolves causation into invariable
+sequence, but are necessarily implied in that doctrine. It is evident,
+that from a limited number of unconditional sequences, there will
+result a much greater number of conditional ones. Certain causes being
+given, that is, certain antecedents which are unconditionally followed
+by certain consequents; the mere coexistence of these causes will give
+rise to an unlimited number of additional uniformities. If two causes
+exist together, the effects of both will exist together; and if many
+causes coexist, these causes (by what we shall term hereafter the
+intermixture of their laws) will give rise to new effects, accompanying
+or succeeding one another in some particular order, which order will be
+invariable while the causes continue to coexist, but no longer. The
+motion of the earth in a given orbit round the sun, is a series of
+changes which follow one another as antecedents and consequents, and
+will continue to do so while the sun's attraction, and the force with
+which the earth tends to advance in a direct line through space,
+continue to coexist in the same quantities as at present. But vary
+either of these causes, and this particular succession of motions would
+cease to take place. The series of the earth's motions, therefore,
+though a case of sequence invariable within the limits of human
+experience, is not a case of causation. It is not unconditional.
+
+This distinction between the relations of succession which so far as we
+know are unconditional, and those relations, whether of succession or of
+coexistence, which, like the earth's motions, or the succession of day
+and night, depend on the existence or on the coexistence of other
+antecedent facts--corresponds to the great division which Dr. Whewell
+and other writers have made of the field of science, into the
+investigation of what they term the Laws of Phenomena, and the
+investigation of causes; a phraseology, as I conceive, not
+philosophically sustainable, inasmuch as the ascertainment of causes,
+such causes as the human faculties can ascertain, namely, causes which
+are themselves phenomena, is, therefore, merely the ascertainment of
+other and more universal Laws of Phenomena. And let me here observe,
+that Dr. Whewell, and in some degree even Sir John Herschel, seem to
+have misunderstood the meaning of those writers who, like M. Comte,
+limit the sphere of scientific investigation to Laws of Phenomena, and
+speak of the inquiry into causes as vain and futile. The causes which M.
+Comte designates as inaccessible, are efficient causes. The
+investigation of physical, as opposed to efficient, causes (including
+the study of all the active forces in Nature, considered as facts of
+observation) is as important a part of M. Comte's conception of science
+as of Dr. Whewell's. His objection to the _word_ cause is a mere matter
+of nomenclature, in which, as a matter of nomenclature, I consider him
+to be entirely wrong. "Those," it is justly remarked by Mr. Bailey,[19]
+"who, like M. Comte, object to designate _events_ as causes, are
+objecting without any real ground to a mere but extremely convenient
+generalization, to a very useful common name, the employment of which
+involves, or needs involve, no particular theory." To which it may be
+added, that by rejecting this form of expression, M. Comte leaves
+himself without any term for marking a distinction which, however
+incorrectly expressed, is not only real, but is one of the fundamental
+distinctions in science; indeed it is on this alone, as we shall
+hereafter find, that the possibility rests of framing a rigorous Canon
+of Induction. And as things left without a name are apt to be forgotten,
+a Canon of that description is not one of the many benefits which the
+philosophy of Induction has received from M. Comte's great powers.
+
+
+� 6. Does a cause always stand with its effect in the relation of
+antecedent and consequent? Do we not often say of two simultaneous facts
+that they are cause and effect--as when we say that fire is the cause of
+warmth, the sun and moisture the cause of vegetation, and the like?
+Since a cause does not necessarily perish because its effect has been
+produced, the two things do very generally coexist; and there are some
+appearances, and some common expressions, seeming to imply not only that
+causes may, but that they must, be contemporaneous with their effects.
+_Cessante caus� cessat et effectus_, has been a dogma of the schools:
+the necessity for the continued existence of the cause in order to the
+continuance of the effect, seems to have been once a generally received
+doctrine. Kepler's numerous attempts to account for the motions of the
+heavenly bodies on mechanical principles, were rendered abortive by his
+always supposing that the agency which set those bodies in motion must
+continue to operate in order to keep up the motion which it at first
+produced. Yet there were at all times many familiar instances of the
+continuance of effects, long after their causes had ceased. A _coup de
+soleil_ gives a person a brain fever: will the fever go off as soon as
+he is moved out of the sunshine? A sword is run through his body: must
+the sword remain in his body in order that he may continue dead? A
+ploughshare once made, remains a ploughshare, without any continuance of
+heating and hammering, and even after the man who heated and hammered it
+has been gathered to his fathers. On the other hand, the pressure which
+forces up the mercury in an exhausted tube must be continued in order to
+sustain it in the tube. This (it may be replied) is because another
+force is acting without intermission, the force of gravity, which would
+restore it to its level, unless counterpoised by a force equally
+constant. But again; a tight bandage causes pain, which pain will
+sometimes go off as soon as the bandage is removed. The illumination
+which the sun diffuses over the earth ceases when the sun goes down.
+
+There is, therefore, a distinction to be drawn. The conditions which are
+necessary for the first production of a phenomenon, are occasionally
+also necessary for its continuance; though more commonly its continuance
+requires no condition except negative ones. Most things, once produced,
+continue as they are, until something changes or destroys them; but some
+require the permanent presence of the agencies which produced them at
+first. These may, if we please, be considered as instantaneous
+phenomena, requiring to be renewed at each instant by the cause by which
+they were at first generated. Accordingly, the illumination of any given
+point of space has always been looked upon as an instantaneous fact,
+which perishes and is perpetually renewed as long as the necessary
+conditions subsist. If we adopt this language we avoid the necessity of
+admitting that the continuance of the cause is ever required to maintain
+the effect. We may say, it is not required to maintain, but to
+reproduce, the effect, or else to counteract some force tending to
+destroy it. And this may be a convenient phraseology. But it is only a
+phraseology. The fact remains, that in some cases (though these are a
+minority) the continuance of the conditions which produced an effect is
+necessary to the continuance of the effect.
+
+As to the ulterior question, whether it is strictly necessary that the
+cause, or assemblage of conditions, should precede, by ever so short an
+instant, the production of the effect, (a question raised and argued
+with much ingenuity by Sir John Herschel in an Essay already
+quoted,[20]) the inquiry is of no consequence for our present purpose.
+There certainly are cases in which the effect follows without any
+interval perceptible by our faculties: and when there is an interval, we
+cannot tell by how many intermediate links imperceptible to us that
+interval may really be filled up. But even granting that an effect may
+commence simultaneously with its cause, the view I have taken of
+causation is in no way practically affected. Whether the cause and its
+effect be necessarily successive or not, the beginning of a phenomenon
+is what implies a cause, and causation is the law of the succession of
+phenomena. If these axioms be granted, we can afford, though I see no
+necessity for doing so, to drop the words antecedent and consequent as
+applied to cause and effect. I have no objection to define a cause, the
+assemblage of phenomena, which occurring, some other phenomenon
+invariably commences, or has its origin. Whether the effect coincides in
+point of time with, or immediately follows, the hindmost of its
+conditions, is immaterial. At all events it does not precede it; and
+when we are in doubt, between two coexistent phenomena, which is cause
+and which effect, we rightly deem the question solved if we can
+ascertain which of them preceded the other.
+
+
+� 7. It continually happens that several different phenomena, which are
+not in the slightest degree dependent or conditional on one another, are
+found all to depend, as the phrase is, on one and the same agent; in
+other words, one and the same phenomenon is seen to be followed by
+several sorts of effects quite heterogeneous, but which go on
+simultaneously one with another; provided, of course, that all other
+conditions requisite for each of them also exist. Thus, the sun produces
+the celestial motions, it produces daylight, and it produces heat. The
+earth causes the fall of heavy bodies, and it also, in its capacity of a
+great magnet, causes the phenomena of the magnetic needle. A crystal of
+galena causes the sensations of hardness, of weight, of cubical form, of
+grey colour, and many others between which we can trace no
+interdependence. The purpose to which the phraseology of Properties and
+Powers is specially adapted, is the expression of this sort of cases.
+When the same phenomenon is followed (either subject or not to the
+presence of other conditions) by effects of different and dissimilar
+orders, it is usual to say that each different sort of effect is
+produced by a different property of the cause. Thus we distinguish the
+attractive or gravitative property of the earth, and its magnetic
+property: the gravitative, luminiferous, and calorific properties of the
+sun: the colour, shape, weight, and hardness of a crystal. These are
+mere phrases, which explain nothing, and add nothing to our knowledge of
+the subject; but, considered as abstract names denoting the connexion
+between the different effects produced and the object which produces
+them, they are a very powerful instrument of abridgment, and of that
+acceleration of the process of thought which abridgment accomplishes.
+
+This class of considerations leads to a conception which we shall find
+to be of great importance, that of a Permanent Cause, or original
+natural agent. There exist in nature a number of permanent causes, which
+have subsisted ever since the human race has been in existence, and for
+an indefinite and probably an enormous length of time previous. The sun,
+the earth, and planets, with their various constituents, air, water, and
+other distinguishable substances, whether simple or compound, of which
+nature is made up, are such Permanent Causes. These have existed, and
+the effects or consequences which they were fitted to produce have taken
+place (as often as the other conditions of the production met,) from the
+very beginning of our experience. But we can give no account of the
+origin of the Permanent Causes themselves. Why these particular natural
+agents existed originally and no others, or why they are commingled in
+such and such proportions, and distributed in such and such a manner
+throughout space, is a question we cannot answer. More than this: we can
+discover nothing regular in the distribution itself; we can reduce it to
+no uniformity, to no law. There are no means by which, from the
+distribution of these causes or agents in one part of space, we could
+conjecture whether a similar distribution prevails in another. The
+coexistence, therefore, of Primeval Causes, ranks, to us, among merely
+casual concurrences: and all those sequences or coexistences among the
+effects of several such causes, which, though invariable while those
+causes coexist, would, if the coexistence terminated, terminate along
+with it, we do not class as cases of causation, or laws of nature: we
+can only calculate on finding these sequences or coexistences where we
+know by direct evidence, that the natural agents on the properties of
+which they ultimately depend, are distributed in the requisite manner.
+These Permanent Causes are not always objects; they are sometimes
+events, that is to say, periodical cycles of events, that being the only
+mode in which events can possess the property of permanence. Not only,
+for instance, is the earth itself a permanent cause, or primitive
+natural agent, but the earth's rotation is so too: it is a cause which
+has produced, from the earliest period, (by the aid of other necessary
+conditions,) the succession of day and night, the ebb and flow of the
+sea, and many other effects, while, as we can assign no cause (except
+conjecturally) for the rotation itself, it is entitled to be ranked as a
+primeval cause. It is, however, only the _origin_ of the rotation which
+is mysterious to us: once begun, its continuance is accounted for by the
+first law of motion (that of the permanence of rectilinear motion once
+impressed) combined with the gravitation of the parts of the earth
+towards one another.
+
+All phenomena without exception which begin to exist, that is, all
+except the primeval causes, are effects either immediate or remote of
+those primitive facts, or of some combination of them. There is no Thing
+produced, no event happening, in the known universe, which is not
+connected by an uniformity, or invariable sequence, with some one or
+more of the phenomena which preceded it; insomuch that it will happen
+again as often as those phenomena occur again, and as no other
+phenomenon having the character of a counteracting cause shall coexist.
+These antecedent phenomena, again, were connected in a similar manner
+with some that preceded them; and so on, until we reach, as the ultimate
+step attainable by us, either the properties of some one primeval cause,
+or the conjunction of several. The whole of the phenomena of nature were
+therefore the necessary, or in other words, the unconditional,
+consequences of some former collocation of the Permanent Causes.
+
+The state of the whole universe at any instant, we believe to be the
+consequence of its state at the previous instant; insomuch that one who
+knew all the agents which exist at the present moment, their collocation
+in space, and all their properties, in other words, the laws of their
+agency, could predict the whole subsequent history of the universe, at
+least unless some new volition of a power capable of controlling the
+universe should supervene.[21] And if any particular state of the
+entire universe could ever recur a second time, all subsequent states
+would return too, and history would, like a circulating decimal of many
+figures, periodically repeat itself:--
+
+    Jam redit et virgo, redeunt Saturnia regna....
+    Alter erit tum Tiphys, et altera qu� vehat Argo
+    Delectos heroas; erunt quoque altera bella,
+    Atque iterum ad Trojam magnus mittetur Achilles.
+
+And though things do not really revolve in this eternal round, the whole
+series of events in the history of the universe, past and future, is not
+the less capable, in its own nature, of being constructed _� priori_ by
+any one whom we can suppose acquainted with the original distribution of
+all natural agents, and with the whole of their properties, that is, the
+laws of succession existing between them and their effects: saving the
+far more than human powers of combination and calculation which would be
+required, even in one possessing the data, for the actual performance of
+the task.
+
+
+� 8. Since everything which occurs is determined by laws of causation
+and collocations of the original causes, it follows that the
+coexistences which are observable among effects cannot be themselves the
+subject of any similar set of laws, distinct from laws of causation.
+Uniformities there are, as well of coexistence as of succession, among
+effects; but these must in all cases be a mere result either of the
+identity or of the coexistence of their causes: if the causes did not
+coexist, neither could the effects. And these causes being also effects
+of prior causes, and these of others, until we reach the primeval
+causes, it follows that (except in the case of effects which can be
+traced immediately or remotely to one and the same cause) the
+coexistences of phenomena can in no case be universal, unless the
+coexistences of the primeval causes to which the effects are ultimately
+traceable, can be reduced to an universal law: but we have seen that
+they cannot. There are, accordingly, no original and independent, in
+other words no unconditional, uniformities of coexistence, between
+effects of different causes; if they coexist, it is only because the
+causes have casually coexisted. The only independent and unconditional
+coexistences which are sufficiently invariable to have any claim to the
+character of laws, are between different and mutually independent
+effects of the same cause; in other words, between different properties
+of the same natural agent. This portion of the Laws of Nature will be
+treated of in the latter part of the present Book, under the name of the
+Specific Properties of Kinds.
+
+
+� 9. It is proper in this place to advert to a rather ancient doctrine
+respecting causation, which has been revived during the last few years
+in many quarters, and at present gives more signs of life than any other
+theory of causation at variance with that set forth in the preceding
+pages.
+
+According to the theory in question, Mind, or, to speak more precisely,
+Will, is the only cause of phenomena. The type of Causation, as well as
+the exclusive source from which we derive the idea, is our own voluntary
+agency. Here, and here only (it is said) we have direct evidence of
+causation. We know that we can move our bodies. Respecting the phenomena
+of inanimate nature, we have no other direct knowledge than that of
+antecedence and sequence. But in the case of our voluntary actions, it
+is affirmed that we are conscious of power, before we have experience of
+results. An act of volition, whether followed by an effect or not, is
+accompanied by a consciousness of effort, "of force exerted, of power in
+action, which is necessarily causal, or causative." This feeling of
+energy or force, inherent in an act of will, is knowledge _� priori_;
+assurance, prior to experience, that we have the power of causing
+effects. Volition, therefore, it is asserted, is something more than an
+unconditional antecedent; it is a cause, in a different sense from that
+in which physical phenomena are said to cause one another: it is an
+Efficient Cause. From this the transition is easy to the further
+doctrine, that Volition is the _sole_ Efficient Cause of all phenomena.
+"It is inconceivable that dead force could continue unsupported for a
+moment beyond its creation. We cannot even conceive of change or
+phenomena without the energy of a mind." "The word _action_" itself,
+says another writer of the same school, "has no real significance except
+when applied to the doings of an intelligent agent. Let any one
+conceive, if he can, of any power, energy, or force, inherent in a lump
+of matter." Phenomena may have the semblance of being produced by
+physical causes, but they are in reality produced, say these writers, by
+the immediate agency of mind. All things which do not proceed from a
+human (or, I suppose, an animal) will, proceed, they say, directly from
+divine will. The earth is not moved by the combination of a centripetal
+and a projectile force; this is but a mode of speaking, which serves to
+facilitate our conceptions. It is moved by the direct volition of an
+omnipotent Being, in a path coinciding with that which we deduce from
+the hypothesis of these two forces.
+
+As I have so often observed, the general question of the existence of
+Efficient Causes does not fall within the limits of our subject: but a
+theory which represents them as capable of being subjects of human
+knowledge, and which passes off as efficient causes what are only
+physical or phenomenal causes, belongs as much to Logic as to
+Metaphysics, and is a fit subject for discussion here.
+
+To my apprehension, a volition is not an efficient, but simply a
+physical, cause. Our will causes our bodily actions in the same sense,
+and in no other, in which cold causes ice, or a spark causes an
+explosion of gunpowder. The volition, a state of our mind, is the
+antecedent; the motion of our limbs in conformity to the volition, is
+the consequent. This sequence I conceive to be not a subject of direct
+consciousness, in the sense intended by the theory. The antecedent,
+indeed, and the consequent, are subjects of consciousness. But the
+connexion between them is a subject of experience. I cannot admit that
+our consciousness of the volition contains in itself any _� priori_
+knowledge that the muscular motion will follow. If our nerves of motion
+were paralysed, or our muscles stiff and inflexible, and had been so all
+our lives, I do not see the slightest ground for supposing that we
+should ever (unless by information from other people) have known
+anything of volition as a physical power, or been conscious of any
+tendency in feelings of our mind to produce motions of our body, or of
+other bodies. I will not undertake to say whether we should in that case
+have had the physical feeling which I suppose is meant when these
+writers speak of "consciousness of effort:" I see no reason why we
+should not; since that physical feeling is probably a state of nervous
+sensation beginning and ending in the brain, without involving the
+motory apparatus: but we certainly should not have designated it by any
+term equivalent to effort, since effort implies consciously aiming at an
+end, which we should not only in that case have had no reason to do, but
+could not even have had the idea of doing. If conscious at all of this
+peculiar sensation, we should have been conscious of it, I conceive,
+only as a kind of uneasiness, accompanying our feelings of desire.
+
+It is well argued by Sir William Hamilton against the theory in
+question, that it "is refuted by the consideration, that between the
+overt fact of corporeal movement of which we are cognisant, and the
+internal act of mental determination of which we are also cognisant,
+there intervenes a numerous series of intermediate agencies of which we
+have no knowledge; and, consequently, that we can have no consciousness
+of any causal connexion between the extreme links of this chain, the
+volition to move and the limb moving, as this hypothesis asserts. No one
+is immediately conscious, for example, of moving his arm through his
+volition. Previously to this ultimate movement, muscles, nerves, a
+multitude of solid and fluid parts, must be set in motion by the will,
+but of this motion we know, from consciousness, absolutely nothing. A
+person struck with paralysis is conscious of no inability in his limb to
+fulfil the determinations of his will; and it is only after having
+willed, and finding that his limbs do not obey his volition, that he
+learns by this experience, that the external movement does not follow
+the internal act. But as the paralytic learns after the volition that
+his limbs do not obey his mind; so it is only after volition that the
+man in health learns, that his limbs do obey the mandates of his
+will."[22]
+
+Those against whom I am contending have never produced, and do not
+pretend to produce, any positive evidence[23] that the power of our will
+to move our bodies would be known to us independently of experience.
+What they have to say on the subject is, that the production of physical
+events by a will seems to carry its own explanation with it, while the
+action of matter upon matter seems to require something else to explain
+it; and is even, according to them, "inconceivable" on any other
+supposition than that some will intervenes between the apparent cause
+and its apparent effect. They thus rest their case on an appeal to the
+inherent laws of our conceptive faculty; mistaking, as I apprehend, for
+the laws of that faculty its acquired habits, grounded on the
+spontaneous tendencies of its uncultured state. The succession between
+the will to move a limb and the actual motion, is one of the most direct
+and instantaneous of all sequences which come under our observation, and
+is familiar to every moment's experience from our earliest infancy; more
+familiar than any succession of events exterior to our bodies, and
+especially more so than any other case of the apparent origination (as
+distinguished from the mere communication) of motion. Now, it is the
+natural tendency of the mind to be always attempting to facilitate its
+conception of unfamiliar facts by assimilating them to others which are
+familiar. Accordingly, our voluntary acts, being the most familiar to us
+of all cases of causation, are, in the infancy and early youth of the
+human race, spontaneously taken as the type of causation in general, and
+all phenomena are supposed to be directly produced by the will of some
+sentient being. This original Fetichism I shall not characterize in the
+words of Hume, or of any follower of Hume, but in those of a religious
+metaphysician, Dr. Reid, in order more effectually to show the unanimity
+which exists on the subject among all competent thinkers.
+
+"When we turn our attention to external objects, and begin to exercise
+our rational faculties about them, we find that there are some motions
+and changes in them which we have power to produce, and that there are
+many which must have some other cause. Either the objects must have life
+and active power, as we have, or they must be moved or changed by
+something that has life and active power, as external objects are moved
+by us.
+
+"Our first thoughts seem to be, that the objects in which we perceive
+such motion have understanding and active power as we have. 'Savages,'
+says the Abb� Raynal, 'wherever they see motion which they cannot
+account for, there they suppose a soul.' All men may be considered as
+savages in this respect, until they are capable of instruction, and of
+using their faculties in a more perfect manner than savages do.
+
+"The Abb� Raynal's observation is sufficiently confirmed, both from
+fact, and from the structure of all languages.
+
+"Rude nations do really believe sun, moon, and stars, earth, sea, and
+air, fountains, and lakes, to have understanding and active power. To
+pay homage to them, and implore their favour, is a kind of idolatry
+natural to savages.
+
+"All languages carry in their structure the marks of their being formed
+when this belief prevailed. The distinction of verbs and participles
+into active and passive, which is found in all languages, must have been
+originally intended to distinguish what is really active from what is
+merely passive; and in all languages, we find active verbs applied to
+those objects, in which, according to the Abb� Raynal's observation,
+savages suppose a soul.
+
+"Thus we say the sun rises and sets, and comes to the meridian, the moon
+changes, the sea ebbs and flows, the winds blow. Languages were formed
+by men who believed these objects to have life and active power in
+themselves. It was therefore proper and natural to express their motions
+and changes by active verbs.
+
+"There is no surer way of tracing the sentiments of nations before they
+have records, than by the structure of their language, which,
+notwithstanding the changes produced in it by time, will always retain
+some signatures of the thoughts of those by whom it was invented. When
+we find the same sentiments indicated in the structure of all languages,
+those sentiments must have been common to the human species when
+languages were invented.
+
+"When a few, of superior intellectual abilities, find leisure for
+speculation, they begin to philosophize, and soon discover, that many of
+those objects which at first they believed to be intelligent and active
+are really lifeless and passive. This is a very important discovery. It
+elevates the mind, emancipates from many vulgar superstitions, and
+invites to further discoveries of the same kind.
+
+"As philosophy advances, life and activity in natural objects retires,
+and leaves them dead and inactive. Instead of moving voluntarily, we
+find them to be moved necessarily; instead of acting, we find them to be
+acted upon; and Nature appears as one great machine, where one wheel is
+turned by another, that by a third; and how far this necessary
+succession may reach, the philosopher does not know."[24]
+
+There is, then, a spontaneous tendency of the intellect to account to
+itself for all cases of causation by assimilating them to the
+intentional acts of voluntary agents like itself. This is the
+instinctive philosophy of the human mind in its earliest stage, before
+it has become familiar with any other invariable sequences than those
+between its own volitions or those of other human beings and their
+voluntary acts. As the notion of fixed laws of succession among external
+phenomena gradually establishes itself, the propensity to refer all
+phenomena to voluntary agency slowly gives way before it. The
+suggestions, however, of daily life continuing to be more powerful than
+those of scientific thought, the original instinctive philosophy
+maintains its ground in the mind, underneath the growths obtained by
+cultivation, and keeps up a constant resistance to their throwing their
+roots deep into the soil. The theory against which I am contending
+derives its nourishment from that substratum. Its strength does not lie
+in argument, but in its affinity to an obstinate tendency of the infancy
+of the human mind.
+
+That this tendency, however, is not the result of an inherent mental
+law, is proved by superabundant evidence. The history of science, from
+its earliest dawn, shows that mankind have not been unanimous in
+thinking either that the action of matter upon matter was not
+conceivable, or that the action of mind upon matter was. To some
+thinkers, and some schools of thinkers, both in ancient and in modern
+times, this last has appeared much more inconceivable than the former.
+Sequences entirely physical and material, as soon as they had become
+sufficiently familiar to the human mind, came to be thought perfectly
+natural, and were regarded not only as needing no explanation
+themselves, but as being capable of affording it to others, and even of
+serving as the ultimate explanation of things in general.
+
+One of the ablest recent supporters of the Volitional theory has
+furnished an explanation, at once historically true and philosophically
+acute, of the failure of the Greek philosophers in physical inquiry, in
+which, as I conceive, he unconsciously depicts his own state of mind.
+"Their stumbling-block was one as to the nature of the evidence they had
+to expect for their conviction.... They had not seized the idea that
+they must not expect to understand the processes of outward causes, but
+only their results: and consequently, the whole physical philosophy of
+the Greeks was an attempt to identify mentally the effect with its
+cause, to feel after some not only necessary but natural connexion,
+where they meant by natural that which would _per se_ carry some
+presumption to their own mind.... They wanted to see some _reason_ why
+the physical antecedent should produce this particular consequent, and
+their only attempts were in directions where they could find such
+reasons."[25] In other words, they were not content merely to know that
+one phenomenon was always followed by another; they thought that they
+had not attained the true aim of science, unless they could perceive
+something in the nature of the one phenomenon from which it might have
+been known or presumed _previous to trial_ that it would be followed by
+the other: just what the writer, who has so clearly pointed out their
+error, thinks that he perceives in the nature of the phenomenon
+Volition. And to complete the statement of the case, he should have
+added that these early speculators not only made this their aim, but
+were quite satisfied with their success in it; not only sought for
+causes which should carry in their mere statement evidence of their
+efficiency, but fully believed that they had found such causes. The
+reviewer can see plainly that this was an error, because _he_ does not
+believe that there exist any relations between material phenomena which
+can account for their producing one another: but the very fact of the
+persistency of the Greeks in this error, shows that their minds were in
+a very different state: they were able to derive from the assimilation
+of physical facts to other physical facts, the kind of mental
+satisfaction which we connect with the word explanation, and which the
+reviewer would have us think can only be found in referring phenomena to
+a will. When Thales and Hippo held that moisture was the universal
+cause, and external element, of which all other things were but the
+infinitely various sensible manifestations; when Anaximenes predicated
+the same thing of air, Pythagoras of numbers, and the like, they all
+thought that they had found a real explanation; and were content to rest
+in this explanation as ultimate. The ordinary sequences of the external
+universe appeared to them, no less than to their critic, to be
+inconceivable without the supposition of some universal agency to
+connect the antecedents with the consequents; but they did not think
+that Volition, exerted by minds, was the only agency which fulfilled
+this requirement. Moisture, or air, or numbers, carried to their minds a
+precisely similar impression of making intelligible what was otherwise
+inconceivable, and gave the same full satisfaction to the demands of
+their conceptive faculty.
+
+It was not the Greeks alone, who "wanted to see some reason why the
+physical antecedent should produce this particular consequent," some
+connexion "which would _per se_ carry some presumption to their own
+mind." Among modern philosophers, Leibnitz laid it down as a
+self-evident principle that all physical causes without exception must
+contain in their own nature something which makes it intelligible that
+they should be able to produce the effects which they do produce. Far
+from admitting Volition as the only kind of cause which carried internal
+evidence of its own power, and as the real bond of connexion between
+physical antecedents and their consequents, he demanded some naturally
+and _per se_ efficient physical antecedent as the bond of connexion
+between Volition itself and its effects. He distinctly refused to admit
+the will of God as a sufficient explanation of anything except miracles;
+and insisted upon finding something that would account _better_ for the
+phenomena of nature than a mere reference to divine volition.[26]
+
+Again, and conversely, the action of mind upon matter (which, we are now
+told, not only needs no explanation itself, but is the explanation of
+all other effects), has appeared to some thinkers to be itself the grand
+inconceivability. It was to get over this very difficulty that the
+Cartesians invented the system of Occasional Causes. They could not
+conceive that thoughts in a mind could produce movements in a body, or
+that bodily movements could produce thoughts. They could see no
+necessary connexion, no relation _� priori_, between a motion and a
+thought. And as the Cartesians, more than any other school of
+philosophical speculation before or since, made their own minds the
+measure of all things, and refused, on principle, to believe that Nature
+had done what they were unable to see any reason why she must do, they
+affirmed it to be impossible that a material and a mental fact could be
+causes one of another. They regarded them as mere Occasions on which the
+real agent, God, thought fit to exert his power as a Cause. When a man
+wills to move his foot, it is not his will that moves it, but God (they
+said) moves it on the occasion of his will. God, according to this
+system, is the only efficient cause, not _qu�_ mind, or _qu�_ endowed
+with volition, but _qu�_ omnipotent. This hypothesis was, as I said,
+originally suggested by the supposed inconceivability of any real mutual
+action between Mind and Matter: but it was afterwards extended to the
+action of Matter upon Matter, for on a nicer examination they found this
+inconceivable too, and therefore, according to their logic, impossible.
+The _deus ex machin�_ was ultimately called in to produce a spark on the
+occasion of a flint and steel coming together, or to break an egg on the
+occasion of its falling on the ground.
+
+All this, undoubtedly, shows that it is the disposition of mankind in
+general, not to be satisfied with knowing that one fact is invariably
+antecedent and another consequent, but to look out for something which
+may seem to explain their being so. But we also see that this demand may
+be completely satisfied by an agency purely physical, provided it be
+much more familiar than that which it is invoked to explain. To Thales
+and Anaximenes, it appeared inconceivable that the antecedents which we
+see in nature, should produce the consequents; but perfectly natural
+that water, or air, should produce them. The writers whom I oppose
+declare this inconceivable, but can conceive that mind, or volition, is
+_per se_ an efficient cause: while the Cartesians could not conceive
+even that, but peremptorily declared that no mode of production of any
+fact whatever was conceivable, except the direct agency of an omnipotent
+being. Thus giving additional proof of what finds new confirmation in
+every stage of the history of science: that both what persons can, and
+what they cannot, conceive, is very much an affair of accident, and
+depends altogether on their experience, and their habits of thought;
+that by cultivating the requisite associations of ideas, people may make
+themselves unable to conceive any given thing; and may make themselves
+able to conceive most things, however inconceivable these may at first
+appear: and the same facts in each person's mental history which
+determine what is or is not conceivable to him, determine also which
+among the various sequences in nature will appear to him so natural and
+plausible, as to need no other proof of their existence; to be evident
+by their own light, independent equally of experience and of
+explanation.
+
+By what rule is any one to decide between one theory of this description
+and another? The theorists do not direct us to any external evidence;
+they appeal each to his own subjective feelings. One says, the
+succession C, B, appears to me more natural, conceivable, and credible
+_per se_, than the succession A, B; you are therefore mistaken in
+thinking that B depends upon A; I am certain, though I can give no other
+evidence of it, that C comes in between A and B, and is the real and
+only cause of B. The other answers--the successions C, B, and A, B,
+appear to me equally natural and conceivable, or the latter more so than
+the former: A is quite capable of producing B without any other
+intervention. A third agrees with the first in being unable to conceive
+that A can produce B, but finds the sequence D, B, still more natural
+than C, B, or of nearer kin to the subject matter, and prefers his D
+theory to the C theory. It is plain that there is no universal law
+operating here, except the law that each person's conceptions are
+governed and limited by his individual experience and habits of thought.
+We are warranted in saying of all three, what each of them already
+believes of the other two, namely, that they exalt into an original law
+of the human intellect and of outward nature, one particular sequence of
+phenomena, which appears to them more natural and more conceivable than
+other sequences, only because it is more familiar. And from this
+judgment I am unable to except the theory, that Volition is an Efficient
+Cause.
+
+I am unwilling to leave the subject without adverting to the additional
+fallacy contained in the corollary from this theory; in the inference
+that because Volition is an efficient cause, therefore it is the only
+cause, and the direct agent in producing even what is apparently
+produced by something else. Volitions are not known to produce anything
+directly except nervous action, for the will influences even the muscles
+only through the nerves. Though it were granted, then, that every
+phenomenon has an efficient, and not merely a phenomenal cause, and that
+volition, in the case of the peculiar phenomena which are known to be
+produced by it, is that efficient cause; are we therefore to say, with
+these writers, that since we know of no other efficient cause, and ought
+not to assume one without evidence, there _is_ no other, and volition is
+the direct cause of all phenomena? A more outrageous stretch of
+inference could hardly be made. Because among the infinite variety of
+the phenomena of nature there is one, namely, a particular mode of
+action of certain nerves, which has for its cause, and as we are now
+supposing for its efficient cause, a state of our mind; and because this
+is the only efficient cause of which we are conscious, being the only
+one of which in the nature of the case we _can_ be conscious, since it
+is the only one which exists within ourselves; does this justify us in
+concluding that all other phenomena must have the same kind of efficient
+cause with that one eminently special, narrow, and peculiarly human or
+animal, phenomenon? The nearest parallel to this specimen of
+generalization is suggested by the recently revived controversy on the
+old subject of Plurality of Worlds, in which the contending parties have
+been so conspicuously successful in overthrowing one another. Here also
+we have experience only of a single case, that of the world in which we
+live, but that this is inhabited we know absolutely, and without
+possibility of doubt. Now if on this evidence any one were to infer that
+every heavenly body without exception, sun, planet, satellite, comet,
+fixed star or nebula, is inhabited, and must be so from the inherent
+constitution of things, his inference would exactly resemble that of the
+writers who conclude that because volition is the efficient cause of our
+own bodily motions, it must be the efficient cause of everything else in
+the universe. It is true there are cases in which, with acknowledged
+propriety, we generalize from a single instance to a multitude of
+instances. But they must be instances which resemble the one known
+instance, and not such as have no circumstance in common with it except
+that of being instances. I have, for example, no direct evidence that
+any creature is alive except myself: yet I attribute, with full
+assurance, life and sensation to other human beings and animals. But I
+do not conclude that all other things are alive merely because I am. I
+ascribe to certain other creatures a life like my own, because they
+manifest it by the same sort of indications by which mine is manifested.
+I find that their phenomena and mine conform to the same laws, and it is
+for this reason that I believe both to arise from a similar cause.
+Accordingly I do not extend the conclusion beyond the grounds for it.
+Earth, fire, mountains, trees, are remarkable agencies, but their
+phenomena do not conform to the same laws as my actions do, and I
+therefore do not believe earth or fire, mountains or trees, to possess
+animal life. But the supporters of the Volition Theory ask us to infer
+that volition causes everything, for no reason except that it causes one
+particular thing; although that one phenomenon, far from being a type of
+all natural phenomena, is eminently peculiar; its laws bearing scarcely
+any resemblance to those of any other phenomenon, whether of inorganic
+or of organic nature.
+
+
+NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
+
+     The author of the Second Burnett Prize Essay (Dr. Tulloch), who
+     has employed a considerable number of pages in controverting
+     the doctrines of the preceding chapter, has somewhat surprised
+     me by denying a fact, which I imagined too well known to
+     require proof--that there have been philosophers who found in
+     physical explanations of phenomena the same complete mental
+     satisfaction which we are told is only given by volitional
+     explanation, and others who denied the Volitional Theory on the
+     same ground of inconceivability on which it is defended. The
+     assertion of the Essayist is countersigned still more
+     positively by an able reviewer of the Essay:[27] "Two
+     illustrations," says the reviewer, "are advanced by Mr. Mill:
+     the case of Thales and Anaximenes, stated by him to have
+     maintained, the one Moisture and the other Air to be the origin
+     of all things; and that of Descartes and Leibnitz, whom he
+     asserts to have found the action of Mind upon Matter the grand
+     inconceivability. In counterstatement as to the first of these
+     cases the author shows--what we believe now hardly admits of
+     doubt--that the Greek philosophers distinctly recognised as
+     beyond and above their primal material source, the [Greek:
+     nous], or Divine Intelligence, as the efficient and originating
+     Source of all: and as to the second, by proof that it was the
+     _mode_, not the _fact_, of that action on matter, which was
+     represented as inconceivable."
+
+     A greater quantity of historical error has seldom been
+     comprised in a single sentence. With regard to Thales, the
+     assertion that he considered water as a mere material in the
+     hands of [Greek: nous] rests on a passage of Cicero _de Natur�
+     Deorum_: and whoever will refer to any of the accurate
+     historians of philosophy, will find that they treat this as a
+     mere fancy of Cicero, resting on no authority, opposed to all
+     the evidence; and make surmises as to the manner in which
+     Cicero may have been led into the error. (See Ritter, vol. i.
+     p. 211, 2nd ed.; Brandis, vol. i. pp. 118-9, 1st ed.; Preller,
+     _Historia Philosophi� Gr�co-Roman�_, p. 10. "Schiefe Ansicht,
+     durchaus zu verwerfen;" "augenscheinlich folgernd statt zu
+     berichten;" "quibus vera sententia Thaletis plane detorquetur;"
+     are the expressions of these writers.) As for Anaximenes, he,
+     even according to Cicero, maintained, not that air was the
+     material out of which God made the world, but that the air was
+     a god: "Anaximenes a�ra deum statuit:" or according to St.
+     Augustine, that it was the material out of which the gods were
+     made; "non tamen ab ipsis [Diis] a�rem factum, sed ipsos ex
+     a�re ortos credidit." Those who are not familiar with the
+     metaphysical terminology of antiquity, must not be misled by
+     finding it stated that Anaximenes attributed [Greek: psych�]
+     (translated _soul_, or _life_) to his universal element, the
+     air. The Greek philosophers acknowledged several kinds of
+     [Greek: psych�], the nutritive, the sensitive, and the
+     intellective.[28] Even the moderns with admitted correctness
+     attribute life to plants. As far as we can make out the meaning
+     of Anaximenes, he made choice of Air as the universal agent, on
+     the ground that it is perpetually in motion, without any
+     apparent cause external to itself: so that he conceived it as
+     exercising spontaneous force, and as the principle of life and
+     activity in all things, men and gods inclusive. If this be not
+     representing it as the Efficient Cause, the dispute altogether
+     has no meaning.
+
+     If either Anaximenes, or Thales, or any of their cotemporaries,
+     had held the doctrine that [Greek: nous] was the Efficient
+     Cause, that doctrine could not have been reputed, as it was
+     throughout antiquity, to have originated with Anaxagoras. The
+     testimony of Aristotle, in the first book of his Metaphysics,
+     is perfectly decisive with respect to these early speculations.
+     After enumerating four kinds of causes, or rather four
+     different meanings of the word Cause, viz. the Essence of a
+     thing, the Matter of it, the Origin of Motion (Efficient
+     Cause), and the End or Final Cause, he proceeds to say, that
+     most of the early philosophers recognised only the second kind
+     of Cause, the Matter of a thing, [Greek: tas en hyl�s eidei
+     monas ��th�san archas einai pant�n]. As his first example he
+     specifies Thales, whom he describes as taking the lead in this
+     view of the subject, [Greek: ho t�s toiaut�s arch�gos
+     philosophias], and goes on to Hippon, Anaximenes, Diogenes (of
+     Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.
+     Anaxagoras, however, (he proceeds to say,) taught a different
+     doctrine, as we know, and it is _alleged_ that Hermotimus of
+     Clazomen� taught it before him. Anaxagoras represented, that
+     even if these various theories of the universal material were
+     true, there would be need of some other cause to account for
+     the transformations of the material, since the material cannot
+     originate its own changes: [Greek: ou gar d� to ge hypokeimenon
+     auto poiei metaballein heauto; leg� d' oion oute to xylon oute
+     ho chalkos aitios tou metaballein hekateron aut�n, oude poiei
+     to men xylon klin�n ho de chalkos andrianta, all' heteron ti
+     t�s metabol�s aition], viz., the other kind of cause [Greek:
+     hothen h� arch� t�s kin�se�s]--an Efficient Cause. Aristotle
+     expresses great approbation of this doctrine (which he says
+     made its author appear the only sober man among persons raving,
+     [Greek: oion n�ph�n ephan� par' eik� legontas tous proteron]);
+     but while describing the influence which it exercised over
+     subsequent speculation, he remarks that the philosophers
+     against whom this, as he thinks, insuperable difficulty was
+     urged, had not felt it to be any difficulty: [Greek: ouden
+     edyscheranan en heautois]. It is surely unnecessary to say more
+     in proof of the matter of fact which Dr. Tulloch and his
+     reviewer deny.
+
+     Having pointed out what he thinks the error of these early
+     speculators in not recognising the need of an efficient cause,
+     Aristotle goes on to mention two other efficient causes to
+     which they might have had recourse, instead of intelligence:
+     [Greek: tych�], chance, and [Greek: to automaton], spontaneity.
+     He indeed puts these aside as not sufficiently worthy causes
+     for the order in the universe, [Greek: oud' au t� automat� kai
+     t� tych� tosouton epitrepsai pragma kal�s eichen]: but he does
+     not reject them as incapable of producing any effect, but only
+     as incapable of producing _that_ effect. He himself recognises
+     [Greek: tych�] and [Greek: to automaton] as co-ordinate agents
+     with Mind in producing the phenomena of the universe; the
+     department allotted to them being composed of all the classes
+     of phenomena which are not supposed to follow any uniform law.
+     By thus including Chance among efficient causes, Aristotle fell
+     into an error which philosophy has now outgrown, but which is
+     by no means so alien to the spirit even of modern speculation
+     as it may at first sight appear. Up to quite a recent period
+     philosophers went on ascribing, and many of them have not yet
+     ceased to ascribe, a real existence to the results of
+     abstraction. Chance could make out as good a title to that
+     dignity as many other of the mind's abstract creations: it had
+     had a name given to it, and why should it not be a reality? As
+     for [Greek: to automaton], it is recognised even yet as one of
+     the modes of origination of phenomena, by all those thinkers
+     who maintain what is called the Freedom of the Will. The same
+     self-determining power which that doctrine attributes to
+     volitions, was supposed by the ancients to be possessed also by
+     some other natural phenomena: a circumstance which throws
+     considerable light on more than one of the supposed invincible
+     necessities of belief. I have introduced it here, because this
+     belief of Aristotle, or rather of the Greek philosophers
+     generally, is as fatal as the doctrines of Thales and the Ionic
+     school, to the theory that the human mind is compelled by its
+     constitution to conceive volition as the origin of all force,
+     and the efficient cause of all phenomena.[29]
+
+     With regard to the modern philosophers (Leibnitz and the
+     Cartesians) whom I had cited as having maintained that the
+     action of mind upon matter, so far from being the only
+     conceivable origin of material phenomena, is itself
+     inconceivable; the attempt to rebut this argument by asserting
+     that the mode, not the fact, of the action of mind on matter
+     was represented as inconceivable, is an abuse of the privilege
+     of writing confidently about authors without reading them: for
+     any knowledge whatever of Leibnitz would have taught those who
+     thus speak of him, that the inconceivability of the mode, and
+     the impossibility of the thing, were in his mind convertible
+     expressions. What was his famous Principle of the Sufficient
+     Reason, the very corner stone of his philosophy, from which the
+     Preestablished Harmony, the doctrine of Monads, and all the
+     opinions most characteristic of Leibnitz, were corollaries? It
+     was, that nothing exists, the existence of which is not capable
+     of being proved and explained _� priori_; the proof and
+     explanation in the case of contingent facts being derived from
+     the nature of their causes; which could not be the causes
+     unless there was something in their nature showing them to be
+     capable of producing those particular effects. And this
+     "something" which accounts for the production of physical
+     effects, he was able to find in many physical causes, but could
+     not find it in any finite minds, which therefore he
+     unhesitatingly asserted to be incapable of producing any
+     physical effects whatever. "On ne saurait concevoir," he says,
+     "une action r�ciproque de la mati�re et de l'intelligence l'une
+     sur l'autre," and there is therefore (he contends) no choice
+     but between the Occasional Causes of the Cartesians, and his
+     own Preestablished Harmony, according to which there is no more
+     connexion between our volitions and our muscular actions than
+     there is between two clocks which are wound up to strike at the
+     same instant. But he felt no similar difficulty as to physical
+     causes: and throughout his speculations, as in the passage I
+     have already cited respecting gravitation, he distinctly
+     refuses to consider as part of the order of nature any fact
+     which is not explicable from the nature of its physical cause.
+
+     With regard to the Cartesians (not Descartes; I did not make
+     that mistake, though the reviewer of Dr. Tulloch's Essay
+     attributes it to me) I take a passage almost at random from
+     Malebranche, who is the best known of the Cartesians, and,
+     though not the inventor of the system of Occasional Causes, is
+     its principal expositor. In Part 2, chap. 3, of his Sixth Book,
+     having first said that matter cannot have the power of moving
+     itself, he proceeds to argue that neither can mind have the
+     power of moving it. "Quand on examine l'id�e que l'on a de tous
+     les esprits finis, on ne voit point de liaison n�cessaire entre
+     leur volont� et le mouvement de quelque corps que ce soit, on
+     voit au contraire qu'il n'y en a point, et qu'il n'y en peut
+     avoir;" (there is nothing in the idea of finite mind which can
+     account for its causing the motion of a body;) "on doit aussi
+     conclure, si on veut raisonner selon ses lumi�res, qu'il n'y a
+     aucun esprit cr�� qui puisse remuer quelque corps que ce soit
+     comme cause v�ritable ou principale, de m�me que l'on a dit
+     qu'aucun corps ne se pouvait remuer soi-m�me:" thus the idea of
+     Mind is according to him as incompatible as the idea of Matter
+     with the exercise of active force. But when, he continues, we
+     consider not a created but a Divine Mind, the case is altered;
+     for the idea of a Divine Mind includes omnipotence; and the
+     idea of omnipotence does contain the idea of being able to move
+     bodies. Thus it is the nature of omnipotence which renders the
+     motion of bodies even by the divine mind credible or
+     conceivable, while, so far as depended on the mere nature of
+     mind, it would have been inconceivable and incredible. If
+     Malebranche had not believed in an omnipotent being, he would
+     have held all action of mind on body to be a demonstrated
+     impossibility.[30]
+
+     A doctrine more precisely the reverse of the Volitional theory
+     of causation cannot well be imagined. The volitional theory is,
+     that we know by intuition or by direct experience the action of
+     our own mental volitions on matter; that we may hence infer all
+     other action upon matter to be that of volition, and might thus
+     know, without any other evidence, that matter is under the
+     government of a divine mind. Leibnitz and the Cartesians, on
+     the contrary, maintain that our volitions do not and cannot act
+     upon matter, and that it is only the existence of an
+     all-governing Being, and that Being omnipotent, which can
+     account for the sequence between our volitions and our bodily
+     actions. When we consider that each of these two theories,
+     which, as theories of causation, stand at the opposite extremes
+     of possible divergence from one another, invokes not only as
+     its evidence, but as its sole evidence, the absolute
+     inconceivability of any theory but itself, we are enabled to
+     measure the worth of this kind of evidence; and when we find
+     the Volitional theory entirely built upon the assertion that by
+     our mental constitution we are compelled to recognise our
+     volitions as efficient causes, and then find other thinkers
+     maintaining that we know that they are not, and cannot be such
+     causes, and cannot conceive them to be so, I think we have a
+     right to say, that this supposed law of our mental constitution
+     does not exist.
+
+     Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this,
+     that Leibnitz and the Cartesians were Theists, and believed the
+     will of God to be an efficient cause. Doubtless they did, and
+     the Cartesians even believed, though Leibnitz did not, that it
+     is the only such cause. Dr. Tulloch mistakes the nature of the
+     question. I was not writing on Theism, as Dr. Tulloch is, but
+     against a particular theory of causation, which if it be
+     unfounded, can give no effective support to Theism or to
+     anything else. I found it asserted that volition is the only
+     efficient cause, on the ground that no other efficient cause is
+     conceivable. To this assertion I oppose the instances of
+     Leibnitz and of the Cartesians, who affirmed with equal
+     positiveness that volition as an efficient cause is itself not
+     conceivable, and that omnipotence, which renders all things
+     conceivable, can alone take away the impossibility. This I
+     thought, and think, a conclusive answer to the argument on
+     which this theory of causation avowedly depends. But I
+     certainly did not imagine that Theism was bound up with that
+     theory; nor expected to be charged with denying Leibnitz and
+     the Cartesians to be Theists because I denied that they held
+     the theory.
+
+
+
+
+CHAPTER VI.
+
+ON THE COMPOSITION OF CAUSES.
+
+
+� 1. To complete the general notion of causation on which the rules of
+experimental inquiry into the laws of nature must be founded, one
+distinction still remains to be pointed out: a distinction so radical,
+and of so much importance, as to require a chapter to itself.
+
+The preceding discussions have rendered us familiar with the case in
+which several agents, or causes, concur as conditions to the production
+of an effect: a case, in truth, almost universal, there being very few
+effects to the production of which no more than one agent contributes.
+Suppose, then, that two different agents, operating jointly, are
+followed, under a certain set of collateral conditions, by a given
+effect. If either of these agents, instead of being joined with the
+other, had operated alone, under the same set of conditions in all other
+respects, some effect would probably have followed; which would have
+been different from the joint effect of the two, and more or less
+dissimilar to it. Now, if we happen to know what would be the effect of
+each cause when acting separately from the other, we are often able to
+arrive deductively, or _� priori_, at a correct prediction of what will
+arise from their conjunct agency. To enable us to do this, it is only
+necessary that the same law which expresses the effect of each cause
+acting by itself, shall also correctly express the part due to that
+cause, of the effect which follows from the two together. This condition
+is realized in the extensive and important class of phenomena commonly
+called mechanical, namely the phenomena of the communication of motion
+(or of pressure, which is tendency to motion) from one body to another.
+In this important class of cases of causation, one cause never, properly
+speaking, defeats or frustrates another; both have their full effect.
+If a body is propelled in two directions by two forces, one tending to
+drive it to the north and the other to the east, it is caused to move in
+a given time exactly as far in both directions as the two forces would
+separately have carried it; and is left precisely where it would have
+arrived if it had been acted upon first by one of the two forces, and
+afterwards by the other. This law of nature is called, in dynamics, the
+principle of the Composition of Forces: and in imitation of that
+well-chosen expression, I shall give the name of the Composition of
+Causes to the principle which is exemplified in all cases in which the
+joint effect of several causes is identical with the sum of their
+separate effects.
+
+This principle, however, by no means prevails in all departments of the
+field of nature. The chemical combination of two substances produces, as
+is well known, a third substance with properties entirely different from
+those of either of the two substances separately, or both of them taken
+together. Not a trace of the properties of hydrogen or of oxygen is
+observable in those of their compound, water. The taste of sugar of lead
+is not the sum of the tastes of its component elements, acetic acid and
+lead or its oxide; nor is the colour of blue vitriol a mixture of the
+colours of sulphuric acid and copper. This explains why mechanics is a
+deductive or demonstrative science, and chemistry not. In the one, we
+can compute the effects of all combinations of causes, whether real or
+hypothetical, from the laws which we know to govern those causes when
+acting separately; because they continue to observe the same laws when
+in combination which they observed when separate: whatever would have
+happened in consequence of each cause taken by itself, happens when they
+are together, and we have only to cast up the results. Not so in the
+phenomena which are the peculiar subject of the science of chemistry.
+There, most of the uniformities to which the causes conformed when
+separate, cease altogether when they are conjoined; and we are not, at
+least in the present state of our knowledge, able to foresee what result
+will follow from any new combination, until we have tried the specific
+experiment.
+
+If this be true of chemical combinations, it is still more true of those
+far more complex combinations of elements which constitute organized
+bodies; and in which those extraordinary new uniformities arise, which
+are called the laws of life. All organized bodies are composed of parts
+similar to those composing inorganic nature, and which have even
+themselves existed in an inorganic state; but the phenomena of life,
+which result from the juxtaposition of those parts in a certain manner,
+bear no analogy to any of the effects which would be produced by the
+action of the component substances considered as mere physical agents.
+To whatever degree we might imagine our knowledge of the properties of
+the several ingredients of a living body to be extended and perfected,
+it is certain that no mere summing up of the separate actions of those
+elements will ever amount to the action of the living body itself. The
+tongue, for instance, is, like all other parts of the animal frame,
+composed of gelatine, fibrin, and other products of the chemistry of
+digestion, but from no knowledge of the properties of those substances
+could we ever predict that it could taste, unless gelatine or fibrin
+could themselves taste; for no elementary fact can be in the conclusion,
+which was not in the premises.
+
+There are thus two different modes of the conjunct action of causes;
+from which arise two modes of conflict, or mutual interference, between
+laws of nature. Suppose, at a given point of time and space, two or more
+causes, which, if they acted separately, would produce effects contrary,
+or at least conflicting with each other; one of them tending to undo,
+wholly or partially, what the other tends to do. Thus, the expansive
+force of the gases generated by the ignition of gunpowder tends to
+project a bullet towards the sky, while its gravity tends to make it
+fall to the ground. A stream running into a reservoir at one end tends
+to fill it higher and higher, while a drain at the other extremity tends
+to empty it. Now, in such cases as these, even if the two causes which
+are in joint action exactly annul one another, still the laws of both
+are fulfilled; the effect is the same as if the drain had been open for
+half an hour first,[31] and the stream had flowed in for as long
+afterwards. Each agent produced the same amount of effect as if it had
+acted separately, though the contrary effect which was taking place
+during the same time obliterated it as fast as it was produced. Here
+then are two causes, producing by their joint operation an effect which
+at first seems quite dissimilar to those which they produce separately,
+but which on examination proves to be really the sum of those separate
+effects. It will be noticed that we here enlarge the idea of the sum of
+two effects, so as to include what is commonly called their difference,
+but which is in reality the result of the addition of opposites; a
+conception to which mankind are indebted for that admirable extension of
+the algebraical calculus, which has so vastly increased its powers as an
+instrument of discovery, by introducing into its reasonings (with the
+sign of subtraction prefixed, and under the name of Negative Quantities)
+every description whatever of positive phenomena, provided they are of
+such a quality in reference to those previously introduced, that to add
+the one is equivalent to subtracting an equal quantity of the other.
+
+There is, then, one mode of the mutual interference of laws of nature,
+in which, even when the concurrent causes annihilate each other's
+effects, each exerts its full efficacy according to its own law, its law
+as a separate agent. But in the other description of cases, the agencies
+which are brought together cease entirely, and a totally different set
+of phenomena arise: as in the experiment of two liquids which, when
+mixed in certain proportions, instantly become, not a larger amount of
+liquid, but a solid mass.
+
+
+� 2. This difference between the case in which the joint effect of
+causes is the sum of their separate effects, and the case in which it
+is heterogeneous to them; between laws which work together without
+alteration, and laws which, when called upon to work together, cease and
+give place to others; is one of the fundamental distinctions in nature.
+The former case, that of the Composition of Causes, is the general one;
+the other is always special and exceptional. There are no objects which
+do not, as to some of their phenomena, obey the principle of the
+Composition of Causes; none that have not some laws which are rigidly
+fulfilled in every combination into which the objects enter. The weight
+of a body, for instance, is a property which it retains in all the
+combinations in which it is placed. The weight of a chemical compound,
+or of an organized body, is equal to the sum of the weights of the
+elements which compose it. The weight either of the elements or of the
+compound will vary, if they be carried farther from their centre of
+attraction, or brought nearer to it; but whatever affects the one
+affects the other. They always remain precisely equal. So again, the
+component parts of a vegetable or animal substance do not lose their
+mechanical and chemical properties as separate agents, when, by a
+peculiar mode of juxtaposition, they, as an aggregate whole, acquire
+physiological or vital properties in addition. Those bodies continue, as
+before, to obey mechanical and chemical laws, in so far as the operation
+of those laws is not counteracted by the new laws which govern them as
+organized beings. When, in short, a concurrence of causes takes place
+which calls into action new laws bearing no analogy to any that we can
+trace in the separate operation of the causes, the new laws, while they
+supersede one portion of the previous laws, may coexist with another
+portion, and may even compound the effect of those previous laws with
+their own.
+
+Again, laws which were themselves generated in the second mode, may
+generate others in the first. Though there are laws which, like those of
+chemistry and physiology, owe their existence to a breach of the
+principle of Composition of Causes, it does not follow that these
+peculiar, or as they might be termed, _heteropathic_ laws, are not
+capable of composition with one another. The causes which by one
+combination have had their laws altered, may carry their new laws with
+them unaltered into their ulterior combinations. And hence there is no
+reason to despair of ultimately raising chemistry and physiology to the
+condition of deductive sciences; for though it is impossible to deduce
+all chemical and physiological truths from the laws or properties of
+simple substances or elementary agents, they may possibly be deducible
+from laws which commence when these elementary agents are brought
+together into some moderate number of not very complex combinations. The
+Laws of Life will never be deducible from the mere laws of the
+ingredients, but the prodigiously complex Facts of Life may all be
+deducible from comparatively simple laws of life; which laws (depending
+indeed on combinations, but on comparatively simple combinations, of
+antecedents) may, in more complex circumstances, be strictly compounded
+with one another, and with the physical and chemical laws of the
+ingredients. The details of the vital phenomena, even now, afford
+innumerable exemplifications of the Composition of Causes; and in
+proportion as these phenomena are more accurately studied, there appears
+more reason to believe that the same laws which operate in the simpler
+combinations of circumstances do, in fact, continue to be observed in
+the more complex. This will be found equally true in the phenomena of
+mind; and even in social and political phenomena, the results of the
+laws of mind. It is in the case of chemical phenomena that the least
+progress has yet been made in bringing the special laws under general
+ones from which they may be deduced; but there are even in chemistry
+many circumstances to encourage the hope that such general laws will
+hereafter be discovered. The different actions of a chemical compound
+will never, undoubtedly, be found to be the sums of the actions of its
+separate elements; but there may exist, between the properties of the
+compound and those of its elements, some constant relation, which, if
+discoverable by a sufficient induction, would enable us to foresee the
+sort of compound which will result from a new combination before we have
+actually tried it, and to judge of what sort of elements some new
+substance is compounded before we have analysed it. The law of definite
+proportions, first discovered in its full generality by Dalton, is a
+complete solution of this problem in one, though but a secondary aspect,
+that of quantity: and in respect to quality, we have already some
+partial generalizations sufficient to indicate the possibility of
+ultimately proceeding farther. We can predicate some common properties
+of the kind of compounds which result from the combination, in each of
+the small number of possible proportions, of any acid whatever with any
+base. We have also the curious law, discovered by Berthollet, that two
+soluble salts mutually decompose one another whenever the new
+combinations which result produce an insoluble compound, or one less
+soluble than the two former. Another uniformity is that called the law
+of isomorphism; the identity of the crystalline forms of substances
+which possess in common certain peculiarities of chemical composition.
+Thus it appears that even heteropathic laws, such laws of combined
+agency as are not compounded of the laws of the separate agencies, are
+yet, at least in some cases, derived from them according to a fixed
+principle. There may, therefore, be laws of the generation of laws from
+others dissimilar to them; and in chemistry, these undiscovered laws of
+the dependence of the properties of the compound on the properties of
+its elements, may, together with the laws of the elements themselves,
+furnish the premises by which the science is perhaps destined one day to
+be rendered deductive.
+
+It would seem, therefore, that there is no class of phenomena in which
+the Composition of Causes does not obtain: that as a general rule,
+causes in combination produce exactly the same effects as when acting
+singly: but that this rule, though general, is not universal: that in
+some instances, at some particular points in the transition from
+separate to united action, the laws change, and an entirely new set of
+effects are either added to, or take the place of, those which arise
+from the separate agency of the same causes: the laws of these new
+effects being again susceptible of composition, to an indefinite extent,
+like the laws which they superseded.
+
+
+� 3. That effects are proportional to their causes is laid down by some
+writers as an axiom in the theory of causation; and great use is
+sometimes made of this principle in reasonings respecting the laws of
+nature, though it is incumbered with many difficulties and apparent
+exceptions, which much ingenuity has been expended in showing not to be
+real ones. This proposition, in so far as it is true, enters as a
+particular case into the general principle of the Composition of Causes;
+the causes compounded being, in this instance, homogeneous; in which
+case, if in any, their joint effect might be expected to be identical
+with the sum of their separate effects. If a force equal to one hundred
+weight will raise a certain body along an inclined plane, a force equal
+to two hundred weight will raise two bodies exactly similar, and thus
+the effect is proportional to the cause. But does not a force equal to
+two hundred weight actually contain in itself two forces each equal to
+one hundred weight, which, if employed apart, would separately raise the
+two bodies in question? The fact, therefore, that when exerted jointly
+they raise both bodies at once, results from the Composition of Causes,
+and is a mere instance of the general fact that mechanical forces are
+subject to the law of Composition. And so in every other case which can
+be supposed. For the doctrine of the proportionality of effects to their
+causes cannot of course be applicable to cases in which the augmentation
+of the cause alters the _kind_ of effect; that is, in which the surplus
+quantity superadded to the cause does not become compounded with it, but
+the two together generate an altogether new phenomenon. Suppose that the
+application of a certain quantity of heat to a body merely increases its
+bulk, that a double quantity melts it, and a triple quantity decomposes
+it: these three effects being heterogeneous, no ratio, whether
+corresponding or not to that of the quantities of heat applied, can be
+established between them. Thus the supposed axiom of the proportionality
+of effects to their causes fails at the precise point where the
+principle of the Composition of Causes also fails; viz., where the
+concurrence of causes is such as to determine a change in the properties
+of the body generally, and render it subject to new laws, more or less
+dissimilar to those to which it conformed in its previous state. The
+recognition, therefore, of any such law of proportionality, is
+superseded by the more comprehensive principle, in which as much of it
+as is true is implicitly asserted.
+
+The general remarks on causation, which seemed necessary as an
+introduction to the theory of the inductive process, may here terminate.
+That process is essentially an inquiry into cases of causation. All the
+uniformities which exist in the succession of phenomena, and most of the
+uniformities in their coexistence, are either, as we have seen,
+themselves laws of causation, or consequences resulting from, and
+corollaries capable of being deduced from, such laws. If we could
+determine what causes are correctly assigned to what effects, and what
+effects to what causes, we should be virtually acquainted with the whole
+course of nature. All those uniformities which are mere results of
+causation, might then be explained and accounted for; and every
+individual fact or event might be predicted, provided we had the
+requisite data, that is, the requisite knowledge of the circumstances
+which, in the particular instance, preceded it.
+
+To ascertain, therefore, what are the laws of causation which exist in
+nature; to determine the effect of every cause, and the causes of all
+effects,--is the main business of Induction; and to point out how this
+is done is the chief object of Inductive Logic.
+
+
+
+
+CHAPTER VII.
+
+OF OBSERVATION AND EXPERIMENT.
+
+
+� 1. It results from the preceding exposition, that the process of
+ascertaining what consequents, in nature, are invariably connected with
+what antecedents, or in other words what phenomena are related to each
+other as causes and effects, is in some sort a process of analysis. That
+every fact which begins to exist has a cause, and that this cause must
+be found somewhere among the facts which immediately preceded the
+occurrence, may be taken for certain. The whole of the present facts are
+the infallible result of all past facts, and more immediately of all the
+facts which existed at the moment previous. Here, then, is a great
+sequence, which we know to be uniform. If the whole prior state of the
+entire universe could again recur, it would again be followed by the
+present state. The question is, how to resolve this complex uniformity
+into the simpler uniformities which compose it, and assign to each
+portion of the vast antecedent the portion of the consequent which is
+attendant on it.
+
+This operation, which we have called analytical, inasmuch as it is the
+resolution of a complex whole into the component elements, is more than
+a merely mental analysis. No mere contemplation of the phenomena, and
+partition of them by the intellect alone, will of itself accomplish the
+end we have now in view. Nevertheless, such a mental partition is an
+indispensable first step. The order of nature, as perceived at a first
+glance, presents at every instant a chaos followed by another chaos. We
+must decompose each chaos into single facts. We must learn to see in the
+chaotic antecedent a multitude of distinct antecedents, in the chaotic
+consequent a multitude of distinct consequents. This, supposing it done,
+will not of itself tell us on which of the antecedents each consequent
+is invariably attendant. To determine that point, we must endeavour to
+effect a separation of the facts from one another, not in our minds
+only, but in nature. The mental analysis, however, must take place
+first. And every one knows that in the mode of performing it, one
+intellect differs immensely from another. It is the essence of the act
+of observing; for the observer is not he who merely sees the thing which
+is before his eyes, but he who sees what parts that thing is composed
+of. To do this well is a rare talent. One person, from inattention, or
+attending only in the wrong place, overlooks half of what he sees:
+another sets down much more than he sees, confounding it with what he
+imagines, or with what he infers; another takes note of the _kind_ of
+all the circumstances, but being inexpert in estimating their degree,
+leaves the quantity of each vague and uncertain; another sees indeed the
+whole, but makes such an awkward division of it into parts, throwing
+things into one mass which require to be separated, and separating
+others which might more conveniently be considered as one, that the
+result is much the same, sometimes even worse, than if no analysis had
+been attempted at all. It would be possible to point out what qualities
+of mind, and modes of mental culture, fit a person for being a good
+observer: that, however, is a question not of Logic, but of the Theory
+of Education, in the most enlarged sense of the term. There is not
+properly an Art of Observing. There may be rules for observing. But
+these, like rules for inventing, are properly instructions for the
+preparation of one's own mind; for putting it into the state in which it
+will be most fitted to observe, or most likely to invent. They are,
+therefore, essentially rules of self-education, which is a different
+thing from Logic. They do not teach how to do the thing, but how to make
+ourselves capable of doing it. They are an art of strengthening the
+limbs, not an art of using them.
+
+The extent and minuteness of observation which may be requisite, and the
+degree of decomposition to which it may be necessary to carry the mental
+analysis, depend on the particular purpose in view. To ascertain the
+state of the whole universe at any particular moment is impossible, but
+would also be useless. In making chemical experiments, we do not think
+it necessary to note the position of the planets; because experience has
+shown, as a very superficial experience is sufficient to show, that in
+such cases that circumstance is not material to the result: and,
+accordingly, in the ages when men believed in the occult influences of
+the heavenly bodies, it might have been unphilosophical to omit
+ascertaining the precise condition of those bodies at the moment of the
+experiment. As to the degree of minuteness of the mental subdivision; if
+we were obliged to break down what we observe into its very simplest
+elements, that is, literally into single facts, it would be difficult to
+say where we should find them: we can hardly ever affirm that our
+divisions of any kind have reached the ultimate unit. But this too is
+fortunately unnecessary. The only object of the mental separation is to
+suggest the requisite physical separation, so that we may either
+accomplish it ourselves, or seek for it in nature; and we have done
+enough when we have carried the subdivision as far as the point at which
+we are able to see what observations or experiments we require. It is
+only essential, at whatever point our mental decomposition of facts may
+for the present have stopped, that we should hold ourselves ready and
+able to carry it farther as occasion requires, and should not allow the
+freedom of our discriminating faculty to be imprisoned by the swathes
+and bands of ordinary classification; as was the case with all early
+speculative inquirers, not excepting the Greeks, to whom it seldom
+occurred that what was called by one abstract name might, in reality, be
+several phenomena, or that there was a possibility of decomposing the
+facts of the universe into any elements but those which ordinary
+language already recognised.
+
+
+� 2. The different antecedents and consequents, being, then, supposed to
+be, so far as the case requires, ascertained and discriminated from one
+another; we are to inquire which is connected with which. In every
+instance which comes under our observation, there are many antecedents
+and many consequents. If those antecedents could not be severed from
+one another except in thought, or if those consequents never were found
+apart, it would be impossible for us to distinguish (_� posteriori_ at
+least) the real laws, or to assign to any cause its effect, or to any
+effect its cause. To do so, we must be able to meet with some of the
+antecedents apart from the rest, and observe what follows from them; or
+some of the consequents, and observe by what they are preceded. We must,
+in short, follow the Baconian rule of _varying the circumstances_. This
+is, indeed, only the first rule of physical inquiry, and not, as some
+have thought, the sole rule; but it is the foundation of all the rest.
+
+For the purpose of varying the circumstances, we may have recourse
+(according to a distinction commonly made) either to observation or to
+experiment; we may either _find_ an instance in nature, suited to our
+purposes, or, by an artificial arrangement of circumstances, _make_ one.
+The value of the instance depends on what it is in itself, not on the
+mode in which it is obtained: its employment for the purposes of
+induction depends on the same principles in the one case and in the
+other; as the uses of money are the same whether it is inherited or
+acquired. There is, in short, no difference in kind, no real logical
+distinction, between the two processes of investigation. There are,
+however, practical distinctions to which it is of considerable
+importance to advert.
+
+
+� 3. The first and most obvious distinction between Observation and
+Experiment is, that the latter is an immense extension of the former. It
+not only enables us to produce a much greater number of variations in
+the circumstances than nature spontaneously offers, but also, in
+thousands of cases, to produce the precise _sort_ of variation which we
+are in want of for discovering the law of the phenomenon; a service
+which nature, being constructed on a quite different scheme from that of
+facilitating our studies, is seldom so friendly as to bestow upon us.
+For example, in order to ascertain what principle in the atmosphere
+enables it to sustain life, the variation we require is that a living
+animal should be immersed in each component element of the atmosphere
+separately. But nature does not supply either oxygen or azote in a
+separate state. We are indebted to artificial experiment for our
+knowledge that it is the former, and not the latter, which supports
+respiration; and for our knowledge of the very existence of the two
+ingredients.
+
+Thus far the advantage of experimentation over simple observation is
+universally recognised: all are aware that it enables us to obtain
+innumerable combinations of circumstances which are not to be found in
+nature, and so add to nature's experiments a multitude of experiments of
+our own. But there is another superiority (or, as Bacon would have
+expressed it, another prerogative) of instances artificially obtained
+over spontaneous instances,--of our own experiments over even the same
+experiments when made by nature,--which is not of less importance, and
+which is far from being felt and acknowledged in the same degree.
+
+When we can produce a phenomenon artificially, we can take it, as it
+were, home with us, and observe it in the midst of circumstances with
+which in all other respects we are accurately acquainted. If we desire
+to know what are the effects of the cause A, and are able to produce A
+by means at our disposal, we can generally determine at our own
+discretion, so far as is compatible with the nature of the phenomenon A,
+the whole of the circumstances which shall be present along with it: and
+thus, knowing exactly the simultaneous state of everything else which is
+within the reach of A's influence, we have only to observe what
+alteration is made in that state by the presence of A.
+
+For example, by the electric machine we can produce in the midst of
+known circumstances, the phenomena which nature exhibits on a grander
+scale in the form of lightning and thunder. Now let any one consider
+what amount of knowledge of the effects and laws of electric agency
+mankind could have obtained from the mere observation of thunder-storms,
+and compare it with that which they have gained, and may expect to gain,
+from electrical and galvanic experiments. This example is the more
+striking, now that we have reason to believe that electric action is of
+all natural phenomena (except heat) the most pervading and universal,
+which, therefore, it might antecedently have been supposed could stand
+least in need of artificial means of production to enable it to be
+studied; while the fact is so much the contrary, that without the
+electric machine, the Leyden jar, and the voltaic battery, we probably
+should never have suspected the existence of electricity as one of the
+great agents in nature; the few electric phenomena we should have known
+of would have continued to be regarded either as supernatural, or as a
+sort of anomalies and eccentricities in the order of the universe.
+
+When we have succeeded in insulating the phenomenon which is the subject
+of inquiry, by placing it among known circumstances, we may produce
+further variations of circumstances to any extent, and of such kinds as
+we think best calculated to bring the laws of the phenomenon into a
+clear light. By introducing one well-defined circumstance after another
+into the experiment, we obtain assurance of the manner in which the
+phenomenon behaves under an indefinite variety of possible
+circumstances. Thus, chemists, after having obtained some
+newly-discovered substance in a pure state, (that is, having made sure
+that there is nothing present which can interfere with and modify its
+agency,) introduce various other substances, one by one, to ascertain
+whether it will combine with them, or decompose them, and with what
+result; and also apply heat, or electricity, or pressure, to discover
+what will happen to the substance under each of these circumstances.
+
+But if, on the other hand, it is out of our power to produce the
+phenomenon, and we have to seek for instances in which nature produces
+it, the task before us is very different. Instead of being able to
+choose what the concomitant circumstances shall be, we now have to
+discover what they are; which, when we go beyond the simplest and most
+accessible cases, it is next to impossible to do, with any precision and
+completeness. Let us take, as an exemplification of a phenomenon which
+we have no means of fabricating artificially, a human mind. Nature
+produces many; but the consequence of our not being able to produce
+them by art is, that in every instance in which we see a human mind
+developing itself, or acting upon other things, we see it surrounded and
+obscured by an indefinite multitude of unascertainable circumstances,
+rendering the use of the common experimental methods almost delusive. We
+may conceive to what extent this is true, if we consider, among other
+things, that whenever nature produces a human mind, she produces, in
+close connexion with it, a body; that is, a vast complication of
+physical facts, in no two cases perhaps exactly similar, and most of
+which (except the mere structure, which we can examine in a sort of
+coarse way after it has ceased to act), are radically out of the reach
+of our means of exploration. If, instead of a human mind, we suppose the
+subject of investigation to be a human society or State, all the same
+difficulties recur in a greatly augmented degree.
+
+We have thus already come within sight of a conclusion, which the
+progress of the inquiry will, I think, bring before us with the clearest
+evidence: namely, that in the sciences which deal with phenomena in
+which artificial experiments are impossible (as in the case of
+astronomy), or in which they have a very limited range (as in mental
+philosophy, social science, and even physiology), induction from direct
+experience is practised at a disadvantage in most cases equivalent to
+impracticability: from which it follows that the methods of those
+sciences, in order to accomplish anything worthy of attainment, must be
+to a great extent, if not principally, deductive. This is already known
+to be the case with the first of the sciences we have mentioned,
+astronomy; that it is not generally recognised as true of the others, is
+probably one of the reasons why they are not in a more advanced state.
+
+
+� 4. If what is called pure observation is at so great a disadvantage,
+compared with artificial experimentation, in one department of the
+direct exploration of phenomena, there is another branch in which the
+advantage is all on the side of the former.
+
+Inductive inquiry having for its object to ascertain what causes are
+connected with what effects, we may begin this search at either end of
+the road which leads from the one point to the other: we may either
+inquire into the effects of a given cause, or into the causes of a given
+effect. The fact that light blackens chloride of silver might have been
+discovered either by experiments on light, trying what effect it would
+produce on various substances, or by observing that portions of the
+chloride had repeatedly become black, and inquiring into the
+circumstances. The effect of the urali poison might have become known
+either by administering it to animals, or by examining how it happened
+that the wounds which the Indians of Guiana inflict with their arrows
+prove so uniformly mortal. Now it is manifest from the mere statement of
+the examples, without any theoretical discussion, that artificial
+experimentation is applicable only to the former of these modes of
+investigation. We can take a cause, and try what it will produce: but we
+cannot take an effect, and try what it will be produced by. We can only
+watch till we see it produced, or are enabled to produce it by accident.
+
+This would be of little importance, if it always depended on our choice
+from which of the two ends of the sequence we would undertake our
+inquiries. But we have seldom any option. As we can only travel from the
+known to the unknown, we are obliged to commence at whichever end we are
+best acquainted with. If the agent is more familiar to us than its
+effects, we watch for, or contrive, instances of the agent, under such
+varieties of circumstances as are open to us, and observe the result.
+If, on the contrary, the conditions on which a phenomenon depends are
+obscure, but the phenomenon itself familiar, we must commence our
+inquiry from the effect. If we are struck with the fact that chloride of
+silver has been blackened, and have no suspicion of the cause, we have
+no resource but to compare instances in which the fact has chanced to
+occur, until by that comparison we discover that in all those instances
+the substances had been exposed to light. If we knew nothing of the
+Indian arrows but their fatal effect, accident alone could turn our
+attention to experiments on the urali; in the regular course of
+investigation, we could only inquire, or try to observe, what had been
+done to the arrows in particular instances.
+
+Wherever, having nothing to guide us to the cause, we are obliged to set
+out from the effect, and to apply the rule of varying the circumstances
+to the consequents, not the antecedents, we are necessarily destitute of
+the resource of artificial experimentation. We cannot, at our choice,
+obtain consequents, as we can antecedents, under any set of
+circumstances compatible with their nature. There are no means of
+producing effects but through their causes, and by the supposition the
+causes of the effect in question are not known to us. We have therefore
+no expedient but to study it where it offers itself spontaneously. If
+nature happens to present us with instances sufficiently varied in their
+circumstances, and if we are able to discover, either among the
+proximate antecedents or among some other order of antecedents,
+something which is always found when the effect is found, however
+various the circumstances, and never found when it is not; we may
+discover, by mere observation without experiment, a real uniformity in
+nature.
+
+But though this is certainly the most favourable case for sciences of
+pure observation, as contrasted with those in which artificial
+experiments are possible, there is in reality no case which more
+strikingly illustrates the inherent imperfection of direct induction
+when not founded on experimentation. Suppose that, by a comparison of
+cases of the effect, we have found an antecedent which appears to be,
+and perhaps is, invariably connected with it: we have not yet proved
+that antecedent to be the cause, until we have reversed the process, and
+produced the effect by means of that antecedent. If we can produce the
+antecedent artificially, and if, when we do so, the effect follows, the
+induction is complete; that antecedent is the cause of that
+consequent.[32] But we have then added the evidence of experiment to
+that of simple observation. Until we had done so, we had only proved
+_invariable_ antecedence within the limits of experience, but not
+_unconditional_ antecedence, or causation. Until it had been shown by
+the actual production of the antecedent under known circumstances, and
+the occurrence thereupon of the consequent, that the antecedent was
+really the condition on which it depended; the uniformity of succession
+which was proved to exist between them might, for aught we knew, be
+(like the succession of day and night) not a case of causation at all;
+both antecedent and consequent might be successive stages of the effect
+of an ulterior cause. Observation, in short, without experiment
+(supposing no aid from deduction) can ascertain sequences and
+coexistences, but cannot prove causation.
+
+In order to see these remarks verified by the actual state of the
+sciences, we have only to think of the condition of natural history. In
+zoology, for example, there is an immense number of uniformities
+ascertained, some of coexistence, others of succession, to many of
+which, notwithstanding considerable variations of the attendant
+circumstances, we know not any exception: but the antecedents, for the
+most part, are such as we cannot artificially produce; or if we can, it
+is only by setting in motion the exact process by which nature produces
+them; and this being to us a mysterious process, of which the main
+circumstances are not only unknown but unobservable, we do not succeed
+in obtaining the antecedents under known circumstances. What is the
+result? That on this vast subject, which affords so much and such varied
+scope for observation, we have made most scanty progress in ascertaining
+any laws of causation. We know not with certainty, in the case of most
+of the phenomena that we find conjoined, which is the condition of the
+other; which is cause, and which effect, or whether either of them is
+so, or they are not rather conjunct effects of causes yet to be
+discovered, complex results of laws hitherto unknown.
+
+Although some of the foregoing observations may be, in technical
+strictness of arrangement, premature in this place, it seemed that a few
+general remarks on the difference between sciences of mere observation
+and sciences of experimentation, and the extreme disadvantage under
+which directly inductive inquiry is necessarily carried on in the
+former, were the best preparation for discussing the methods of direct
+induction; a preparation rendering superfluous much that must otherwise
+have been introduced, with some inconvenience, into the heart of that
+discussion. To the consideration of these methods we now proceed.
+
+
+
+
+CHAPTER VIII.
+
+OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.
+
+
+� 1. The simplest and most obvious modes of singling out from among the
+circumstances which precede or follow a phenomenon, those with which it
+is really connected by an invariable law, are two in number. One is, by
+comparing together different instances in which the phenomenon occurs.
+The other is, by comparing instances in which the phenomenon does occur,
+with instances in other respects similar in which it does not. These two
+methods may be respectively denominated, the Method of Agreement, and
+the Method of Difference.
+
+In illustrating these methods, it will be necessary to bear in mind the
+twofold character of inquiries into the laws of phenomena; which may be
+either inquiries into the cause of a given effect, or into the effects
+or properties of a given cause. We shall consider the methods in their
+application to either order of investigation, and shall draw our
+examples equally from both.
+
+We shall denote antecedents by the large letters of the alphabet, and
+the consequents corresponding to them by the small. Let A, then, be an
+agent or cause, and let the object of our inquiry be to ascertain what
+are the effects of this cause. If we can either find, or produce, the
+agent A in such varieties of circumstances, that the different cases
+have no circumstance in common except A; then whatever effect we find to
+be produced in all our trials, is indicated as the effect of A. Suppose,
+for example, that A is tried along with B and C, and that the effect is
+_a b c_; and suppose that A is next tried with D and E, but without B
+and C, and that the effect is _a d e_. Then we may reason thus: _b_ and
+_c_ are not effects of A, for they were not produced by it in the second
+experiment; nor are _d_ and _e_, for they were not produced in the
+first. Whatever is really the effect of A must have been produced in
+both instances; now this condition is fulfilled by no circumstance
+except _a_. The phenomenon _a_ cannot have been the effect of B or C,
+since it was produced where they were not; nor of D or E, since it was
+produced where they were not. Therefore it is the effect of A.
+
+For example, let the antecedent A be the contact of an alkaline
+substance and an oil. This combination being tried under several
+varieties of circumstances, resembling each other in nothing else, the
+results agree in the production of a greasy and detersive or saponaceous
+substance: it is therefore concluded that the combination of an oil and
+an alkali causes the production of a soap. It is thus we inquire, by the
+Method of Agreement, into the effect of a given cause.
+
+In a similar manner we may inquire into the cause of a given effect. Let
+_a_ be the effect. Here, as shown in the last chapter, we have only the
+resource of observation without experiment: we cannot take a phenomenon
+of which we know not the origin, and try to find its mode of production
+by producing it: if we succeeded in such a random trial it could only be
+by accident. But if we can observe _a_ in two different combinations, _a
+b c_, and _a d e_; and if we know, or can discover, that the antecedent
+circumstances in these cases respectively were A B C and A D E; we may
+conclude by a reasoning similar to that in the preceding example, that A
+is the antecedent connected with the consequent _a_ by a law of
+causation. B and C, we may say, cannot be causes of _a_, since on its
+second occurrence they were not present; nor are D and E, for they were
+not present on its first occurrence. A, alone of the five circumstances,
+was found among the antecedents of _a_ in both instances.
+
+For example, let the effect _a_ be crystallization. We compare instances
+in which bodies are known to assume crystalline structure, but which
+have no other point of agreement; and we find them to have one, and as
+far as we can observe, only one, antecedent in common: the deposition of
+a solid matter from a liquid state, either a state of fusion or of
+solution. We conclude, therefore, that the solidification of a
+substance from a liquid state is an invariable antecedent of its
+crystallization.
+
+In this example we may go farther, and say, it is not only the
+invariable antecedent but the cause; or at least the proximate event
+which completes the cause. For in this case we are able, after detecting
+the antecedent A, to produce it artificially, and by finding that _a_
+follows it, verify the result of our induction. The importance of thus
+reversing the proof was strikingly manifested when by keeping a phial of
+water charged with siliceous particles undisturbed for years, a chemist
+(I believe Dr. Wollaston) succeeded in obtaining crystals of quartz: and
+in the equally interesting experiment in which Sir James Hall produced
+artificial marble, by the cooling of its materials from fusion under
+immense pressure: two admirable examples of the light which may be
+thrown upon the most secret processes of nature by well-contrived
+interrogation of her.
+
+But if we cannot artificially produce the phenomenon A, the conclusion
+that it is the cause of _a_ remains subject to very considerable doubt.
+Though an invariable, it may not be the unconditional antecedent of _a_,
+but may precede it as day precedes night or night day. This uncertainty
+arises from the impossibility of assuring ourselves that A is the _only_
+immediate antecedent common to both the instances. If we could be
+certain of having ascertained all the invariable antecedents, we might
+be sure that the unconditional invariable antecedent, or cause, must be
+found somewhere among them. Unfortunately it is hardly ever possible to
+ascertain all the antecedents, unless the phenomenon is one which we can
+produce artificially. Even then, the difficulty is merely lightened, not
+removed: men knew how to raise water in pumps long before they adverted
+to what was really the operating circumstance in the means they
+employed, namely, the pressure of the atmosphere on the open surface of
+the water. It is, however, much easier to analyse completely a set of
+arrangements made by ourselves, than the whole complex mass of the
+agencies which nature happens to be exerting at the moment of the
+production of a given phenomenon. We may overlook some of the material
+circumstances in an experiment with an electrical machine; but we shall,
+at the worst, be better acquainted with them than with those of a
+thunder-storm.
+
+The mode of discovering and proving laws of nature, which we have now
+examined, proceeds on the following axiom: Whatever circumstances can be
+excluded, without prejudice to the phenomenon, or can be absent
+notwithstanding its presence, is not connected with it in the way of
+causation. The casual circumstances being thus eliminated, if only one
+remains, that one is the cause which we are in search of: if more than
+one, they either are, or contain among them, the cause; and so, _mutatis
+mutandis_, of the effect. As this method proceeds by comparing different
+instances to ascertain in what they agree, I have termed it the Method
+of Agreement: and we may adopt as its regulating principle the following
+canon:--
+
+FIRST CANON.
+
+_If two or more instances of the phenomenon under investigation have
+only one circumstance in common, the circumstance in which alone all the
+instances agree, is the cause (or effect) of the given phenomenon._
+
+Quitting for the present the Method of Agreement, to which we shall
+almost immediately return, we proceed to a still more potent instrument
+of the investigation of nature, the Method of Difference.
+
+
+� 2. In the Method of Agreement, we endeavoured to obtain instances
+which agreed in the given circumstance but differed in every other: in
+the present method we require, on the contrary, two instances resembling
+one another in every other respect, but differing in the presence or
+absence of the phenomenon we wish to study. If our object be to discover
+the effects of an agent A, we must procure A in some set of ascertained
+circumstances, as A B C, and having noted the effects produced, compare
+them with the effect of the remaining circumstances B C, when A is
+absent. If the effect of A B C is _a b c_, and the effect of B C, _b c_,
+it is evident that the effect of A is _a_. So again, if we begin at the
+other end, and desire to investigate the cause of an effect _a_, we must
+select an instance, as _a b c_, in which the effect occurs, and in which
+the antecedents were A B C, and we must look out for another instance in
+which the remaining circumstances, _b c_, occur without _a_. If the
+antecedents, in that instance, are B C, we know that the cause of _a_
+must be A: either A alone, or A in conjunction with some of the other
+circumstances present.
+
+It is scarcely necessary to give examples of a logical process to which
+we owe almost all the inductive conclusions we draw in daily life. When
+a man is shot through the heart, it is by this method we know that it
+was the gun-shot which killed him: for he was in the fulness of life
+immediately before, all circumstances being the same, except the wound.
+
+The axioms implied in this method are evidently the following. Whatever
+antecedent cannot be excluded without preventing the phenomenon, is the
+cause, or a condition, of that phenomenon: Whatever consequent can be
+excluded, with no other difference in the antecedents than the absence
+of a particular one, is the effect of that one. Instead of comparing
+different instances of a phenomenon, to discover in what they agree,
+this method compares an instance of its occurrence with an instance of
+its non-occurrence, to discover in what they differ. The canon which is
+the regulating principle of the Method of Difference may be expressed as
+follows:
+
+SECOND CANON.
+
+_If an instance in which the phenomenon under investigation occurs, and
+an instance in which it does not occur, have every circumstance in
+common save one, that one occurring only in the former; the circumstance
+in which alone the two instances differ, is the effect, or the cause, or
+an indispensable part of the cause, of the phenomenon._
+
+
+� 3. The two methods which we have now stated have many features of
+resemblance, but there are also many distinctions between them. Both
+are methods of _elimination_. This term (employed in the theory of
+equations to denote the process by which one after another of the
+elements of a question is excluded, and the solution made to depend on
+the relation between the remaining elements only) is well suited to
+express the operation, analogous to this, which has been understood
+since the time of Bacon to be the foundation of experimental inquiry:
+namely, the successive exclusion of the various circumstances which are
+found to accompany a phenomenon in a given instance, in order to
+ascertain what are those among them which can be absent consistently
+with the existence of the phenomenon. The Method of Agreement stands on
+the ground that whatever can be eliminated, is not connected with the
+phenomenon by any law. The Method of Difference has for its foundation,
+that whatever cannot be eliminated, is connected with the phenomenon by
+a law.
+
+Of these methods, that of Difference is more particularly a method of
+artificial experiment; while that of Agreement is more especially the
+resource employed where experimentation is impossible. A few reflections
+will prove the fact, and point out the reason of it.
+
+It is inherent in the peculiar character of the Method of Difference,
+that the nature of the combinations which it requires is much more
+strictly defined than in the Method of Agreement. The two instances
+which are to be compared with one another must be exactly similar, in
+all circumstances except the one which we are attempting to investigate:
+they must be in the relation of A B C and B C, or of _a b c_ and _b c_.
+It is true that this similarity of circumstances needs not extend to
+such as are already known to be immaterial to the result. And in the
+case of most phenomena we learn at once, from the commonest experience,
+that most of the coexistent phenomena of the universe may be either
+present or absent without affecting the given phenomenon; or, if
+present, are present indifferently when the phenomenon does not happen
+and when it does. Still, even limiting the identity which is required
+between the two instances, A B C and B C, to such circumstances as are
+not already known to be indifferent; it is very seldom that nature
+affords two instances, of which we can be assured that they stand in
+this precise relation to one another. In the spontaneous operations of
+nature there is generally such complication and such obscurity, they are
+mostly either on so overwhelmingly large or on so inaccessibly minute a
+scale, we are so ignorant of a great part of the facts which really take
+place, and even those of which we are not ignorant are so multitudinous,
+and therefore so seldom exactly alike in any two cases, that a
+spontaneous experiment, of the kind required by the Method of
+Difference, is commonly not to be found. When, on the contrary, we
+obtain a phenomenon by an artificial experiment, a pair of instances
+such as the method requires is obtained almost as a matter of course,
+provided the process does not last a long time. A certain state of
+surrounding circumstances existed before we commenced the experiment;
+this is B C. We then introduce A; say, for instance, by merely bringing
+an object from another part of the room, before there has been time for
+any change in the other elements. It is, in short (as M. Comte
+observes), the very nature of an experiment, to introduce into the
+pre-existing state of circumstances a change perfectly definite. We
+choose a previous state of things with which we are well acquainted, so
+that no unforeseen alteration in that state is likely to pass
+unobserved; and into this we introduce, as rapidly as possible, the
+phenomenon which we wish to study; so that in general we are entitled to
+feel complete assurance that the pre-existing state, and the state which
+we have produced, differ in nothing except the presence or absence of
+that phenomenon. If a bird is taken from a cage, and instantly plunged
+into carbonic acid gas, the experimentalist may be fully assured (at all
+events after one or two repetitions) that no circumstance capable of
+causing suffocation had supervened in the interim, except the change
+from immersion in the atmosphere to immersion in carbonic acid gas.
+There is one doubt, indeed, which may remain in some cases of this
+description; the effect may have been produced not by the change, but by
+the means employed to produce the change. The possibility, however, of
+this last supposition generally admits of being conclusively tested by
+other experiments. It thus appears that in the study of the various
+kinds of phenomena which we can, by our voluntary agency, modify or
+control, we can in general satisfy the requisitions of the Method of
+Difference; but that by the spontaneous operations of nature those
+requisitions are seldom fulfilled.
+
+The reverse of this is the case with the Method of Agreement. We do not
+here require instances of so special and determinate a kind. Any
+instances whatever, in which nature presents us with a phenomenon, may
+be examined for the purposes of this method; and if all such instances
+agree in anything, a conclusion of considerable value is already
+attained. We can seldom, indeed, be sure that the one point of agreement
+is the only one; but this ignorance does not, as in the Method of
+Difference, vitiate the conclusion; the certainty of the result, as far
+as it goes, is not affected. We have ascertained one invariable
+antecedent or consequent, however many other invariable antecedents or
+consequents may still remain unascertained. If A B C, A D E, A F G, are
+all equally followed by _a_, then _a_ is an invariable consequent of A.
+If _a b c_, _a d e_, _a f g_, all number A among their antecedents, then
+A is connected as an antecedent, by some invariable law, with _a_. But
+to determine whether this invariable antecedent is a cause, or this
+invariable consequent an effect, we must be able, in addition, to
+produce the one by means of the other; or, at least, to obtain that
+which alone constitutes our assurance of having produced anything,
+namely, an instance in which the effect, _a_, has come into existence,
+with no other change in the pre-existing circumstances than the addition
+of A. And this, if we can do it, is an application of the Method of
+Difference, not of the Method of Agreement.
+
+It thus appears to be by the Method of Difference alone that we can
+ever, in the way of direct experience, arrive with certainty at causes.
+The Method of Agreement leads only to laws of phenomena (as some writers
+call them, but improperly, since laws of causation are also laws of
+phenomena): that is, to uniformities, which either are not laws of
+causation, or in which the question of causation must for the present
+remain undecided. The Method of Agreement is chiefly to be resorted to,
+as a means of suggesting applications of the Method of Difference (as in
+the last example the comparison of A B C, A D E, A F G, suggested that A
+was the antecedent on which to try the experiment whether it could
+produce _a_); or as an inferior resource, in case the Method of
+Difference is impracticable; which, as we before showed, generally
+arises from the impossibility of artificially producing the phenomena.
+And hence it is that the Method of Agreement, though applicable in
+principle to either case, is more emphatically the method of
+investigation on those subjects where artificial experimentation is
+impossible: because on those it is, generally, our only resource of a
+directly inductive nature; while, in the phenomena which we can produce
+at pleasure, the Method of Difference generally affords a more
+efficacious process, which will ascertain causes as well as mere laws.
+
+
+� 4. There are, however, many cases in which, though our power of
+producing the phenomenon is complete, the Method of Difference either
+cannot be made available at all, or not without a previous employment of
+the Method of Agreement. This occurs when the agency by which we can
+produce the phenomenon is not that of one single antecedent, but a
+combination of antecedents, which we have no power of separating from
+each other, and exhibiting apart. For instance, suppose the subject of
+inquiry to be the cause of the double refraction of light. We can
+produce this phenomenon at pleasure, by employing any one of the many
+substances which are known to refract light in that peculiar manner. But
+if, taking one of those substances, as Iceland spar for example, we wish
+to determine on which of the properties of Iceland spar this remarkable
+phenomenon depends, we can make no use, for that purpose, of the Method
+of Difference; for we cannot find another substance precisely resembling
+Iceland spar except in some one property. The only mode, therefore, of
+prosecuting this inquiry is that afforded by the Method of Agreement; by
+which, in fact, through a comparison of all the known substances which
+have the property of doubly refracting light, it was ascertained that
+they agree in the circumstance of being crystalline substances; and
+though the converse does not hold, though all crystalline substances
+have not the property of double refraction, it was concluded, with
+reason, that there is a real connexion between these two properties;
+that either crystalline structure, or the cause which gives rise to that
+structure, is one of the conditions of double refraction.
+
+Out of this employment of the Method of Agreement arises a peculiar
+modification of that method, which is sometimes of great avail in the
+investigation of nature. In cases similar to the above, in which it is
+not possible to obtain the precise pair of instances which our second
+canon requires--instances agreeing in every antecedent except A, or in
+every consequent except _a_; we may yet be able, by a double employment
+of the Method of Agreement, to discover in what the instances which
+contain A or _a_, differ from those which do not.
+
+If we compare various instances in which _a_ occurs, and find that they
+all have in common the circumstance A, and (as far as can be observed)
+no other circumstance, the Method of Agreement, so far, bears testimony
+to a connexion between A and _a_. In order to convert this evidence of
+connexion into proof of causation by the direct Method of Difference, we
+ought to be able, in some one of these instances, as for example A B C,
+to leave out A, and observe whether by doing so, _a_ is prevented. Now
+supposing (what is often the case) that we are not able to try this
+decisive experiment; yet, provided we can by any means discover what
+would be its result if we could try it, the advantage will be the same.
+Suppose, then, that as we previously examined a variety of instances in
+which _a_ occurred, and found them to agree in containing A, so we now
+observe a variety of instances in which _a_ does not occur, and find
+them agree in not containing A; which establishes, by the Method of
+Agreement, the same connexion between the absence of A and the absence
+of _a_, which was before established between their presence. As, then,
+it had been shown that whenever A is present _a_ is present, so it being
+now shown that when A is taken away _a_ is removed along with it, we
+have by the one proposition A B C, _a b c_, by the other B C, _b c_,
+the positive and negative instances which the Method of Difference
+requires.
+
+This method may be called the Indirect Method of Difference, or the
+Joint Method of Agreement and Difference; and consists in a double
+employment of the Method of Agreement, each proof being independent of
+the other, and corroborating it. But it is not equivalent to a proof by
+the direct Method of Difference. For the requisitions of the Method of
+Difference are not satisfied, unless we can be quite sure either that
+the instances affirmative of _a_ agree in no antecedent whatever but A,
+or that the instances negative of _a_ agree in nothing but the negation
+of A. Now if it were possible, which it never is, to have this
+assurance, we should not need the joint method; for either of the two
+sets of instances separately would then be sufficient to prove
+causation. This indirect method, therefore, can only be regarded as a
+great extension and improvement of the Method of Agreement, but not as
+participating in the more cogent nature of the Method of Difference. The
+following may be stated as its canon:--
+
+THIRD CANON.
+
+_If two or more instances in which the phenomenon occurs have only one
+circumstance in common, while two or more instances in which it does not
+occur have nothing in common save the absence of that circumstance; the
+circumstance in which alone the two sets of instances differ, is the
+effect, or the cause, or an indispensable part of the cause, of the
+phenomenon._
+
+We shall presently see that the Joint Method of Agreement and Difference
+constitutes, in another respect not yet adverted to, an improvement upon
+the common Method of Agreement, namely, in being unaffected by a
+characteristic imperfection of that method, the nature of which still
+remains to be pointed out. But as we cannot enter into this exposition
+without introducing a new element of complexity into this long and
+intricate discussion, I shall postpone it to a subsequent chapter, and
+shall at once proceed to a statement of two other methods, which will
+complete the enumeration of the means which mankind possess for
+exploring the laws of nature by specific observation and experience.
+
+
+� 5. The first of these has been aptly denominated the Method of
+Residues. Its principle is very simple. Subducting from any given
+phenomenon all the portions which, by virtue of preceding inductions,
+can be assigned to known causes, the remainder will be the effect of the
+antecedents which had been overlooked, or of which the effect was as yet
+an unknown quantity.
+
+Suppose, as before, that we have the antecedents A B C, followed by the
+consequents _a b c_, and that by previous inductions (founded, we will
+suppose, on the Method of Difference) we have ascertained the causes of
+some of these effects, or the effects of some of these causes; and are
+thence apprised that the effect of A is _a_, and that the effect of B is
+_b_. Subtracting the sum of these effects from the total phenomenon,
+there remains _c_, which now, without any fresh experiments, we may know
+to be the effect of C. This Method of Residues is in truth a peculiar
+modification of the Method of Difference. If the instance A B C, _a b
+c_, could have been compared with a single instance A B, _a b_, we
+should have proved C to be the cause of _c_, by the common process of
+the Method of Difference. In the present case, however, instead of a
+single instance A B, we have had to study separately the causes A and B,
+and to infer from the effects which they produce separately, what effect
+they must produce in the case A B C where they act together. Of the two
+instances, therefore, which the Method of Difference requires,--the one
+positive, the other negative,--the negative one, or that in which the
+given phenomenon is absent, is not the direct result of observation and
+experiment, but has been arrived at by deduction. As one of the forms of
+the Method of Difference, the Method of Residues partakes of its
+rigorous certainty, provided the previous inductions, those which gave
+the effects of A and B, were obtained by the same infallible method, and
+provided we are certain that C is the _only_ antecedent to which the
+residual phenomenon _c_ can be referred; the only agent of which we had
+not already calculated and subducted the effect. But as we can never be
+quite certain of this, the evidence derived from the Method of Residues
+is not complete unless we can obtain C artificially and try it
+separately, or unless its agency, when once suggested, can be accounted
+for, and proved deductively from known laws.
+
+Even with these reservations, the Method of Residues is one of the most
+important among our instruments of discovery. Of all the methods of
+investigating laws of nature, this is the most fertile in unexpected
+results; often informing us of sequences in which neither the cause nor
+the effect were sufficiently conspicuous to attract of themselves the
+attention of observers. The agent C may be an obscure circumstance, not
+likely to have been perceived unless sought for, nor likely to have been
+sought for until attention had been awakened by the insufficiency of the
+obvious causes to account for the whole of the effect. And _c_ may be so
+disguised by its intermixture with _a_ and _b_, that it would scarcely
+have presented itself spontaneously as a subject of separate study. Of
+these uses of the method, we shall presently cite some remarkable
+examples. The canon of the Method of Residues is as follows:--
+
+FOURTH CANON.
+
+_Subduct from any phenomenon such part as is known by previous
+inductions to be the effect of certain antecedents, and the residue of
+the phenomenon is the effect of the remaining antecedents._
+
+
+� 6. There remains a class of laws which it is impracticable to
+ascertain by any of the three methods which I have attempted to
+characterize; namely, the laws of those Permanent Causes, or
+indestructible natural agents, which it is impossible either to exclude
+or to isolate; which we can neither hinder from being present, nor
+contrive that they shall be present alone. It would appear at first
+sight that we could by no means separate the effects of these agents
+from the effects of those other phenomena with which they cannot be
+prevented from coexisting. In respect, indeed, to most of the permanent
+causes, no such difficulty exists; since though we cannot eliminate
+them as coexisting facts, we can eliminate them as influencing agents,
+by simply trying our experiment in a local situation beyond the limits
+of their influence. The pendulum, for example, has its oscillations
+disturbed by the vicinity of a mountain: we remove the pendulum to a
+sufficient distance from the mountain, and the disturbance ceases: from
+these data we can determine by the Method of Difference, the amount of
+effect due to the mountain; and beyond a certain distance everything
+goes on precisely as it would do if the mountain exercised no influence
+whatever, which, accordingly, we, with sufficient reason, conclude to be
+the fact.
+
+The difficulty, therefore, in applying the methods already treated of to
+determine the effects of Permanent Causes, is confined to the cases in
+which it is impossible for us to get out of the local limits of their
+influence. The pendulum can be removed from the influence of the
+mountain, but it cannot be removed from the influence of the earth: we
+cannot take away the earth from the pendulum, nor the pendulum from the
+earth, to ascertain whether it would continue to vibrate if the action
+which the earth exerts upon it were withdrawn. On what evidence, then,
+do we ascribe its vibrations to the earth's influence? Not on any
+sanctioned by the Method of Difference; for one of the two instances,
+the negative instance, is wanting. Nor by the Method of Agreement; for
+though all pendulums agree in this, that during their oscillations the
+earth is always present, why may we not as well ascribe the phenomenon
+to the sun, which is equally a coexistent fact in all the experiments?
+It is evident that to establish even so simple a fact of causation as
+this, there was required some method over and above those which we have
+yet examined.
+
+As another example, let us take the phenomenon Heat. Independently of
+all hypothesis as to the real nature of the agency so called, this fact
+is certain, that we are unable to exhaust any body of the whole of its
+heat. It is equally certain, that no one ever perceived heat not
+emanating from a body. Being unable, then, to separate Body and Heat, we
+cannot effect such a variation of circumstances as the foregoing three
+methods require; we cannot ascertain, by those methods, what portion of
+the phenomena exhibited by any body is due to the heat contained in it.
+If we could observe a body with its heat, and the same body entirely
+divested of heat, the Method of Difference would show the effect due to
+the heat, apart from that due to the body. If we could observe heat
+under circumstances agreeing in nothing but heat, and therefore not
+characterized also by the presence of a body, we could ascertain the
+effects of heat, from an instance of heat with a body and an instance of
+heat without a body, by the Method of Agreement; or we could determine
+by the Method of Difference what effect was due to the body, when the
+remainder which was due to the heat would be given by the Method of
+Residues. But we can do none of these things; and without them the
+application of any of the three methods to the solution of this problem
+would be illusory. It would be idle, for instance, to attempt to
+ascertain the effect of heat by subtracting from the phenomena exhibited
+by a body, all that is due to its other properties; for as we have never
+been able to observe any bodies without a portion of heat in them,
+effects due to that heat might form a part of the very results, which we
+were affecting to subtract in order that the effect of heat might be
+shown by the residue.
+
+If, therefore, there were no other methods of experimental investigation
+than these three, we should be unable to determine the effects due to
+heat as a cause. But we have still a resource. Though we cannot exclude
+an antecedent altogether, we may be able to produce, or nature may
+produce for us, some modification in it. By a modification is here
+meant, a change in it, not amounting to its total removal. If some
+modification in the antecedent A is always followed by a change in the
+consequent _a_, the other consequents _b_ and _c_ remaining the same; or
+_vice vers�_, if every change in _a_ is found to have been preceded by
+some modification in A, none being observable in any of the other
+antecedents; we may safely conclude that _a_ is, wholly or in part, an
+effect traceable to A, or at least in some way connected with it through
+causation. For example, in the case of heat, though we cannot expel it
+altogether from any body, we can modify it in quantity, we can increase
+or diminish it; and doing so, we find by the various methods of
+experimentation or observation already treated of, that such increase or
+diminution of heat is followed by expansion or contraction of the body.
+In this manner we arrive at the conclusion, otherwise unattainable by
+us, that one of the effects of heat is to enlarge the dimensions of
+bodies; or what is the same thing in other words, to widen the distances
+between their particles.
+
+A change in a thing, not amounting to its total removal, that is, a
+change which leaves it still the same thing it was, must be a change
+either in its quantity, or in some of its variable relations to other
+things, of which variable relations the principal is its position in
+space. In the previous example, the modification which was produced in
+the antecedent was an alteration in its quantity. Let us now suppose the
+question to be, what influence the moon exerts on the surface of the
+earth. We cannot try an experiment in the absence of the moon, so as to
+observe what terrestrial phenomena her annihilation would put an end to;
+but when we find that all the variations in the _position_ of the moon
+are followed by corresponding variations in the time and place of high
+water, the place being always either the part of the earth which is
+nearest to, or that which is most remote from, the moon, we have ample
+evidence that the moon is, wholly or partially, the cause which
+determines the tides. It very commonly happens, as it does in this
+instance, that the variations of an effect are correspondent, or
+analogous, to those of its cause; as the moon moves farther towards the
+east, the high water point does the same: but this is not an
+indispensable condition; as may be seen in the same example, for along
+with that high water point there is at the same instant another high
+water point diametrically opposite to it, and which, therefore, of
+necessity, moves towards the west, as the moon, followed by the nearer
+of the tide waves, advances towards the east: and yet both these motions
+are equally effects of the moon's motion.
+
+That the oscillations of the pendulum are caused by the earth, is proved
+by similar evidence. Those oscillations take place between equidistant
+points on the two sides of a line, which, being perpendicular to the
+earth, varies with every variation in the earth's position, either in
+space or relatively to the object. Speaking accurately, we only know by
+the method now characterized, that all terrestrial bodies tend to the
+earth, and not to some unknown fixed point lying in the same direction.
+In every twenty-four hours, by the earth's rotation, the line drawn from
+the body at right angles to the earth coincides successively with all
+the radii of a circle, and in the course of six months the place of that
+circle varies by nearly two hundred millions of miles; yet in all these
+changes of the earth's position, the line in which bodies tend to fall
+continues to be directed towards it: which proves that terrestrial
+gravity is directed to the earth, and not, as was once fancied by some,
+to a fixed point of space.
+
+The method by which these results were obtained, may be termed the
+Method of Concomitant Variations: it is regulated by the following
+canon:--
+
+FIFTH CANON.
+
+_Whatever phenomenon varies in any manner whenever another phenomenon
+varies in some particular manner, is either a cause or an effect of that
+phenomenon, or is connected with it through some fact of causation._
+
+The last clause is subjoined, because it by no means follows when two
+phenomena accompany each other in their variations, that the one is
+cause and the other effect. The same thing may, and indeed must happen,
+supposing them to be two different effects of a common cause: and by
+this method alone it would never be possible to ascertain which of the
+suppositions is the true one. The only way to solve the doubt would be
+that which we have so often adverted to, viz. by endeavouring to
+ascertain whether we can produce the one set of variations by means of
+the other. In the case of heat, for example, by increasing the
+temperature of a body we increase its bulk, but by increasing its bulk
+we do not increase its temperature; on the contrary, (as in the
+rarefaction of air under the receiver of an air-pump,) we generally
+diminish it: therefore heat is not an effect, but a cause, of increase
+of bulk. If we cannot ourselves produce the variations, we must
+endeavour, though it is an attempt which is seldom successful, to find
+them produced by nature in some case in which the pre-existing
+circumstances are perfectly known to us.
+
+It is scarcely necessary to say, that in order to ascertain the uniform
+concomitance of variations in the effect with variations in the cause,
+the same precautions must be used as in any other case of the
+determination of an invariable sequence. We must endeavour to retain all
+the other antecedents unchanged, while that particular one is subjected
+to the requisite series of variations; or in other words, that we may be
+warranted in inferring causation from concomitance of variations, the
+concomitance itself must be proved by the Method of Difference.
+
+It might at first appear that the Method of Concomitant Variations
+assumes a new axiom, or law of causation in general, namely, that every
+modification of the cause is followed by a change in the effect. And it
+does usually happen that when a phenomenon A causes a phenomenon _a_,
+any variation in the quantity or in the various relations of A, is
+uniformly followed by a variation in the quantity or relations of _a_.
+To take a familiar instance, that of gravitation. The sun causes a
+certain tendency to motion in the earth; here we have cause and effect;
+but that tendency is _towards_ the sun, and therefore varies in
+direction as the sun varies in the relation of position; and moreover
+the tendency varies in intensity, in a certain numerical correspondence
+to the sun's distance from the earth, that is, according to another
+relation of the sun. Thus we see that there is not only an invariable
+connexion between the sun and the earth's gravitation, but that two of
+the relations of the sun, its position with respect to the earth and its
+distance from the earth, are invariably connected as antecedents with
+the quantity and direction of the earth's gravitation. The cause of the
+earth's gravitating at all, is simply the sun; but the cause of its
+gravitating with a given intensity and in a given direction, is the
+existence of the sun in a given direction and at a given distance. It is
+not strange that a modified cause, which is in truth a different cause,
+should produce a different effect.
+
+Although it is for the most part true that a modification of the cause
+is followed by a modification of the effect, the Method of Concomitant
+Variations does not, however, presuppose this as an axiom. It only
+requires the converse proposition; that anything on whose modifications,
+modifications of an effect are invariably consequent, must be the cause
+(or connected with the cause) of that effect; a proposition, the truth
+of which is evident; for if the thing itself had no influence on the
+effect, neither could the modifications of the thing have any influence.
+If the stars have no power over the fortunes of mankind, it is implied
+in the very terms, that the conjunctions or oppositions of different
+stars can have no such power.
+
+Although the most striking applications of the Method of Concomitant
+Variations take place in the cases in which the Method of Difference,
+strictly so called, is impossible, its use is not confined to those
+cases; it may often usefully follow after the Method of Difference, to
+give additional precision to a solution which that has found. When by
+the Method of Difference it has first been ascertained that a certain
+object produces a certain effect, the Method of Concomitant Variations
+may be usefully called in, to determine according to what law the
+quantity or the different relations of the effect follow those of the
+cause.
+
+
+� 7. The case in which this method admits of the most extensive
+employment, is that in which the variations of the cause are variations
+of quantity. Of such variations we may in general affirm with safety,
+that they will be attended not only with variations, but with similar
+variations, of the effect: the proposition, that more of the cause is
+followed by more of the effect, being a corollary from the principle of
+the Composition of Causes, which, as we have seen, is the general rule
+of causation; cases of the opposite description, in which causes change
+their properties on being conjoined with one another, being, on the
+contrary, special and exceptional. Suppose, then, that when A changes
+in quantity, _a_ also changes in quantity, and in such a manner that we
+can trace the numerical relation which the changes of the one bear to
+such changes of the other as take place within our limits of
+observation. We may then, with certain precautions, safely conclude that
+the same numerical relation will hold beyond those limits. If, for
+instance, we find that when A is double, _a_ is double; that when A is
+treble or quadruple, _a_ is treble or quadruple; we may conclude that if
+A were a half or a third, _a_ would be a half or a third, and finally,
+that if A were annihilated, _a_ would be annihilated, and that _a_ is
+wholly the effect of A, or wholly the effect of the same cause with A.
+And so with any other numerical relation according to which A and _a_
+would vanish simultaneously; as for instance, if _a_ were proportional
+to the square of A. If, on the other hand, _a_ is not wholly the effect
+of A, but yet varies when A varies, it is probably a mathematical
+function not of A alone, but of A and something else: its changes, for
+example, may be such as would occur if part of it remained constant, or
+varied on some other principle, and the remainder varied in some
+numerical relation to the variations of A. In that case, when A
+diminishes, _a_ will be seen to approach not towards zero, but towards
+some other limit: and when the series of variations is such as to
+indicate what that limit is, if constant, or the law of its variation if
+variable, the limit will exactly measure how much of _a_ is the effect
+of some other and independent cause, and the remainder will be the
+effect of A (or of the cause of A).
+
+These conclusions, however, must not be drawn without certain
+precautions. In the first place, the possibility of drawing them at all,
+manifestly supposes that we are acquainted not only with the variations,
+but with the absolute quantities both of A and _a_. If we do not know
+the total quantities, we cannot, of course, determine the real numerical
+relation according to which those quantities vary. It is therefore an
+error to conclude, as some have concluded, that because increase of heat
+expands bodies, that is, increases the distance between their particles,
+therefore the distance is wholly the effect of heat, and that if we
+could entirely exhaust the body of its heat, the particles would be in
+complete contact. This is no more than a guess, and of the most
+hazardous sort, not a legitimate induction: for since we neither know
+how much heat there is in any body, nor what is the real distance
+between any two of its particles, we cannot judge whether the
+contraction of the distance does or does not follow the diminution of
+the quantity of heat according to such a numerical relation that the two
+quantities would vanish simultaneously.
+
+In contrast with this, let us consider a case in which the absolute
+quantities are known; the case contemplated in the first law of motion;
+viz. that all bodies in motion continue to move in a straight line with
+uniform velocity until acted upon by some new force. This assertion is
+in open opposition to first appearances; all terrestrial objects, when
+in motion, gradually abate their velocity and at last stop; which
+accordingly the ancients, with their _inductio per enumerationem
+simplicem_, imagined to be the law. Every moving body, however,
+encounters various obstacles, as friction, the resistance of the
+atmosphere, &c., which we know by daily experience to be causes capable
+of destroying motion. It was suggested that the whole of the retardation
+might be owing to these causes. How was this inquired into? If the
+obstacles could have been entirely removed, the case would have been
+amenable to the Method of Difference. They could not be removed, they
+could only be diminished, and the case, therefore, admitted only of the
+Method of Concomitant Variations. This accordingly being employed, it
+was found that every diminution of the obstacles diminished the
+retardation of the motion: and inasmuch as in this case (unlike the case
+of heat) the total quantities both of the antecedent and of the
+consequent were known; it was practicable to estimate, with an approach
+to accuracy, both the amount of the retardation and the amount of the
+retarding causes, or resistances, and to judge how near they both were
+to being exhausted; and it appeared that the effect dwindled as rapidly,
+and at each step was as far on the road towards annihilation, as the
+cause was. The simple oscillation of a weight suspended from a fixed
+point, and moved a little out of the perpendicular, which in ordinary
+circumstances lasts but a few minutes, was prolonged in Borda's
+experiments to more than thirty hours, by diminishing as much as
+possible the friction at the point of suspension, and by making the body
+oscillate in a space exhausted as nearly as possible of its air. There
+could therefore be no hesitation in assigning the whole of the
+retardation of motion to the influence of the obstacles; and since,
+after subducting this retardation from the total phenomenon, the
+remainder was an uniform velocity, the result was the proposition known
+as the first law of motion.
+
+There is also another characteristic uncertainty affecting the inference
+that the law of variation which the quantities observe within our limits
+of observation, will hold beyond those limits. There is of course, in
+the first instance, the possibility that beyond the limits, and in
+circumstances therefore of which we have no direct experience, some
+counteracting cause might develop itself; either a new agent, or a new
+property of the agents concerned, which lies dormant in the
+circumstances we are able to observe. This is an element of uncertainty
+which enters largely into all our predictions of effects; but it is not
+peculiarly applicable to the Method of Concomitant Variations. The
+uncertainty, however, of which I am about to speak, is characteristic of
+that method; especially in the cases in which the extreme limits of our
+observation are very narrow, in comparison with the possible variations
+in the quantities of the phenomena. Any one who has the slightest
+acquaintance with mathematics, is aware that very different laws of
+variation may produce numerical results which differ but slightly from
+one another within narrow limits; and it is often only when the absolute
+amounts of variation are considerable, that the difference between the
+results given by one law and by another becomes appreciable. When,
+therefore, such variations in the quantity of the antecedents as we have
+the means of observing, are small in comparison with the total
+quantities, there is much danger lest we should mistake the numerical
+law, and be led to miscalculate the variations which would take place
+beyond the limits; a miscalculation which would vitiate any conclusion
+respecting the dependence of the effect upon the cause, that could be
+founded on those variations. Examples are not wanting of such mistakes.
+"The formul�," says Sir John Herschel,[33] "which have been empirically
+deduced for the elasticity of steam, (till very recently,) and those for
+the resistance of fluids, and other similar subjects," when relied on
+beyond the limits of the observations from which they were deduced,
+"have almost invariably failed to support the theoretical structures
+which have been erected on them."
+
+In this uncertainty, the conclusion we may draw from the concomitant
+variations of _a_ and A, to the existence of an invariable and exclusive
+connexion between them, or to the permanency of the same numerical
+relation between their variations when the quantities are much greater
+or smaller than those which we have had the means of observing, cannot
+be considered to rest on a complete induction. All that in such a case
+can be regarded as proved on the subject of causation is, that there is
+some connexion between the two phenomena; that A, or something which can
+influence A, must be _one_ of the causes which collectively determine
+_a_. We may, however, feel assured that the relation which we have
+observed to exist between the variations of A and _a_, will hold true in
+all cases which fall between the same extreme limits; that is, wherever
+the utmost increase or diminution in which the result has been found by
+observation to coincide with the law, is not exceeded.
+
+The four methods which it has now been attempted to describe, are the
+only possible modes of experimental inquiry--of direct induction _�
+posteriori_, as distinguished from deduction: at least, I know not, nor
+am able to imagine, any others. And even of these, the Method of
+Residues, as we have seen, is not independent of deduction; though, as
+it also requires specific experience, it may, without impropriety, be
+included among methods of direct observation and experiment.
+
+These, then, with such assistance as can be obtained from Deduction,
+compose the available resources of the human mind for ascertaining the
+laws of the succession of phenomena. Before proceeding to point out
+certain circumstances, by which the employment of these methods is
+subjected to an immense increase of complication and of difficulty, it
+is expedient to illustrate the use of the methods, by suitable examples
+drawn from actual physical investigations. These, accordingly, will form
+the subject of the succeeding chapter.
+
+
+
+
+CHAPTER IX.
+
+MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.
+
+
+� 1. I shall select, as a first example, an interesting speculation of
+one of the most eminent of theoretical chemists, Baron Liebig. The
+object in view, is to ascertain the immediate cause of the death
+produced by metallic poisons.
+
+Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
+introduced into the animal organism, except in the smallest doses,
+destroy life. These facts have long been known, as insulated truths of
+the lowest order of generalization; but it was reserved for Liebig, by
+an apt employment of the first two of our methods of experimental
+inquiry, to connect these truths together by a higher induction,
+pointing out what property, common to all these deleterious substances,
+is the really operating cause of their fatal effect.
+
+When solutions of these substances are placed in sufficiently close
+contact with many animal products, albumen, milk, muscular fibre, and
+animal membranes, the acid or salt leaves the water in which it was
+dissolved, and enters into combination with the animal substance: which
+substance, after being thus acted upon, is found to have lost its
+tendency to spontaneous decomposition, or putrefaction.
+
+Observation also shows, in cases where death has been produced by these
+poisons, that the parts of the body with which the poisonous substances
+have been brought into contact, do not afterwards putrefy.
+
+And, finally, when the poison has been supplied in too small a quantity
+to destroy life, eschars are produced, that is, certain superficial
+portions of the tissues are destroyed, which are afterwards thrown off
+by the reparative process taking place in the healthy parts.
+
+These three sets of instances admit of being treated according to the
+Method of Agreement. In all of them the metallic compounds are brought
+into contact with the substances which compose the human or animal body;
+and the instances do not seem to agree in any other circumstance. The
+remaining antecedents are as different, and even opposite, as they could
+possibly be made; for in some the animal substances exposed to the
+action of the poisons are in a state of life, in others only in a state
+of organization, in others not even in that. And what is the result
+which follows in all the cases? The conversion of the animal substance
+(by combination with the poison) into a chemical compound, held together
+by so powerful a force as to resist the subsequent action of the
+ordinary causes of decomposition. Now, organic life (the necessary
+condition of sensitive life) consisting in a continual state of
+decomposition and recomposition of the different organs and tissues;
+whatever incapacitates them for this decomposition destroys life. And
+thus the proximate cause of the death produced by this description of
+poisons, is ascertained, as far as the Method of Agreement can ascertain
+it.
+
+Let us now bring our conclusion to the test of the Method of Difference.
+Setting out from the cases already mentioned, in which the antecedent is
+the presence of substances forming with the tissues a compound incapable
+of putrefaction, (and _� fortiori_ incapable of the chemical actions
+which constitute life,) and the consequent is death, either of the whole
+organism, or of some portion of it; let us compare with these cases
+other cases, as much resembling them as possible, but in which that
+effect is not produced. And, first, "many insoluble basic salts of
+arsenious acid are known not to be poisonous. The substance called
+alkargen, discovered by Bunsen, which contains a very large quantity of
+arsenic, and approaches very closely in composition to the organic
+arsenious compounds found in the body, has not the slightest injurious
+action upon the organism." Now when these substances are brought into
+contact with the tissues in any way, they do not combine with them; they
+do not arrest their progress to decomposition. As far, therefore, as
+these instances go, it appears that when the effect is absent, it is by
+reason of the absence of that antecedent which we had already good
+ground for considering as the proximate cause.
+
+But the rigorous conditions of the Method of Difference are not yet
+satisfied; for we cannot be sure that these unpoisonous bodies agree
+with the poisonous substances in every property, except the particular
+one, of entering into a difficultly decomposable compound with the
+animal tissues. To render the method strictly applicable, we need an
+instance, not of a different substance, but of one of the very same
+substances, in circumstances which would prevent it from forming, with
+the tissues, the sort of compound in question; and then, if death does
+not follow, our case is made out. Now such instances are afforded by the
+antidotes to these poisons. For example, in case of poisoning by
+arsenious acid, if hydrated peroxide of iron is administered, the
+destructive agency is instantly checked. Now this peroxide is known to
+combine with the acid, and form a compound, which, being insoluble,
+cannot act at all on animal tissues. So, again, sugar is a well-known
+antidote to poisoning by salts of copper; and sugar reduces those salts
+either into metallic copper, or into the red suboxide, neither of which
+enters into combination with animal matter. The disease called painter's
+colic, so common in manufactories of white lead, is unknown where the
+workmen are accustomed to take, as a preservative, sulphuric acid
+lemonade (a solution of sugar rendered acid by sulphuric acid). Now
+diluted sulphuric acid has the property of decomposing all compounds of
+lead with organic matter, or of preventing them from being formed.
+
+There is another class of instances, of the nature required by the
+Method of Difference, which seem at first sight to conflict with the
+theory. Soluble salts of silver, such for instance as the nitrate, have
+the same stiffening antiseptic effect on decomposing animal substances
+as corrosive sublimate and the most deadly metallic poisons; and when
+applied to the external parts of the body, the nitrate is a powerful
+caustic; depriving those parts of all active vitality, and causing them
+to be thrown off by the neighbouring living structures, in the form of
+an eschar. The nitrate and the other salts of silver ought, then, it
+would seem, if the theory be correct, to be poisonous; yet they may be
+administered internally with perfect impunity. From this apparent
+exception arises the strongest confirmation which the theory has yet
+received. Nitrate of silver, in spite of its chemical properties, does
+not poison when introduced into the stomach; but in the stomach, as in
+all animal liquids, there is common salt; and in the stomach there is
+also free muriatic acid. These substances operate as natural antidotes,
+combining with the nitrate, and if its quantity is not too great,
+immediately converting it into chloride of silver; a substance very
+slightly soluble, and therefore incapable of combining with the tissues,
+although to the extent of its solubility it has a medicinal influence,
+though an entirely different class of organic actions.
+
+The preceding instances have afforded an induction of a high order of
+conclusiveness, illustrative of the two simplest of our four methods;
+though not rising to the maximum of certainty which the Method of
+Difference, in its most perfect exemplification, is capable of
+affording. For (let us not forget) the positive instance and the
+negative one which the rigour of that method requires, ought to differ
+only in the presence or absence of one single circumstance. Now, in the
+preceding argument, they differ in the presence or absence not of a
+single _circumstance_, but of a single _substance_: and as every
+substance has innumerable properties, there is no knowing what number of
+real differences are involved in what is nominally and apparently only
+one difference. It is conceivable that the antidote, the peroxide of
+iron for example, may counteract the poison through some other of its
+properties than that of forming an insoluble compound with it; and if
+so, the theory would fall to the ground, so far as it is supported by
+that instance. This source of uncertainty, which is a serious hindrance
+to all extensive generalizations in chemistry, is however reduced in the
+present case to almost the lowest degree possible, when we find that
+not only one substance, but many substances, possess the capacity of
+acting as antidotes to metallic poisons, and that all these agree in the
+property of forming insoluble compounds with the poisons, while they
+cannot be ascertained to agree in any other property whatsoever. We have
+thus, in favour of the theory, all the evidence which can be obtained by
+what we termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference; the evidence of which, though it never can
+amount to that of the Method of Difference properly so called, may
+approach indefinitely near to it.
+
+
+� 2. Let the object be[34] to ascertain the law of what is termed
+_induced_ electricity; to find under what conditions any electrified
+body, whether positively or negatively electrified, gives rise to a
+contrary electric state in some other body adjacent to it.
+
+The most familiar exemplification of the phenomenon to be investigated
+is the following. Around the prime conductors of an electrical machine,
+the atmosphere to some distance, or any conducting surface suspended in
+that atmosphere, is found to be in an electric condition opposite to
+that of the prime conductor itself. Near and around the positive prime
+conductor there is negative electricity, and near and around the
+negative prime conductor there is positive electricity. When pith balls
+are brought near to either of the conductors, they become electrified
+with the opposite electricity to it; either receiving a share from the
+already electrified atmosphere by conduction, or acted upon by the
+direct inductive influence of the conductor itself: they are then
+attracted by the conductor to which they are in opposition; or, if
+withdrawn in their electrified state, they will be attracted by any
+other oppositely charged body. In like manner the hand, if brought near
+enough to the conductor, receives or gives an electric discharge; now we
+have no evidence that a charged conductor can be suddenly discharged
+unless by the approach of a body oppositely electrified. In the case,
+therefore, of the electric machine, it appears that the accumulation of
+electricity in an insulated conductor is always accompanied by the
+excitement of the contrary electricity in the surrounding atmosphere,
+and in every conductor placed near the former conductor. It does not
+seem possible, in this case, to produce one electricity by itself.
+
+Let us now examine all the other instances which we can obtain,
+resembling this instance in the given consequent, namely, the evolution
+of an opposite electricity in the neighbourhood of an electrified body.
+As one remarkable instance we have the Leyden jar; and after the
+splendid experiments of Faraday in complete and final establishment of
+the substantial identity of magnetism and electricity, we may cite the
+magnet, both the natural and the electro-magnet, in neither of which it
+is possible to produce one kind of electricity by itself, or to charge
+one pole without charging an opposite pole with the contrary electricity
+at the same time. We cannot have a magnet with one pole: if we break a
+natural loadstone into a thousand pieces, each piece will have its two
+oppositely electrified poles complete within itself. In the voltaic
+circuit, again, we cannot have one current without its opposite. In the
+ordinary electric machine, the glass cylinder or plate, and the rubber,
+acquire opposite electricities.
+
+From all these instances, treated by the Method of Agreement, a general
+law appears to result. The instances embrace all the known modes in
+which a body can become charged with electricity; and in all of them
+there is found, as a concomitant or consequent, the excitement of the
+opposite electric state in some other body or bodies. It seems to follow
+that the two facts are invariably connected, and that the excitement of
+electricity in any body has for one of its necessary conditions the
+possibility of a simultaneous excitement of the opposite electricity in
+some neighbouring body.
+
+As the two contrary electricities can only be produced together, so
+they can only cease together. This may be shown by an application of the
+Method of Difference to the example of the Leyden jar. It needs scarcely
+be here remarked that in the Leyden jar, electricity can be accumulated
+and retained in considerable quantity, by the contrivance of having two
+conducting surfaces of equal extent, and parallel to each other through
+the whole of that extent, with a non-conducting substance such as glass
+between them. When one side of the jar is charged positively, the other
+is charged negatively, and it was by virtue of this fact that the Leyden
+jar served just now as an instance in our employment of the Method of
+Agreement. Now it is impossible to discharge one of the coatings unless
+the other can be discharged at the same time. A conductor held to the
+positive side cannot convey away any electricity unless an equal
+quantity be allowed to pass from the negative side: if one coating be
+perfectly insulated, the charge is safe. The dissipation of one must
+proceed _pari passu_ with that of the other.
+
+The law thus strongly indicated admits of corroboration by the Method of
+Concomitant Variations. The Leyden jar is capable of receiving a much
+higher charge than can ordinarily be given to the conductor of an
+electrical machine. Now in the case of the Leyden jar, the metallic
+surface which receives the induced electricity is a conductor exactly
+similar to that which receives the primary charge, and is therefore as
+susceptible of receiving and retaining the one electricity, as the
+opposite surface of receiving and retaining the other; but in the
+machine, the neighbouring body which is to be oppositely electrified is
+the surrounding atmosphere, or any body casually brought near to the
+conductor; and as these are generally much inferior in their capacity of
+becoming electrified, to the conductor itself, their limited power
+imposes a corresponding limit to the capacity of the conductor for being
+charged. As the capacity of the neighbouring body for supporting the
+opposition increases, a higher charge becomes possible: and to this
+appears to be owing the great superiority of the Leyden jar.
+
+A further and most decisive confirmation by the Method of Difference,
+is to be found in one of Faraday's experiments in the course of his
+researches on the subject of induced electricity.
+
+Since common or machine electricity, and voltaic electricity, may be
+considered for the present purpose to be identical, Faraday wished to
+know whether, as the prime conductor develops opposite electricity upon
+a conductor in its vicinity, so a voltaic current running along a wire
+would induce an opposite current upon another wire laid parallel to it
+at a short distance. Now this case is similar to the cases previously
+examined, in every circumstance except the one to which we have ascribed
+the effect. We found in the former instances that whenever electricity
+of one kind was excited in one body, electricity of the opposite kind
+must be excited in a neighbouring body. But in Faraday's experiment this
+indispensable opposition exists within the wire itself. From the nature
+of a voltaic charge, the two opposite currents necessary to the
+existence of each other are both accommodated in one wire; and there is
+no need of another wire placed beside it to contain one of them, in the
+same way as the Leyden jar must have a positive and a negative surface.
+The exciting cause can and does produce all the effect which its laws
+require, independently of any electric excitement of a neighbouring
+body. Now the result of the experiment with the second wire was, that no
+opposite current was produced. There was an instantaneous effect at the
+closing and breaking of the voltaic circuit; electric inductions
+appeared when the two wires were moved to and from one another; but
+these are phenomena of a different class. There was no induced
+electricity in the sense in which this is predicated of the Leyden jar;
+there was no sustained current running up the one wire while an opposite
+current ran down the neighbouring wire; and this alone would have been a
+true parallel case to the other.
+
+It thus appears by the combined evidence of the Method of Agreement, the
+Method of Concomitant Variations, and the most rigorous form of the
+Method of Difference, that neither of the two kinds of electricity can
+be excited without an equal excitement of the other and opposite kind:
+that both are effects of the same cause; that the possibility of the one
+is a condition of the possibility of the other, and the quantity of the
+one an impassable limit to the quantity of the other. A scientific
+result of considerable interest in itself, and illustrating those three
+methods in a manner both characteristic and easily intelligible.[35]
+
+
+� 3. Our third example shall be extracted from Sir John Herschel's
+_Discourse on the Study of Natural Philosophy_, a work replete with
+happily-selected exemplifications of inductive processes from almost
+every department of physical science, and in which alone, of all books
+which I have met with, the four methods of induction are distinctly
+recognised, though not so clearly characterized and defined, nor their
+correlation so fully shown, as has appeared to me desirable. The present
+example is described by Sir John Herschel as "one of the most beautiful
+specimens" which can be cited "of inductive experimental inquiry lying
+within a moderate compass;" the theory of dew, first promulgated by the
+late Dr. Wells, and now universally adopted by scientific authorities.
+The passages in inverted commas are extracted verbatim from the
+Discourse.[36]
+
+"Suppose _dew_ were the phenomenon proposed, whose cause we would know.
+In the first place" we must determine precisely what we mean by dew:
+what the fact really is, whose cause we desire to investigate. "We must
+separate dew from rain, and the moisture of fogs, and limit the
+application of the term to what is really meant, which is the
+spontaneous appearance of moisture on substances exposed in the open air
+when no rain or _visible_ wet is falling." This answers to a preliminary
+operation which will be characterized in the ensuing book, treating of
+operations subsidiary to induction.[37]
+
+"Now, here we have analogous phenomena in the moisture which bedews a
+cold metal or stone when we breathe upon it; that which appears on a
+glass of water fresh from the well in hot weather; that which appears on
+the inside of windows when sudden rain or hail chills the external air;
+that which runs down our walls when, after a long frost, a warm moist
+thaw comes on." Comparing these cases, we find that they all contain the
+phenomenon which was proposed as the subject of investigation. Now "all
+these instances agree in one point, the coldness of the object dewed, in
+comparison with the air in contact with it." But there still remains the
+most important case of all, that of nocturnal dew: does the same
+circumstance exist in this case? "Is it a fact that the object dewed is
+colder than the air? Certainly not, one would at first be inclined to
+say; for what is to _make_ it so? But ... the experiment is easy: we
+have only to lay a thermometer in contact with the dewed substance, and
+hang one at a little distance above it, out of reach of its influence.
+The experiment has been therefore made, the question has been asked, and
+the answer has been invariably in the affirmative. Whenever an object
+contracts dew, it _is_ colder than the air."
+
+Here then is a complete application of the Method of Agreement,
+establishing the fact of an invariable connexion between the deposition
+of dew on a surface, and the coldness of that surface compared with the
+external air. But which of these is cause, and which effect? or are they
+both effects of something else? On this subject the Method of Agreement
+can afford us no light: we must call in a more potent method. "We must
+collect more facts, or, which comes to the same thing, vary the
+circumstances; since every instance in which the circumstances differ is
+a fresh fact: and especially, we must note the contrary or negative
+cases, _i.e._ where no dew is produced:" a comparison between instances
+of dew and instances of no dew, being the condition necessary to bring
+the Method of Difference into play.
+
+"Now, first, no dew is produced on the surface of polished metals, but
+it _is_ very copiously on glass, both exposed with their faces upwards,
+and in some cases the under side of a horizontal plate of glass is also
+dewed." Here is an instance in which the effect is produced, and another
+instance in which it is not produced; but we cannot yet pronounce, as
+the canon of the Method of Difference requires, that the latter instance
+agrees with the former in all its circumstances except one; for the
+differences between glass and polished metals are manifold, and the only
+thing we can as yet be sure of is, that the cause of dew will be found
+among the circumstances by which the former substance is distinguished
+from the latter. But if we could be sure that glass, and the various
+other substances on which dew is deposited, have only one quality in
+common, and that polished metals and the other substances on which dew
+is not deposited have also nothing in common but the one circumstance,
+of not having the one quality which the others have; the requisitions of
+the Method of Difference would be completely satisfied, and we should
+recognise, in that quality of the substances, the cause of dew. This,
+accordingly, is the path of inquiry which is next to be pursued.
+
+"In the cases of polished metal and polished glass, the contrast shows
+evidently that the _substance_ has much to do with the phenomenon;
+therefore let the substance _alone_ be diversified as much as possible,
+by exposing polished surfaces of various kinds. This done, a _scale of
+intensity_ becomes obvious. Those polished substances are found to be
+most strongly dewed which conduct heat worst; while those which conduct
+well, resist dew most effectually." The complication increases; here is
+the Method of Concomitant Variations called to our assistance; and no
+other method was practicable on this occasion; for the quality of
+conducting heat could not be excluded, since all substances conduct heat
+in some degree. The conclusion obtained is, that _c�teris paribus_ the
+deposition of dew is in some proportion to the power which the body
+possesses of resisting the passage of heat; and that this, therefore,
+(or something connected with this,) must be at least one of the causes
+which assist in producing the deposition of dew on the surface.
+
+"But if we expose rough surfaces instead of polished, we sometimes find
+this law interfered with. Thus, roughened iron, especially if painted
+over or blackened, becomes dewed sooner than varnished paper; the kind
+of _surface_, therefore, has a great influence. Expose, then, the _same_
+material in very diversified states as to surface," (that is, employ the
+Method of Difference to ascertain concomitance of variations,) "and
+another scale of intensity becomes at once apparent; those _surfaces_
+which _part with their heat_ most readily by radiation, are found to
+contract dew most copiously." Here, therefore, are the requisites for a
+second employment of the Method of Concomitant Variations; which in this
+case also is the only method available, since all substances radiate
+heat in some degree or other. The conclusion obtained by this new
+application of the method is, that _c�teris paribus_ the deposition of
+dew is also in some proportion to the power of radiating heat; and that
+the quality of doing this abundantly (or some cause on which that
+quality depends) is another of the causes which promote the deposition
+of dew on the substance.
+
+"Again, the influence ascertained to exist of _substance_ and _surface_
+leads us to consider that of _texture_: and here, again, we are
+presented on trial with remarkable differences, and with a third scale
+of intensity, pointing out substances of a close firm texture, such as
+stones, metals, &c., as unfavourable, but those of a loose one, as
+cloth, velvet, wool, eider-down, cotton, &c., as eminently favourable to
+the contraction of dew." The Method of Concomitant Variations is here,
+for the third time, had recourse to; and, as before, from necessity,
+since the texture of no substance is absolutely firm or absolutely
+loose. Looseness of texture, therefore, or something which is the cause
+of that quality, is another circumstance which promotes the deposition
+of dew; but this third cause resolves itself into the first, viz. the
+quality of resisting the passage of heat: for substances of loose
+texture "are precisely those which are best adapted for clothing, or for
+impeding the free passage of heat from the skin into the air, so as to
+allow their outer surfaces to be very cold, while they remain warm
+within;" and this last is, therefore, an induction (from fresh
+instances) simply _corroborative_ of a former induction.
+
+It thus appears that the instances in which much dew is deposited, which
+are very various, agree in this, and, so far as we are able to observe,
+in this only, that they either radiate heat rapidly or conduct it
+slowly: qualities between which there is no other circumstance of
+agreement, than that by virtue of either, the body tends to lose heat
+from the surface more rapidly than it can be restored from within. The
+instances, on the contrary, in which no dew, or but a small quantity of
+it, is formed, and which are also extremely various, agree (as far as we
+can observe) in nothing except in _not_ having this same property. We
+seem, therefore, to have detected the characteristic difference between
+the substances on which dew is produced, and those on which it is not
+produced. And thus have been realized the requisitions of what we have
+termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference. The example afforded of this indirect method,
+and of the manner in which the data are prepared for it by the Methods
+of Agreement and of Concomitant Variations, is the most important of all
+the illustrations of induction afforded by this interesting speculation.
+
+We might now consider the question, on what the deposition of dew
+depends, to be completely solved, if we could be quite sure that the
+substances on which dew is produced differ from those on which it is
+not, in _nothing_ but in the property of losing heat from the surface
+faster than the loss can be repaired from within. And though we never
+can have that complete certainty, this is not of so much importance as
+might at first be supposed; for we have, at all events, ascertained
+that even if there be any other quality hitherto unobserved which is
+present in all the substances which contract dew, and absent in those
+which do not, this other property must be one which, in all that great
+number of substances, is present or absent exactly where the property of
+being a better radiator than conductor is present or absent; an extent
+of coincidence which affords a strong presumption of a community of
+cause, and a consequent invariable coexistence between the two
+properties; so that the property of being a better radiator than
+conductor, if not itself the cause, almost certainly always accompanies
+the cause, and, for purposes of prediction, no error is likely to be
+committed by treating it as if it were really such.
+
+Reverting now to an earlier stage of the inquiry, let us remember that
+we had ascertained that, in every instance where dew is formed, there is
+actual coldness of the surface below the temperature of the surrounding
+air; but we were not sure whether this coldness was the cause of dew, or
+its effect. This doubt we are now able to resolve. We have found that,
+in every such instance, the substance is one which, by its own
+properties or laws, would, if exposed in the night, become colder than
+the surrounding air. The coldness therefore being accounted for
+independently of the dew, while it is proved that there is a connexion
+between the two, it must be the dew which depends on the coldness; or in
+other words, the coldness is the cause of the dew.
+
+This law of causation, already so amply established, admits, however, of
+efficient additional corroboration in no less than three ways. First, by
+deduction from the known laws of aqueous vapour when diffused through
+air or any other gas; and though we have not yet come to the Deductive
+Method, we will not omit what is necessary to render this speculation
+complete. It is known by direct experiment that only a limited quantity
+of water can remain suspended in the state of vapour at each degree of
+temperature, and that this maximum grows less and less as the
+temperature diminishes. From this it follows, deductively, that if there
+is already as much vapour suspended as the air will contain at its
+existing temperature, any lowering of that temperature will cause a
+portion of the vapour to be condensed, and become water. But, again, we
+know deductively, from the laws of heat, that the contact of the air
+with a body colder than itself, will necessarily lower the temperature
+of the stratum of air immediately applied to its surface; and will
+therefore cause it to part with a portion of its water, which
+accordingly will, by the ordinary laws of gravitation or cohesion,
+attach itself to the surface of the body, thereby constituting dew. This
+deductive proof, it will have been seen, has the advantage of at once
+proving causation as well as coexistence; and it has the additional
+advantage that it also accounts for the exceptions to the occurrence of
+the phenomenon, the cases in which, although the body is colder than the
+air, yet no dew is deposited; by showing that this will necessarily be
+the case when the air is so under-supplied with aqueous vapour,
+comparatively to its temperature, that even when somewhat cooled by the
+contact of the colder body, it can still continue to hold in suspension
+all the vapour which was previously suspended in it: thus in a very dry
+summer there are no dews, in a very dry winter no hoar frost. Here,
+therefore, is an additional condition of the production of dew, which
+the methods we previously made use of failed to detect, and which might
+have remained still undetected, if recourse had not been had to the plan
+of deducing the effect from the ascertained properties of the agents
+known to be present.
+
+The second corroboration of the theory is by direct experiment,
+according to the canon of the Method of Difference. We can, by cooling
+the surface of any body, find in all cases some temperature, (more or
+less inferior to that of the surrounding air, according to its
+hygrometric condition,) at which dew will begin to be deposited. Here,
+too, therefore, the causation is directly proved. We can, it is true,
+accomplish this only on a small scale; but we have ample reason to
+conclude that the same operation, if conducted in Nature's great
+laboratory, would equally produce the effect.
+
+And, finally, even on that great scale we are able to verify the result.
+The case is one of those rare cases, as we have shown them to be, in
+which nature works the experiment for us in the same manner in which we
+ourselves perform it; introducing into the previous state of things a
+single and perfectly definite new circumstance, and manifesting the
+effect so rapidly that there is not time for any other material change
+in the pre-existing circumstances. "It is observed that dew is never
+copiously deposited in situations much screened from the open sky, and
+not at all in a cloudy night; but _if the clouds withdraw even for a few
+minutes, and leave a clear opening, a deposition of dew presently
+begins_, and goes on increasing.... Dew formed in clear intervals will
+often even evaporate again when the sky becomes thickly overcast." The
+proof, therefore, is complete, that the presence or absence of an
+uninterrupted communication with the sky causes the deposition or
+non-deposition of dew. Now, since a clear sky is nothing but the absence
+of clouds, and it is a known property of clouds, as of all other bodies
+between which and any given object nothing intervenes but an elastic
+fluid, that they tend to raise or keep up the superficial temperature of
+the object by radiating heat to it, we see at once that the
+disappearance of clouds will cause the surface to cool; so that Nature,
+in this case, produces a change in the antecedent by definite and known
+means, and the consequent follows accordingly: a natural experiment
+which satisfies the requisitions of the Method of Difference.[38]
+
+The accumulated proof of which the Theory of Dew has been found
+susceptible, is a striking instance of the fulness of assurance which
+the inductive evidence of laws of causation may attain, in cases in
+which the invariable sequence is by no means obvious to a superficial
+view.
+
+
+� 4. The admirable physiological investigations of Dr. Brown-S�quard
+afford brilliant examples of the application of the Inductive Methods to
+a class of inquiries in which, for reasons which will presently be
+given, direct induction takes place under peculiar difficulties and
+disadvantages. As one of the most apt instances I select his speculation
+(in the Proceedings of the Royal Society for May 16, 1861) on the
+relations between muscular irritability, cadaveric rigidity, and
+putrefaction.
+
+The law which Dr. Brown-S�quard's investigation tends to establish, is
+the following:--"The greater the degree of muscular irritability at the
+time of death, the later the cadaveric rigidity sets in, and the longer
+it lasts, and the later also putrefaction appears, and the slower it
+progresses." One would say at first sight that the method here required
+must be that of Concomitant Variations. But this is a delusive
+appearance, arising from the circumstance that the conclusion to be
+tested is itself a fact of concomitant variation. For the establishment
+of that fact any of the Methods may be put in requisition, and it will
+be found that the fourth Method, though really employed, has only a
+subordinate place in this particular investigation.
+
+The evidences by which Dr. Brown-S�quard establishes the law may be
+enumerated as follows:--
+
+1st. Paralysed muscles have greater irritability than healthy muscles.
+Now, paralysed muscles are later in assuming the cadaveric rigidity than
+healthy muscles, the rigidity lasts longer, and putrefaction sets in
+later and proceeds more slowly.
+
+Both these propositions had to be proved by experiment; and for the
+experiments which prove them, science is also indebted to Dr.
+Brown-S�quard. The former of the two--that paralysed muscles have
+greater irritability than healthy muscles--he ascertained in various
+ways, but most decisively by "comparing the duration of irritability in
+a paralysed muscle and in the corresponding healthy one of the opposite
+side, while they are both submitted to the same excitation." He "often
+found in experimenting in that way, that the paralysed muscle remained
+irritable twice, three times, or even four times as long as the healthy
+one." This is a case of induction by the Method of Difference. The two
+limbs, being those of the same animal, were presumed to differ in no
+circumstance material to the case except the paralysis, to the presence
+and absence of which, therefore, the difference in the muscular
+irritability was to be attributed. This assumption of complete
+resemblance in all material circumstances save one, evidently could not
+be safely made in any one pair of experiments, because the two legs of
+any given animal might be accidentally in very different pathological
+conditions; but if, besides taking pains to avoid any such difference,
+the experiment was repeated sufficiently often in different animals to
+exclude the supposition that any abnormal circumstance could be present
+in them all, the conditions of the Method of Difference were adequately
+secured.
+
+In the same manner in which Dr. Brown-S�quard proved that paralysed
+muscles have greater irritability, he also proved the correlative
+proposition respecting cadaveric rigidity and putrefaction. Having, by
+section of the roots of the sciatic nerve, and again of a lateral half
+of the spinal cord, produced paralysis in one hind leg of an animal
+while the other remained healthy, he found that not only did muscular
+irritability last much longer in the paralysed limb, but rigidity set in
+later and ended later, and putrefaction began later and was less rapid
+than on the healthy side. This is a common case of the Method of
+Difference, requiring no comment. A further and very important
+corroboration was obtained by the same method. When the animal was
+killed, not shortly after the section of the nerve, but a month later,
+the effect was reversed; rigidity set in sooner, and lasted a shorter
+time, than in the healthy muscles. But after this lapse of time, the
+paralysed muscles, having been kept by the paralysis in a state of rest,
+had lost a great part of their irritability, and instead of more, had
+become less irritable than those on the healthy side. This gives the A B
+C, a b c, and B C, b c, of the Method of Difference. One antecedent,
+increased irritability, being changed, and the other circumstances being
+the same, the consequence did not follow; and moreover, when a new
+antecedent, contrary to the first, was supplied, it was followed by a
+contrary consequent. This instance is attended with the special
+advantage, of proving that the retardation and prolongation of the
+rigidity do not depend directly on the paralysis, since that was the
+same in both the instances; but specifically on one effect of the
+paralysis, namely, the increased irritability; since they ceased when it
+ceased, and were reversed when it was reversed.
+
+2ndly. Diminution of the temperature of muscles before death increases
+their irritability. But diminution of their temperature also retards
+cadaveric rigidity and putrefaction.
+
+Both these truths were first made known by Dr. Brown-S�quard himself,
+through experiments which conclude according to the Method of
+Difference. There is nothing in the nature of the process requiring
+specific analysis.
+
+3rdly. Muscular exercise, prolonged to exhaustion, diminishes the
+muscular irritability. This is a well-known truth, dependent on the most
+general laws of muscular action, and proved by experiments under the
+Method of Difference, constantly repeated. Now it has been shown by
+observation that overdriven cattle, if killed before recovery from their
+fatigue, become rigid and putrefy in a surprisingly short time. A
+similar fact has been observed in the case of animals hunted to death;
+cocks killed during or shortly after a fight; and soldiers slain in the
+field of battle. These various cases agree in no circumstance, directly
+connected with the muscles, except that these have just been subjected
+to exhausting exercise. Under the canon, therefore, of the Method of
+Agreement, it may be inferred that there is a connexion between the two
+facts. The Method of Agreement, indeed, as has been shown, is not
+competent to prove causation. The present case, however, is already
+known to be a case of causation, it being certain that the state of the
+body after death must somehow depend upon its state at the time of
+death. We are therefore warranted in concluding that the single
+circumstance in which all the instances agree, is the part of the
+antecedent which is the cause of that particular consequent.
+
+4thly. In proportion as the nutrition of muscles is in a good state,
+their irritability is high. This fact also rests on the general evidence
+of the laws of physiology, grounded on many familiar applications of the
+Method of Difference. Now, in the case of those who die from accident or
+violence, with their muscles in a good state of nutrition, the muscular
+irritability continues long after death, rigidity sets in late, and
+persists long without the putrefactive change. On the contrary, in cases
+of disease in which nutrition has been diminished for a long time before
+death, all these effects are reversed. These are the conditions of the
+Joint Method of Agreement and Difference. The cases of retarded and long
+continued rigidity here in question, agree only in being preceded by a
+high state of nutrition of the muscles; the cases of rapid and brief
+rigidity agree only in being preceded by a low state of muscular
+nutrition; a connexion is therefore inductively proved between the
+degree of the nutrition, and the slowness and prolongation of the
+rigidity.
+
+5thly. Convulsions, like exhausting exercise, but in a still greater
+degree, diminish the muscular irritability. Now, when death follows
+violent and prolonged convulsions, as in tetanus, hydrophobia, some
+cases of cholera, and certain poisons, rigidity sets in very rapidly,
+and after a very brief duration, gives place to putrefaction. This is
+another example of the Method of Agreement, of the same character with
+No. 3.
+
+6thly. The series of instances which we shall take last, is of a more
+complex character, and requires a more minute analysis.
+
+It has long been observed that in some cases of death by lightning,
+cadaveric rigidity either does not take place at all, or is of such
+extremely brief duration as to escape notice, and that in these cases
+putrefaction is very rapid. In other cases, however, the usual cadaveric
+rigidity appears. There must be some difference in the cause, to account
+for this difference in the effect. Now "death by lightning may be the
+result of, 1st, a syncope by fright, or in consequence of a direct or
+reflex influence of lightning on the par vagum; 2ndly, hemorrhage in or
+around the brain, or in the lungs, the pericardium, &c.; 3rdly,
+concussion, or some other alteration in the brain;" none of which
+phenomena have any known property capable of accounting for the
+suppression, or almost suppression, of the cadaveric rigidity. But the
+cause of death may also be that the lightning produces "a violent
+convulsion of every muscle in the body," of which, if of sufficient
+intensity, the known effect would be that "muscular irritability ceases
+almost at once." If Dr. Brown-S�quard's generalization is a true law,
+these will be the very cases in which rigidity is so much abridged as to
+escape notice; and the cases in which, on the contrary, rigidity takes
+place as usual, will be those in which the stroke of lightning operates
+in some of the other modes which have been enumerated. How, then, is
+this brought to the test? By experiments not on lightning, which cannot
+be commanded at pleasure, but on the same natural agency in a manageable
+form, that of artificial galvanism. Dr. Brown-S�quard galvanized the
+entire bodies of animals immediately after death. Galvanism cannot
+operate in any of the modes in which the stroke of lightning may have
+operated, except the single one of producing muscular convulsions. If,
+therefore, after the bodies have been galvanized, the duration of
+rigidity is much shortened and putrefaction much accelerated, it is
+reasonable to ascribe the same effects when produced by lightning, to
+the property which galvanism shares with lightning, and not to those
+which it does not. Now this Dr. Brown-S�quard found to be the fact. The
+galvanic experiment was tried with charges of very various degrees of
+strength; and the more powerful the charge, the shorter was found to be
+the duration of rigidity, and the more speedy and rapid the
+putrefaction. In the experiment in which the charge was strongest, and
+the muscular irritability most promptly destroyed, the rigidity only
+lasted fifteen minutes. On the principle, therefore, of the Method of
+Concomitant Variations, it maybe inferred that the duration of the
+rigidity depends on the degree of the irritability; and that if the
+charge had been as much stronger than Dr. Brown-S�quard's strongest, as
+a stroke of lightning must be stronger than any electric shock which we
+can produce artificially, the rigidity would have been shortened in a
+corresponding ratio, and might have disappeared altogether. This
+conclusion having been arrived at, the case of an electric shock,
+whether natural or artificial, becomes an instance in addition to all
+those already ascertained, of correspondence between the irritability of
+the muscle and the duration of rigidity.
+
+All these instances are summed up in the following statement:--"That
+when the degree of muscular irritability at the time of death is
+considerable, either in consequence of a good state of nutrition, as in
+persons who die in full health from an accidental cause, or in
+consequence of rest, as in cases of paralysis, or on account of the
+influence of cold, cadaveric rigidity in all these cases sets in late
+and lasts long, and putrefaction appears late, and progresses slowly:"
+but "that when the degree of muscular irritability at the time of death
+is slight, either in consequence of a bad state of nutrition, or of
+exhaustion from over-exertion, or from convulsions caused by disease or
+poison, cadaveric rigidity sets in and ceases soon, and putrefaction
+appears and progresses quickly." These facts present, in all their
+completeness, the conditions of the Joint Method of Agreement and
+Difference. Early and brief rigidity takes place in cases which agree
+only in the circumstance of a low state of muscular irritability.
+Rigidity begins late and lasts long in cases which agree only in the
+contrary circumstance, of a muscular irritability high and unusually
+prolonged. It follows that there is a connexion through causation
+between the degree of muscular irritability after death, and the
+tardiness and prolongation of the cadaveric rigidity. This
+investigation places in a strong light the value and efficacy of the
+Joint Method. For, as we have already seen, the defect of that Method
+is, that like the Method of Agreement, of which it is only an improved
+form, it cannot prove causation. But in the present case (as in one of
+the steps in the argument which led up to it) causation is already
+proved; since there could never be any doubt that the rigidity
+altogether, and the putrefaction which follows it, are caused by the
+fact of death: the observations and experiments on which this rests are
+too familiar to need analysis, and fall under the Method of Difference.
+It being, therefore, beyond doubt that the aggregate antecedent, the
+death, is the actual cause of the whole train of consequents, whatever
+of the circumstances attending the death can be shown to be followed in
+all its variations by variations in the effect under investigation, must
+be the particular feature of the fact of death on which that effect
+depends. The degree of muscular irritability at the time of death
+fulfils this condition. The only point that could be brought into
+question, would be whether the effect depended on the irritability
+itself, or on something which always accompanied the irritability: and
+this doubt is set at rest by establishing, as the instances do, that by
+whatever cause the high or low irritability is produced, the effect
+equally follows; and cannot, therefore, depend upon the causes of
+irritability, nor upon the other effects of those causes, which are as
+various as the causes themselves; but upon the irritability, solely.
+
+
+� 5. The last two examples will have conveyed to any one by whom they
+have been duly followed, so clear a conception of the use and practical
+management of three of the four methods of experimental inquiry, as to
+supersede the necessity of any further exemplification of them. The
+remaining method, that of Residues, not having found a place in any of
+the preceding investigations, I shall quote from Sir John Herschel some
+examples of that method, with the remarks by which they are introduced.
+
+"It is by this process, in fact, that science, in its present advanced
+state, is chiefly promoted. Most of the phenomena which Nature presents
+are very complicated; and when the effects of all known causes are
+estimated with exactness, and subducted, the residual facts are
+constantly appearing in the form of phenomena altogether new, and
+leading to the most important conclusions.
+
+"For example: the return of the comet predicted by Professor Encke, a
+great many times in succession, and the general good agreement of its
+calculated with its observed place during any one of its periods of
+visibility, would lead us to say that its gravitation towards the sun
+and planets is the sole and sufficient cause of all the phenomena of its
+orbitual motion; but when the effect of this cause is strictly
+calculated and subducted from the observed motion, there is found to
+remain behind a _residual phenomenon_, which would never have been
+otherwise ascertained to exist, which is a small anticipation of the
+time of its reappearance, or a diminution of its periodic time, which
+cannot be accounted for by gravity, and whose cause is therefore to be
+inquired into. Such an anticipation would be caused by the resistance of
+a medium disseminated through the celestial regions; and as there are
+other good reasons for believing this to be a _vera causa_," (an
+actually existing antecedent,) "it has therefore been ascribed to such a
+resistance.[39]
+
+"M. Arago, having suspended a magnetic needle by a silk thread, and set
+it in vibration, observed, that it came much sooner to a state of rest
+when suspended over a plate of copper, than when no such plate was
+beneath it. Now, in both cases there were two _ver� caus�_" (antecedents
+known to exist) "why it _should_ come at length to rest, viz. the
+resistance of the air, which opposes, and at length destroys, all
+motions performed in it; and the want of perfect mobility in the silk
+thread. But the effect of these causes being exactly known by the
+observation made in the absence of the copper, and being thus allowed
+for and subducted, a residual phenomenon appeared, in the fact that a
+retarding influence was exerted by the copper itself; and this fact,
+once ascertained, speedily led to the knowledge of an entirely new and
+unexpected class of relations." This example belongs, however, not to
+the Method of Residues but to the Method of Difference, the law being
+ascertained by a direct comparison of the results of two experiments,
+which differed in nothing but the presence or absence of the plate of
+copper. To have made it exemplify the Method of Residues, the effect of
+the resistance of the air and that of the rigidity of the silk should
+have been calculated _� priori_, from the laws obtained by separate and
+foregone experiments.
+
+"Unexpected and peculiarly striking confirmations of inductive laws
+frequently occur in the form of residual phenomena, in the course of
+investigations of a widely different nature from those which gave rise
+to the inductions themselves. A very elegant example may be cited in the
+unexpected confirmation of the law of the development of heat in elastic
+fluids by compression, which is afforded by the phenomena of sound. The
+inquiry into the cause of sound had led to conclusions respecting its
+mode of propagation, from which its velocity in the air could be
+precisely calculated. The calculations were performed; but, when
+compared with fact, though the agreement was quite sufficient to show
+the general correctness of the cause and mode of propagation assigned,
+yet the _whole_ velocity could not be shown to arise from this theory.
+There was still a residual velocity to be accounted for, which placed
+dynamical philosophers for a long time in great dilemma. At length
+Laplace struck on the happy idea, that this might arise from the _heat_
+developed in the act of that condensation which necessarily takes place
+at every vibration by which sound is conveyed. The matter was subjected
+to exact calculation, and the result was at once the complete
+explanation of the residual phenomenon, and a striking confirmation of
+the general law of the development of heat by compression, under
+circumstances beyond artificial imitation."
+
+"Many of the new elements of chemistry have been detected in the
+investigation of residual phenomena. Thus Arfwedson discovered lithia by
+perceiving an excess of weight in the sulphate produced from a small
+portion of what he considered as magnesia present in a mineral he had
+analysed. It is on this principle, too, that the small concentrated
+residues of great operations in the arts are almost sure to be the
+lurking places of new chemical ingredients: witness iodine, brome,
+selenium, and the new metals accompanying platina in the experiments of
+Wollaston and Tennant. It was a happy thought of Glauber to examine what
+everybody else threw away."[40]
+
+"Almost all the greatest discoveries in Astronomy," says the same
+author,[41] "have resulted from the consideration of residual phenomena
+of a quantitative or numerical kind.... It was thus that the grand
+discovery of the precession of the equinoxes resulted as a residual
+phenomenon, from the imperfect explanation of the return of the seasons
+by the return of the sun to the same apparent place among the fixed
+stars. Thus, also, aberration and nutation resulted as residual
+phenomena from that portion of the changes of the apparent places of the
+fixed stars which was left unaccounted for by precession. And thus again
+the apparent proper motions of the stars are the observed residues of
+their apparent movements outstanding and unaccounted for by strict
+calculation of the effects of precession, nutation, and aberration. The
+nearest approach which human theories can make to perfection is to
+diminish this residue, this _caput mortuum_ of observation, as it may be
+considered, as much as practicable, and, if possible, to reduce it to
+nothing, either by showing that something has been neglected in our
+estimation of known causes, or by reasoning upon it as a new fact, and
+on the principle of the inductive philosophy ascending from the effect
+to its cause or causes."
+
+The disturbing effects mutually produced by the earth and planets upon
+each other's motions were first brought to light as residual phenomena,
+by the difference which appeared between the observed places of those
+bodies, and the places calculated on a consideration solely of their
+gravitation towards the sun. It was this which determined astronomers
+to consider the law of gravitation as obtaining between all bodies
+whatever, and therefore between all particles of matter; their first
+tendency having been to regard it as a force acting only between each
+planet or satellite and the central body to whose system it belonged.
+Again, the catastrophists, in geology, be their opinion right or wrong,
+support it on the plea, that after the effect of all causes now in
+operation has been allowed for, there remains in the existing
+constitution of the earth a large residue of facts, proving the
+existence at former periods either of other forces, or of the same
+forces in a much greater degree of intensity. To add one more example:
+those who assert, what no one has shown any real ground for believing,
+that there is in one human individual, one sex, or one race of mankind
+over another, an inherent and inexplicable superiority in mental
+faculties, could only substantiate their proposition by subtracting from
+the differences of intellect which we in fact see, all that can be
+traced by known laws either to the ascertained differences of physical
+organization, or to the differences which have existed in the outward
+circumstances in which the subjects of the comparison have hitherto been
+placed. What these causes might fail to account for, would constitute a
+residual phenomenon, which and which alone would be evidence of an
+ulterior original distinction, and the measure of its amount. But the
+assertors of such supposed differences have not provided themselves with
+these necessary logical conditions of the establishment of their
+doctrine.
+
+The spirit of the Method of Residues being, it is hoped, sufficiently
+intelligible from these examples, and the other three methods having
+already been so fully exemplified, we may here close our exposition of
+the four methods, considered as employed in the investigation of the
+simpler and more elementary order of the combinations of phenomena.
+
+
+� 6. Dr. Whewell has expressed a very unfavourable opinion of the
+utility of the Four Methods, as well as of the aptness of the examples
+by which I have attempted to illustrate them. His words are these:--[42]
+
+"Upon these methods, the obvious thing to remark is, that they take for
+granted the very thing which is most difficult to discover, the
+reduction of the phenomena to formul� such as are here presented to us.
+When we have any set of complex facts offered to us; for instance, those
+which were offered in the cases of discovery which I have
+mentioned,--the facts of the planetary paths, of falling bodies, of
+refracted rays, of cosmical motions, of chemical analysis; and when, in
+any of these cases, we would discover the law of nature which governs
+them, or, if any one chooses so to term it, the feature in which all the
+cases agree, where are we to look for our A, B, C, and _a_, _b_, _c_?
+Nature does not present to us the cases in this form; and how are we to
+reduce them to this form? You say, _when_ we find the combination of A B
+C with _a b c_ and A B D with _a b d_, then we may draw our inference.
+Granted; but when and where are we to find such combinations? Even now
+that the discoveries are made, who will point out to us what are the A,
+B, C, and _a_, _b_, _c_ elements of the cases which have just been
+enumerated? Who will tell us which of the methods of inquiry those
+historically real and successful inquiries exemplify? Who will carry
+these formul� through the history of the sciences, as they have really
+grown up; and show us that these four methods have been operative in
+their formation; or that any light is thrown upon the steps of their
+progress by reference to these formul�?"
+
+He adds that, in this work, the methods have not been applied "to a
+large body of conspicuous and undoubted examples of discovery, extending
+along the whole history of science;" which ought to have been done in
+order that the methods might be shown to possess the "advantage" (which
+he claims as belonging to his own) of being those "by which all great
+discoveries in science have really been made."--(p. 277.)
+
+There is a striking similarity between the objections here made against
+Canons of Induction, and what was alleged, in the last century, by as
+able men as Dr. Whewell, against the acknowledged Canon of
+Ratiocination. Those who protested against the Aristotelian Logic said
+of the Syllogism, what Dr. Whewell says of the Inductive Methods, that
+it "takes for granted the very thing which is most difficult to
+discover, the reduction of the argument to formul� such as are here
+presented to us." The grand difficulty, they said, is to obtain your
+syllogism, not to judge of its correctness when obtained. On the matter
+of fact, both they and Dr. Whewell are right. The greatest difficulty in
+both cases is first that of obtaining the evidence, and next, of
+reducing it to the form which tests its conclusiveness. But if we try to
+reduce it without knowing _to what_, we are not likely to make much
+progress. It is a more difficult thing to solve a geometrical problem,
+than to judge whether a proposed solution is correct: but if people were
+not able to judge of the solution when found, they would have little
+chance of finding it. And it cannot be pretended that to judge of an
+induction when found, is perfectly easy, is a thing for which aids and
+instruments are superfluous; for erroneous inductions, false inferences
+from experience, are quite as common, on some subjects much commoner,
+than true ones. The business of Inductive Logic is to provide rules and
+models (such as the Syllogism and its rules are for ratiocination) to
+which if inductive arguments conform, those arguments are conclusive,
+and not otherwise. This is what the Four Methods profess to be, and what
+I believe they are universally considered to be by experimental
+philosophers, who had practised all of them long before any one sought
+to reduce the practice to theory.
+
+The assailants of the Syllogism had also anticipated Dr. Whewell in the
+other branch of his argument. They said that no discoveries were ever
+made by syllogism; and Dr. Whewell says, or seems to say, that none were
+ever made by the four Methods of Induction. To the former objectors,
+Archbishop Whately very pertinently answered, that their argument, if
+good at all, was good against the reasoning process altogether; for
+whatever cannot be reduced to syllogism, is not reasoning. And Dr.
+Whewell's argument, if good at all, is good against all inferences from
+experience. In saying that no discoveries were ever made by the four
+Methods, he affirms that none were ever made by observation and
+experiment; for assuredly if any were, it was by processes reducible to
+one or other of those methods.
+
+This difference between us accounts for the dissatisfaction which my
+examples give him; for I did not select them with a view to satisfy any
+one who required to be convinced that observation and experiment are
+modes of acquiring knowledge: I confess that in the choice of them I
+thought only of illustration, and of facilitating the _conception_ of
+the Methods by concrete instances. If it had been my object to justify
+the processes themselves as means of investigation, there would have
+been no need to look far off, or make use of recondite or complicated
+instances. As a specimen of a truth ascertained by the Method of
+Agreement, I might have chosen the proposition "Dogs bark." This dog,
+and that dog, and the other dog, answer to A B C, A D E, A F G. The
+circumstance of being a dog, answers to A. Barking answers to _a_. As a
+truth made known by the Method of Difference, "Fire burns" might have
+sufficed. Before I touch the fire I am not burnt; this is B C; I touch
+it, and am burnt; this is A B C, _a_ B C.
+
+Such familiar experimental processes are not regarded as inductions by
+Dr. Whewell; but they are perfectly homogeneous with those by which,
+even on his own showing, the pyramid of science is supplied with its
+base. In vain he attempts to escape from this conclusion by laying the
+most arbitrary restrictions on the choice of examples admissible as
+instances of Induction: they must neither be such as are still matter of
+discussion (p. 265), nor must any of them be drawn from mental and
+social subjects (p. 269), nor from ordinary observation and practical
+life (pp. 241-247). They must be taken exclusively from the
+generalizations by which scientific thinkers have ascended to great and
+comprehensive laws of natural phenomena. Now it is seldom possible, in
+these complicated inquiries, to go much beyond the initial steps,
+without calling in the instrument of Deduction, and the temporary aid of
+hypotheses; as I myself, in common with Dr. Whewell, have maintained
+against the purely empirical school. Since therefore such cases could
+not conveniently be selected to illustrate the principles of mere
+observation and experiment, Dr. Whewell is misled by their absence into
+representing the Experimental Methods as serving no purpose in
+scientific investigation; forgetting that if those methods had not
+supplied the first generalizations, there would have been no materials
+for his own conception of Induction to work upon.
+
+His challenge, however, to point out which of the four methods are
+exemplified in certain important cases of scientific inquiry, is easily
+answered. "The planetary paths," as far as they are a case of induction
+at all,[43] fall under the Method of Agreement. The law of "falling
+bodies," namely that they describe spaces proportional to the squares of
+the times, was historically a deduction from the first law of motion;
+but the experiments by which it was verified, and by which it might have
+been discovered, were examples of the Method of Agreement; and the
+apparent variation from the true law, caused by the resistance of the
+air, was cleared up by experiments _in vacuo_, constituting an
+application of the Method of Difference. The law of "refracted rays"
+(the constancy of the ratio between the sines of incidence and of
+refraction for each refracting substance) was ascertained by direct
+measurement, and therefore by the Method of Agreement. The "cosmical
+motions" were determined by highly complex processes of thought, in
+which Deduction was predominant, but the Methods of Agreement and of
+Concomitant Variations had a large part in establishing the empirical
+laws. Every case without exception of "chemical analysis" constitutes a
+well-marked example of the Method of Difference. To any one acquainted
+with the subjects--to Dr. Whewell himself, there would not be the
+smallest difficulty in setting out "the A B C and _a b c_ elements" of
+these cases.
+
+If discoveries are ever made by observation and experiment without
+Deduction, the four methods are methods of discovery: but even if they
+were not methods of discovery, it would not be the less true that they
+are the sole methods of Proof; and in that character, even the results
+of deduction are amenable to them. The great generalizations which begin
+as Hypotheses, must end by being proved, and are in reality (as will be
+shown hereafter) proved, by the Four Methods. Now it is with Proof, as
+such, that Logic is principally concerned. This distinction has indeed
+no chance of finding favour with Dr. Whewell; for it is the peculiarity
+of his system, not to recognise, in cases of Induction, any necessity
+for proof. If, after assuming an hypothesis and carefully collating it
+with facts, nothing is brought to light inconsistent with it, that is,
+if experience does not _disprove_ it, he is content: at least until a
+simpler hypothesis, equally consistent with experience, presents itself.
+If this be Induction, doubtless there is no necessity for the four
+methods. But to suppose that it is so, appears to me a radical
+misconception of the nature of the evidence of physical truths.
+
+So real and practical is the need of a test for induction, similar to
+the syllogistic test of ratiocination, that inferences which bid
+defiance to the most elementary notions of inductive logic are put forth
+without misgiving by persons eminent in physical science, as soon as
+they are off the ground on which they are conversant with the facts, and
+not reduced to judge only by the arguments; and as for educated persons
+in general, it may be doubted if they are better judges of a good or a
+bad induction than they were before Bacon wrote. The improvement in the
+results of thinking has seldom extended to the processes; or has
+reached, if any process, that of investigation only, not that of proof.
+A knowledge of many laws of nature has doubtless been arrived at, by
+framing hypotheses and finding that the facts corresponded to them; and
+many errors have been got rid of by coming to a knowledge of facts which
+were inconsistent with them, but not by discovering that the mode of
+thought which led to the errors was itself faulty, and might have been
+known to be such independently of the facts which disproved the
+specific conclusion. Hence it is, that while the thoughts of mankind
+have on many subjects worked themselves practically right, the thinking
+power remains as weak as ever: and on all subjects on which the facts
+which would check the result are not accessible, as in what relates to
+the invisible world, and even, as has been seen lately, to the visible
+world of the planetary regions, men of the greatest scientific
+acquirements argue as pitiably as the merest ignoramus. For though they
+have made many sound inductions, they have not learnt from them (and Dr.
+Whewell thinks there is no necessity that they should learn) the
+principles of inductive _evidence_.
+
+
+
+
+CHAPTER X.
+
+OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS.
+
+
+� 1. In the preceding exposition of the four methods of observation and
+experiment, by which we contrive to distinguish among a mass of
+coexistent phenomena the particular effect due to a given cause, or the
+particular cause which gave birth to a given effect; it has been
+necessary to suppose, in the first instance, for the sake of
+simplification, that this analytical operation is encumbered by no other
+difficulties than what are essentially inherent in its nature; and to
+represent to ourselves, therefore, every effect, on the one hand as
+connected exclusively with a single cause, and on the other hand as
+incapable of being mixed and confounded with any other coexistent
+effect. We have regarded _a b c d e_, the aggregate of the phenomena
+existing at any moment, as consisting of dissimilar facts, _a_, _b_,
+_c_, _d_, and _e_, for each of which one, and only one, cause needs be
+sought; the difficulty being only that of singling out this one cause
+from the multitude of antecedent circumstances, A, B, C, D, and E. The
+cause indeed may not be simple; it may consist of an assemblage of
+conditions; but we have supposed that there was only one possible
+assemblage of conditions, from which the given effect could result.
+
+If such were the fact, it would be comparatively an easy task to
+investigate the laws of nature. But the supposition does not hold, in
+either of its parts. In the first place, it is not true that the same
+phenomenon is always produced by the same cause: the effect _a_ may
+sometimes arise from A, sometimes from B. And, secondly, the effects of
+different causes are often not dissimilar, but homogeneous, and marked
+out by no assignable boundaries from one another: A and B may produce
+not _a_ and _b_, but different portions of an effect _a_. The obscurity
+and difficulty of the investigation of the laws of phenomena is
+singularly increased by the necessity of adverting to these two
+circumstances; Intermixture of Effects, and Plurality of Causes. To the
+latter, being the simpler of the two considerations, we shall first
+direct our attention.
+
+It is not true, then, that one effect must be connected with only one
+cause, or assemblage of conditions; that each phenomenon can be produced
+only in one way. There are often several independent modes in which the
+same phenomenon could have originated. One fact may be the consequent in
+several invariable sequences; it may follow, with equal uniformity, any
+one of several antecedents, or collections of antecedents. Many causes
+may produce motion: many causes may produce some kinds of sensation:
+many causes may produce death. A given effect may really be produced by
+a certain cause, and yet be perfectly capable of being produced without
+it.
+
+
+� 2. One of the principal consequences of this fact of Plurality of
+Causes is, to render the first of the inductive methods, that of
+Agreement, uncertain. To illustrate that method, we supposed two
+instances, A B C followed by _a b c_, and A D E followed by _a d e_.
+From these instances it might apparently be concluded that A is an
+invariable antecedent of _a_, and even that it is the unconditional
+invariable antecedent, or cause, if we could be sure that there is no
+other antecedent common to the two cases. That this difficulty may not
+stand in the way, let us suppose the two cases positively ascertained to
+have no antecedent in common except A. The moment, however, that we let
+in the possibility of a plurality of causes, the conclusion fails. For
+it involves a tacit supposition, that _a_ must have been produced in
+both instances by the same cause. If there can possibly have been two
+causes, those two may, for example, be C and E: the one may have been
+the cause of _a_ in the former of the instances, the other in the
+latter, A having no influence in either case.
+
+Suppose, for example, that two great artists, or great philosophers,
+that two extremely selfish, or extremely generous characters, were
+compared together as to the circumstances of their education and
+history, and the two cases were found to agree only in one circumstance:
+would it follow that this one circumstance was the cause of the quality
+which characterized both those individuals? Not at all; for the causes
+which may produce any type of character are innumerable; and the two
+persons might equally have agreed in their character, though there had
+been no manner of resemblance in their previous history.
+
+This, therefore, is a characteristic imperfection of the Method of
+Agreement; from which imperfection the Method of Difference is free. For
+if we have two instances, A B C and B C, of which B C gives _b c_, and A
+being added converts it into _a b c_, it is certain that in this
+instance at least, A was either the cause of _a_, or an indispensable
+portion of its cause, even though the cause which produces it in other
+instances may be altogether different. Plurality of Causes, therefore,
+not only does not diminish the reliance due to the Method of Difference,
+but does not even render a greater number of observations or experiments
+necessary: two instances, the one positive and the other negative, are
+still sufficient for the most complete and rigorous induction. Not so,
+however, with the Method of Agreement. The conclusions which that
+yields, when the number of instances compared is small, are of no real
+value, except as, in the character of suggestions, they may lead either
+to experiments bringing them to the test of the Method of Difference, or
+to reasonings which may explain and verify them deductively.
+
+It is only when the instances, being indefinitely multiplied and varied,
+continue to suggest the same result, that this result acquires any high
+degree of independent value. If there are but two instances, A B C and A
+D E, though these instances have no antecedent in common except A, yet
+as the effect may possibly have been produced in the two cases by
+different causes, the result is at most only a slight probability in
+favour of A; there may be causation, but it is almost equally probable
+that there was only a coincidence. But the oftener we repeat the
+observation, varying the circumstances, the more we advance towards a
+solution of this doubt. For if we try A F G, A H K, &c., all unlike one
+another except in containing the circumstance A, and if we find the
+effect _a_ entering into the result in all these cases, we must suppose
+one of two things, either that it is caused by A, or that it has as many
+different causes as there are instances. With each addition, therefore,
+to the number of instances, the presumption is strengthened in favour of
+A. The inquirer, of course, will not neglect, if an opportunity present
+itself, to exclude A from some one of these combinations, from A H K for
+instance, and by trying H K separately, appeal to the Method of
+Difference in aid of the Method of Agreement. By the Method of
+Difference alone can it be ascertained that A is the cause of _a_; but
+that it is either the cause, or another effect of the same cause, may be
+placed beyond any reasonable doubt by the Method of Agreement, provided
+the instances are very numerous, as well as sufficiently various.
+
+After how great a multiplication, then, of varied instances, all
+agreeing in no other antecedent except A, is the supposition of a
+plurality of causes sufficiently rebutted, and the conclusion that _a_
+is connected with A divested of the characteristic imperfection, and
+reduced to a virtual certainty? This is a question which we cannot be
+exempted from answering: but the consideration of it belongs to what is
+called the Theory of Probability, which will form the subject of a
+chapter hereafter. It is seen, however, at once, that the conclusion
+does amount to a practical certainty after a sufficient number of
+instances, and that the method, therefore, is not radically vitiated by
+the characteristic imperfection. The result of these considerations is
+only, in the first place, to point out a new source of inferiority in
+the Method of Agreement as compared with other modes of investigation,
+and new reasons for never resting contented with the results obtained by
+it, without attempting to confirm them either by the Method of
+Difference, or by connecting them deductively with some law or laws
+already ascertained by that superior method. And, in the second place,
+we learn from this the true theory of the value of mere _number_ of
+instances in inductive inquiry. The Plurality of Causes is the only
+reason why mere number is of any importance. The tendency of
+unscientific inquirers is to rely too much on number, without analysing
+the instances; without looking closely enough into their nature, to
+ascertain what circumstances are or are not eliminated by means of them.
+Most people hold their conclusions with a degree of assurance
+proportioned to the mere _mass_ of the experience on which they appear
+to rest; not considering that by the addition of instances to instances,
+all of the same kind, that is, differing from one another only in points
+already recognised as immaterial, nothing whatever is added to the
+evidence of the conclusion. A single instance eliminating some
+antecedent which existed in all the other cases, is of more value than
+the greatest multitude of instances which are reckoned by their number
+alone. It is necessary, no doubt, to assure ourselves, by repetition of
+the observation or experiment, that no error has been committed
+concerning the individual facts observed; and until we have assured
+ourselves of this, instead of varying the circumstances, we cannot too
+scrupulously repeat the same experiment or observation without any
+change. But when once this assurance has been obtained, the
+multiplication of instances which do not exclude any more circumstances
+is entirely useless, provided there have been already enough to exclude
+the supposition of Plurality of Causes.
+
+It is of importance to remark, that the peculiar modification of the
+Method of Agreement, which, as partaking in some degree of the nature of
+the Method of Difference, I have called the Joint Method of Agreement
+and Difference, is not affected by the characteristic imperfection now
+pointed out. For, in the joint method, it is supposed not only that the
+instances in which _a_ is, agree only in containing A, but also that the
+instances in which _a_ is not, agree only in not containing A. Now, if
+this be so, A must be not only the cause of _a_, but the only possible
+cause: for if there were another, as for example B, then in the
+instances in which _a_ is not, B must have been absent as well as A, and
+it would not be true that these instances agree _only_ in not containing
+A. This, therefore, constitutes an immense advantage of the joint
+method over the simple Method of Agreement. It may seem, indeed, that
+the advantage does not belong so much to the joint method, as to one of
+its two premises, (if they may be so called,) the negative premise. The
+Method of Agreement, when applied to negative instances, or those in
+which a phenomenon does _not_ take place, is certainly free from the
+characteristic imperfection which affects it in the affirmative case.
+The negative premise, it might therefore be supposed, could be worked as
+a simple case of the Method of Agreement, without requiring an
+affirmative premise to be joined with it. But though this is true in
+principle, it is generally altogether impossible to work the Method of
+Agreement by negative instances without positive ones: it is so much
+more difficult to exhaust the field of negation than that of
+affirmation. For instance, let the question be, what is the cause of the
+transparency of bodies; with what prospect of success could we set
+ourselves to inquire directly in what the multifarious substances which
+are _not_ transparent, agree? But we might hope much sooner to seize
+some point of resemblance among the comparatively few and definite
+species of objects which _are_ transparent; and this being attained, we
+should quite naturally be put upon examining whether the _absence_ of
+this one circumstance be not precisely the point in which all opaque
+substances will be found to resemble.
+
+The Joint Method of Agreement and Difference, therefore, or, as I have
+otherwise called it, the Indirect Method of Difference (because, like
+the Method of Difference properly so called, it proceeds by ascertaining
+how and in what the cases where the phenomenon is present, differ from
+those in which it is absent) is, after the Direct Method of Difference,
+the most powerful of the remaining instruments of inductive
+investigation; and in the sciences which depend on pure observation,
+with little or no aid from experiment, this method, so well exemplified
+in the speculation on the cause of dew, is the primary resource, so far
+as direct appeals to experience are concerned.
+
+
+� 3. We have thus far treated Plurality of Causes only as a possible
+supposition, which, until removed, renders our inductions uncertain; and
+have only considered by what means, where the plurality does not really
+exist, we may be enabled to disprove it. But we must also consider it as
+a case actually occurring in nature, and which, as often as it does
+occur, our methods of induction ought to be capable of ascertaining and
+establishing. For this, however, there is required no peculiar method.
+When an effect is really producible by two or more causes, the process
+for detecting them is in no way different from that by which we discover
+single causes. They may (first) be discovered as separate sequences, by
+separate sets of instances. One set of observations or experiments shows
+that the sun is a cause of heat, another that friction is a source of
+it, another that percussion, another that electricity, another that
+chemical action is such a source. Or (secondly) the plurality may come
+to light in the course of collating a number of instances, when we
+attempt to find some circumstance in which they all agree, and fail in
+doing so. We find it impossible to trace, in all the cases in which the
+effect is met with, any common circumstance. We find that we can
+eliminate _all_ the antecedents; that no one of them is present in all
+the instances, no one of them indispensable to the effect. On closer
+scrutiny, however, it appears that though no one is always present, one
+or other of several always is. If, on further analysis, we can detect in
+these any common element, we may be able to ascend from them to some one
+cause which is the really operative circumstance in them all. Thus it is
+now thought that in the production of heat by friction, percussion,
+chemical action, &c., the ultimate source is one and the same. But if
+(as continually happens) we cannot take this ulterior step, the
+different antecedents must be set down provisionally as distinct causes,
+each sufficient of itself to produce the effect.
+
+We here close our remarks on the Plurality of Causes, and proceed to the
+still more peculiar and more complex case of the Intermixture of
+Effects, and the interference of causes with one another: a case
+constituting the principal part of the complication and difficulty of
+the study of nature; and with which the four only possible methods of
+directly inductive investigation by observation and experiment, are for
+the most part, as will appear presently, quite unequal to cope. The
+instrument of Deduction alone is adequate to unravel the complexities
+proceeding from this source; and the four methods have little more in
+their power than to supply premises for, and a verification of, our
+deductions.
+
+
+� 4. A concurrence of two or more causes, not separately producing each
+its own effect, but interfering with or modifying the effects of one
+another, takes place, as has already been explained, in two different
+ways. In the one, which is exemplified by the joint operation of
+different forces in mechanics, the separate effects of all the causes
+continue to be produced, but are compounded with one another, and
+disappear in one total. In the other, illustrated by the case of
+chemical action, the separate effects cease entirely, and are succeeded
+by phenomena altogether different, and governed by different laws.
+
+Of these cases the former is by far the more frequent, and this case it
+is which, for the most part, eludes the grasp of our experimental
+methods. The other and exceptional case is essentially amenable to them.
+When the laws of the original agents cease entirely, and a phenomenon
+makes its appearance, which, with reference to those laws, is quite
+heterogeneous; when, for example, two gaseous substances, hydrogen and
+oxygen, on being brought together, throw off their peculiar properties,
+and produce the substance called water; in such cases the new fact may
+be subjected to experimental inquiry, like any other phenomenon; and the
+elements which are said to compose it may be considered as the mere
+agents of its production; the conditions on which it depends, the facts
+which make up its cause.
+
+The _effects_ of the new phenomenon, the _properties_ of water, for
+instance, are as easily found by experiment as the effects of any other
+cause. But to discover the _cause_ of it, that is, the particular
+conjunction of agents from which it results, is often difficult enough.
+In the first place, the origin and actual production of the phenomenon
+are most frequently inaccessible to our observation. If we could not
+have learned the composition of water until we found instances in which
+it was actually produced from oxygen and hydrogen, we should have been
+forced to wait until the casual thought struck some one of passing an
+electric spark through a mixture of the two gases, or inserting a
+lighted taper into it, merely to try what would happen. Besides, many
+substances, though they can be analysed, cannot by any known artificial
+means be recompounded. Further, even if we could have ascertained, by
+the Method of Agreement, that oxygen and hydrogen were both present when
+water is produced, no experimentation on oxygen and hydrogen separately,
+no knowledge of their laws, could have enabled us deductively to infer
+that they would produce water. We require a specific experiment on the
+two combined.
+
+Under these difficulties, we should generally have been indebted for our
+knowledge of the causes of this class of effects, not to any inquiry
+directed specifically towards that end, but either to accident, or to
+the gradual progress of experimentation on the different combinations of
+which the producing agents are susceptible; if it were not for a
+peculiarity belonging to effects of this description, that they often,
+under some particular combination of circumstances, reproduce their
+causes. If water results from the juxtaposition of hydrogen and oxygen
+whenever this can be made sufficiently close and intimate, so, on the
+other hand, if water itself be placed in certain situations, hydrogen
+and oxygen are reproduced from it: an abrupt termination is put to the
+new laws, and the agents reappear separately with their own properties
+as at first. What is called chemical analysis is the process of
+searching for the causes of a phenomenon among its effects, or rather
+among the effects produced by the action of some other causes upon it.
+
+Lavoisier, by heating mercury to a high temperature in a close vessel
+containing air, found that the mercury increased in weight, and became
+what was then called red precipitate, while the air, on being examined
+after the experiment, proved to have lost weight, and to have become
+incapable of supporting life or combustion. When red precipitate was
+exposed to a still greater heat, it became mercury again, and gave off a
+gas which did support life and flame. Thus the agents which by their
+combination produced red precipitate, namely the mercury and the gas,
+reappear as effects resulting from that precipitate when acted upon by
+heat. So, if we decompose water by means of iron filings, we produce two
+effects, rust and hydrogen: now rust is already known by experiments
+upon the component substances, to be an effect of the union of iron and
+oxygen: the iron we ourselves supplied, but the oxygen must have been
+produced from the water. The result therefore is that water has
+disappeared, and hydrogen and oxygen have appeared in its stead: or in
+other words, the original laws of these gaseous agents, which had been
+suspended by the superinduction of the new laws called the properties of
+water, have again started into existence, and the causes of water are
+found among its effects.
+
+Where two phenomena, between the laws or properties of which considered
+in themselves no connexion can be traced, are thus reciprocally cause
+and effect, each capable in its turn of being produced from the other,
+and each, when it produces the other, ceasing itself to exist (as water
+is produced from oxygen and hydrogen, and oxygen and hydrogen are
+reproduced from water); this causation of the two phenomena by one
+another, each being generated by the other's destruction, is properly
+transformation. The idea of chemical composition is an idea of
+transformation, but of a transformation which is incomplete; since we
+consider the oxygen and hydrogen to be present in the water _as_ oxygen
+and hydrogen, and capable of being discovered in it if our senses were
+sufficiently keen: a supposition (for it is no more) grounded solely on
+the fact, that the weight of the water is the sum of the separate
+weights of the two ingredients. If there had not been this exception to
+the entire disappearance, in the compound, of the laws of the separate
+ingredients; if the combined agents had not, in this one particular of
+weight, preserved their own laws, and produced a joint result equal to
+the sum of their separate results; we should never, probably, have had
+the notion now implied by the words chemical composition: and, in the
+facts of water produced from hydrogen and oxygen, and hydrogen and
+oxygen produced from water, as the transformation would have been
+complete, we should have seen only a transformation.
+
+The very promising generalization now commonly known as the Conservation
+or Persistence of Force, bears a close resemblance to what the
+conception of chemical composition would become, if divested of the one
+circumstance which now distinguishes it from simple transformation. It
+has long been known that heat is capable of producing electricity, and
+electricity heat; that mechanical motion in numerous cases produces and
+is produced by them both; and so of all other physical forces. It has of
+late become the general belief of scientific inquirers that mechanical
+force, electricity, magnetism, heat, light, and chemical action (to
+which has subsequently been added vital action) are not so much causes
+of one another as convertible into one another; and they are now
+generally spoken of as forms of one and the same force, varying only in
+its manifestations. This doctrine may be admitted, without by any means
+implying that Force is a real entity, a Thing in itself, distinct from
+all its phenomenal manifestations to our organs. Supposing the doctrine
+true, the several kinds of phenomena which it identifies in respect of
+their origin would nevertheless remain different facts; facts which
+would be causes of one another--reciprocally causes and effects, which
+is the first element in the form of causation properly called
+transformation. What the doctrine contains more than this, is, that in
+each of these cases of reciprocal causation, the causes are reproduced
+without alteration in quantity. This is what takes place in the
+transformations of matter: when water has been converted into hydrogen
+and oxygen, these can be reconverted into precisely the same quantity of
+water from which they were produced. To establish a corresponding law in
+regard to Force, it has to be proved that heat is capable of being
+converted into electricity, electricity into chemical action, chemical
+action into mechanical force, and mechanical force back again into the
+exact quantity of heat which was originally expended; and so through
+all the interchanges. Were this proved, it would establish what
+constitutes transformation, as distinguished from the simple fact of
+reciprocal causation. The fact in issue is simply the quantitative
+equivalence of all these natural agencies; whereby a given quantity of
+any one is convertible into, and interchangeable with, a given, and
+always the same, quantity of any other: this, no less, but also no more.
+It cannot yet be said that the law has been fully proved of any case,
+except that of interchange between heat and mechanical motion. It does
+seem to be ascertained, not only that these two are convertible into
+each other, but that after any number of conversions the original
+quantities reappear without addition or diminution, like the original
+quantities of hydrogen and oxygen after passing through the condition of
+water. If the same thing comes to be proved true of all the other
+forces, in relation to these two and to one another, the law of
+Conservation will be established; and it will be a legitimate mode of
+expressing the fact, to speak of Force, as we already speak of Matter,
+as indestructible. But Force will not the less remain, to the
+philosopher, a mere abstraction of the mind. All that will have been
+proved is, that in the phenomena of Nature, nothing actually ceases
+without generating a calculable, and always the same, quantity of some
+other natural phenomenon, which again, when it ceases, will in its turn
+either generate a calculable, and always the same, quantity of some
+third phenomenon, or reproduce the original quantity of the first.
+
+In these cases, where the heteropathic effect (as we called it in a
+former chapter)[44] is but a transformation of its cause, or in other
+words, where the effect and its cause are reciprocally such, and
+mutually convertible into each other; the problem of finding the cause
+resolves itself into the far easier one of finding an effect, which is
+the kind of inquiry that admits of being prosecuted by direct
+experiment. But there are other cases of heteropathic effects to which
+this mode of investigation is not applicable. Take, for instance, the
+heteropathic laws of mind; that portion of the phenomena of our mental
+nature which are analogous to chemical rather than to dynamical
+phenomena; as when a complex passion is formed by the coalition of
+several elementary impulses, or a complex emotion by several simple
+pleasures or pains, of which it is the result without being the
+aggregate, or in any respect homogeneous with them. The product, in
+these cases, is generated by its various factors; but the factors cannot
+be reproduced from the product; just as a youth can grow into an old
+man, but an old man cannot grow into a youth. We cannot ascertain from
+what simple feelings any of our complex states of mind are generated, as
+we ascertain the ingredients of a chemical compound, by making it, in
+its turn, generate them. We can only, therefore, discover these laws by
+the slow process of studying the simple feelings themselves, and
+ascertaining synthetically, by experimenting on the various combinations
+of which they are susceptible, what they, by their mutual action upon
+one another, are capable of generating.
+
+
+� 5. It might have been supposed that the other, and apparently simpler
+variety of the mutual interference of causes, where each cause continues
+to produce its own proper effect according to the same laws to which it
+conforms in its separate state, would have presented fewer difficulties
+to the inductive inquirer than that of which we have just finished the
+consideration. It presents, however, so far as direct induction apart
+from deduction is concerned, infinitely greater difficulties. When a
+concurrence of causes gives rise to a new effect, bearing no relation to
+the separate effects of those causes, the resulting phenomenon stands
+forth undisguised, inviting attention to its peculiarity, and presenting
+no obstacle to our recognising its presence or absence among any number
+of surrounding phenomena. It admits therefore of being easily brought
+under the canons of Induction, provided instances can be obtained such
+as those canons require: and the non-occurrence of such instances, or
+the want of means to produce them artificially, is the real and only
+difficulty in such investigations; a difficulty not logical, but in some
+sort physical. It is otherwise with cases of what, in a preceding
+chapter, has been denominated the Composition of Causes. There, the
+effects of the separate causes do not terminate and give place to
+others, thereby ceasing to form any part of the phenomenon to be
+investigated; on the contrary, they still take place, but are
+intermingled with, and disguised by, the homogeneous and closely allied
+effects of other causes. They are no longer _a_, _b_, _c_, _d_, _e_,
+existing side by side, and continuing to be separately discernible; they
+are + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of which cancel one
+another, while many others do not appear distinguishably, but merge in
+one sum: forming altogether a result, between which and the causes
+whereby it was produced there is often an insurmountable difficulty in
+tracing by observation any fixed relation whatever.
+
+The general idea of the Composition of Causes has been seen to be, that
+though two or more laws interfere with one another, and apparently
+frustrate or modify one another's operation, yet in reality all are
+fulfilled, the collective effect being the exact sum of the effects of
+the causes taken separately. A familiar instance is that of a body kept
+in equilibrium by two equal and contrary forces. One of the forces if
+acting alone would carry the body in a given time a certain distance to
+the west, the other if acting alone would carry it exactly as far
+towards the east; and the result is the same as if it had been first
+carried to the west as far as the one force would carry it, and then
+back towards the east as far as the other would carry it, that is,
+precisely the same distance; being ultimately left where it was found at
+first.
+
+All laws of causation are liable to be in this manner counteracted, and
+seemingly frustrated, by coming into conflict with other laws, the
+separate result of which is opposite to theirs, or more or less
+inconsistent with it. And hence, with almost every law, many instances
+in which it really is entirely fulfilled, do not, at first sight, appear
+to be cases of its operation at all. It is so in the example just
+adduced: a force, in mechanics, means neither more nor less than a cause
+of motion, yet the sum of the effects of two causes of motion may be
+rest. Again, a body solicited by two forces in directions making an
+angle with one another, moves in the diagonal; and it seems a paradox to
+say that motion in the diagonal is the sum of two motions in two other
+lines. Motion, however, is but change of place, and at every instant the
+body is in the exact place it would have been in if the forces had acted
+during alternate instants instead of acting in the same instant; (saving
+that if we suppose two forces to act successively which are in truth
+simultaneous, we must of course allow them double the time.) It is
+evident, therefore, that each force has had, during each instant, all
+the effect which belonged to it; and that the modifying influence which
+one of two concurrent causes is said to exercise with respect to the
+other, may be considered as exerted not over the action of the cause
+itself, but over the effect after it is completed. For all purposes of
+predicting, calculating, or explaining their joint result, causes which
+compound their effects may be treated as if they produced simultaneously
+each of them its own effect, and all these effects coexisted visibly.
+
+Since the laws of causes are as really fulfilled when the causes are
+said to be counteracted by opposing causes, as when they are left to
+their own undisturbed action, we must be cautious not to express the
+laws in such terms as would render the assertion of their being
+fulfilled in those cases a contradiction. If, for instance, it were
+stated as a law of nature that a body to which a force is applied moves
+in the direction of the force, with a velocity proportioned to the force
+directly, and to its own mass inversely; when in point of fact some
+bodies to which a force is applied do not move at all, and those which
+do move (at least in the region of our earth) are, from the very first,
+retarded by the action of gravity and other resisting forces, and at
+last stopped altogether; it is clear that the general proposition,
+though it would be true under a certain hypothesis, would not express
+the facts as they actually occur. To accommodate the expression of the
+law to the real phenomena, we must say, not that the object moves, but
+that it _tends_ to move, in the direction and with the velocity
+specified. We might, indeed, guard our expression in a different mode,
+by saying that the body moves in that manner unless prevented, or except
+in so far as prevented, by some counteracting cause. But the body does
+not only move in that manner unless counteracted; it _tends_ to move in
+that manner even when counteracted; it still exerts, in the original
+direction, the same energy of movement as if its first impulse had been
+undisturbed, and produces, by that energy, an exactly equivalent
+quantity of effect. This is true even when the force leaves the body as
+it found it, in a state of absolute rest; as when we attempt to raise a
+body of three tons weight with a force equal to one ton. For if, while
+we are applying this force, wind or water or any other agent supplies an
+additional force just exceeding two tons, the body will be raised; thus
+proving that the force we applied exerted its full effect, by
+neutralizing an equivalent portion of the weight which it was
+insufficient altogether to overcome. And if while we are exerting this
+force of one ton upon the object in a direction contrary to that of
+gravity, it be put into a scale and weighed, it will be found to have
+lost a ton of its weight, or in other words, to press downwards with a
+force only equal to the difference of the two forces.
+
+These facts are correctly indicated by the expression _tendency_. All
+laws of causation, in consequence of their liability to be counteracted,
+require to be stated in words affirmative of tendencies only, and not of
+actual results. In those sciences of causation which have an accurate
+nomenclature, there are special words which signify a tendency to the
+particular effect with which the science is conversant; thus _pressure_,
+in mechanics, is synonymous with tendency to motion, and forces are not
+reasoned on as causing actual motion, but as exerting pressure. A
+similar improvement in terminology would be very salutary in many other
+branches of science.
+
+The habit of neglecting this necessary element in the precise expression
+of the laws of nature, has given birth to the popular prejudice that all
+general truths have exceptions; and much unmerited distrust has thence
+accrued to the conclusions of science, when they have been submitted to
+the judgment of minds insufficiently disciplined and cultivated. The
+rough generalizations suggested by common observation usually have
+exceptions; but principles of science, or in other words, laws of
+causation, have not. "What is thought to be an exception to a
+principle," (to quote words used on a different occasion,) "is always
+some other and distinct principle cutting into the former; some other
+force which impinges[45] against the first force, and deflects it from
+its direction. There are not a law and an exception to that law, the law
+acting in ninety-nine cases, and the exception in one. There are two
+laws, each possibly acting in the whole hundred cases, and bringing
+about a common effect by their conjunct operation. If the force which,
+being the less conspicuous of the two, is called the _disturbing_ force,
+prevails sufficiently over the other force in some one case, to
+constitute that case what is commonly called an exception, the same
+disturbing force probably acts as a modifying cause in many other cases
+which no one will call exceptions.
+
+"Thus if it were stated to be a law of nature that all heavy bodies fall
+to the ground, it would probably be said that the resistance of the
+atmosphere, which prevents a balloon from falling, constitutes the
+balloon an exception to that pretended law of nature. But the real law
+is, that all heavy bodies _tend_ to fall; and to this there is no
+exception, not even the sun and moon; for even they, as every astronomer
+knows, tend towards the earth, with a force exactly equal to that with
+which the earth tends towards them. The resistance of the atmosphere
+might, in the particular case of the balloon, from a misapprehension of
+what the law of gravitation is, be said to _prevail over_ the law; but
+its disturbing effect is quite as real in every other case, since though
+it does not prevent, it retards the fall of all bodies whatever. The
+rule, and the so-called exception, do not divide the cases between them;
+each of them is a comprehensive rule extending to all cases. To call one
+of these concurrent principles an exception to the other, is
+superficial, and contrary to the correct principles of nomenclature and
+arrangement. An effect of precisely the same kind, and arising from the
+same cause, ought not to be placed in two different categories, merely
+as there does or does not exist another cause preponderating over
+it."[46]
+
+
+� 6. We have now to consider according to what method these complex
+effects, compounded of the effects of many causes, are to be studied;
+how we are enabled to trace each effect to the concurrence of causes in
+which it originated, and ascertain the conditions of its recurrence--the
+circumstances in which it may be expected again to occur. The conditions
+of a phenomenon which arises from a composition of causes, may be
+investigated either deductively or experimentally.
+
+The case, it is evident, is naturally susceptible of the deductive mode
+of investigation. The law of an effect of this description is a result
+of the laws of the separate causes on the combination of which it
+depends, and is therefore in itself capable of being deduced from these
+laws. This is called the method _� priori_. The other, or _� posteriori_
+method, professes to proceed according to the canons of experimental
+inquiry. Considering the whole assemblage of concurrent causes which
+produced the phenomenon, as one single cause, it attempts to ascertain
+the cause in the ordinary manner, by a comparison of instances. This
+second method subdivides itself into two different varieties. If it
+merely collates instances of the effect, it is a method of pure
+observation. If it operates upon the causes, and tries different
+combinations of them, in hopes of ultimately hitting the precise
+combination which will produce the given total effect, it is a method of
+experiment.
+
+In order more completely to clear up the nature of each of these three
+methods, and determine which of them deserves the preference, it will be
+expedient (conformably to a favourite maxim of Lord Chancellor Eldon, to
+which, though it has often incurred philosophical ridicule, a deeper
+philosophy will not refuse its sanction) to "clothe them in
+circumstances." We shall select for this purpose a case which as yet
+furnishes no very brilliant example of the success of any of the three
+methods, but which is all the more suited to illustrate the difficulties
+inherent in them. Let the subject of inquiry be, the conditions of
+health and disease in the human body; or (for greater simplicity) the
+conditions of recovery from a given disease; and in order to narrow the
+question still more, let it be limited, in the first instance, to this
+one inquiry: Is, or is not some particular medicament (mercury, for
+instance) a remedy for the given disease.
+
+Now, the deductive method would set out from known properties of
+mercury, and known laws of the human body, and by reasoning from these,
+would attempt to discover whether mercury will act upon the body when in
+the morbid condition supposed, in such a manner as to restore health.
+The experimental method would simply administer mercury in as many cases
+as possible, noting the age, sex, temperament, and other peculiarities
+of bodily constitution, the particular form or variety of the disease,
+the particular stage of its progress, &c., remarking in which of these
+cases it produced a salutary effect, and with what circumstances it was
+on those occasions combined. The method of simple observation would
+compare instances of recovery, to find whether they agreed in having
+been preceded by the administration of mercury; or would compare
+instances of recovery with instances of failure, to find cases which,
+agreeing in all other respects, differed only in the fact that mercury
+had been administered, or that it had not.
+
+
+� 7. That the last of these three modes of investigation is applicable
+to the case, no one has ever seriously contended. No conclusions of
+value on a subject of such intricacy, ever were obtained in that way.
+The utmost that could result would be a vague general impression for or
+against the efficacy of mercury, of no avail for guidance unless
+confirmed by one of the other two methods. Not that the results, which
+this method strives to obtain, would not be of the utmost possible value
+if they could be obtained. If all the cases of recovery which presented
+themselves, in an examination extending to a great number of instances,
+were cases in which mercury had been administered, we might generalize
+with confidence from this experience, and should have obtained a
+conclusion of real value. But no such basis for generalization can we,
+in a case of this description, hope to obtain. The reason is that which
+we have spoken of as constituting the characteristic imperfection of the
+Method of Agreement; Plurality of Causes. Supposing even that mercury
+does tend to cure the disease, so many other causes, both natural and
+artificial, also tend to cure it, that there are sure to be abundant
+instances of recovery in which mercury has not been administered:
+unless, indeed, the practice be to administer it in all cases; on which
+supposition it will equally be found in the cases of failure.
+
+When an effect results from the union of many causes, the share which
+each has in the determination of the effect cannot in general be great:
+and the effect is not likely, even in its presence or absence, still
+less in its variations, to follow, even approximately, any one of the
+causes. Recovery from a disease is an event to which, in every case,
+many influences must concur. Mercury may be one such influence; but from
+the very fact that there are many other such, it will necessarily happen
+that although mercury is administered, the patient, for want of other
+concurring influences, will often not recover, and that he often will
+recover when it is not administered, the other favourable influences
+being sufficiently powerful without it. Neither, therefore, will the
+instances of recovery agree in the administration of mercury, nor will
+the instances of failure agree in its non-administration. It is much if,
+by multiplied and accurate returns from hospitals and the like, we can
+collect that there are rather more recoveries and rather fewer failures
+when mercury is administered than when it is not; a result of very
+secondary value even as a guide to practice, and almost worthless as a
+contribution to the theory of the subject.
+
+
+� 8. The inapplicability of the method of simple observation to
+ascertain the conditions of effects dependent on many concurring
+causes, being thus recognised; we shall next inquire whether any greater
+benefit can be expected from the other branch of the _� posteriori_
+method, that which proceeds by directly trying different combinations of
+causes, either artificially produced or found in nature, and taking
+notice what is their effect: as, for example, by actually trying the
+effect of mercury, in as many different circumstances as possible. This
+method differs from the one which we have just examined, in turning our
+attention directly to the causes or agents, instead of turning it to the
+effect, recovery from the disease. And since, as a general rule, the
+effects of causes are far more accessible to our study than the causes
+of effects, it is natural to think that this method has a much better
+chance of proving successful than the former.
+
+The method now under consideration is called the Empirical Method; and
+in order to estimate it fairly, we must suppose it to be completely, not
+incompletely, empirical. We must exclude from it everything which
+partakes of the nature not of an experimental but of a deductive
+operation. If for instance we try experiments with mercury upon a person
+in health, in order to ascertain the general laws of its action upon the
+human body, and then reason from these laws to determine how it will act
+upon persons affected with a particular disease, this may be a really
+effectual method, but this is deduction. The experimental method does
+not derive the law of a complex case from the simpler laws which
+conspire to produce it, but makes its experiments directly upon the
+complex case. We must make entire abstraction of all knowledge of the
+simpler tendencies, the _modi operandi_ of mercury in detail. Our
+experimentation must aim at obtaining a direct answer to the specific
+question, Does or does not mercury tend to cure the particular disease?
+
+Let us see, therefore, how far the case admits of the observance of
+those rules of experimentation, which it is found necessary to observe
+in other cases. When we devise an experiment to ascertain the effect of
+a given agent, there are certain precautions which we never, if we can
+help it, omit. In the first place, we introduce the agent into the midst
+of a set of circumstances which we have exactly ascertained. It needs
+hardly be remarked how far this condition is from being realized in any
+case connected with the phenomena of life; how far we are from knowing
+what are all the circumstances which pre-exist in any instance in which
+mercury is administered to a living being. This difficulty, however,
+though insuperable in most cases, may not be so in all; there are
+sometimes concurrences of many causes, in which we yet know accurately
+what the causes are. Moreover, the difficulty may be attenuated by
+sufficient multiplication of experiments, in circumstances rendering it
+improbable that any of the unknown causes should exist in them all. But
+when we have got clear of this obstacle, we encounter another still more
+serious. In other cases, when we intend to try an experiment, we do not
+reckon it enough that there be no circumstance in the case the presence
+of which is unknown to us. We require also that none of the
+circumstances which we do know, shall have effects susceptible of being
+confounded with those of the agent whose properties we wish to study. We
+take the utmost pains to exclude all causes capable of composition with
+the given cause; or if forced to let in any such causes, we take care to
+make them such that we can compute and allow for their influence, so
+that the effect of the given cause may, after the subduction of those
+other effects, be apparent as a residual phenomenon.
+
+These precautions are inapplicable to such cases as we are now
+considering. The mercury of our experiment being tried with an unknown
+multitude (or even let it be a known multitude) of other influencing
+circumstances, the mere fact of their being influencing circumstances
+implies that they disguise the effect of the mercury, and preclude us
+from knowing whether it has any effect or not. Unless we already knew
+what and how much is owing to every other circumstance, (that is, unless
+we suppose the very problem solved which we are considering the means of
+solving,) we cannot tell that those other circumstances may not have
+produced the whole of the effect, independently or even in spite of the
+mercury. The Method of Difference, in the ordinary mode of its use,
+namely by comparing the state of things following the experiment with
+the state which preceded it, is thus, in the case of intermixture of
+effects, entirely unavailing; because other causes than that whose
+effect we are seeking to determine, have been operating during the
+transition. As for the other mode of employing the Method of Difference,
+namely by comparing, not the same case at two different periods, but
+different cases, this in the present instance is quite chimerical. In
+phenomena so complicated it is questionable if two cases, similar in all
+respects but one, ever occurred; and were they to occur, we could not
+possibly know that they were so exactly similar.
+
+Anything like a scientific use of the method of experiment, in these
+complicated cases, is therefore out of the question. We can in the most
+favourable cases only discover, by a succession of trials, that a
+certain cause is _very often_ followed by a certain effect. For, in one
+of these conjunct effects, the portion which is determined by any one of
+the influencing agents, is generally, as we before remarked, but small;
+and it must be a more potent cause than most, if even the tendency which
+it really exerts is not thwarted by other tendencies in nearly as many
+cases as it is fulfilled.
+
+If so little can be done by the experimental method to determine the
+conditions of an effect of many combined causes, in the case of medical
+science; still less is this method applicable to a class of phenomena
+more complicated than even those of physiology, the phenomena of
+politics and history. There, Plurality of Causes exists in almost
+boundless excess, and effects are, for the most part, inextricably
+interwoven with one another. To add to the embarrassment, most of the
+inquiries in political science relate to the production of effects of a
+most comprehensive description, such as the public wealth, public
+security, public morality, and the like: results liable to be affected
+directly or indirectly either in _plus_ or in _minus_ by nearly every
+fact which exists, or event which occurs, in human society. The vulgar
+notion, that the safe methods on political subjects are those of
+Baconian induction--that the true guide is not general reasoning, but
+specific experience--will one day be quoted as among the most
+unequivocal marks of a low state of the speculative faculties in any
+age in which it is accredited. Nothing can be more ludicrous than the
+sort of parodies on experimental reasoning which one is accustomed to
+meet with, not in popular discussion only, but in grave treatises, when
+the affairs of nations are the theme. "How," it is asked, "can an
+institution be bad, when the country has prospered under it?" "How can
+such or such causes have contributed to the prosperity of one country,
+when another has prospered without them?" Whoever makes use of an
+argument of this kind, not intending to deceive, should be sent back to
+learn the elements of some one of the more easy physical sciences. Such
+reasoners ignore the fact of Plurality of Causes in the very case which
+affords the most signal example of it. So little could be concluded, in
+such a case, from any possible collation of individual instances, that
+even the impossibility, in social phenomena, of making artificial
+experiments, a circumstance otherwise so prejudicial to directly
+inductive inquiry, hardly affords, in this case, additional reason of
+regret. For even if we could try experiments upon a nation or upon the
+human race, with as little scruple as M. Magendie tried them on dogs and
+rabbits, we should never succeed in making two instances identical in
+every respect except the presence or absence of some one definite
+circumstance. The nearest approach to an experiment in the philosophical
+sense, which takes place in politics, is the introduction of a new
+operative element into national affairs by some special and assignable
+measure of government, such as the enactment or repeal of a particular
+law. But where there are so many influences at work, it requires some
+time for the influence of any new cause upon national phenomena to
+become apparent; and as the causes operating in so extensive a sphere
+are not only infinitely numerous, but in a state of perpetual
+alteration, it is always certain that before the effect of the new cause
+becomes conspicuous enough to be a subject of induction, so many of the
+other influencing circumstances will have changed as to vitiate the
+experiment.
+
+Two, therefore, of the three possible methods for the study of phenomena
+resulting from the composition of many causes, being, from the very
+nature of the case, inefficient and illusory, there remains only the
+third,--that which considers the causes separately, and infers the
+effect from the balance of the different tendencies which produce it: in
+short, the deductive, or _� priori_ method. The more particular
+consideration of this intellectual process requires a chapter to itself.
+
+
+
+
+CHAPTER XI.
+
+OF THE DEDUCTIVE METHOD.
+
+
+� 1. The mode of investigation which, from the proved inapplicability of
+direct methods of observation and experiment, remains to us as the main
+source of the knowledge we possess or can acquire respecting the
+conditions, and laws of recurrence, of the more complex phenomena, is
+called, in its most general expression, the Deductive Method; and
+consists of three operations: the first, one of direct induction; the
+second, of ratiocination; the third, of verification.
+
+I call the first step in the process an inductive operation, because
+there must be a direct induction as the basis of the whole; though in
+many particular investigations the place of the induction may be
+supplied by a prior deduction; but the premises of this prior deduction
+must have been derived from induction.
+
+The problem of the Deductive Method is, to find the law of an effect,
+from the laws of the different tendencies of which it is the joint
+result. The first requisite, therefore, is to know the laws of those
+tendencies; the law of each of the concurrent causes: and this supposes
+a previous process of observation or experiment upon each cause
+separately; or else a previous deduction, which also must depend for its
+ultimate premises on observation or experiment. Thus, if the subject be
+social or historical phenomena, the premises of the Deductive Method
+must be the laws of the causes which determine that class of phenomena;
+and those causes are human actions, together with the general outward
+circumstances under the influence of which mankind are placed, and which
+constitute man's position on the earth. The Deductive Method, applied to
+social phenomena, must begin, therefore, by investigating, or must
+suppose to have been already investigated, the laws of human action,
+and those properties of outward things by which the actions of human
+beings in society are determined. Some of these general truths will
+naturally be obtained by observation and experiment, others by
+deduction: the more complex laws of human action, for example, may be
+deduced from the simpler ones; but the simple or elementary laws will
+always, and necessarily, have been obtained by a directly inductive
+process.
+
+To ascertain, then, the laws of each separate cause which takes a share
+in producing the effect, is the first desideratum of the Deductive
+Method. To know what the causes are, which must be subjected to this
+process of study, may or may not be difficult. In the case last
+mentioned, this first condition is of easy fulfilment. That social
+phenomena depend on the acts and mental impressions of human beings,
+never could have been a matter of any doubt, however imperfectly it may
+have been known either by what laws those impressions and actions are
+governed, or to what social consequences their laws naturally lead.
+Neither, again, after physical science had attained a certain
+development, could there be any real doubt where to look for the laws on
+which the phenomena of life depend, since they must be the mechanical
+and chemical laws of the solid and fluid substances composing the
+organized body and the medium in which it subsists, together with the
+peculiar vital laws of the different tissues constituting the organic
+structure. In other cases, really far more simple than these, it was
+much less obvious in what quarter the causes were to be looked for: as
+in the case of the celestial phenomena. Until, by combining the laws of
+certain causes, it was found that those laws explained all the facts
+which experience had proved concerning the heavenly motions, and led to
+predictions which it always verified, mankind never knew that those
+_were_ the causes. But whether we are able to put the question before,
+or not until after, we have become capable of answering it, in either
+case it must be answered; the laws of the different causes must be
+ascertained, before we can proceed to deduce from them the conditions of
+the effect.
+
+The mode of ascertaining those laws neither is, nor can be, any other
+than the fourfold method of experimental inquiry, already discussed. A
+few remarks on the application of that method to cases of the
+Composition of Causes, are all that is requisite.
+
+It is obvious that we cannot expect to find the law of a tendency, by an
+induction from cases in which the tendency is counteracted. The laws of
+motion could never have been brought to light from the observation of
+bodies kept at rest by the equilibrium of opposing forces. Even where
+the tendency is not, in the ordinary sense of the word, counteracted,
+but only modified, by having its effects compounded with the effects
+arising from some other tendency or tendencies, we are still in an
+unfavourable position for tracing, by means of such cases, the law of
+the tendency itself. It would have been scarcely possible to discover
+the law that every body in motion tends to continue moving in a straight
+line, by an induction from instances in which the motion is deflected
+into a curve, by being compounded with the effect of an accelerating
+force. Notwithstanding the resources afforded in this description of
+cases by the Method of Concomitant Variations, the principles of a
+judicious experimentation prescribe that the law of each of the
+tendencies should be studied, if possible, in cases in which that
+tendency operates alone, or in combination with no agencies but those of
+which the effect can, from previous knowledge, be calculated and allowed
+for.
+
+Accordingly, in the cases, unfortunately very numerous and important, in
+which the causes do not suffer themselves to be separated and observed
+apart, there is much difficulty in laying down with due certainty the
+inductive foundation necessary to support the deductive method. This
+difficulty is most of all conspicuous in the case of physiological
+phenomena; it being seldom possible to separate the different agencies
+which collectively compose an organized body, without destroying the
+very phenomena which it is our object to investigate:
+
+    --following life, in creatures we dissect,
+    We lose it, in the moment we detect.
+
+And for this reason I am inclined to the opinion, that physiology
+(greatly and rapidly progressive as it now is) is embarrassed by
+greater natural difficulties, and is probably susceptible of a less
+degree of ultimate perfection, than even the social science; inasmuch as
+it is possible to study the laws and operations of one human mind apart
+from other minds, much less imperfectly than we can study the laws of
+one organ or tissue of the human body apart from the other organs or
+tissues.
+
+It has been judiciously remarked that pathological facts, or, to speak
+in common language, diseases in their different forms and degrees,
+afford in the case of physiological investigation the most valuable
+equivalent to experimentation properly so called; inasmuch as they often
+exhibit to us a definite disturbance in some one organ or organic
+function, the remaining organs and functions being, in the first
+instance at least, unaffected. It is true that from the perpetual
+actions and reactions which are going on among all parts of the organic
+economy, there can be no prolonged disturbance in any one function
+without ultimately involving many of the others; and when once it has
+done so, the experiment for the most part loses its scientific value.
+All depends on observing the early stages of the derangement; which,
+unfortunately, are of necessity the least marked. If, however, the
+organs and functions not disturbed in the first instance, become
+affected in a fixed order of succession, some light is thereby thrown
+upon the action which one organ exercises over another: and we
+occasionally obtain a series of effects which we can refer with some
+confidence to the original local derangement; but for this it is
+necessary that we should know that the original derangement _was_ local.
+If it was what is termed constitutional, that is, if we do not know in
+what part of the animal economy it took its rise, or the precise nature
+of the disturbance which took place in that part, we are unable to
+determine which of the various derangements was cause and which effect;
+which of them were produced by one another, and which by the direct,
+though perhaps tardy, action of the original cause.
+
+Besides natural pathological facts, we can produce pathological facts
+artificially; we can try experiments, even in the popular sense of the
+term, by subjecting the living being to some external agent, such as the
+mercury of our former example, or the section of a nerve to ascertain
+the functions of different parts of the nervous system. As this
+experimentation is not intended to obtain a direct solution of any
+practical question, but to discover general laws, from which afterwards
+the conditions of any particular effect may be obtained by deduction;
+the best cases to select are those of which the circumstances can be
+best ascertained: and such are generally not those in which there is any
+practical object in view. The experiments are best tried, not in a state
+of disease, which is essentially a changeable state, but in the
+condition of health, comparatively a fixed state. In the one, unusual
+agencies are at work, the results of which we have no means of
+predicting; in the other, the course of the accustomed physiological
+phenomena would, it may generally be presumed, remain undisturbed, were
+it not for the disturbing cause which we introduce.
+
+Such, with the occasional aid of the Method of Concomitant Variations,
+(the latter not less incumbered than the more elementary methods by the
+peculiar difficulties of the subject,) are our inductive resources for
+ascertaining the laws of the causes considered separately, when we have
+it not in our power to make trial of them in a state of actual
+separation. The insufficiency of these resources is so glaring, that no
+one can be surprised at the backward state of the science of physiology;
+in which indeed our knowledge of causes is so imperfect, that we can
+neither explain, nor could without specific experience have predicted,
+many of the facts which are certified to us by the most ordinary
+observation. Fortunately, we are much better informed as to the
+empirical laws of the phenomena, that is, the uniformities respecting
+which we cannot yet decide whether they are cases of causation, or mere
+results of it. Not only has the order in which the facts of organization
+and life successively manifest themselves, from the first germ of
+existence to death, been found to be uniform, and very accurately
+ascertainable; but, by a great application of the Method of Concomitant
+Variations to the entire facts of comparative anatomy and physiology,
+the characteristic organic structure corresponding to each class of
+functions has been determined with considerable precision. Whether these
+organic conditions are the whole of the conditions, and in many cases
+whether they are conditions at all, or mere collateral effects of some
+common cause, we are quite ignorant: nor are we ever likely to know,
+unless we could construct an organized body, and try whether it would
+live.
+
+Under such disadvantages do we, in cases of this description, attempt
+the initial, or inductive step, in the application of the Deductive
+Method to complex phenomena. But such, fortunately, is not the common
+case. In general, the laws of the causes on which the effect depends may
+be obtained by an induction from comparatively simple instances, or, at
+the worst, by deduction from the laws of simpler causes, so obtained. By
+simple instances are meant, of course, those in which the action of each
+cause was not intermixed or interfered with, or not to any great extent,
+by other causes whose laws were unknown. And only when the induction
+which furnished the premises to the Deductive method rested on such
+instances, has the application of such a method to the ascertainment of
+the laws of a complex effect, been attended with brilliant results.
+
+
+� 2. When the laws of the causes have been ascertained, and the first
+stage of the great logical operation now under discussion satisfactorily
+accomplished, the second part follows; that of determining from the laws
+of the causes, what effect any given combination of those causes will
+produce. This is a process of calculation, in the wider sense of the
+term; and very often involves processes of calculation in the narrowest
+sense. It is a ratiocination; and when our knowledge of the causes is so
+perfect, as to extend to the exact numerical laws which they observe in
+producing their effects, the ratiocination may reckon among its premises
+the theorems of the science of number, in the whole immense extent of
+that science. Not only are the most advanced truths of mathematics often
+required to enable us to compute an effect, the numerical law of which
+we already know; but, even by the aid of those most advanced truths, we
+can go but a little way. In so simple a case as the common problem of
+three bodies gravitating towards one another, with a force directly as
+their mass and inversely as the square of the distance, all the
+resources of the calculus have not hitherto sufficed to obtain any
+general solution but an approximate one. In a case a little more
+complex, but still one of the simplest which arise in practice, that of
+the motion of a projectile, the causes which affect the velocity and
+range (for example) of a cannon-ball may be all known and estimated; the
+force of the gunpowder, the angle of elevation, the density of the air,
+the strength and direction of the wind; but it is one of the most
+difficult of mathematical problems to combine all these, so as to
+determine the effect resulting from their collective action.
+
+Besides the theorems of number, those of geometry also come in as
+premises, where the effects take place in space, and involve motion and
+extension, as in mechanics, optics, acoustics, astronomy. But when the
+complication increases, and the effects are under the influence of so
+many and such shifting causes as to give no room either for fixed
+numbers, or for straight lines and regular curves, (as in the case of
+physiological, to say nothing of mental and social phenomena,) the laws
+of number and extension are applicable, if at all, only on that large
+scale on which precision of details becomes unimportant. Although these
+laws play a conspicuous part in the most striking examples of the
+investigation of nature by the Deductive Method, as for example in the
+Newtonian theory of the celestial motions, they are by no means an
+indispensable part of every such process. All that is essential in it is
+reasoning from a general law to a particular case, that is, determining
+by means of the particular circumstances of that case, what result is
+required in that instance to fulfil the law. Thus in the Torricellian
+experiment, if the fact that air has weight had been previously known,
+it would have been easy, without any numerical data, to deduce from the
+general law of equilibrium, that the mercury would stand in the tube at
+such a height that the column of mercury would exactly balance a column
+of the atmosphere of equal diameter; because, otherwise, equilibrium
+would not exist.
+
+By such ratiocinations from the separate laws of the causes, we may, to
+a certain extent, succeed in answering either of the following
+questions: Given a certain combination of causes, what effect will
+follow? and, What combination of causes, if it existed, would produce a
+given effect? In the one case, we determine the effect to be expected in
+any complex circumstances of which the different elements are known: in
+the other case we learn, according to what law--under what antecedent
+conditions--a given complex effect will occur.
+
+
+� 3. But (it may here be asked) are not the same arguments by which the
+methods of direct observation and experiment were set aside as illusory
+when applied to the laws of complex phenomena, applicable with equal
+force against the Method of Deduction? When in every single instance a
+multitude, often an unknown multitude, of agencies, are clashing and
+combining, what security have we that in our computation _� priori_ we
+have taken all these into our reckoning? How many must we not generally
+be ignorant of? Among those which we know, how probable that some have
+been overlooked; and, even were all included, how vain the pretence of
+summing up the effects of many causes, unless we know accurately the
+numerical law of each,--a condition in most cases not to be fulfilled;
+and even when fulfilled, to make the calculation transcends, in any but
+very simple cases, the utmost power of mathematical science with all its
+most modern improvements.
+
+These objections have real weight, and would be altogether unanswerable,
+if there were no test by which, when we employ the Deductive Method, we
+might judge whether an error of any of the above descriptions had been
+committed or not. Such a test however there is: and its application
+forms, under the name of Verification, the third essential component
+part of the Deductive Method; without which all the results it can give
+have little other value than that of conjecture. To warrant reliance on
+the general conclusions arrived at by deduction, these conclusions must
+be found, on careful comparison, to accord with the results of direct
+observation wherever it can be had. If, when we have experience to
+compare with them, this experience confirms them, we may safely trust to
+them in other cases of which our specific experience is yet to come. But
+if our deductions have led to the conclusion that from a particular
+combination of causes a given effect would result, then in all known
+cases where that combination can be shown to have existed, and where the
+effect has not followed, we must be able to show (or at least to make a
+probable surmise) what frustrated it: if we cannot, the theory is
+imperfect, and not yet to be relied upon. Nor is the verification
+complete, unless some of the cases in which the theory is borne out by
+the observed result, are of at least equal complexity with any other
+cases in which its application could be called for.
+
+If direct observation and collation of instances have furnished us with
+any empirical laws of the effect (whether true in all observed cases, or
+only true for the most part), the most effectual verification of which
+the theory could be susceptible would be, that it led deductively to
+those empirical laws; that the uniformities, whether complete or
+incomplete, which were observed to exist among the phenomena, were
+accounted for by the laws of the causes--were such as could not but
+exist if those be really the causes by which the phenomena are produced.
+Thus it was very reasonably deemed an essential requisite of any true
+theory of the causes of the celestial motions, that it should lead by
+deduction to Kepler's laws: which, accordingly, the Newtonian theory
+did.
+
+In order, therefore, to facilitate the verification of theories obtained
+by deduction, it is important that as many as possible of the empirical
+laws of the phenomena should be ascertained, by a comparison of
+instances, conformably to the Method of Agreement: as well as (it must
+be added) that the phenomena themselves should be described, in the most
+comprehensive as well as accurate manner possible; by collecting from
+the observation of parts, the simplest possible correct expressions for
+the corresponding wholes: as when the series of the observed places of a
+planet was first expressed by a circle, then by a system of epicycles,
+and subsequently by an ellipse.
+
+It is worth remarking, that complex instances which would have been of
+no use for the discovery of the simple laws into which we ultimately
+analyse their phenomena, nevertheless, when they have served to verify
+the analysis, become additional evidence of the laws themselves.
+Although we could not have got at the law from complex cases, still when
+the law, got at otherwise, is found to be in accordance with the result
+of a complex case, that case becomes a new experiment on the law, and
+helps to confirm what it did not assist to discover. It is a new trial
+of the principle in a different set of circumstances; and occasionally
+serves to eliminate some circumstance not previously excluded, and the
+exclusion of which might require an experiment impossible to be
+executed. This was strikingly conspicuous in the example formerly
+quoted, in which the difference between the observed and the calculated
+velocity of sound was ascertained to result from the heat extricated by
+the condensation which takes place in each sonorous vibration. This was
+a trial, in new circumstances, of the law of the development of heat by
+compression; and it added materially to the proof of the universality of
+that law. Accordingly any law of nature is deemed to have gained in
+point of certainty, by being found to explain some complex case which
+had not previously been thought of in connexion with it; and this indeed
+is a consideration to which it is the habit of scientific inquirers to
+attach rather too much value than too little.
+
+To the Deductive Method, thus characterized in its three constituent
+parts, Induction, Ratiocination, and Verification, the human mind is
+indebted for its most conspicuous triumphs in the investigation of
+nature. To it we owe all the theories by which vast and complicated
+phenomena are embraced under a few simple laws, which, considered as the
+laws of those great phenomena, could never have been detected by their
+direct study. We may form some conception of what the method has done
+for us, from the case of the celestial motions; one of the simplest
+among the greater instances of the Composition of Causes, since (except
+in a few cases not of primary importance) each of the heavenly bodies
+may be considered, without material inaccuracy, to be never at one time
+influenced by the attraction of more than two bodies, the sun and one
+other planet or satellite; making, with the reaction of the body itself,
+and the force generated by the body's own motion and acting in the
+direction of the tangent, only four different agents on the concurrence
+of which the motions of that body depend; a much smaller number, no
+doubt, than that by which any other of the great phenomena of nature is
+determined or modified. Yet how could we ever have ascertained the
+combination of forces on which the motions of the earth and planets are
+dependent, by merely comparing the orbits or velocities of different
+planets, or the different velocities or positions of the same planet?
+Notwithstanding the regularity which manifests itself in those motions,
+in a degree so rare among the effects of a concurrence of causes; and
+although the periodical recurrence of exactly the same effect, affords
+positive proof that all the combinations of causes which occur at all,
+recur periodically; we should not have known what the causes were, if
+the existence of agencies precisely similar on our own earth had not,
+fortunately, brought the causes themselves within the reach of
+experimentation under simple circumstances. As we shall have occasion to
+analyse, further on, this great example of the Method of Deduction, we
+shall not occupy any time with it here, but shall proceed to that
+secondary application of the Deductive Method, the result of which is
+not to prove laws of phenomena, but to explain them.
+
+
+
+
+CHAPTER XII.
+
+OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+� 1. The deductive operation by which we derive the law of an effect
+from the laws of the causes, the concurrence of which gives rise to it,
+may be undertaken either for the purpose of discovering the law, or of
+explaining a law already discovered. The word _explanation_ occurs so
+continually and holds so important a place in philosophy, that a little
+time spent in fixing the meaning of it will be profitably employed.
+
+An individual fact is said to be explained, by pointing out its cause,
+that is, by stating the law or laws of causation, of which its
+production is an instance. Thus, a conflagration is explained, when it
+is proved to have arisen from a spark falling into the midst of a heap
+of combustibles. And in a similar manner, a law or uniformity in nature
+is said to be explained, when another law or laws are pointed out, of
+which that law itself is but a case, and from which it could be deduced.
+
+
+� 2. There are three distinguishable sets of circumstances in which a
+law of causation may be explained from, or, as it also is often
+expressed, resolved into, other laws.
+
+The first is the case already so fully considered; an intermixture of
+laws, producing a joint effect equal to the sum of the effects of the
+causes taken separately. The law of the complex effect is explained, by
+being resolved into the separate laws of the causes which contribute to
+it. Thus, the law of the motion of a planet is resolved into the law of
+the acquired force, which tends to produce an uniform motion in the
+tangent, and the law of the centripetal force which tends to produce an
+accelerating motion towards the sun; the real motion being a compound of
+the two.
+
+It is necessary here to remark, that in this resolution of the law of a
+complex effect, the laws of which it is compounded are not the only
+elements. It is resolved into the laws of the separate causes, together
+with the fact of their coexistence. The one is as essential an
+ingredient as the other; whether the object be to discover the law of
+the effect, or only to explain it. To deduce the laws of the heavenly
+motions, we require not only to know the law of a rectilineal and that
+of a gravitative force, but the existence of both these forces in the
+celestial regions, and even their relative amount. The complex laws of
+causation are thus resolved into two distinct kinds of elements: the
+one, simpler laws of causation, the other (in the aptly selected
+expression of Dr. Chalmers) collocations; the collocations consisting in
+the existence of certain agents or powers, in certain circumstances of
+place and time. We shall hereafter have occasion to return to this
+distinction, and to dwell on it at such length as dispenses with the
+necessity of further insisting on it here. The first mode, then, of the
+explanation of Laws of Causation, is when the law of an effect is
+resolved into the various tendencies of which it is the result, together
+with the laws of those tendencies.
+
+
+� 3. A second case is when, between what seemed the cause and what was
+supposed to be its effect, further observation detects an intermediate
+link; a fact caused by the antecedent, and in its turn causing the
+consequent; so that the cause at first assigned is but the remote cause,
+operating through the intermediate phenomenon. A seemed the cause of C,
+but it subsequently appeared that A was only the cause of B, and that it
+is B which was the cause of C. For example: mankind were aware that the
+act of touching an outward object caused a sensation. It was
+subsequently discovered, that after we have touched the object, and
+before we experience the sensation, some change takes place in a kind of
+thread called a nerve, which extends from our outward organs to the
+brain. Touching the object, therefore, is only the remote cause of our
+sensation; that is, not the cause, properly speaking, but the cause of
+the cause;--the real cause of the sensation is the change in the state
+of the nerve. Future experience may not only give us more knowledge than
+we now have of the particular nature of this change, but may also
+interpolate another link: between the contact (for example) of the
+object with our outward organs, and the production of the change of
+state in the nerve, there may take place some electric phenomenon; or
+some phenomenon of a nature not resembling the effects of any known
+agency. Hitherto, however, no such intermediate link has been
+discovered; and the touch of the object must be considered,
+provisionally, as the proximate cause of the affection of the nerve. The
+sequence, therefore, of a sensation of touch on contact with an object,
+is ascertained not to be an ultimate law; it is resolved, as the phrase
+is, into two other laws,--the law, that contact with an object produces
+an affection of the nerve; and the law, that an affection of the nerve
+produces sensation.
+
+To take another example: the more powerful acids corrode or blacken
+organic compounds. This is a case of causation, but of remote causation;
+and is said to be explained when it is shown that there is an
+intermediate link, namely, the separation of some of the chemical
+elements of the organic structure from the rest, and their entering into
+combination with the acid. The acid causes this separation of the
+elements, and the separation of the elements causes the disorganization,
+and often the charring of the structure. So, again, chlorine extracts
+colouring matters, (whence its efficacy in bleaching,) and purifies the
+air from infection. This law is resolved into the two following laws.
+Chlorine has a powerful affinity for bases of all kinds, particularly
+metallic bases and hydrogen. Such bases are essential elements of
+colouring matters and contagious compounds: which substances, therefore,
+are decomposed and destroyed by chlorine.
+
+
+� 4. It is of importance to remark, that when a sequence of phenomena is
+thus resolved into other laws, they are always laws more general than
+itself. The law that A is followed by C, is less general than either of
+the laws which connect B with C and A with B. This will appear from very
+simple considerations.
+
+All laws of causation are liable to be counteracted or frustrated, by
+the non-fulfilment of some negative condition: the tendency, therefore,
+of B to produce C may be defeated. Now the law that A produces B, is
+equally fulfilled whether B is followed by C or not; but the law that A
+produces C by means of B, is of course only fulfilled when B is really
+followed by C, and is therefore less general than the law that A
+produces B. It is also less general than the law that B produces C. For
+B may have other causes besides A; and as A produces C only by means of
+B, while B produces C whether it has itself been produced by A or by
+anything else, the second law embraces a greater number of instances,
+covers as it were a greater space of ground, than the first.
+
+Thus, in our former example, the law that the contact of an object
+causes a change in the state of the nerve, is more general than the law
+that contact with an object causes sensation, since, for aught we know,
+the change in the nerve may equally take place when, from a
+counteracting cause, as for instance, strong mental excitement, the
+sensation does not follow; as in a battle, where wounds are sometimes
+received without any consciousness of receiving them. And again, the law
+that change in the state of a nerve produces sensation, is more general
+than the law that contact with an object produces sensation; since the
+sensation equally follows the change in the nerve when not produced by
+contact with an object, but by some other cause; as in the well-known
+case, when a person who has lost a limb, feels the same sensation which
+he has been accustomed to call a pain in the limb.
+
+Not only are the laws of more immediate sequence into which the law of a
+remote sequence is resolved, laws of greater generality than that law
+is, but (as a consequence of, or rather as implied in, their greater
+generality) they are more to be relied on; there are fewer chances of
+their being ultimately found not to be universally true. From the moment
+when the sequence of A and C is shown not to be immediate, but to
+depend on an intervening phenomenon, then, however constant and
+invariable the sequence of A and C has hitherto been found,
+possibilities arise of its failure, exceeding those which can affect
+either of the more immediate sequences, A, B, and B, C. The tendency of
+A to produce C may be defeated by whatever is capable of defeating
+either the tendency of A to produce B, or the tendency of B to produce
+C; it is therefore twice as liable to failure as either of those more
+elementary tendencies; and the generalization that A is always followed
+by C, is twice as likely to be found erroneous. And so of the converse
+generalization, that C is always preceded and caused by A; which will be
+erroneous not only if there should happen to be a second immediate mode
+of production of C itself, but moreover if there be a second mode of
+production of B, the immediate antecedent of C in the sequence.
+
+The resolution of the one generalization into the other two, not only
+shows that there are possible limitations of the former, from which its
+two elements are exempt, but shows also where these are to be looked
+for. As soon as we know that B intervenes between A and C, we also know
+that if there be cases in which the sequence of A and C does not hold,
+these are most likely to be found by studying the effects or the
+conditions of the phenomenon B.
+
+It appears, then, that in the second of the three modes in which a law
+may be resolved into other laws, the latter are more general, that is,
+extend to more cases, and are also less likely to require limitation
+from subsequent experience, than the law which they serve to explain.
+They are more nearly unconditional; they are defeated by fewer
+contingencies; they are a nearer approach to the universal truth of
+nature. The same observations are still more evidently true with regard
+to the first of the three modes of resolution. When the law of an effect
+of combined causes is resolved into the separate laws of the causes, the
+nature of the case implies that the law of the effect is less general
+than the law of any of the causes, since it only holds when they are
+combined; while the law of any one of the causes holds good both then,
+and also when that cause acts apart from the rest. It is also manifest
+that the complex law is liable to be oftener unfulfilled than any one
+of the simpler laws of which it is the result, since every contingency
+which defeats any of the laws prevents so much of the effect as depends
+on it, and thereby defeats the complex law. The mere rusting, for
+example, of some small part of a great machine, often suffices entirely
+to prevent the effect which ought to result from the joint action of all
+the parts. The law of the effect of a combination of causes is always
+subject to the whole of the negative conditions which attach to the
+action of all the causes severally.
+
+There is another and an equally strong reason why the law of a complex
+effect must be less general than the laws of the causes which conspire
+to produce it. The same causes, acting according to the same laws, and
+differing only in the proportions in which they are combined, often
+produce effects which differ not merely in quantity, but in kind. The
+combination of a centripetal with a projectile force, in the proportions
+which obtain in all the planets and satellites of our solar system,
+gives rise to an elliptical motion; but if the ratio of the two forces
+to each other were slightly altered, it is demonstrated that the motion
+produced would be in a circle, or a parabola, or an hyperbola: and it is
+thought that in the case of some comets one of these is probably the
+fact. Yet the law of the parabolic motion would be resolvable into the
+very same simple laws into which that of the elliptical motion is
+resolved, namely, the law of the permanence of rectilineal motion, and
+the law of gravitation. If, therefore, in the course of ages, some
+circumstance were to manifest itself which, without defeating the law of
+either of those forces, should merely alter their proportion to one
+another, (such as the shock of some solid body, or even the accumulating
+effect of the resistance of the medium in which astronomers have been
+led to surmise that the motions of the heavenly bodies take place,) the
+elliptical motion might be changed into a motion in some other conic
+section; and the complex law, that the planetary motions take place in
+ellipses, would be deprived of its universality, though the discovery
+would not at all detract from the universality of the simpler laws into
+which that complex law is resolved. The law, in short, of each of the
+concurrent causes remains the same, however their collocations may vary;
+but the law of their joint effect varies with every difference in the
+collocations. There needs no more to show how much more general the
+elementary laws must be, than any of the complex laws which are derived
+from them.
+
+
+� 5. Besides the two modes which have been treated of, there is a third
+mode in which laws are resolved into one another; and in this it is
+self-evident that they are resolved into laws more general than
+themselves. This third mode is the _subsumption_ (as it has been called)
+of one law under another: or (what comes to the same thing) the
+gathering up of several laws into one more general law which includes
+them all. The most splendid example of this operation was when
+terrestrial gravity and the central force of the solar system were
+brought together under the general law of gravitation. It had been
+proved antecedently that the earth and the other planets tend to the
+sun; and it had been known from the earliest times that terrestrial
+bodies tend towards the earth. These were similar phenomena; and to
+enable them both to be subsumed under one law, it was only necessary to
+prove that, as the effects were similar in quality, so also they, as to
+quantity, conform to the same rules. This was first shown to be true of
+the moon, which agreed with terrestrial objects not only in tending to a
+centre, but in the fact that this centre was the earth. The tendency of
+the moon towards the earth being ascertained to vary as the inverse
+square of the distance, it was deduced from this, by direct calculation,
+that if the moon were as near to the earth as terrestrial objects are,
+and the acquired force in the direction of the tangent were suspended,
+the moon would fall towards the earth through exactly as many feet in a
+second as those objects do by virtue of their weight. Hence the
+inference was irresistible, that the moon also tends to the earth by
+virtue of its weight: and that the two phenomena, the tendency of the
+moon to the earth and the tendency of terrestrial objects to the earth,
+being not only similar in quality, but, when in the same circumstances,
+identical in quantity, are cases of one and the same law of causation.
+But the tendency of the moon to the earth, and the tendency of the earth
+and planets to the sun, were already known to be cases of the same law
+of causation: and thus the law of all these tendencies, and the law of
+terrestrial gravity, were recognised as identical, and were subsumed
+under one general law, that of gravitation.
+
+In a similar manner, the laws of magnetic phenomena have more recently
+been subsumed under known laws of electricity. It is thus that the most
+general laws of nature are usually arrived at: we mount to them by
+successive steps. For, to arrive by correct induction at laws which hold
+under such an immense variety of circumstances, laws so general as to be
+independent of any varieties of space or time which we are able to
+observe, requires for the most part many distinct sets of experiments or
+observations, conducted at different times and by different people. One
+part of the law is first ascertained, afterwards another part: one set
+of observations teaches us that the law holds good under some
+conditions, another that it holds good under other conditions, by
+combining which observations we find that it holds good under conditions
+much more general, or even universally. The general law, in this case,
+is literally the sum of all the partial ones; it is the recognition of
+the same sequence in different sets of instances; and may, in fact, be
+regarded as merely one step in the process of elimination. That tendency
+of bodies towards one another, which we now call gravity, had at first
+been observed only on the earth's surface, where it manifested itself
+only as a tendency of all bodies towards the earth, and might,
+therefore, be ascribed to a peculiar property of the earth itself: one
+of the circumstances, namely, the proximity of the earth, had not been
+eliminated. To eliminate this circumstance required a fresh set of
+instances in other parts of the universe: these we could not ourselves
+create; and though nature had created them for us, we were placed in
+very unfavourable circumstances for observing them. To make these
+observations, fell naturally to the lot of a different set of persons
+from those who studied terrestrial phenomena; and had, indeed, been a
+matter of great interest at a time when the idea of explaining celestial
+facts by terrestrial laws was looked upon as the confounding of an
+indefeasible distinction. When, however, the celestial motions were
+accurately ascertained, and the deductive processes performed, from
+which it appeared that their laws and those of terrestrial gravity
+corresponded, those celestial observations became a set of instances
+which exactly eliminated the circumstance of proximity to the earth; and
+proved that in the original case, that of terrestrial objects, it was
+not the earth, as such, that caused the motion or the pressure, but the
+circumstance common to that case with the celestial instances, namely,
+the presence of some great body within certain limits of distance.
+
+
+� 6. There are, then, three modes of explaining laws of causation, or,
+which is the same thing, resolving them into other laws. First, when the
+law of an effect of combined causes is resolved into the separate laws
+of the causes, together with the fact of their combination. Secondly,
+when the law which connects any two links, not proximate, in a chain of
+causation, is resolved into the laws which connect each with the
+intermediate links. Both of these are cases of resolving one law into
+two or more; in the third, two or more are resolved into one: when,
+after the law has been shown to hold good in several different classes
+of cases, we decide that what is true in each of these classes of cases,
+is true under some more general supposition, consisting of what all
+those classes of cases have in common. We may here remark that this last
+operation involves none of the uncertainties attendant on induction by
+the Method of Agreement, since we need not suppose the result to be
+extended by way of inference to any new class of cases, different from
+those by the comparison of which it was engendered.
+
+In all these three processes, laws are, as we have seen, resolved into
+laws more general than themselves; laws extending to all the cases which
+the former extended to, and others besides. In the first two modes they
+are also resolved into laws more certain, in other words, more
+universally true than themselves; they are, in fact, proved not to be
+themselves laws of nature, the character of which is to be universally
+true, but _results_ of laws of nature, which may be only true
+conditionally, and for the most part. No difference of this sort exists
+in the third case; since here the partial laws are, in fact, the very
+same law as the general one, and any exception to them would be an
+exception to it too.
+
+By all the three processes, the range of deductive science is extended;
+since the laws, thus resolved, may be thenceforth deduced
+demonstratively from the laws into which they are resolved. As already
+remarked, the same deductive process which proves a law or fact of
+causation if unknown, serves to explain it when known.
+
+The word explanation is here used in its philosophical sense. What is
+called explaining one law of nature by another, is but substituting one
+mystery for another; and does nothing to render the general course of
+nature other than mysterious: we can no more assign a _why_ for the more
+extensive laws than for the partial ones. The explanation may substitute
+a mystery which has become familiar, and has grown to _seem_ not
+mysterious, for one which is still strange. And this is the meaning of
+explanation, in common parlance. But the process with which we are here
+concerned often does the very contrary: it resolves a phenomenon with
+which we are familiar, into one of which we previously knew little or
+nothing; as when the common fact of the fall of heavy bodies was
+resolved into the tendency of all particles of matter towards one
+another. It must be kept constantly in view, therefore, that in science,
+those who speak of explaining any phenomenon mean (or should mean)
+pointing out not some more familiar, but merely some more general,
+phenomenon, of which it is a partial exemplification; or some laws of
+causation which produce it by their joint or successive action, and from
+which, therefore, its conditions may be determined deductively. Every
+such operation brings us a step nearer towards answering the question
+which was stated in a previous chapter as comprehending the whole
+problem of the investigation of nature, viz. What are the fewest
+assumptions, which being granted, the order of nature as it exists
+would be the result? What are the fewest general propositions from which
+all the uniformities existing in nature could be deduced?
+
+The laws, thus explained or resolved, are sometimes said to be
+_accounted for_; but the expression is incorrect, if taken to mean
+anything more than what has been already stated. In minds not habituated
+to accurate thinking, there is often a confused notion that the general
+laws are the _causes_ of the partial ones; that the law of general
+gravitation, for example, causes the phenomenon of the fall of bodies to
+the earth. But to assert this, would be a misuse of the word cause:
+terrestrial gravity is not an effect of general gravitation, but a
+_case_ of it; that is, one kind of the particular instances in which
+that general law obtains. To account for a law of nature means, and can
+mean, nothing more than to assign other laws more general, together with
+collocations, which laws and collocations being supposed, the partial
+law follows without any additional supposition.
+
+
+
+
+CHAPTER XIII.
+
+MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+� 1. The most striking example which the history of science presents, of
+the explanation of laws of causation and other uniformities of sequence
+among special phenomena, by resolving them into laws of greater
+simplicity and generality, is the great Newtonian generalization:
+respecting which typical instance so much having already been said, it
+is sufficient to call attention to the great number and variety of the
+special observed uniformities which are in this case accounted for,
+either as particular cases or as consequences of one very simple law of
+universal nature. The simple fact of a tendency of every particle of
+matter towards every other particle, varying inversely as the square of
+the distance, explains the fall of bodies to the earth, the revolutions
+of the planets and satellites, the motions (so far as known) of comets,
+and all the various regularities which have been observed in these
+special phenomena; such as the elliptical orbits, and the variations
+from exact ellipses; the relation between the solar distances of the
+planets and the duration of their revolutions; the precession of the
+equinoxes; the tides, and a vast number of minor astronomical truths.
+
+Mention has also been made in the preceding chapter of the explanation
+of the phenomena of magnetism from laws of electricity; the special laws
+of magnetic agency having been affiliated by deduction to observed laws
+of electric action, in which they have ever since been considered to be
+included as special cases. An example not so complete in itself, but
+even more fertile in consequences, having been the starting point of the
+really scientific study of physiology, is the affiliation, commenced by
+Bichat, and carried on by subsequent biologists, of the properties of
+the bodily organs, to the elementary properties of the tissues into
+which they are anatomically decomposed.
+
+Another striking instance is afforded by Dalton's generalization,
+commonly known as the atomic theory. It had been known from the very
+commencement of accurate chemical observation, that any two bodies
+combine chemically with one another in only a certain number of
+proportions; but those proportions were in each case expressed by a
+percentage--so many parts (by weight) of each ingredient, in 100 of the
+compound; (say 35 and a fraction of one element, 64 and a fraction of
+the other): in which mode of statement no relation was perceived between
+the proportion in which a given element combines with one substance, and
+that in which it combines with others. The great step made by Dalton
+consisted in perceiving, that a unit of weight might be established for
+each substance, such that by supposing the substance to enter into all
+its combinations in the ratio either of that unit, or of some low
+multiple of that unit, all the different proportions, previously
+expressed by percentages, were found to result. Thus 1 being assumed as
+the unit of hydrogen, if 8 were then taken as that of oxygen, the
+combination of one unit of hydrogen with one unit of oxygen would
+produce the exact proportion of weight between the two substances which
+is known to exist in water; the combination of one unit of hydrogen with
+two units of oxygen would produce the proportion which exists in the
+other compound of the same two elements, called peroxide of hydrogen;
+and the combinations of hydrogen and of oxygen with all other
+substances, would correspond with the supposition that those elements
+enter into combination by single units, or twos, or threes, of the
+numbers assigned to them, 1 and 8, and the other substances by ones or
+twos or threes of other determinate numbers proper to each. The result
+is that a table of the equivalent numbers, or, as they are called,
+atomic weights, of all the elementary substances, comprises in itself,
+and scientifically explains, all the proportions in which any substance,
+elementary or compound, is found capable of entering into chemical
+combination with any other substance whatever.
+
+
+� 2. Some interesting cases of the explanation of old uniformities by
+newly ascertained laws are afforded by the researches of Professor
+Graham. That eminent chemist was the first who drew attention to the
+distinction which may be made of all substances into two classes, termed
+by him crystalloids and colloids; or rather, of all states of matter
+into the crystalloid and the colloidal states, for many substances are
+capable of existing in either. When in the colloidal state, their
+sensible properties are very different from those of the same substance
+when crystallized, or when in a state easily susceptible of
+crystallization. Colloid substances pass with extreme difficulty and
+slowness into the crystalline state, and are extremely inert in all the
+ordinary chemical relations. Substances in the colloid state are almost
+always, when combined with water, more or less viscous or gelatinous.
+The most prominent examples of the state are certain animal and
+vegetable substances, particularly gelatine, albumen, starch, the gums,
+caramel, tannin, and some others. Among substances not of organic
+origin, the most notable instances are hydrated silicic acid, and
+hydrated alumina, with other metallic peroxides of the aluminous class.
+
+Now it is found, that while colloidal substances are easily penetrated
+by water, and by the solutions of crystalloid substances, they are very
+little penetrable by one another: which enabled Professor Graham to
+introduce a highly effective process (termed dialysis) for separating
+the crystalloid substances contained in any liquid mixture, by passing
+them through a thin septum of colloidal matter, which does not suffer
+anything colloidal to pass, or suffers it only in very minute quantity.
+This property of colloids enabled Mr. Graham to account for a number of
+special results of observation, not previously explained.
+
+For instance, "while soluble crystalloids are always highly sapid,
+soluble colloids are singularly insipid," as might be expected; for, as
+the sentient extremities of the nerves of the palate "are probably
+protected by a colloidal membrane," impermeable to other colloids, a
+colloid, when tasted, probably never reaches those nerves. Again, "it
+has been observed that vegetable gum is not digested in the stomach; the
+coats of that organ dialyse the soluble food, absorbing crystalloids,
+and rejecting all colloids." One of the mysterious processes
+accompanying digestion, the secretion of free muriatic acid by the coats
+of the stomach, obtains a probable hypothetical explanation through the
+same law. Finally, much light is thrown upon the observed phenomena of
+osmose (the passage of fluids outward and inward through animal
+membranes) by the fact that the membranes are colloidal. In consequence,
+the water and saline solutions contained in the animal body pass easily
+and rapidly through the membranes, while the substances directly
+applicable to nutrition, which are mostly colloidal, are detained by
+them.[47]
+
+The property which salt possesses of preserving animal substances from
+putrefaction is resolved by Liebig into two more general laws, the
+strong attraction of salt for water, and the necessity of the presence
+of water as a condition of putrefaction. The intermediate phenomenon
+which is interpolated between the remote cause and the effect, can here
+be not merely inferred but seen; for it is a familiar fact, that flesh
+upon which salt has been thrown is speedily found swimming in brine.
+
+The second of the two factors (as they may be termed) into which the
+preceding law has been resolved, the necessity of water to putrefaction,
+itself affords an additional example of the Resolution of Laws. The law
+itself is proved by the Method of Difference, since flesh completely
+dried and kept in a dry atmosphere does not putrefy; as we see in the
+case of dried provisions, and human bodies in very dry climates. A
+deductive explanation of this same law results from Liebig's
+speculations. The putrefaction of animal and other azotised bodies is a
+chemical process, by which they are gradually dissipated in a gaseous
+form, chiefly in that of carbonic acid and ammonia; now to convert the
+carbon of the animal substance into carbonic acid requires oxygen, and
+to convert the azote into ammonia requires hydrogen, which are the
+elements of water. The extreme rapidity of the putrefaction of azotised
+substances, compared with the gradual decay of non-azotised bodies (such
+as wood and the like) by the action of oxygen alone, he explains from
+the general law that substances are much more easily decomposed by the
+action of two different affinities upon two of their elements, than by
+the action of only one.
+
+
+� 3. Among the many important properties of the nervous system, which
+have either been first discovered or strikingly illustrated by Dr.
+Brown-S�quard, I select the reflex influence of the nervous system on
+nutrition and secretion. By reflex nervous action is meant, action which
+one part of the nervous system exerts over another part, without any
+intermediate action on the brain, and consequently without
+consciousness; or which, if it does pass through the brain, at least
+produces its effects independently of the will. There are many
+experiments which prove that irritation of a nerve in one part of the
+body may in this manner excite powerful action in another part; for
+example, food injected into the stomach through a divided oesophagus,
+nevertheless produces secretion of saliva; warm water injected into the
+bowels, and various other irritations of the lower intestines, have been
+found to excite secretion of the gastric juice, and so forth. The
+reality of the power being thus proved, its agency explains a great
+variety of apparently anomalous phenomena; of which I select the
+following from Dr. Brown-S�quard's _Lectures on the Nervous System_.
+
+The production of tears by irritation of the eye, or of the mucous
+membrane of the nose:
+
+The secretions of the eye and nose increased by exposure of other parts
+of the body to cold:
+
+Inflammation of the eye, especially when of traumatic origin, very
+frequently excites a similar affection in the other eye, which may be
+cured by section of the intervening nerve:
+
+Loss of sight sometimes produced by neuralgia; and has been known to be
+at once cured by the extirpation (for instance) of a carious tooth:
+
+Even cataract has been produced in a healthy eye by cataract in the
+other eye, or by neuralgia, or by a wound of the frontal nerve:
+
+The well-known phenomenon of a sudden stoppage of the heart's action,
+and consequent death, produced by irritation of some of the nervous
+extremities: _e.g._, by drinking very cold water; or by a blow on the
+abdomen, or other sudden excitation of the abdominal sympathetic nerve;
+though this nerve may be irritated to any extent without stopping the
+heart's action, if a section be made of the communicating nerves:
+
+The extraordinary effects produced on the internal organs by an
+extensive burn on the surface of the body; consisting in violent
+inflammation of the tissues of the abdomen, chest, or head: which, when
+death ensues from this kind of injury, is one of the most frequent
+causes of it:
+
+Paralysis and an�sthesia of one part of the body from neuralgia in
+another part; and muscular atrophy from neuralgia, even when there is no
+paralysis:
+
+Tetanus produced by the lesion of a nerve; Dr. Brown-S�quard thinks it
+highly probable that hydrophobia is a phenomenon of a similar nature:
+
+Morbid changes in the nutrition of the brain and spinal cord,
+manifesting themselves by epilepsy, chorea, hysteria, and other
+diseases, occasioned by lesion of some of the nervous extremities in
+remote places, as by worms, calculi, tumours, carious bones, and in some
+cases even by very slight irritations of the skin.
+
+
+� 4. From the foregoing and similar instances, we may see the
+importance, when a law of nature previously unknown has been brought to
+light, or when new light has been thrown upon a known law by experiment,
+of examining all cases which present the conditions necessary for
+bringing that law into action; a process fertile in demonstrations of
+special laws previously unsuspected, and explanations of others already
+empirically known.
+
+For instance, Faraday discovered by experiment, that voltaic electricity
+could be evolved from a natural magnet, provided a conducting body were
+set in motion at right angles to the direction of the magnet: and this
+he found to hold not only of small magnets, but of that great magnet,
+the earth. The law being thus established experimentally, that
+electricity is evolved, by a magnet, and a conductor moving at right
+angles to the direction of its poles, we may now look out for fresh
+instances in which these conditions meet. Wherever a conductor moves or
+revolves at right angles to the direction of the earth's magnetic poles,
+there we may expect an evolution of electricity. In the northern
+regions, where the polar direction is nearly perpendicular to the
+horizon, all horizontal motions of conductors will produce electricity;
+horizontal wheels, for example, made of metal; likewise all running
+streams will evolve a current of electricity, which will circulate round
+them; and the air thus charged with electricity may be one of the causes
+of the Aurora Borealis. In the equatorial regions, on the contrary,
+upright wheels placed parallel to the equator will originate a voltaic
+circuit, and waterfalls will naturally become electric.
+
+For a second example; it has been proved, chiefly by the researches of
+Professor Graham, that gases have a strong tendency to permeate animal
+membranes, and diffuse themselves through the spaces which such
+membranes inclose, notwithstanding the presence of other gases in those
+spaces. Proceeding from this general law, and reviewing a variety of
+cases in which gases lie contiguous to membranes, we are enabled to
+demonstrate or to explain the following more special laws: 1st. The
+human or animal body, when surrounded with any gas not already contained
+within the body, absorbs it rapidly; such, for instance, as the gases of
+putrefying matters: which helps to explain malaria. 2nd. The carbonic
+acid gas of effervescing drinks, evolved in the stomach, permeates its
+membranes, and rapidly spreads through the system. 3rd. Alcohol taken
+into the stomach passes into vapour and spreads through the system with
+great rapidity; (which, combined with the high combustibility of
+alcohol, or in other words its ready combination with oxygen, may
+perhaps help to explain the bodily warmth immediately consequent on
+drinking spirituous liquors.) 4th. In any state of the body in which
+peculiar gases are formed within it, these will rapidly exhale through
+all parts of the body; and hence the rapidity with which, in certain
+states of disease, the surrounding atmosphere becomes tainted. 5th. The
+putrefaction of the interior parts of a carcase will proceed as rapidly
+as that of the exterior, from the ready passage outwards of the gaseous
+products. 6th. The exchange of oxygen and carbonic acid in the lungs is
+not prevented, but rather promoted, by the intervention of the membrane
+of the lungs and the coats of the blood-vessels between the blood and
+the air. It is necessary, however, that there should be a substance in
+the blood with which the oxygen of the air may immediately combine;
+otherwise instead of passing into the blood, it would permeate the whole
+organism: and it is necessary that the carbonic acid, as it is formed in
+the capillaries, should also find a substance in the blood with which it
+can combine; otherwise it would leave the body at all points, instead of
+being discharged through the lungs.
+
+
+� 5. The following is a deduction which confirms, by explaining, the old
+but not undisputed empirical generalization, that soda powders weaken
+the human system. These powders, consisting of a mixture of tartaric
+acid with bicarbonate of soda, from which the carbonic acid is set free,
+must pass into the stomach as tartrate of soda. Now, neutral tartrates,
+citrates, and acetates of the alkalis are found, in their passage
+through the system, to be changed into carbonates; and to convert a
+tartrate into a carbonate requires an additional quantity of oxygen, the
+abstraction of which must lessen the oxygen destined for assimilation
+with the blood, on the quantity of which the vigorous action of the
+human system partly depends.
+
+The instances of new theories agreeing with and explaining old
+empiricisms, are innumerable. All the just remarks made by experienced
+persons on human character and conduct, are so many special laws, which
+the general laws of the human mind explain and resolve. The empirical
+generalizations on which the operations of the arts have usually been
+founded, are continually justified and confirmed on the one hand, or
+corrected and improved on the other, by the discovery of the simpler
+scientific laws on which the efficacy of those operations depends. The
+effects of the rotation of crops, of the various manures, and other
+processes of improved agriculture, have been for the first time resolved
+in our own day into known laws of chemical and organic action, by Davy,
+Liebig, and others. The processes of the medical art are even now mostly
+empirical: their efficacy is concluded, in each instance, from a special
+and most precarious experimental generalization: but as science advances
+in discovering the simple laws of chemistry and physiology, progress is
+made in ascertaining the intermediate links in the series of phenomena,
+and the more general laws on which they depend; and thus, while the old
+processes are either exploded, or their efficacy, in so far as real,
+explained, better processes, founded on the knowledge of proximate
+causes, are continually suggested and brought into use.[48] Many even of
+the truths of geometry were generalizations from experience before they
+were deduced from first principles. The quadrature of the cycloid is
+said to have been first effected by measurement, or rather by weighing a
+cycloidal card, and comparing its weight with that of a piece of similar
+card of known dimensions.
+
+
+� 6. To the foregoing examples from physical science, let us add another
+from mental. The following is one of the simple laws of mind: Ideas of a
+pleasurable or painful character form associations more easily and
+strongly than other ideas, that is, they become associated after fewer
+repetitions, and the association is more durable. This is an
+experimental law, grounded on the Method of Difference. By deduction
+from this law, many of the more special laws which experience shows to
+exist among particular mental phenomena may be demonstrated and
+explained:--the ease and rapidity, for instance, with which thoughts
+connected with our passions or our more cherished interests are excited,
+and the firm hold which the facts relating to them have on our memory;
+the vivid recollection we retain of minute circumstances which
+accompanied any object or event that deeply interested us, and of the
+times and places in which we have been very happy or very miserable; the
+horror with which we view the accidental instrument of any occurrence
+which shocked us, or the locality where it took place, and the pleasure
+we derive from any memorial of past enjoyment; all these effects being
+proportional to the sensibility of the individual mind, and to the
+consequent intensity of the pain or pleasure from which the association
+originated. It has been suggested by the able writer of a biographical
+sketch of Dr. Priestley in a monthly periodical,[49] that the same
+elementary law of our mental constitution, suitably followed out, would
+explain a variety of mental phenomena previously inexplicable, and in
+particular some of the fundamental diversities of human character and
+genius. Associations being of two sorts, either between synchronous, or
+between successive impressions; and the influence of the law which
+renders associations stronger in proportion to the pleasurable or
+painful character of the impressions, being felt with peculiar force in
+the synchronous class of associations; it is remarked by the writer
+referred to, that in minds of strong organic sensibility synchronous
+associations will be likely to predominate, producing a tendency to
+conceive things in pictures and in the concrete, richly clothed in
+attributes and circumstances, a mental habit which is commonly called
+Imagination, and is one of the peculiarities of the painter and the
+poet; while persons of more moderate susceptibility to pleasure and pain
+will have a tendency to associate facts chiefly in the order of their
+succession, and such persons, if they possess mental superiority, will
+addict themselves to history or science rather than to creative art.
+This interesting speculation the author of the present work has
+endeavoured, on another occasion, to pursue farther, and to examine how
+far it will avail towards explaining the peculiarities of the poetical
+temperament.[50] It is at least an example which may serve, instead of
+many others, to show the extensive scope which exists for deductive
+investigation in the important and hitherto so imperfect Science of
+Mind.
+
+
+� 7. The copiousness with which the discovery and explanation of special
+laws of phenomena by deduction from simpler and more general ones has
+here been exemplified, was prompted by a desire to characterize clearly,
+and place in its due position of importance, the Deductive Method;
+which, in the present state of knowledge, is destined henceforth
+irrevocably to predominate in the course of scientific investigation. A
+revolution is peaceably and progressively effecting itself in
+philosophy, the reverse of that to which Bacon has attached his name.
+That great man changed the method of the sciences from deductive to
+experimental, and it is now rapidly reverting from experimental to
+deductive. But the deductions which Bacon abolished were from premises
+hastily snatched up, or arbitrarily assumed. The principles were neither
+established by legitimate canons of experimental inquiry, nor the
+results tested by that indispensable element of a rational Deductive
+Method, verification by specific experience. Between the primitive
+method of Deduction and that which I have attempted to characterize,
+there is all the difference which exists between the Aristotelian
+physics and the Newtonian theory of the heavens.
+
+It would, however, be a mistake to expect that those great
+generalizations, from which the subordinate truths of the more backward
+sciences will probably at some future period be deduced by reasoning (as
+the truths of astronomy are deduced from the generalities of the
+Newtonian theory), will be found, in all, or even in most cases, among
+truths now known and admitted. We may rest assured, that many of the
+most general laws of nature are as yet entirely unthought of; and that
+many others, destined hereafter to assume the same character, are known,
+if at all, only as laws or properties of some limited class of
+phenomena; just as electricity, now recognised as one of the most
+universal of natural agencies, was once known only as a curious property
+which certain substances acquired by friction, of first attracting and
+then repelling light bodies. If the theories of heat, cohesion,
+crystallization, and chemical action, are destined, as there can be
+little doubt that they are, to become deductive, the truths which will
+then be regarded as the _principia_ of those sciences would probably, if
+now announced, appear quite as novel[51] as the law of gravitation
+appeared to the cotemporaries of Newton; possibly even more so, since
+Newton's law, after all, was but an extension of the law of weight--that
+is, of a generalization familiar from of old, and which already
+comprehended a not inconsiderable body of natural phenomena. The general
+laws of a similarly commanding character, which we still look forward to
+the discovery of, may not always find so much of their foundations
+already laid.
+
+These general truths will doubtless make their first appearance in the
+character of hypotheses; not proved, nor even admitting of proof, in
+the first instance, but assumed as premises for the purpose of deducing
+from them the known laws of concrete phenomena. But this, though their
+initial, cannot be their final state. To entitle an hypothesis to be
+received as one of the truths of nature, and not as a mere technical
+help to the human faculties, it must be capable of being tested by the
+canons of legitimate induction, and must actually have been submitted to
+that test. When this shall have been done, and done successfully,
+premises will have been obtained from which all the other propositions
+of the science will thenceforth be presented as conclusions, and the
+science will, by means of a new and unexpected Induction, be rendered
+Deductive.
+
+FOOTNOTES:
+
+[1] Dr. Whewell thinks it improper to apply the term Induction to any
+operation not terminating in the establishment of a general truth.
+Induction, he says (_Philosophy of Discovery_, p. 245), "is not the same
+thing as experience and observation. Induction is experience or
+observation _consciously_ looked at in a _general_ form. This
+consciousness and generality are necessary parts of that knowledge which
+is science." And he objects (p. 241) to the mode in which the word
+Induction is employed in this work, as an undue extension of that term
+"not only to the cases in which the general induction is consciously
+applied to a particular instance, but to the cases in which the
+particular instance is dealt with by means of experience in that rude
+sense in which experience can be asserted of brutes, and in which of
+course we can in no way imagine that the law is possessed or understood
+as a general proposition." This use of the term he deems a "confusion of
+knowledge with practical tendencies."
+
+I disclaim, as strongly as Dr. Whewell can do, the application of such
+terms as induction, inference, or reasoning, to operations performed by
+mere instinct, that is, from an animal impulse, without the exertion of
+any intelligence. But I perceive no ground for confining the use of
+those terms to cases in which the inference is drawn in the forms and
+with the precautions required by scientific propriety. To the idea of
+Science, an express recognition and distinct apprehension of general
+laws as such, is essential: but nine-tenths of the conclusions drawn
+from experience in the course of practical life, are drawn without any
+such recognition: they are direct inferences from known cases, to a case
+supposed to be similar. I have endeavoured to show that this is not only
+as legitimate an operation, but substantially the same operation, as
+that of ascending from known cases to a general proposition; except that
+the latter process has one great security for correctness which the
+former does not possess. In Science, the inference must necessarily pass
+through the intermediate stage of a general proposition, because Science
+wants its conclusions for record, and not for instantaneous use. But the
+inferences drawn for the guidance of practical affairs, by persons who
+would often be quite incapable of expressing in unexceptionable terms
+the corresponding generalizations, may and frequently do exhibit
+intellectual powers quite equal to any which have ever been displayed in
+Science: and if these inferences are not inductive, what are they? The
+limitation imposed on the term by Dr. Whewell seems perfectly arbitrary;
+neither justified by any fundamental distinction between what he
+includes and what he desires to exclude, nor sanctioned by usage, at
+least from the time of Reid and Stewart, the principal legislators (as
+far as the English language is concerned) of modern metaphysical
+terminology.
+
+[2] Supra, p. 214.
+
+[3] _Novum Organum Renovatum_, pp. 72, 73.
+
+[4] _Novum Organum Renovatum_, p. 32.
+
+[5] _Cours de Philosophie Positive_, vol. ii. p. 202.
+
+[6] Dr. Whewell, in his reply, contests the distinction here drawn, and
+maintains, that not only different descriptions, but different
+explanations of a phenomenon, may all be true. Of the three theories
+respecting the motions of the heavenly bodies, he says (_Philosophy of
+Discovery_, p. 231): "Undoubtedly all these explanations may be true and
+consistent with each other, and would be so if each had been followed
+out so as to show in what manner it could be made consistent with the
+facts. And this was, in reality, in a great measure done. The doctrine
+that the heavenly bodies were moved by vortices was successfully
+modified, so that it came to coincide in its results with the doctrine
+of an inverse-quadratic centripetal force.... When this point was
+reached, the vortex was merely a machinery, well or ill devised, for
+producing such a centripetal force, and therefore did not contradict the
+doctrine of a centripetal force. Newton himself does not appear to have
+been averse to explaining gravity by impulse. So little is it true that
+if one theory be true the other must be false. The attempt to explain
+gravity by the impulse of streams of particles flowing through the
+universe in all directions, which I have mentioned in the _Philosophy_,
+is so far from being inconsistent with the Newtonian theory, that it is
+founded entirely upon it. And even with regard to the doctrine, that the
+heavenly bodies move by an inherent virtue; if this doctrine had been
+maintained in any such way that it was brought to agree with the facts,
+the inherent virtue must have had its laws determined; and then it would
+have been found that the virtue had a reference to the central body; and
+so, the 'inherent virtue' must have coincided in its effect with the
+Newtonian force; and then, the two explanations would agree, except so
+far as the word 'inherent' was concerned. And if such a part of an
+earlier theory as this word _inherent_ indicates, is found to be
+untenable, it is of course rejected in the transition to later and more
+exact theories, in Inductions of this kind, as well as in what Mr. Mill
+calls Descriptions. There is, therefore, still no validity discoverable
+in the distinction which Mr. Mill attempts to draw between descriptions
+like Kepler's law of elliptical orbits, and other examples of
+induction."
+
+If the doctrine of vortices had meant, not that vortices existed, but
+only that the planets moved _in the same manner_ as if they had been
+whirled by vortices; if the hypothesis had been merely a mode of
+representing the facts, not an attempt to account for them; if, in
+short, it had been only a Description; it would, no doubt, have been
+reconcileable with the Newtonian theory. The vortices, however, were not
+a mere aid to conceiving the motions of the planets, but a supposed
+physical agent, actively impelling them; a material fact, which might be
+true or not true, but could not be both true and not true. According to
+Descartes' theory it was true, according to Newton's it was not true.
+Dr. Whewell probably means that since the phrases, centripetal and
+projectile force, do not declare the nature but only the direction of
+the forces, the Newtonian theory does not absolutely contradict any
+hypothesis which may be framed respecting the mode of their production.
+The Newtonian theory, regarded as a mere _description_ of the planetary
+motions, does not; but the Newtonian theory as an _explanation_ of them
+does. For in what does the explanation consist? In ascribing those
+motions to a general law which obtains between all particles of matter,
+and in identifying this with the law by which bodies fall to the ground.
+If the planets are kept in their orbits by a force which draws the
+particles composing them towards every other particle of matter in the
+solar system, they are not kept in those orbits by the impulsive force
+of certain streams of matter which whirl them round. The one explanation
+absolutely excludes the other. Either the planets are not moved by
+vortices, or they do not move by a law common to all matter. It is
+impossible that both opinions can be true. As well might it be said that
+there is no contradiction between the assertions, that a man died
+because somebody killed him, and that he died a natural death.
+
+So, again, the theory that the planets move by a virtue inherent in
+their celestial nature, is incompatible with either of the two others:
+either that of their being moved by vortices, or that which regards them
+as moving by a property which they have in common with the earth and all
+terrestrial bodies. Dr. Whewell says that the theory of an inherent
+virtue agrees with Newton's when the word inherent is left out, which of
+course it would be (he says) if "found to be untenable." But leave that
+out, and where is the theory? The word inherent _is_ the theory. When
+that is omitted, there remains nothing except that the heavenly bodies
+move by "a virtue," _i.e._ by a power of some sort; or by virtue of
+their celestial nature, which directly contradicts the doctrine that
+terrestrial bodies fall by the same law.
+
+If Dr. Whewell is not yet satisfied, any other subject will serve
+equally well to test his doctrine. He will hardly say that there is no
+contradiction between the emission theory and the undulatory theory of
+light; or that there can be both one and two electricities; or that the
+hypothesis of the production of the higher organic forms by development
+from the lower, and the supposition of separate and successive acts of
+creation, are quite reconcileable; or that the theory that volcanoes are
+fed from a central fire, and the doctrines which ascribe them to
+chemical action at a comparatively small depth below the earth's
+surface, are consistent with one another, and all true as far as they
+go.
+
+If different explanations of the same fact cannot both be true, still
+less, surely, can different predictions. Dr. Whewell quarrels (on what
+ground it is not necessary here to consider) with the example I had
+chosen on this point, and thinks an objection to an illustration a
+sufficient answer to a theory. Examples not liable to his objection are
+easily found, if the proposition that conflicting predictions cannot
+both be true, can be made clearer by any examples. Suppose the
+phenomenon to be a newly-discovered comet, and that one astronomer
+predicts its return once in every 300 years--another once in every 400:
+can they both be right? When Columbus predicted that by sailing
+constantly westward he should in time return to the point from which he
+set out, while others asserted that he could never do so except by
+turning back, were both he and his opponents true prophets? Were the
+predictions which foretold the wonders of railways and steamships, and
+those which averred that the Atlantic could never be crossed by steam
+navigation, nor a railway train propelled ten miles an hour, both (in
+Dr. Whewell's words) "true, and consistent with one another"?
+
+Dr. Whewell sees no distinction between holding contradictory opinions
+on a question of fact, and merely employing different analogies to
+facilitate the conception of the same fact. The case of different
+Inductions belongs to the former class, that of different Descriptions
+to the latter.
+
+[7] _Phil. of Discov._ p. 256.
+
+[8] _Essays on the Pursuit of Truth._
+
+[9] In the first edition a note was appended at this place, containing
+some criticism on Archbishop Whately's mode of conceiving the relation
+between Syllogism and Induction. In a subsequent issue of his _Logic_,
+the Archbishop made a reply to the criticism, which induced me to cancel
+part of the note, incorporating the remainder in the text. In a still
+later edition, the Archbishop observes in a tone of something like
+disapprobation, that the objections, "doubtless from their being fully
+answered and found untenable, were silently suppressed," and that hence
+he might appear to some of his readers to be combating a shadow. On this
+latter point, the Archbishop need give himself no uneasiness. His
+readers, I make bold to say, will fully credit his mere affirmation that
+the objections have actually been made.
+
+But as he seems to think that what he terms the suppression of the
+objections ought not to have been made "silently," I now break that
+silence, and state exactly what it is that I suppressed, and why. I
+suppressed that alone which might be regarded as personal criticism on
+the Archbishop. I had imputed to him the having omitted to ask himself a
+particular question. I found that he had asked himself the question, and
+could give it an answer consistent with his own theory. I had also,
+within the compass of a parenthesis, hazarded some remarks on certain
+general characteristics of Archbishop Whately as a philosopher. These
+remarks, though their tone, I hope, was neither disrespectful nor
+arrogant, I felt, on reconsideration, that I was hardly entitled to
+make; least of all, when the instance which I had regarded as an
+illustration of them, failed, as I now saw, to bear them out. The real
+matter at the bottom of the whole dispute, the different view we take of
+the function of the major premise, remains exactly where it was; and so
+far was I from thinking that my opinion had been "fully answered" and
+was "untenable," that in the same edition in which I cancelled the note,
+I not only enforced the opinion by further arguments, but answered
+(though without naming him) those of the Archbishop.
+
+For not having made this statement before, I do not think it needful to
+apologize. It would be attaching very great importance to one's smallest
+sayings, to think a formal retractation requisite every time that one
+commits an error. Nor is Archbishop Whately's well-earned fame of so
+tender a quality as to require, that in withdrawing a slight criticism
+on him I should have been bound to offer a public _amende_ for having
+made it.
+
+[10] But though it is a condition of the validity of every induction
+that there be uniformity in the course of nature, it is not a necessary
+condition that the uniformity should pervade all nature. It is enough
+that it pervades the particular class of phenomena to which the
+induction relates. An induction concerning the motions of the planets,
+or the properties of the magnet, would not be vitiated though we were to
+suppose that wind and weather are the sport of chance, provided it be
+assumed that astronomical and magnetic phenomena are under the dominion
+of general laws. Otherwise the early experience of mankind would have
+rested on a very weak foundation; for in the infancy of science it could
+not be known that _all_ phenomena are regular in their course.
+
+Neither would it be correct to say that every induction by which we
+infer any truth, implies the general fact of uniformity _as foreknown_,
+even in reference to the kind of phenomena concerned. It implies,
+_either_ that this general fact is already known, _or_ that we may now
+know it: as the conclusion, the Duke of Wellington is mortal, drawn from
+the instances A, B, and C, implies either that we have already concluded
+all men to be mortal, or that we are now entitled to do so from the same
+evidence. A vast amount of confusion and paralogism respecting the
+grounds of Induction would be dispelled by keeping in view these simple
+considerations.
+
+[11] Infra, chap. xxi.
+
+[12] Infra, chap. xxi. xxii.
+
+[13] Dr. Whewell (_Phil. of Discov._ p. 246) will not allow these and
+similar erroneous judgments to be called inductions; inasmuch as such
+superstitious fancies "were not collected from the facts by seeking a
+law of their occurrence, but were suggested by an imagination of the
+anger of superior powers, shown by such deviations from the ordinary
+course of nature." I conceive the question to be, not in what manner
+these notions were at first suggested, but by what evidence they have,
+from time to time, been supposed to be substantiated. If the believers
+in these erroneous opinions had been put on their defence, they would
+have referred to experience: to the comet which preceded the
+assassination of Julius C�sar, or to oracles and other prophecies known
+to have been fulfilled. It is by such appeals to facts that all
+analogous superstitions, even in our day, attempt to justify themselves;
+the supposed evidence of experience is necessary to their hold on the
+mind. I quite admit that the influence of such coincidences would not be
+what it is, if strength were not lent to it by an antecedent
+presumption; but this is not peculiar to such cases; preconceived
+notions of probability form part of the explanation of many other cases
+of belief on insufficient evidence. The _� priori_ prejudice does not
+prevent the erroneous opinion from being sincerely regarded as a
+legitimate conclusion from experience; though it improperly predisposes
+the mind to that interpretation of experience.
+
+Thus much in defence of the sort of examples objected to. But it would
+be easy to produce instances, equally adapted to the purpose, and in
+which no antecedent prejudice is at all concerned. "For many ages," says
+Archbishop Whately, "all farmers and gardeners were firmly
+convinced--and convinced of their knowing it by experience--that the
+crops would never turn out good unless the seed were sown during the
+increase of the moon." This was induction, but bad induction: just as a
+vicious syllogism is reasoning, but bad reasoning.
+
+[14] The assertion, that any and every one of the conditions of a
+phenomenon may be and is, on some occasions and for some purposes,
+spoken of as the cause, has been disputed by an intelligent reviewer of
+this work in the _Prospective Review_ (the predecessor of the justly
+esteemed _National Review_), who maintains that "we always apply the
+word cause rather to that element in the antecedents which exercises
+_force_, and which would _tend_ at all times to produce the same or a
+similar effect to that which, under certain conditions, it would
+actually produce." And he says, that "every one would feel" the
+expression, that the cause of a surprise was the sentinel's being off
+his post, to be incorrect; but that the "allurement or force which
+_drew_ him off his post, might be so called, because in doing so it
+removed a resisting power which would have prevented the surprise." I
+cannot think that it would be wrong to say, that the event took place
+because the sentinel was absent, and yet right to say that it took place
+because he was bribed to be absent. Since the only direct effect of the
+bribe was his absence, the bribe could be called the remote cause of the
+surprise, only on the supposition that the absence was the proximate
+cause; nor does it seem to me that any one (who had not a theory to
+support) would use the one expression and reject the other.
+
+The reviewer observes, that when a person dies of poison, his possession
+of bodily organs is a necessary condition, but that no one would ever
+speak of it as the cause. I admit the fact; but I believe the reason to
+be, that the occasion could never arise for so speaking of it; for when
+in the inaccuracy of common discourse we are led to speak of some one
+condition of a phenomenon as its cause, the condition so spoken of is
+always one which it is at least possible that the hearer may require to
+be informed of. The possession of bodily organs is a known condition,
+and to give that as the answer, when asked the cause of a person's
+death, would not supply the information sought. Once conceive that a
+doubt could exist as to his having bodily organs, or that he were to be
+compared with some being who had them not, and cases may be imagined in
+which it might be said that his possession of them was the cause of his
+death. If Faust and Mephistopheles together took poison, it might be
+said that Faust died because he was a human being, and had a body, while
+Mephistopheles survived because he was a spirit.
+
+It is for the same reason that no one (as the reviewer remarks) "calls
+the cause of a leap, the muscles or sinews of the body, though they are
+necessary conditions; nor the cause of a self-sacrifice, the knowledge
+which was necessary for it; nor the cause of writing a book, that a man
+has time for it, which is a necessary condition." These conditions
+(besides that they are antecedent _states_, and not proximate antecedent
+_events_, and are therefore never the conditions in closest apparent
+proximity to the effect) are all of them so obviously implied, that it
+is hardly possible there should exist that necessity for insisting on
+them, which alone gives occasion for speaking of a single condition as
+if it were the cause. Wherever this necessity exists in regard to some
+one condition, and does not exist in regard to any other, I conceive
+that it is consistent with usage, when scientific accuracy is not aimed
+at, to apply the name cause to that one condition. If the only condition
+which can be supposed to be unknown is a negative condition, the
+negative condition may be spoken of as the cause. It might be said that
+a person died for want of medical advice: though this would not be
+likely to be said, unless the person was already understood to be ill,
+and in order to indicate that this negative circumstance was what made
+the illness fatal, and not the weakness of his constitution, or the
+original virulence of the disease. It might be said that a person was
+drowned because he could not swim; the positive condition, namely, that
+he fell into the water, being already implied in the word drowned. And
+here let me remark, that his falling into the water is in this case the
+only positive condition: all the conditions not expressly or virtually
+included in this (as that he could not swim, that nobody helped him, and
+so forth) are negative. Yet, if it were simply said that the cause of a
+man's death was falling into the water, there would be quite as great a
+sense of impropriety in the expression, as there would be if it were
+said that the cause was his inability to swim; because, though the one
+condition is positive and the other negative, it would be felt that
+neither of them was sufficient, without the other, to produce death.
+
+With regard to the assertion that nothing is termed the cause, except
+the element which exerts active force; I wave the question as to the
+meaning of active force, and accepting the phrase in its popular sense,
+I revert to a former example, and I ask, would it be more agreeable to
+custom to say that a man fell because his foot slipped in climbing a
+ladder, or that he fell because of his weight? for his weight, and not
+the motion of his foot, was the active force which determined his fall.
+If a person walking out in a frosty day, stumbled and fell, it might be
+said that he stumbled because the ground was slippery, or because he was
+not sufficiently careful; but few people, I suppose, would say, that he
+stumbled because he walked. Yet the only active force concerned was that
+which he exerted in walking: the others were mere negative conditions;
+but they happened to be the only ones which there could be any necessity
+to state; for he walked, most likely, in exactly his usual manner, and
+the negative conditions made all the difference. Again, if a person were
+asked why the army of Xerxes defeated that of Leonidas, he would
+probably say, because they were a thousand times the number; but I do
+not think he would say, it was because they fought, though that was the
+element of active force. To borrow another example, used by Mr. Grove
+and by Mr. Baden Powell, the opening of floodgates is said to be the
+cause of the flow of water; yet the active force is exerted by the water
+itself, and opening the floodgates merely supplies a negative condition.
+The reviewer adds, "there are some conditions absolutely passive, and
+yet absolutely necessary to physical phenomena, viz. the relations of
+space and time; and to these no one ever applies the word cause without
+being immediately arrested by those who hear him." Even from this
+statement I am compelled to dissent. Few persons would feel it
+incongruous to say (for example) that a secret became known because it
+was spoken of when A. B. was within hearing; which is a condition of
+space: or that the cause why one of two particular trees is taller than
+the other, is that it has been longer planted; which is a condition of
+time.
+
+[15] There are a few exceptions; for there are some properties of
+objects which seem to be purely preventive; as the property of opaque
+bodies, by which they intercept the passage of light. This, as far as we
+are able to understand it, appears an instance not of one cause
+counteracting another by the same law whereby it produces its own
+effects, but of an agency which manifests itself in no other way than in
+defeating the effects of another agency. If we knew on what other
+relations to light, or on what peculiarities of structure, opacity
+depends, we might find that this is only an apparent, not a real,
+exception to the general proposition in the text. In any case it needs
+not affect the practical application. The formula which includes all the
+negative conditions of an effect in the single one of the absence of
+counteracting causes, is not violated by such cases as this; though, if
+all counteracting agencies were of this description, there would be no
+purpose served by employing the formula, since we should still have to
+enumerate specially the negative conditions of each phenomenon, instead
+of regarding them as implicitly contained in the positive laws of the
+various other agencies in nature.
+
+[16] I mean by this expression, the ultimate laws of nature (whatever
+they may be) as distinguished from the derivative laws and from the
+collocations. The diurnal revolution of the earth (for example) is not a
+part of the constitution of things, because nothing can be so called
+which might possibly be terminated or altered by natural causes.
+
+[17] I use the words "straight line" for brevity and simplicity. In
+reality the line in question is not exactly straight, for, from the
+effect of refraction, we actually see the sun for a short interval
+during which the opaque mass of the earth is interposed in a direct line
+between the sun and our eyes; thus realizing, though but to a limited
+extent, the coveted desideratum of seeing round a corner.
+
+[18] _Second Burnett Prize Essay_, by Principal Tulloch, p. 25.
+
+[19] _Letters on the Philosophy of the Human Mind_, First Series, p.
+219.
+
+[20] _Essays_, pp. 206-208.
+
+[21] To the universality which mankind are agreed in ascribing to the
+Law of Causation, there is one claim of exception, one disputed case,
+that of the Human Will; the determinations of which, a large class of
+metaphysicians are not willing to regard as following the causes called
+motives, according to as strict laws as those which they suppose to
+exist in the world of mere matter. This controverted point will undergo
+a special examination when we come to treat particularly of the Logic of
+the Moral Sciences (Book vi. ch. 2). In the mean time I may remark that
+these metaphysicians, who, it must be observed, ground the main part of
+their objection on the supposed repugnance of the doctrine in question
+to our consciousness, seem to me to mistake the fact which consciousness
+testifies against. What is really in contradiction to consciousness,
+they would, I think, on strict self-examination, find to be, the
+application to human actions and volitions of the ideas involved in the
+common use of the term Necessity; which I agree with them in objecting
+to. But if they would consider that by saying that a person's actions
+_necessarily_ follow from his character, all that is really meant (for
+no more is meant in any case whatever of causation) is that he
+invariably _does_ act in conformity to his character, and that any one
+who thoroughly knew his character would certainly predict how he would
+act in any supposable case; they probably would not find this doctrine
+either contrary to their experience or revolting to their feelings. And
+no more than this is contended for by any one but an Asiatic fatalist.
+
+[22] _Lectures on Metaphysics_, vol. ii. Lect. xxxix. pp. 391-2.
+
+I regret that I cannot invoke the authority of Sir William Hamilton in
+favour of my own opinions on Causation, as I can against the particular
+theory which I am now combating. But that acute thinker has a theory of
+Causation peculiar to himself, which has never yet, as far as I know,
+been analytically examined, but which, I venture to think, admits of as
+complete refutation as any one of the false or insufficient
+psychological theories which strew the ground in such numbers under his
+potent metaphysical scythe. (Since examined and controverted in the
+sixteenth chapter of _An Examination of Sir William Hamilton's
+Philosophy_).
+
+[23] Unless we are to consider as such the following statement, by one
+of the writers quoted in the text: "In the case of mental exertion, the
+result to be accomplished is preconsidered or meditated, and is
+therefore known _� priori_, or before experience."--(Bowen's _Lowell
+Lectures on the Application of Metaphysical and Ethical Science to the
+Evidence of Religion_, Boston, 1849.) This is merely saying that when we
+will a thing we have an idea of it. But to have an idea of what we wish
+to happen, does not imply a prophetic knowledge that it will happen.
+Perhaps it will be said that the _first time_ we exerted our will, when
+we had of course no experience of any of the powers residing in us, we
+nevertheless must already have known that we possessed them, since we
+cannot will that which we do not believe to be in our power. But the
+impossibility is perhaps in the words only, and not in the facts; for we
+may _desire_ what we do not know to be in our power; and finding by
+experience that our bodies move according to our _desire_, we may then,
+and only then, pass into the more complicated mental state which is
+termed will.
+
+After all, even if we had an instinctive knowledge that our actions
+would follow our will, this, as Brown remarks, would prove nothing as to
+the nature of Causation. Our knowing, previous to experience, that an
+antecedent will be followed by a certain consequent, would not prove the
+relation between them to be anything more than antecedence and
+consequence.
+
+[24] Reid's _Essays on the Active Powers_, Essay iv. ch. 3.
+
+[25] _Prospective Review_ for February 1850.
+
+[26] Vide supra, p. 270, note.
+
+[27] _Westminster Review_ for October 1855.
+
+[28] See the whole doctrine in Aristotle _de Anim�_: where the [Greek:
+threptik� psych�] is treated as exactly equivalent to [Greek: threptik�
+dynamis].
+
+[29] It deserves notice that the parts of nature, which Aristotle
+regards as presenting evidence of design, are the Uniformities: the
+phenomena in so far as reducible to law. [Greek: Tych�] and [Greek: to
+automaton] satisfy him as explanations of the variable element in
+phenomena, but their occurring according to a fixed rule can only, to
+his conceptions, be accounted for by an Intelligent Will. The common, or
+what may be called the instinctive, religious interpretation of nature,
+is the reverse of this. The events in which men spontaneously see the
+hand of a supernatural being, are those which cannot, as they think, be
+reduced to a physical law. What they can distinctly connect with
+physical causes, and especially what they can predict, though of course
+ascribed to an Author of Nature if they already recognise such an
+author, might be conceived, they think, to arise from a blind fatality,
+and in any case do not appear to them to bear so obviously the mark of a
+divine will. And this distinction has been countenanced by eminent
+writers on Natural Theology, in particular by Dr. Chalmers: who thinks
+that though design is present everywhere, the irresistible evidence of
+it is to be found not in the _laws_ of nature but in the collocations,
+_i.e._ in the part of nature in which it is impossible to trace any law.
+A few properties of dead matter might, he thinks, conceivably account
+for the regular and invariable succession of effects and causes; but
+that the different kinds of matter have been so placed as to promote
+beneficent ends, is what he regards as the proof of a Divine Providence.
+Mr. Baden Powell, in his Essay entitled "Philosophy of Creation," has
+returned to the point of view of Aristotle and the ancients, and
+vigorously reasserts the doctrine that the indication of design in the
+universe is not special adaptations, but Uniformity and Law, these being
+the evidences of mind, and not what appears to us to be a provision for
+our uses. While I decline to express any opinion here on this _vexata
+qu�stio_, I ought not to mention Mr. Powell's volume without the
+acknowledgment due to the philosophic spirit which pervades generally
+the three Essays composing it, forming in the case of one of them (the
+"Unity of Worlds") an honourable contrast with the other dissertations,
+so far as they have come under my notice, which have appeared on either
+side of that controversy.
+
+[30] In the words of Fontenelle, another celebrated Cartesian, "les
+philosophes aussi bien que le peuple avaient cru que l'�me et le corps
+agissaient r�ellement et physiquement l'un sur l'autre. Descartes vint,
+qui prouva que leur nature ne permettait point cette sorte de
+communication v�ritable, et qu'ils n'en pouvaient avoir qu'une
+apparente, dont Dieu �tait le M�diateur."--_Oeuvres de Fontenelle_,
+ed. 1767, tom. v. p. 534.
+
+[31] I omit, for simplicity, to take into account the effect, in this
+latter case, of the diminution of pressure, in diminishing the flow of
+water through the drain; which evidently in no way affects the truth or
+applicability of the principle, since when the two causes act
+simultaneously the conditions of that diminution of pressure do not
+arise.
+
+[32] Unless, indeed, the consequent was generated not by the antecedent,
+but by the means employed to produce the antecedent. As, however, these
+means are under our power, there is so far a probability that they are
+also sufficiently within our knowledge, to enable us to judge whether
+that could be the case or not.
+
+[33] _Discourse on the Study of Natural Philosophy_, p. 179.
+
+[34] For this speculation, as for many other of my scientific
+illustrations, I am indebted to Professor Bain, of Aberdeen, who has
+since, in his profound treatises entitled "The Senses and the
+Intellect," and "The Emotions and the Will," carried the analytic
+investigation of the mental phenomena according to the methods of
+physical science, to the most advanced point which it has yet reached,
+and has worthily inscribed his name among the successive constructors of
+an edifice to which Hartley, Brown, and James Mill had each contributed
+their part.
+
+[35] This view of the necessary coexistence of opposite excitements
+involves a great extension of the original doctrine of two
+electricities. The early theorists assumed that, when amber was rubbed,
+the amber was made positive and the rubber negative to the same degree;
+but it never occurred to them to suppose that the existence of the amber
+charge was dependent on an opposite charge in the bodies with which the
+amber was contiguous, while the existence of the negative charge on the
+rubber was equally dependent on a contrary state of the surfaces that
+might accidentally be confronted with it; that, in fact, in a case of
+electrical excitement by friction, four charges were the minimum that
+could exist. But this double electrical action is essentially implied in
+the explanation now universally adopted in regard to the phenomena of
+the common electric machine.
+
+[36] Pp. 159-162.
+
+[37] Infra, book iv. ch. ii. On Abstraction.
+
+[38] I must, however, remark, that this example, which seems to militate
+against the assertion we made of the comparative inapplicability of the
+Method of Difference to cases of pure observation, is really one of
+those exceptions which, according to a proverbial expression, prove the
+general rule. For in this case, in which Nature, in her experiment,
+seems to have imitated the type of the experiments made by man, she has
+only succeeded in producing the likeness of man's most imperfect
+experiments; namely, those in which, though he succeeds in producing the
+phenomenon, he does so by employing complex means, which he is unable
+perfectly to analyse, and can form therefore no sufficient judgment what
+portion of the effects may be due, not to the supposed cause, but to
+some unknown agency of the means by which that cause was produced. In
+the natural experiment which we are speaking of, the means used was the
+clearing off a canopy of clouds; and we certainly do not know
+sufficiently in what this process consists, or on what it depends, to be
+certain _� priori_ that it might not operate upon the deposition of dew
+independently of any thermometric effect at the earth's surface. Even,
+therefore, in a case so favourable as this to Nature's experimental
+talents, her experiment is of little value except in corroboration of a
+conclusion already attained through other means.
+
+[39] In his subsequent work, _Outlines of Astronomy_ (� 570), Sir John
+Herschel suggests another possible explanation of the acceleration of
+the revolution of a comet.
+
+[40] Discourse, pp. 156-8, and 171.
+
+[41] _Outlines of Astronomy_, � 856.
+
+[42] _Philosophy of Discovery_, pp. 263, 264.
+
+[43] See, on this point, the second chapter of the present Book.
+
+[44] Ante, ch. vii. � 1.
+
+[45] It seems hardly necessary to say that the word _impinge_, as a
+general term to express collision of forces, is here used by a figure of
+speech, and not as expressive of any theory respecting the nature of
+force.
+
+[46] _Essays on some Unsettled Questions of Political Economy_, Essay V.
+
+[47] _Vide_ Memoir by Thomas Graham, F.R.S., Master of the Mint, "On
+Liquid Diffusion Applied to Analysis," in the _Philosophical
+Transactions_ for 1862, reprinted in the _Journal of the Chemical
+Society_, and also separately as a pamphlet.
+
+[48] It was an old generalization in surgery, that tight bandaging had a
+tendency to prevent or dissipate local inflammation. This sequence,
+being, in the progress of physiological knowledge, resolved into more
+general laws, led to the important surgical invention made by Dr.
+Arnott, the treatment of local inflammation and tumours by means of an
+equable pressure, produced by a bladder partially filled with air. The
+pressure, by keeping back the blood from the part, prevents the
+inflammation, or the tumour, from being nourished: in the case of
+inflammation, it removes the stimulus, which the organ is unfit to
+receive; in the case of tumours, by keeping back the nutritive fluid, it
+causes the absorption of matter to exceed the supply, and the diseased
+mass is gradually absorbed and disappears.
+
+[49] Since acknowledged and reprinted in Mr. Martineau's _Miscellanies_.
+
+[50] _Dissertations and Discussions_, vol. i., fourth paper.
+
+[51] Written before the rise of the new views respecting the relation of
+heat to mechanical force; but confirmed rather than contradicted by
+them.
+
+
+END OF VOL. I.
+
+
+
+
+  LONDON:
+  SAVILL, EDWARDS AND CO., PRINTERS, CHANDOS STREET,
+  COVENT GARDEN.
+
+
+
+
+Transcriber's Notes
+
+
+Spelling irregularities where there was no obviously preferred version
+were left as is. Variants include: "alkalies" and "alkalis;" "apprise"
+and "apprize;" "coexistent" and "co-existent" (along with derivatives);
+"coextensive" and "co-extensive;" "e. g." and "e.g."; "encumbered" and
+"incumbered;" "formul�" and "formulas;" "i. e." and "i.e."; "nonentity"
+and "non-entity;" "recal" and "recall" (and derivatives); "rectilinear"
+and "rectilineal;" "stopt" and "stopped."
+
+Changed "3" to "4" on page xiii: "4. --and from descriptions."
+
+Inserted missing page number, "167," for Chapter VIII, section 7 on page
+xiii.
+
+Moved the semi-colon inside the quotation marks in the footnote on page
+14: "the Science of the Formal Laws of Thought;".
+
+Changed "sub-divisions" to "subdivisions" on page 59: "three
+subdivisions."
+
+Changed "pre-supposed" to "presupposed" on page 75: "they are
+presupposed."
+
+In the footnote to page 122, changed the Greek character upsilon with
+dasia and oxia to upsilon with psili and oxia, making the
+transliteration "deuterai ousiai."
+
+Changed "he" to "be" on page 189: "to which it may be reduced."
+
+Changed "cb." to "ch." in footnote on page 227: "Theory of Reasoning,
+ch. iv."
+
+Changed "reconcilable" to "reconcileable" on page 240: "not easily
+reconcileable."
+
+Preserved the hyphen in "counter-acting" on page 280. Usually this is
+spelled without the hyphen, but this instance is in a quotation.
+
+Moved parenthesis that was after "to" to before it on page 321: "(to
+return to a former example)."
+
+Put "i.e." in italics on page 335: "_i.e._ by a power of some sort."
+
+Changed "paralyzed" to "paralysed" on page 389: "nerves of motion were
+paralysed."
+
+The footnote from page 396 refers to the footnote on page 270. There is
+no such footnote. The intent may be to refer to the footnote on page
+268. However, the text was not changed.
+
+Added the dropped "w" in "which" on page 420: "which the progress of the
+inquiry."
+
+Changed "developes" to "develops" on page 456: "the prime conductor
+develops."
+
+Removed the additional period at the end of the footnote on page 457:
+"Pp. 159-162."
+
+Added the dropped "l" to "essential" on page 515: "an essential
+requisite."
+
+Removed extra opening quotation mark before "gum" on page 532:
+"vegetable gum is not digested."
+
+In the Latin-1 text version, the oe-ligature was replaced by the two
+characters, "oe" (or "Oe" when capitalized).
+
+
+
+
+
+End of the Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
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+<pre>
+
+The Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A System of Logic: Ratiocinative and Inductive
+       7th Edition, Vol. I
+
+Author: John Stuart Mill
+
+Release Date: February 27, 2011 [EBook #35420]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL I ***
+
+
+
+
+Produced by David Clarke, Stephen H. Sentoff and the Online
+Distributed Proofreading Team at https://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+</pre>
+
+
+
+
+<p class="center">
+A<br />
+SYSTEM OF LOGIC<br />
+<br />
+RATIOCINATIVE AND INDUCTIVE</p>
+<hr class="tb" />
+<p class="center">
+VOL. I.
+</p>
+
+
+
+
+<hr class="chap" />
+<h1>
+A<br />
+SYSTEM OF LOGIC<br />
+<br />
+RATIOCINATIVE AND INDUCTIVE<br />
+</h1>
+<div class="likeheading2">
+BEING A CONNECTED VIEW OF THE<br />
+PRINCIPLES OF EVIDENCE<br />
+AND THE<br />
+METHODS OF SCIENTIFIC INVESTIGATION<br />
+</div>
+<div class="likeheading3">BY</div>
+
+<div class="likeheading2">JOHN STUART MILL</div>
+
+<hr class="tb" />
+<div class="likeheading2">
+IN TWO VOLUMES<br />
+<br />
+VOL. I.</div>
+<div class="likeheading2">
+SEVENTH EDITION</div>
+
+<p class="center">
+LONDON:<br />
+LONGMANS, GREEN, READER, AND DYER<br />
+<br />
+MDCCCLXVIII
+</p>
+
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p>
+<h2><a name="PREFACE_TO_THE_FIRST_EDITION" id="PREFACE_TO_THE_FIRST_EDITION"></a>PREFACE TO THE FIRST EDITION.</h2>
+
+
+<p>This book makes no pretence of giving to the world a new theory of the
+intellectual operations. Its claim to attention, if it possess any, is
+grounded on the fact that it is an attempt not to supersede, but to
+embody and systematize, the best ideas which have been either
+promulgated on its subject by speculative writers, or conformed to by
+accurate thinkers in their scientific inquiries.</p>
+
+<p>To cement together the detached fragments of a subject, never yet
+treated as a whole; to harmonize the true portions of discordant
+theories, by supplying the links of thought necessary to connect them,
+and by disentangling them from the errors with which they are always
+more or less interwoven; must necessarily require a considerable amount
+of original speculation. To other originality than this, the present
+work lays no claim. In the existing state of the cultivation of the
+sciences, there would be a very strong presumption against any one who
+should imagine that he had effected a revolution in the theory of the
+investigation of truth, or added any fundamentally new process to the
+practice of it. The improvement which remains to be effected in the
+methods of philosophizing (and the author believes that they have much
+need of improvement) can only consist in performing, more systematically
+<span class="pagenum"><a name="Page_vi" id="Page_vi">[Pg vi]</a></span>and accurately, operations with which, at least in their elementary
+form, the human intellect in some one or other of its employments is
+already familiar.</p>
+
+<p>In the portion of the work which treats of Ratiocination, the author has
+not deemed it necessary to enter into technical details which may be
+obtained in so perfect a shape from the existing treatises on what is
+termed the Logic of the Schools. In the contempt entertained by many
+modern philosophers for the syllogistic art, it will be seen that he by
+no means participates; though the scientific theory on which its defence
+is usually rested appears to him erroneous: and the view which he has
+suggested of the nature and functions of the Syllogism may, perhaps,
+afford the means of conciliating the principles of the art with as much
+as is well grounded in the doctrines and objections of its assailants.</p>
+
+<p>The same abstinence from details could not be observed in the First
+Book, on Names and Propositions; because many useful principles and
+distinctions which were contained in the old Logic, have been gradually
+omitted from the writings of its later teachers; and it appeared
+desirable both to revive these, and to reform and rationalize the
+philosophical foundation on which they stood. The earlier chapters of
+this preliminary Book will consequently appear, to some readers,
+needlessly elementary and scholastic. But those who know in what
+darkness the nature of our knowledge, and of the processes by which it
+is obtained, is often involved by a confused apprehension of the import
+of the different classes of Words and Assertions, will not regard these
+discussions as either frivolous, or irrelevant to the topics considered
+in the later Books.</p>
+
+<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a></span></p><p>On the subject of Induction, the task to be performed was that of
+generalizing the modes of investigating truth and estimating evidence,
+by which so many important and recondite laws of nature have, in the
+various sciences, been aggregated to the stock of human knowledge. That
+this is not a task free from difficulty may be presumed from the fact,
+that even at a very recent period, eminent writers (among whom it is
+sufficient to name Archbishop Whately, and the author of a celebrated
+article on Bacon in the <i>Edinburgh Review</i>) have not scrupled to
+pronounce it impossible.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> The author has endeavoured to combat their
+theory in the manner in which Diogenes confuted the sceptical reasonings
+against the possibility of motion; remembering that Diogenes' argument
+would have been equally conclusive, though his individual perambulations
+might not have extended beyond the circuit of his own tub.</p>
+
+<p>Whatever may be the value of what the author has succeeded in effecting
+on this branch of his subject, it is a duty to acknowledge that for much
+of it <span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span>he has been indebted to several important treatises, partly
+historical and partly philosophical, on the generalities and processes
+of physical science, which have been published within the last few
+years. To these treatises, and to their authors, he has endeavoured to
+do justice in the body of the work. But as with one of these writers,
+Dr. Whewell, he has occasion frequently to express differences of
+opinion, it is more particularly incumbent on him in this place to
+declare, that without the aid derived from the facts and ideas contained
+in that gentleman's <i>History of the Inductive Sciences</i>, the
+corresponding portion of this work would probably not have been written.</p>
+
+<p>The concluding Book is an attempt to contribute towards the solution of
+a question, which the decay of old opinions, and the agitation that
+disturbs European society to its inmost depths, render as important in
+the present day to the practical interests of human life, as it must at
+all times be to the completeness of our speculative knowledge: viz.
+Whether moral and social phenomena are really exceptions to the general
+certainty and uniformity of the course of nature; and how far the
+methods, by which so many of the laws of the physical world have been
+numbered among truths irrevocably acquired and universally assented to,
+can be made instrumental to the formation of a similar body of received
+doctrine in moral and political science.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span></p>
+<h2><a name="PREFACE_TO_THE_THIRD_AND_FOURTH_EDITIONS" id="PREFACE_TO_THE_THIRD_AND_FOURTH_EDITIONS"></a>PREFACE TO THE THIRD AND FOURTH EDITIONS.</h2>
+
+
+<p>Several criticisms, of a more or less controversial character, on this
+work, have appeared since the publication of the second edition; and Dr.
+Whewell has lately published a reply to those parts of it in which some
+of his opinions were controverted.<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a></p>
+
+<p>I have carefully reconsidered all the points on which my conclusions
+have been assailed. But I have not to announce a change of opinion on
+any matter of importance. Such minor oversights as have been detected,
+either by myself or by my critics, I have, in general silently,
+corrected: but it is not to be inferred that I agree with the objections
+which have been made to a passage, in every instance in which I have
+altered or cancelled it. I have often done so, merely that it might not
+remain a stumbling-block, when the amount of discussion necessary to
+place the matter in its true light would have exceeded what was suitable
+to the occasion.</p>
+
+<p>To several of the arguments which have been urged against me, I have
+thought it useful to reply with some degree of minuteness; not from any
+taste <span class="pagenum"><a name="Page_x" id="Page_x">[Pg x]</a></span>for controversy, but because the opportunity was favourable for
+placing my own conclusions, and the grounds of them, more clearly and
+completely before the reader. Truth, on these subjects, is militant, and
+can only establish itself by means of conflict. The most opposite
+opinions can make a plausible show of evidence while each has the
+statement of its own case; and it is only possible to ascertain which of
+them is in the right, after hearing and comparing what each can say
+against the other, and what the other can urge in its defence.</p>
+
+<p>Even the criticisms from which I most dissent have been of great service
+to me, by showing in what places the exposition most needed to be
+improved, or the argument strengthened. And I should have been well
+pleased if the book had undergone a much greater amount of attack; as in
+that case I should probably have been enabled to improve it still more
+than I believe I have now done.</p>
+
+<hr class="tb" />
+
+<p>In the subsequent editions, the attempt to improve the work by additions
+and corrections, suggested by criticism or by thought, has been
+continued. In the present (seventh) edition, a few further corrections
+have been made, but no material additions.</p>
+
+<div class="footnotes"><h3>FOOTNOTES:</h3>
+
+<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> In the later editions of Archbishop Whately's <i>Logic</i>, he
+states his meaning to be, not that "rules" for the ascertainment of
+truths by inductive investigation cannot be laid down, or that they may
+not be "of eminent service," but that they "must always be comparatively
+vague and general, and incapable of being built up into a regular
+demonstrative theory like that of the Syllogism." (Book IV. ch. iv. �
+3.) And he observes, that to devise a system for this purpose, capable
+of being "brought into a scientific form," would be an achievement which
+"he must be more sanguine than scientific who expects." (Book IV. ch.
+ii. � 4.) To effect this, however, being the express object of the
+portion of the present work which treats of Induction, the words in the
+text are no overstatement of the difference of opinion between
+Archbishop Whately and me on the subject.</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> Now forming a chapter in his volume on <i>The Philosophy of
+Discovery</i>.</p></div>
+</div>
+
+<hr class="chap" />
+<p><span class="pagenum"><a name="Page_xi" id="Page_xi">[Pg xi]</a></span></p>
+<h2>
+CONTENTS<br />
+OF<br />
+THE FIRST VOLUME.<br />
+</h2>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td></td><td><div class="tocbook"><a href="#INTRODUCTION">INTRODUCTION.</a></div></td></tr>
+
+
+<tr><td align="right" valign="top" style="width:3em;">� <a href="#INTRODUCTION_1">1.</a></td><td align="left" style="width:80%;">A definition at the commencement of a subject must be provisional</td><td align="right" valign="top" style="width:10%;"><a href="#Page_1">1</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_2">2.</a></td><td align="left">Is logic the art and science of reasoning?</td><td align="right" valign="top"><a href="#Page_2">2</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_3">3.</a></td><td align="left">Or the art and science of the pursuit of truth?</td><td align="right" valign="top"><a href="#Page_3">3</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_4">4.</a></td><td align="left">Logic is concerned with inferences, not with intuitive truths</td><td align="right" valign="top"><a href="#Page_5">5</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_5">5.</a></td><td align="left">Relation of logic to the other sciences</td><td align="right" valign="top"><a href="#Page_8">8</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_6">6.</a></td><td align="left">Its utility, how shown</td><td align="right" valign="top"><a href="#Page_10">10</a></td></tr>
+<tr><td align="right" valign="top"><a href="#INTRODUCTION_7">7.</a></td><td align="left">Definition of logic stated and illustrated</td><td align="right" valign="top"><a href="#Page_11">11</a></td></tr>
+
+
+<tr><td></td><td><div class="tocbook"><a href="#BOOK_I">BOOK I.</a><br />
+OF NAMES AND PROPOSITIONS.</div></td></tr>
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_I">Chapter I.</a></span> <i>Of the Necessity of commencing with an
+Analysis of Language.</i></div></td></tr>
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_I_1">1.</a></td><td align="left">Theory of names, why a necessary part of logic</td><td align="right" valign="top"><a href="#Page_17">17</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_I_2">2.</a></td><td align="left">First step in the analysis of Propositions</td><td align="right" valign="top"><a href="#Page_18">18</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_I_3">3.</a></td><td align="left">Names must be studied before Things</td><td align="right" valign="top"><a href="#Page_21">21</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_II">Chapter II.</a></span> <i>Of Names.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_II_1">1.</a></td><td align="left">Names are names of things, not of our ideas</td><td align="right" valign="top"><a href="#Page_23">23</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_2">2.</a></td><td align="left">Words which are not names, but parts of names</td><td align="right" valign="top"><a href="#Page_24">24</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_3">3.</a></td><td align="left">General and Singular names</td><td align="right" valign="top"><a href="#Page_26">26</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_4">4.</a></td><td align="left">Concrete and Abstract</td><td align="right" valign="top"><a href="#Page_29">29</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_5">5.</a></td><td align="left">Connotative and Non-connotative</td><td align="right" valign="top"><a href="#Page_31">31</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_6">6.</a></td><td align="left">Positive and Negative</td><td align="right" valign="top"><a href="#Page_42">42</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_7">7.</a></td><td align="left">Relative and Absolute</td><td align="right" valign="top"><a href="#Page_44">44</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_II_8">8.</a></td><td align="left">Univocal and �quivocal</td><td align="right" valign="top"><a href="#Page_47">47</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xii" id="Page_xii">[Pg xii]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_III">Chapter III.</a></span> <i>Of the Things denoted by Names.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_III_1">1.</a></td><td align="left">Necessity of an enumeration of Nameable Things. The Categories of Aristotle</td><td align="right" valign="top"><a href="#Page_49">49</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_2">2.</a></td><td align="left">Ambiguity of the most general names</td><td align="right" valign="top"><a href="#Page_51">51</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_3">3.</a></td><td align="left">Feelings, or states of consciousness</td><td align="right" valign="top"><a href="#Page_54">54</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_4">4.</a></td><td align="left">Feelings must be distinguished from their physical antecedents. Perceptions, what</td><td align="right" valign="top"><a href="#Page_56">56</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_5">5.</a></td><td align="left">Volitions, and Actions, what</td><td align="right" valign="top"><a href="#Page_58">58</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_6">6.</a></td><td align="left">Substance and Attribute</td><td align="right" valign="top"><a href="#Page_59">59</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_7">7.</a></td><td align="left">Body</td><td align="right" valign="top"><a href="#Page_61">61</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_8">8.</a></td><td align="left">Mind</td><td align="right" valign="top"><a href="#Page_67">67</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_9">9.</a></td><td align="left">Qualities</td><td align="right" valign="top"><a href="#Page_69">69</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_10">10.</a></td><td align="left">Relations</td><td align="right" valign="top"><a href="#Page_72">72</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_11">11.</a></td><td align="left">Resemblance</td><td align="right" valign="top"><a href="#Page_74">74</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_12">12.</a></td><td align="left">Quantity</td><td align="right" valign="top"><a href="#Page_78">78</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_13">13.</a></td><td align="left">All attributes of bodies are grounded on states of consciousness</td><td align="right" valign="top"><a href="#Page_79">79</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_14">14.</a></td><td align="left">So also all attributes of mind</td><td align="right" valign="top"><a href="#Page_80">80</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_III_15">15.</a></td><td align="left">Recapitulation</td><td align="right" valign="top"><a href="#Page_81">81</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_IV">Chapter IV.</a></span> <i>Of Propositions.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_IV_1">1.</a></td><td align="left">Nature and office of the copula</td><td align="right" valign="top"><a href="#Page_85">85</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_IV_2">2.</a></td><td align="left">Affirmative and Negative propositions</td><td align="right" valign="top"><a href="#Page_87">87</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_IV_3">3.</a></td><td align="left">Simple and Complex</td><td align="right" valign="top"><a href="#Page_89">89</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_IV_4">4.</a></td><td align="left">Universal, Particular, and Singular</td><td align="right" valign="top"><a href="#Page_93">93</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_V">Chapter V.</a></span> <i>Of the Import of Propositions.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_V_1">1.</a></td><td align="left">Doctrine that a proposition is the expression of a relation between two ideas</td><td align="right" valign="top"><a href="#Page_96">96</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_2">2.</a></td><td align="left">Doctrine that it is the expression of a relation between the meanings of two names</td><td align="right" valign="top"><a href="#Page_99">99</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_3">3.</a></td><td align="left">Doctrine that it consists in referring something to, or excluding something from, a class</td><td align="right" valign="top"><a href="#Page_103">103</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_4">4.</a></td><td align="left">What it really is</td><td align="right" valign="top"><a href="#Page_107">107</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_5">5.</a></td><td align="left">It asserts (or denies) a sequence, a coexistence, a simple existence, a causation</td><td align="right" valign="top"><a href="#Page_110">110</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_6">6.</a></td><td align="left">&mdash;or a resemblance</td><td align="right" valign="top"><a href="#Page_112">112</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_V_7">7.</a></td><td align="left">Propositions of which the terms are abstract</td><td align="right" valign="top"><a href="#Page_115">115</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xiii" id="Page_xiii">[Pg xiii]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_VI">Chapter VI.</a></span> <i>Of Propositions merely Verbal.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_VI_1">1.</a></td><td align="left">Essential and Accidental propositions</td><td align="right" valign="top"><a href="#Page_119">119</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VI_2">2.</a></td><td align="left">All essential propositions are identical propositions</td><td align="right" valign="top"><a href="#Page_120">120</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VI_3">3.</a></td><td align="left">Individuals have no essences</td><td align="right" valign="top"><a href="#Page_124">124</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VI_4">4.</a></td><td align="left">Real propositions, how distinguished from verbal</td><td align="right" valign="top"><a href="#Page_126">126</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VI_5">5.</a></td><td align="left">Two modes of representing the import of a Real proposition</td><td align="right" valign="top"><a href="#Page_127">127</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_VII">Chapter VII.</a></span> <i>Of the Nature of Classification, and
+the Five Predicables.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_VII_1">1.</a></td><td align="left">Classification, how connected with Naming</td><td align="right" valign="top"><a href="#Page_129">129</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_2">2.</a></td><td align="left">The Predicables, what</td><td align="right" valign="top"><a href="#Page_131">131</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_3">3.</a></td><td align="left">Genus and Species</td><td align="right" valign="top"><a href="#Page_131">131</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_4">4.</a></td><td align="left">Kinds have a real existence in nature</td><td align="right" valign="top"><a href="#Page_134">134</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_5">5.</a></td><td align="left">Differentia</td><td align="right" valign="top"><a href="#Page_139">139</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_6">6.</a></td><td align="left">Differenti� for general purposes, and differenti� for special or technical purposes</td><td align="right" valign="top"><a href="#Page_141">141</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_7">7.</a></td><td align="left">Proprium</td><td align="right" valign="top"><a href="#Page_144">144</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VII_8">8.</a></td><td align="left">Accidens</td><td align="right" valign="top"><a href="#Page_146">146</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_I_CHAPTER_VIII">Chapter VIII.</a></span> <i>Of Definition.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_I_CHAPTER_VIII_1">1.</a></td><td align="left">A definition, what</td><td align="right" valign="top"><a href="#Page_148">148</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_2">2.</a></td><td align="left">Every name can be defined, whose meaning is susceptible of analysis</td><td align="right" valign="top"><a href="#Page_150">150</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_3">3.</a></td><td align="left">Complete, how distinguished from incomplete definitions</td><td align="right" valign="top"><a href="#Page_152">152</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_4">4.</a></td><td align="left">&mdash;and from descriptions</td><td align="right" valign="top"><a href="#Page_154">154</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_5">5.</a></td><td align="left">What are called definitions of Things, are definitions of Names with an implied assumption of the existence of Things corresponding to them</td><td align="right" valign="top"><a href="#Page_157">157</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_6">6.</a></td><td align="left">&mdash;even when such things do not in reality exist</td><td align="right" valign="top"><a href="#Page_165">165</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_I_CHAPTER_VIII_7">7.</a></td><td align="left">Definitions, though of names only, must be grounded on knowledge of the corresponding Things</td><td align="right" valign="top"><a href="#Page_167">167</a></td></tr>
+
+
+
+<tr><td><span class="pagenum"><a name="Page_xiv" id="Page_xiv">[Pg xiv]</a></span></td><td><div class="tocbook"><a href="#BOOK_II">BOOK II.</a><br />
+
+OF REASONING.</div></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_I">Chapter I.</a></span> <i>Of Inference, or Reasoning, in general.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_I_1">1.</a></td><td align="left">Retrospect of the preceding book</td><td align="right" valign="top"><a href="#Page_175">175</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_I_2">2.</a></td><td align="left">Inferences improperly so called</td><td align="right" valign="top"><a href="#Page_177">177</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_I_3">3.</a></td><td align="left">Inferences proper, distinguished into inductions and ratiocinations</td><td align="right" valign="top"><a href="#Page_181">181</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_II">Chapter II.</a></span> <i>Of Ratiocination, or Syllogism.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_II_1">1.</a></td><td align="left">Analysis of the Syllogism</td><td align="right" valign="top"><a href="#Page_184">184</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_II_2">2.</a></td><td align="left">The <i>dictum de omni</i> not the foundation of reasoning, but a mere identical proposition</td><td align="right" valign="top"><a href="#Page_191">191</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_II_3">3.</a></td><td align="left">What is the really fundamental axiom of Ratiocination</td><td align="right" valign="top"><a href="#Page_196">196</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_II_4">4.</a></td><td align="left">The other form of the axiom</td><td align="right" valign="top"><a href="#Page_199">199</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_III">Chapter III.</a></span> <i>Of the Functions, and Logical Value, of the
+Syllogism.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_III_1">1.</a></td><td align="left">Is the syllogism a <i>petitio principii</i>?</td><td align="right" valign="top"><a href="#Page_202">202</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_2">2.</a></td><td align="left">Insufficiency of the common theory</td><td align="right" valign="top"><a href="#Page_203">203</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_3">3.</a></td><td align="left">All inference is from particulars to particulars</td><td align="right" valign="top"><a href="#Page_205">205</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_4">4.</a></td><td align="left">General propositions are a record of such inferences, and the rules of the syllogism are rules for the interpretation of the record</td><td align="right" valign="top"><a href="#Page_214">214</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_5">5.</a></td><td align="left">The syllogism not the type of reasoning, but a test of it</td><td align="right" valign="top"><a href="#Page_218">218</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_6">6.</a></td><td align="left">The true type, what</td><td align="right" valign="top"><a href="#Page_222">222</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_7">7.</a></td><td align="left">Relation between Induction and Deduction</td><td align="right" valign="top"><a href="#Page_226">226</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_8">8.</a></td><td align="left">Objections answered</td><td align="right" valign="top"><a href="#Page_227">227</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_III_9">9.</a></td><td align="left">Of Formal Logic, and its relation to the Logic of Truth</td><td align="right" valign="top"><a href="#Page_231">231</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_IV">Chapter IV.</a></span> <i>Of Trains of Reasoning, and Deductive
+Sciences.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_IV_1">1.</a></td><td align="left">For what purpose trains of reasoning exist</td><td align="right" valign="top"><a href="#Page_234">234</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_2">2.</a></td><td align="left">A train of reasoning is a series of inductive inferences</td><td align="right" valign="top"><a href="#Page_234">234</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_3">3.</a></td><td align="left">&mdash;from particulars to particulars through marks of marks</td><td align="right" valign="top"><a href="#Page_237">237</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_4">4.</a></td><td align="left">Why there are deductive sciences</td><td align="right" valign="top"><a href="#Page_240">240</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_5">5.</a></td><td align="left">Why other sciences still remain experimental</td><td align="right" valign="top"><a href="#Page_244">244</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_6">6.</a></td><td align="left">Experimental sciences may become deductive by the progress of experiment</td><td align="right" valign="top"><a href="#Page_246">246</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_IV_7">7.</a></td><td align="left">In what manner this usually takes place</td><td align="right" valign="top"><a href="#Page_247">247</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xv" id="Page_xv">[Pg xv]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_V">Chapter V.</a></span> <i>Of Demonstration, and Necessary Truths.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_V_1">1.</a></td><td align="left">The Theorems of geometry are necessary truths only in the sense of necessarily following from hypotheses</td><td align="right" valign="top"><a href="#Page_251">251</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_V_2">2.</a></td><td align="left">Those hypotheses are real facts with some of their circumstances exaggerated or omitted</td><td align="right" valign="top"><a href="#Page_255">255</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_V_3">3.</a></td><td align="left">Some of the first principles of geometry are axioms, and these are not hypothetical</td><td align="right" valign="top"><a href="#Page_256">256</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_V_4">4.</a></td><td align="left">&mdash;but are experimental truths</td><td align="right" valign="top"><a href="#Page_258">258</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_V_5">5.</a></td><td align="left">An objection answered</td><td align="right" valign="top"><a href="#Page_261">261</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_V_6">6.</a></td><td align="left">Dr. Whewell's opinions on axioms examined</td><td align="right" valign="top"><a href="#Page_264">264</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_VI">Chapter VI.</a></span> <i>The same Subject continued.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_VI_1">1.</a></td><td align="left">All deductive sciences are inductive</td><td align="right" valign="top"><a href="#Page_282">281</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VI_2">2.</a></td><td align="left">The propositions of the science of number are not verbal, but generalizations from experience</td><td align="right" valign="top"><a href="#Page_284">284</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VI_3">3.</a></td><td align="left">In what sense hypothetical</td><td align="right" valign="top"><a href="#Page_289">289</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VI_4">4.</a></td><td align="left">The characteristic property of demonstrative science is to be hypothetical</td><td align="right" valign="top"><a href="#Page_290">290</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VI_5">5.</a></td><td align="left">Definition of demonstrative evidence</td><td align="right" valign="top"><a href="#Page_292">292</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_II_CHAPTER_VII">Chapter VII.</a></span> <i>Examination of some Opinions opposed to
+the preceding doctrines.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_II_CHAPTER_VII_1">1.</a></td><td align="left">Doctrine of the Universal Postulate</td><td align="right" valign="top"><a href="#Page_294">294</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VII_2">2.</a></td><td align="left">The test of inconceivability does not represent the aggregate of past experience</td><td align="right" valign="top"><a href="#Page_296">296</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VII_3">3.</a></td><td align="left">&mdash;nor is implied in every process of thought</td><td align="right" valign="top"><a href="#Page_299">299</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_II_CHAPTER_VII_4">4.</a></td><td align="left">Sir W. Hamilton's opinion on the Principles of Contradiction and Excluded Middle</td><td align="right" valign="top"><a href="#Page_306">306</a></td></tr>
+
+
+<tr><td></td><td><div class="tocbook"><a href="#BOOK_III">BOOK III.</a><br />
+
+OF INDUCTION.</div></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_I">Chapter I.</a></span> <i>Preliminary Observations on Induction in general.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_I_1">1.</a></td><td align="left">Importance of an Inductive Logic</td><td align="right" valign="top"><a href="#Page_313">313</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_I_2">2.</a></td><td align="left">The logic of science is also that of business and life</td><td align="right" valign="top"><a href="#Page_314">314</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_II">Chapter II.</a></span> <i>Of Inductions improperly so called.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_II_1">1.</a></td><td align="left">Inductions distinguished from verbal transformations</td><td align="right" valign="top"><a href="#Page_319">319</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_II_2">2.</a></td><td align="left">&mdash;from inductions, falsely so called, in mathematics</td><td align="right" valign="top"><a href="#Page_321">321</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_II_3">3.</a></td><td align="left">&mdash;and from descriptions</td><td align="right" valign="top"><a href="#Page_323">323</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_II_4">4.</a></td><td align="left">Examination of Dr. Whewell's theory of Induction</td><td align="right" valign="top"><a href="#Page_326">326</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_II_5">5.</a></td><td align="left">Further illustration of the preceding remarks</td><td align="right" valign="top"><a href="#Page_336">336</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xvi" id="Page_xvi">[Pg xvi]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_III">Chapter III.</a></span> <i>On the Ground of Induction.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_III_1">1.</a></td><td align="left">Axiom of the uniformity of the course of nature</td><td align="right" valign="top"><a href="#Page_341">341</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_III_2">2.</a></td><td align="left">Not true in every sense. Induction <i>per enumerationem simplicem</i></td><td align="right" valign="top"><a href="#Page_346">346</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_III_3">3.</a></td><td align="left">The question of Inductive Logic stated</td><td align="right" valign="top"><a href="#Page_348">348</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_IV">Chapter IV.</a></span> <i>Of Laws of Nature.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_IV_1">1.</a></td><td align="left">The general regularity in nature is a tissue of partial regularities, called laws</td><td align="right" valign="top"><a href="#Page_351">351</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IV_2">2.</a></td><td align="left">Scientific induction must be grounded on previous spontaneous inductions</td><td align="right" valign="top"><a href="#Page_355">355</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IV_3">3.</a></td><td align="left">Are there any inductions fitted to be a test of all others?</td><td align="right" valign="top"><a href="#Page_357">357</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_V">Chapter V.</a></span> <i>Of the Law of Universal Causation.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_V_1">1.</a></td><td align="left">The universal law of successive phenomena is the Law of Causation</td><td align="right" valign="top"><a href="#Page_360">360</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_2">2.</a></td><td align="left">&mdash;<i>i.e.</i> the law that every consequent has an invariable antecedent</td><td align="right" valign="top"><a href="#Page_363">363</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_3">3.</a></td><td align="left">The cause of a phenomenon is the assemblage of its conditions</td><td align="right" valign="top"><a href="#Page_365">365</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_4">4.</a></td><td align="left">The distinction of agent and patient illusory</td><td align="right" valign="top"><a href="#Page_373">373</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_5">5.</a></td><td align="left">The cause is not the invariable antecedent, but the <i>unconditional</i> invariable antecedent</td><td align="right" valign="top"><a href="#Page_375">375</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_6">6.</a></td><td align="left">Can a cause be simultaneous with its effect?</td><td align="right" valign="top"><a href="#Page_380">380</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_7">7.</a></td><td align="left">Idea of a Permanent Cause, or original natural agent</td><td align="right" valign="top"><a href="#Page_383">383</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_8">8.</a></td><td align="left">Uniformities of coexistence between effects of different permanent causes, are not laws</td><td align="right" valign="top"><a href="#Page_386">386</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_V_9">9.</a></td><td align="left">Doctrine that volition is an efficient cause, examined</td><td align="right" valign="top"><a href="#Page_387">387</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_VI">Chapter VI.</a></span> <i>Of the Composition of Causes.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_VI_1">1.</a></td><td align="left">Two modes of the conjunct action of causes, the mechanical and the chemical</td><td align="right" valign="top"><a href="#Page_405">405</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VI_2">2.</a></td><td align="left">The composition of causes the general rule; the other case exceptional</td><td align="right" valign="top"><a href="#Page_408">408</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VI_3">3.</a></td><td align="left">Are effects proportional to their causes?</td><td align="right" valign="top"><a href="#Page_412">412</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_VII">Chapter VII.</a></span> <i>Of Observation and Experiment.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_VII_1">1.</a></td><td align="left">The first step of inductive inquiry is a mental analysis of complex phenomena into their elements</td><td align="right" valign="top"><a href="#Page_414">414</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VII_2">2.</a></td><td align="left">The next is an actual separation of those elements</td><td align="right" valign="top"><a href="#Page_416">416</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VII_3">3.</a></td><td align="left">Advantages of experiment over observation</td><td align="right" valign="top"><a href="#Page_417">417</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VII_4">4.</a></td><td align="left">Advantages of observation over experiment</td><td align="right" valign="top"><a href="#Page_420">420</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xvii" id="Page_xvii">[Pg xvii]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_VIII">Chapter VIII.</a></span> <i>Of the Four Methods of Experimental
+Inquiry.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_VIII_1">1.</a></td><td align="left">Method of Agreement</td><td align="right" valign="top"><a href="#Page_425">425</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_2">2.</a></td><td align="left">Method of Difference</td><td align="right" valign="top"><a href="#Page_428">428</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_3">3.</a></td><td align="left">Mutual relation of these two methods</td><td align="right" valign="top"><a href="#Page_429">429</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_4">4.</a></td><td align="left">Joint Method of Agreement and Difference</td><td align="right" valign="top"><a href="#Page_433">433</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_5">5.</a></td><td align="left">Method of Residues</td><td align="right" valign="top"><a href="#Page_436">436</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_6">6.</a></td><td align="left">Method of Concomitant Variations</td><td align="right" valign="top"><a href="#Page_437">437</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_VIII_7">7.</a></td><td align="left">Limitations of this last method</td><td align="right" valign="top"><a href="#Page_443">443</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_IX">Chapter IX.</a></span> <i>Miscellaneous Examples of the Four Methods.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_IX_1">1.</a></td><td align="left">Liebig's theory of metallic poisons</td><td align="right" valign="top"><a href="#Page_449">449</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IX_2">2.</a></td><td align="left">Theory of induced electricity</td><td align="right" valign="top"><a href="#Page_453">453</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IX_3">3.</a></td><td align="left">Dr. Wells' theory of dew</td><td align="right" valign="top"><a href="#Page_457">457</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IX_4">4.</a></td><td align="left">Dr. Brown-S�quard's theory of cadaveric rigidity</td><td align="right" valign="top"><a href="#Page_465">465</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IX_5">5.</a></td><td align="left">Examples of the Method of Residues</td><td align="right" valign="top"><a href="#Page_471">471</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_IX_6">6.</a></td><td align="left">Dr. Whewell's objections to the Four Methods</td><td align="right" valign="top"><a href="#Page_475">475</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_X">Chapter X.</a></span> <i>Of Plurality of Causes; and of the Intermixture
+of Effects.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_X_1">1.</a></td><td align="left">One effect may have several causes</td><td align="right" valign="top"><a href="#Page_482">482</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_2">2.</a></td><td align="left">&mdash;which is the source of a characteristic imperfection of the Method of Agreement</td><td align="right" valign="top"><a href="#Page_483">483</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_3">3.</a></td><td align="left">Plurality of Causes, how ascertained</td><td align="right" valign="top"><a href="#Page_487">487</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_4">4.</a></td><td align="left">Concurrence of Causes which do not compound their effects</td><td align="right" valign="top"><a href="#Page_489">489</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_5">5.</a></td><td align="left">Difficulties of the investigation, when causes compound their effects</td><td align="right" valign="top"><a href="#Page_494">494</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_6">6.</a></td><td align="left">Three modes of investigating the laws of complex effects</td><td align="right" valign="top"><a href="#Page_499">499</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_7">7.</a></td><td align="left">The method of simple observation inapplicable</td><td align="right" valign="top"><a href="#Page_500">500</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_X_8">8.</a></td><td align="left">The purely experimental method inapplicable</td><td align="right" valign="top"><a href="#Page_501">501</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XI">Chapter XI.</a></span> <i>Of the Deductive Method.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_XI_1">1.</a></td><td align="left">First stage; ascertainment of the laws of the separate causes by direct induction</td><td align="right" valign="top"><a href="#Page_507">507</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XI_2">2.</a></td><td align="left">Second stage; ratiocination from the simple laws of the complex cases</td><td align="right" valign="top"><a href="#Page_512">512</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XI_3">3.</a></td><td align="left">Third stage; verification by specific experience</td><td align="right" valign="top"><a href="#Page_514">514</a></td></tr>
+
+
+<tr><td></td><td><span class="pagenum"><a name="Page_xviii" id="Page_xviii">[Pg xviii]</a></span><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XII">Chapter XII.</a></span> <i>Of the Explanation of Laws of Nature.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_XII_1">1.</a></td><td align="left">Explanation defined</td><td align="right" valign="top"><a href="#Page_518">518</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XII_2">2.</a></td><td align="left">First mode of explanation, by resolving the law of a complex effect into the laws of the concurrent causes and the fact of their coexistence</td><td align="right" valign="top"><a href="#Page_518">518</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XII_3">3.</a></td><td align="left">Second mode; by the detection of an intermediate link in the sequence</td><td align="right" valign="top"><a href="#Page_519">519</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XII_4">4.</a></td><td align="left">Laws are always resolved into laws more general than themselves</td><td align="right" valign="top"><a href="#Page_520">520</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XII_5">5.</a></td><td align="left">Third mode; the subsumption of less general laws under a more general one</td><td align="right" valign="top"><a href="#Page_524">524</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XII_6">6.</a></td><td align="left">What the explanation of a law of nature amounts to</td><td align="right" valign="top"><a href="#Page_526">526</a></td></tr>
+
+
+<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XIII">Chapter XIII.</a></span> <i>Miscellaneous Examples of the Explanation of
+Laws of Nature.</i></div></td></tr>
+
+
+
+
+<tr><td align="right" valign="top">� <a href="#BOOK_III_CHAPTER_XIII_1">1.</a></td><td align="left">The general theories of the sciences</td><td align="right" valign="top"><a href="#Page_529">529</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_2">2.</a></td><td align="left">Examples from chemical speculations</td><td align="right" valign="top"><a href="#Page_531">531</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_3">3.</a></td><td align="left">Example from Dr. Brown-S�quard's researches on the nervous system</td><td align="right" valign="top"><a href="#Page_533">533</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_4">4.</a></td><td align="left">Examples of following newly-discovered laws into their complex manifestations</td><td align="right" valign="top"><a href="#Page_534">534</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_5">5.</a></td><td align="left">Examples of empirical generalizations, afterwards confirmed and explained deductively</td><td align="right" valign="top"><a href="#Page_536">536</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_6">6.</a></td><td align="left">Example from mental science</td><td align="right" valign="top"><a href="#Page_538">538</a></td></tr>
+<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIII_7">7.</a></td><td align="left">Tendency of all the sciences to become deductive</td><td align="right" valign="top"><a href="#Page_539">539</a></td></tr>
+</table></div>
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<h2><a name="INTRODUCTION" id="INTRODUCTION"></a>INTRODUCTION.</h2>
+
+
+<p class="newsection"><a name="INTRODUCTION_1">� 1.</a> There is as great diversity among authors in the modes which they
+have adopted of defining logic, as in their treatment of the details of
+it. This is what might naturally be expected on any subject on which
+writers have availed themselves of the same language as a means of
+delivering different ideas. Ethics and jurisprudence are liable to the
+remark in common with logic. Almost every writer having taken a
+different view of some of the particulars which these branches of
+knowledge are usually understood to include; each has so framed his
+definition as to indicate beforehand his own peculiar tenets, and
+sometimes to beg the question in their favour.</p>
+
+<p>This diversity is not so much an evil to be complained of, as an
+inevitable and in some degree a proper result of the imperfect state of
+those sciences. It is not to be expected that there should be agreement
+about the definition of anything, until there is agreement about the
+thing itself. To define, is to select from among all the properties of a
+thing, those which shall be understood to be designated and declared by
+its name; and the properties must be well known to us before we can be
+competent to determine which of them are fittest to be chosen for this
+purpose. Accordingly, in the case of so complex an aggregation of
+particulars as are comprehended in anything which can be called a
+science, the definition we set out with is seldom that which a more
+extensive knowledge of the subject shows to be the most appropriate.
+Until we know the particulars themselves, we cannot fix upon the most
+correct and compact mode of circumscribing them by a general
+description. It was not until after an extensive and accurate
+acquaintance with the details of chemical phenomena, <span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span>that it was found
+possible to frame a rational definition of chemistry; and the definition
+of the science of life and organization is still a matter of dispute. So
+long as the sciences are imperfect, the definitions must partake of
+their imperfection; and if the former are progressive, the latter ought
+to be so too. As much, therefore, as is to be expected from a definition
+placed at the commencement of a subject, is that it should define the
+scope of our inquiries: and the definition which I am about to offer of
+the science of logic, pretends to nothing more, than to be a statement
+of the question which I have put to myself, and which this book is an
+attempt to resolve. The reader is at liberty to object to it as a
+definition of logic; but it is at all events a correct definition of the
+subject of these volumes.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_2">� 2.</a> Logic has often been called the Art of Reasoning. A writer<a name="FNanchor_1_3" id="FNanchor_1_3"></a><a href="#Footnote_1_3" class="fnanchor">[1]</a> who
+has done more than any other person to restore this study to the rank
+from which it had fallen in the estimation of the cultivated class in
+our own country, has adopted the above definition with an amendment; he
+has defined Logic to be the Science, as well as the Art, of reasoning;
+meaning by the former term, the analysis of the mental process which
+takes place whenever we reason, and by the latter, the rules, grounded
+on that analysis, for conducting the process correctly. There can be no
+doubt as to the propriety of the emendation. A right understanding of
+the mental process itself, of the conditions it depends on, and the
+steps of which it consists, is the only basis on which a system of
+rules, fitted for the direction of the process, can possibly be founded.
+Art necessarily presupposes knowledge; art, in any but its infant state,
+presupposes scientific knowledge: and if every art does not bear the
+name of a science, it is only because several sciences are often
+necessary to form the groundwork of a single art. So complicated are the
+conditions which govern our practical agency, that to enable one thing
+to be <i>done</i>, it is often requisite to <i>know</i> the nature and properties
+of many things.</p>
+
+<p><span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span></p><p>Logic, then, comprises the science of reasoning, as well as an art,
+founded on that science. But the word Reasoning, again, like most other
+scientific terms in popular use, abounds in ambiguities. In one of its
+acceptations, it means syllogizing; or the mode of inference which may
+be called (with sufficient accuracy for the present purpose) concluding
+from generals to particulars. In another of its senses, to reason is
+simply to infer any assertion, from assertions already admitted: and in
+this sense induction is as much entitled to be called reasoning as the
+demonstrations of geometry.</p>
+
+<p>Writers on logic have generally preferred the former acceptation of the
+term: the latter, and more extensive signification is that in which I
+mean to use it. I do this by virtue of the right I claim for every
+author, to give whatever provisional definition he pleases of his own
+subject. But sufficient reasons will, I believe, unfold themselves as we
+advance, why this should be not only the provisional but the final
+definition. It involves, at all events, no arbitrary change in the
+meaning of the word; for, with the general usage of the English
+language, the wider signification, I believe, accords better than the
+more restricted one.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_3">� 3.</a> But Reasoning, even in the widest sense of which the word is
+susceptible, does not seem to comprehend all that is included, either in
+the best, or even in the most current, conception of the scope and
+province of our science. The employment of the word Logic to denote the
+theory of argumentation, is derived from the Aristotelian, or, as they
+are commonly termed, the scholastic, logicians. Yet even with them, in
+their systematic treatises, argumentation was the subject only of the
+third part: the two former treated of Terms, and of Propositions; under
+one or other of which heads were also included Definition and Division.
+By some, indeed, these previous topics were professedly introduced only
+on account of their connexion with reasoning, and as a preparation for
+the doctrine and rules of the syllogism. Yet they were treated with
+greater minuteness, and dwelt on at greater length, than was required
+for that purpose alone. More recent <span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span>writers on logic have generally
+understood the term as it was employed by the able author of the Port
+Royal Logic; viz. as equivalent to the Art of Thinking. Nor is this
+acceptation confined to books, and scientific inquiries. Even in
+ordinary conversation, the ideas connected with the word Logic include
+at least precision of language, and accuracy of classification: and we
+perhaps oftener hear persons speak of a logical arrangement, or of
+expressions logically defined, than of conclusions logically deduced
+from premises. Again, a man is often called a great logician, or a man
+of powerful logic, not for the accuracy of his deductions, but for the
+extent of his command over premises; because the general propositions
+required for explaining a difficulty or refuting a sophism, copiously
+and promptly occur to him: because, in short, his knowledge, besides
+being ample, is well under his command for argumentative use. Whether,
+therefore, we conform to the practice of those who have made the subject
+their particular study, or to that of popular writers and common
+discourse, the province of logic will include several operations of the
+intellect not usually considered to fall within the meaning of the terms
+Reasoning and Argumentation.</p>
+
+<p>These various operations might be brought within the compass of the
+science, and the additional advantage be obtained of a very simple
+definition, if, by an extension of the term, sanctioned by high
+authorities, we were to define logic as the science which treats of the
+operations of the human understanding in the pursuit of truth. For to
+this ultimate end, naming, classification, definition, and all other
+operations over which logic has ever claimed jurisdiction, are
+essentially subsidiary. They may all be regarded as contrivances for
+enabling a person to know the truths which are needful to him, and to
+know them at the precise moment at which they are needful. Other
+purposes, indeed, are also served by these operations; for instance,
+that of imparting our knowledge to others. But, viewed with regard to
+this purpose, they have never been considered as within the province of
+the logician. The sole object of Logic is the guidance of one's own
+thoughts: the communication of those thoughts to others falls under the
+consideration <span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span>of Rhetoric, in the large sense in which that art was
+conceived by the ancients; or of the still more extensive art of
+Education. Logic takes cognizance of our intellectual operations, only
+as they conduce to our own knowledge, and to our command over that
+knowledge for our own uses. If there were but one rational being in the
+universe, that being might be a perfect logician; and the science and
+art of logic would be the same for that one person as for the whole
+human race.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_4">� 4.</a> But, if the definition which we formerly examined included too
+little, that which is now suggested has the opposite fault of including
+too much.</p>
+
+<p>Truths are known to us in two ways: some are known directly, and of
+themselves; some through the medium of other truths. The former are the
+subject of Intuition, or Consciousness;<a name="FNanchor_2_4" id="FNanchor_2_4"></a><a href="#Footnote_2_4" class="fnanchor">[2]</a> the latter, of Inference. The
+truths known by intuition are the original premises from which all
+others are inferred. Our assent to the conclusion being grounded on the
+truth of the premises, we never could arrive at any knowledge by
+reasoning, unless something could be known antecedently to all
+reasoning.</p>
+
+<p>Examples of truths known to us by immediate consciousness, are our own
+bodily sensations and mental feelings. I know directly, and of my own
+knowledge, that I was vexed yesterday, or that I am hungry to-day.
+Examples of truths which we know only by way of inference, are
+occurrences which took place while we were absent, the events recorded
+in history, or the theorems of mathematics. The two former we infer from
+the testimony adduced, or from the traces of those past occurrences
+which still exist; the latter, from the premises laid down in books of
+geometry, under the title of definitions and axioms. Whatever we are
+capable of knowing <span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span>must belong to the one class or to the other; must
+be in the number of the primitive data, or of the conclusions which can
+be drawn from these.</p>
+
+<p>With the original data, or ultimate premises of our knowledge; with
+their number or nature, the mode in which they are obtained, or the
+tests by which they may be distinguished; logic, in a direct way at
+least, has, in the sense in which I conceive the science, nothing to do.
+These questions are partly not a subject of science at all, partly that
+of a very different science.</p>
+
+<p>Whatever is known to us by consciousness, is known beyond possibility of
+question. What one sees or feels, whether bodily or mentally, one cannot
+but be sure that one sees or feels. No science is required for the
+purpose of establishing such truths; no rules of art can render our
+knowledge of them more certain than it is in itself. There is no logic
+for this portion of our knowledge.</p>
+
+<p>But we may fancy that we see or feel what we in reality infer. A truth,
+or supposed truth, which is really the result of a very rapid inference,
+may seem to be apprehended intuitively. It has long been agreed by
+thinkers of the most opposite schools, that this mistake is actually
+made in so familiar an instance as that of the eyesight. There is
+nothing of which we appear to ourselves to be more directly conscious,
+than the distance of an object from us. Yet it has long been
+ascertained, that what is perceived by the eye, is at most nothing more
+than a variously coloured surface; that when we fancy we see distance,
+all we really see is certain variations of apparent size, and degrees of
+faintness of colour; that our estimate of the object's distance from us
+is the result partly of a rapid inference from the muscular sensations
+accompanying the adjustment of the focal distance of the eye to objects
+unequally remote from us, and partly of a comparison (made with so much
+rapidity that we are unconscious of making it) between the size and
+colour of the object as they appear at the time, and the size and colour
+of the same or of similar objects as they appeared when close at hand,
+or when their degree of remoteness was known by other evidence. The
+perception of distance by the <span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>eye, which seems so like intuition, is
+thus, in reality, an inference grounded on experience; an inference,
+too, which we learn to make; and which we make with more and more
+correctness as our experience increases; though in familiar cases it
+takes place so rapidly as to appear exactly on a par with those
+perceptions of sight which are really intuitive, our perceptions of
+colour.<a name="FNanchor_3_5" id="FNanchor_3_5"></a><a href="#Footnote_3_5" class="fnanchor">[3]</a></p>
+
+<p>Of the science, therefore, which expounds the operations of the human
+understanding in the pursuit of truth, one essential part is the
+inquiry: What are the facts which are the objects of intuition or
+consciousness, and what are those which we merely infer? But this
+inquiry has never been considered a portion of logic. Its place is in
+another and a perfectly distinct department of science, to which the
+name metaphysics more particularly belongs: that portion of mental
+philosophy which attempts to determine what part of the furniture of the
+mind belongs to it originally, and what part is constructed out of
+materials furnished to it from without. To this science appertain the
+great and much debated questions of the existence of matter; the
+existence of spirit, and of a distinction between it and matter; the
+reality of time and space, as things without the mind, and
+distinguishable from the objects which are said to exist in them. For in
+the present state of the discussion on these topics, it is almost
+universally allowed that the existence of matter or of spirit, of space
+or of time, is in its nature unsusceptible of being proved; and that if
+anything is known of them, it must be by immediate intuition. To the
+same science belong the inquiries into the nature of Conception,
+Perception, Memory, and Belief; all of which are operations of the
+understanding in the pursuit of truth; but with which, as phenomena of
+the mind, or with the possibility which may or may not exist of
+analysing any of them into simpler phenomena, the <span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span>logician as such has
+no concern. To this science must also be referred the following, and all
+analogous questions: To what extent our intellectual faculties and our
+emotions are innate&mdash;to what extent the result of association: Whether
+God, and duty, are realities, the existence of which is manifest to us
+<i>� priori</i> by the constitution of our rational faculty; or whether our
+ideas of them are acquired notions, the origin of which we are able to
+trace and explain; and the reality of the objects themselves a question
+not of consciousness or intuition, but of evidence and reasoning.</p>
+
+<p>The province of logic must be restricted to that portion of our
+knowledge which consists of inferences from truths previously known;
+whether those antecedent data be general propositions, or particular
+observations and perceptions. Logic is not the science of Belief, but
+the science of Proof, or Evidence. In so far as belief professes to be
+founded on proof, the office of logic is to supply a test for
+ascertaining whether or not the belief is well grounded. With the claims
+which any proposition has to belief on the evidence of consciousness,
+that is, without evidence in the proper sense of the word, logic has
+nothing to do.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_5">� 5.</a> By far the greatest portion of our knowledge, whether of general
+truths or of particular facts, being avowedly matter of inference,
+nearly the whole, not only of science, but of human conduct, is amenable
+to the authority of logic. To draw inferences has been said to be the
+great business of life. Every one has daily, hourly, and momentary need
+of ascertaining facts which he has not directly observed; not from any
+general purpose of adding to his stock of knowledge, but because the
+facts themselves are of importance to his interests or to his
+occupations. The business of the magistrate, of the military commander,
+of the navigator, of the physician, of the agriculturist, is merely to
+judge of evidence, and to act accordingly. They all have to ascertain
+certain facts, in order that they may afterwards apply certain rules,
+either devised by themselves, or prescribed for their guidance by
+others; and as they do this well or ill, so they discharge well or ill
+the duties <span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>of their several callings. It is the only occupation in
+which the mind never ceases to be engaged; and is the subject, not of
+logic, but of knowledge in general.</p>
+
+<p>Logic, however, is not the same thing with knowledge, though the field
+of logic is coextensive with the field of knowledge. Logic is the common
+judge and arbiter of all particular investigations. It does not
+undertake to find evidence, but to determine whether it has been found.
+Logic neither observes, nor invents, nor discovers; but judges. It is no
+part of the business of logic to inform the surgeon what appearances are
+found to accompany a violent death. This he must learn from his own
+experience and observation, or from that of others, his predecessors in
+his peculiar pursuit. But logic sits in judgment on the sufficiency of
+that observation and experience to justify his rules, and on the
+sufficiency of his rules to justify his conduct. It does not give him
+proofs, but teaches him what makes them proofs, and how he is to judge
+of them. It does not teach that any particular fact proves any other,
+but points out to what conditions all facts must conform, in order that
+they may prove other facts. To decide whether any given fact fulfils
+these conditions, or whether facts can be found which fulfil them in a
+given case, belongs exclusively to the particular art or science, or to
+our knowledge of the particular subject.</p>
+
+<p>It is in this sense that logic is, what Bacon so expressively called it,
+<i>ars artium</i>; the science of science itself. All science consists of
+data and conclusions from those data, of proofs and what they prove: now
+logic points out what relations must subsist between data and whatever
+can be concluded from them, between proof and everything which it can
+prove. If there be any such indispensable relations, and if these can be
+precisely determined, every particular branch of science, as well as
+every individual in the guidance of his conduct, is bound to conform to
+those relations, under the penalty of making false inferences, of
+drawing conclusions which are not grounded in the realities of things.
+Whatever has at any time been concluded justly, whatever knowledge has
+been acquired otherwise than by immediate intuition, depended on <span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>the
+observance of the laws which it is the province of logic to investigate.
+If the conclusions are just, and the knowledge real, those laws, whether
+known or not, have been observed.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_6">� 6.</a> We need not, therefore, seek any farther for a solution of the
+question, so often agitated, respecting the utility of logic. If a
+science of logic exists, or is capable of existing, it must be useful.
+If there be rules to which every mind consciously or unconsciously
+conforms in every instance in which it infers rightly, there seems
+little necessity for discussing whether a person is more likely to
+observe those rules, when he knows the rules, than when he is
+unacquainted with them.</p>
+
+<p>A science may undoubtedly be brought to a certain, not inconsiderable,
+stage of advancement, without the application of any other logic to it
+than what all persons, who are said to have a sound understanding,
+acquire empirically in the course of their studies. Mankind judged of
+evidence, and often correctly, before logic was a science, or they never
+could have made it one. And they executed great mechanical works before
+they understood the laws of mechanics. But there are limits both to what
+mechanicians can do without principles of mechanics, and to what
+thinkers can do without principles of logic. A few individuals, by
+extraordinary genius, or by the accidental acquisition of a good set of
+intellectual habits, may work without principles in the same way, or
+nearly the same way, in which they would have worked if they had been in
+possession of principles. But the bulk of mankind require either to
+understand the theory of what they are doing, or to have rules laid down
+for them by those who have understood the theory. In the progress of
+science from its easiest to its more difficult problems, each great step
+in advance has usually had either as its precursor, or as its
+accompaniment and necessary condition, a corresponding improvement in
+the notions and principles of logic received among the most advanced
+thinkers. And if several of the more difficult sciences are still in so
+defective a state; if not only so little is proved, but disputation has
+not terminated even about the little which <span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>seemed to be so; the reason
+perhaps is, that men's logical notions have not yet acquired the degree
+of extension, or of accuracy, requisite for the estimation of the
+evidence proper to those particular departments of knowledge.</p>
+
+
+<p class="newsection"><a name="INTRODUCTION_7">� 7.</a> Logic, then, is the science of the operations of the understanding
+which are subservient to the estimation of evidence: both the process
+itself of advancing from known truths to unknown, and all other
+intellectual operations in so far as auxiliary to this. It includes,
+therefore, the operation of Naming; for language is an instrument of
+thought, as well as a means of communicating our thoughts. It includes,
+also, Definition, and Classification. For, the use of these operations
+(putting all other minds than one's own out of consideration) is to
+serve not only for keeping our evidences and the conclusions from them
+permanent and readily accessible in the memory, but for so marshalling
+the facts which we may at any time be engaged in investigating, as to
+enable us to perceive more clearly what evidence there is, and to judge
+with fewer chances of error whether it be sufficient. These, therefore,
+are operations specially instrumental to the estimation of evidence,
+and, as such, are within the province of Logic. There are other more
+elementary processes, concerned in all thinking, such as Conception,
+Memory, and the like; but of these it is not necessary that Logic should
+take any peculiar cognizance, since they have no special connexion with
+the problem of Evidence, further than that, like all other problems
+addressed to the understanding, it presupposes them.</p>
+
+<p>Our object, then, will be, to attempt a correct analysis of the
+intellectual process called Reasoning or Inference, and of such other
+mental operations as are intended to facilitate this; as well as, on the
+foundation of this analysis, and <i>pari passu</i> with it, to bring together
+or frame a set of rules or canons for testing the sufficiency of any
+given evidence to prove any given proposition.</p>
+
+<p>With respect to the first part of this undertaking, I do not attempt to
+decompose the mental operations in question into their ultimate
+elements. It is enough if the analysis as <span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>far as it goes is correct,
+and if it goes far enough for the practical purposes of logic considered
+as an art. The separation of a complicated phenomenon into its component
+parts is not like a connected and interdependent chain of proof. If one
+link of an argument breaks, the whole drops to the ground; but one step
+towards an analysis holds good and has an independent value, though we
+should never be able to make a second. The results which have been
+obtained by analytical chemistry are not the less valuable, though it
+should be discovered that all which we now call simple substances are
+really compounds. All other things are at any rate compounded of those
+elements: whether the elements themselves admit of decomposition, is an
+important inquiry, but does not affect the certainty of the science up
+to that point.</p>
+
+<p>I shall, accordingly, attempt to analyse the process of inference, and
+the processes subordinate to inference, so far only as may be requisite
+for ascertaining the difference between a correct and an incorrect
+performance of those processes. The reason for thus limiting our design,
+is evident. It has been said by objectors to logic, that we do not learn
+to use our muscles by studying their anatomy. The fact is not quite
+fairly stated; for if the action of any of our muscles were vitiated by
+local weakness, or other physical defect, a knowledge of their anatomy
+might be very necessary for effecting a cure. But we should be justly
+liable to the criticism involved in this objection, were we, in a
+treatise on logic, to carry the analysis of the reasoning process beyond
+the point at which any inaccuracy which may have crept into it must
+become visible. In learning bodily exercises (to carry on the same
+illustration) we do, and must, analyse the bodily motions so far as is
+necessary for distinguishing those which ought to be performed from
+those which ought not. To a similar extent, and no further, it is
+necessary that the logician should analyse the mental processes with
+which Logic is concerned. Logic has no interest in carrying the analysis
+beyond the point at which it becomes apparent whether the operations
+have in any individual case been rightly or wrongly performed: in the
+same manner as the science of music teaches us to discriminate <span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>between
+musical notes, and to know the combinations of which they are
+susceptible, but not what number of vibrations in a second correspond to
+each; which, though useful to be known, is useful for totally different
+purposes. The extension of Logic as a Science is determined by its
+necessities as an Art: whatever it does not need for its practical ends,
+it leaves to the larger science which may be said to correspond, not to
+any particular art, but to art in general; the science which deals with
+the constitution of the human faculties; and to which, in the part of
+our mental nature which concerns Logic, as well as in all other parts,
+it belongs to decide what are ultimate facts, and what are resolvable
+into other facts. And I believe it will be found that most of the
+conclusions arrived at in this work have no necessary connexion with any
+particular views respecting the ulterior analysis. Logic is common
+ground on which the partisans of Hartley and of Reid, of Locke and of
+Kant, may meet and join hands. Particular and detached opinions of all
+these thinkers will no doubt occasionally be controverted, since all of
+them were logicians as well as metaphysicians; but the field on which
+their principal battles have been fought, lies beyond the boundaries of
+our science.</p>
+
+<p>It cannot, indeed, be pretended that logical principles can be
+altogether irrelevant to those more abstruse discussions; nor is it
+possible but that the view we are led to take of the problem which logic
+proposes, must have a tendency favourable to the adoption of some one
+opinion, on these controverted subjects, rather than another. For
+metaphysics, in endeavouring to solve its own peculiar problem, must
+employ means, the validity of which falls under the cognizance of logic.
+It proceeds, no doubt, as far as possible, merely by a closer and more
+attentive interrogation of our consciousness, or more properly speaking,
+of our memory; and so far is not amenable to logic. But wherever this
+method is insufficient to attain the end of its inquiries, it must
+proceed, like other sciences, by means of evidence. Now, the moment this
+science begins to draw inferences from evidence, logic becomes the
+sovereign judge whether its inferences are well grounded, or what other
+inferences would be so.</p>
+
+<p><span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span></p><p>This, however, constitutes no nearer or other relation between logic
+and metaphysics, than that which exists between logic and every other
+science. And I can conscientiously affirm, that no one proposition laid
+down in this work has been adopted for the sake of establishing, or with
+any reference to its fitness for being employed in establishing,
+preconceived opinions in any department of knowledge or of inquiry on
+which the speculative world is still undecided.<a name="FNanchor_4_6" id="FNanchor_4_6"></a><a href="#Footnote_4_6" class="fnanchor">[4]</a></p>
+
+<div class="footnotes"><h3>FOOTNOTES:</h3>
+
+<div class="footnote"><p><a name="Footnote_1_3" id="Footnote_1_3"></a><a href="#FNanchor_1_3"><span class="label">[1]</span></a> Archbishop Whately.</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_4" id="Footnote_2_4"></a><a href="#FNanchor_2_4"><span class="label">[2]</span></a> I use these terms indiscriminately, because, for the
+purpose in view, there is no need for making any distinction between
+them. But metaphysicians usually restrict the name Intuition to the
+direct knowledge we are supposed to have of things external to our
+minds, and Consciousness to our knowledge of our own mental phenomena.</p></div>
+
+<div class="footnote"><p><a name="Footnote_3_5" id="Footnote_3_5"></a><a href="#FNanchor_3_5"><span class="label">[3]</span></a> This important theory has of late been called in question
+by a writer of deserved reputation, Mr. Samuel Bailey; but I do not
+conceive that the grounds on which it has been admitted as an
+established doctrine for a century past, have been at all shaken by that
+gentleman's objections. I have elsewhere said what appeared to me
+necessary in reply to his arguments. (<i>Westminster Review</i> for October
+1842; reprinted in <i>Dissertations and Discussions</i>, vol. ii.)</p></div>
+
+<div class="footnote"><p><a name="Footnote_4_6" id="Footnote_4_6"></a><a href="#FNanchor_4_6"><span class="label">[4]</span></a> The view taken in the text, of the definition and purpose
+of Logic, stands in marked opposition to that of the school of
+philosophy which, in this country, is represented by the writings of Sir
+William Hamilton and of his numerous pupils. Logic, as this school
+conceives it, is "the Science of the Formal Laws of Thought;" a
+definition framed for the express purpose of excluding, as irrelevant to
+Logic, whatever relates to Belief and Disbelief, or to the pursuit of
+truth as such, and restricting the science to that very limited portion
+of its total province, which has reference to the conditions, not of
+Truth, but of Consistency. What I have thought it useful to say in
+opposition to this limitation of the field of Logic, has been said at
+some length in a separate work, first published in 1865, and entitled
+<i>An Examination of Sir William Hamilton's Philosophy, and of the
+Principal Philosophical Questions discussed in his Writings</i>. For the
+purposes of the present Treatise, I am content that the justification of
+the larger extension which I give to the domain of the science, should
+rest on the sequel of the Treatise itself. Some remarks on the relation
+which the Logic of Consistency bears to the Logic of Truth, and on the
+place which that particular part occupies in the whole to which it
+belongs, will be found in the present volume (<a href="#BOOK_II_CHAPTER_III_9">Book II. chap. iii. � 9</a>).</p></div>
+</div>
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span></p>
+<h2><a name="BOOK_I" id="BOOK_I"></a>BOOK I.<br />
+
+OF NAMES AND PROPOSITIONS.</h2>
+
+
+<p><span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p><blockquote><p>'La scolastique, qui produisit dans la logique, comme dans la morale,
+et dans une partie de la m�taphysique, une subtilit�, une pr�cision
+d'id�es, dont l'habitude inconnue aux anciens, a contribu� plus qu'on ne
+croit au progr�s de la bonne philosophie.'&mdash;<span class="smcap">Condorcet</span>, <i>Vie de Turgot</i>.</p></blockquote>
+
+<blockquote><p>'To the schoolmen the vulgar languages are principally indebted for what
+precision and analytic subtlety they possess.'&mdash;<span class="smcap">Sir W. Hamilton</span>,
+<i>Discussions in Philosophy</i>.</p></blockquote>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_I" id="BOOK_I_CHAPTER_I"></a>CHAPTER I.<br />
+
+OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_I_1">� 1.</a> It is so much the established practice of writers on logic to
+commence their treatises by a few general observations (in most cases,
+it is true, rather meagre) on Terms and their varieties, that it will,
+perhaps, scarcely be required from me in merely following the common
+usage, to be as particular in assigning my reasons, as it is usually
+expected that those should be who deviate from it.</p>
+
+<p>The practice, indeed, is recommended by considerations far too obvious
+to require a formal justification. Logic is a portion of the Art of
+Thinking: Language is evidently, and by the admission of all
+philosophers, one of the principal instruments or helps of thought; and
+any imperfection in the instrument, or in the mode of employing it, is
+confessedly liable, still more than in almost any other art, to confuse
+and impede the process, and destroy all ground of confidence in the
+result. For a mind not previously versed in the meaning and right use of
+the various kinds of words, to attempt the study of methods of
+philosophizing, would be as if some one should attempt to become an
+astronomical observer, having never learned to adjust the focal distance
+of his optical instruments so as to see distinctly.</p>
+
+<p>Since Reasoning, or Inference, the principal subject of logic, is an
+operation which usually takes place by means of words, and in
+complicated cases can take place in no other way; those who have not a
+thorough insight into the signification and purposes of words, will be
+under chances, amounting almost to certainty, of reasoning or inferring
+incorrectly. And logicians have generally felt that unless, in the very
+first stage, they removed this source of error; unless they taught their
+<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>pupil to put away the glasses which distort the object, and to use
+those which are adapted to his purpose in such a manner as to assist,
+not perplex, his vision; he would not be in a condition to practise the
+remaining part of their discipline with any prospect of advantage.
+Therefore it is that an inquiry into language, so far as is needful to
+guard against the errors to which it gives rise, has at all times been
+deemed a necessary preliminary to the study of logic.</p>
+
+<p>But there is another reason, of a still more fundamental nature, why the
+import of words should be the earliest subject of the logician's
+consideration: because without it he cannot examine into the import of
+Propositions. Now this is a subject which stands on the very threshold
+of the science of logic.</p>
+
+<p>The object of logic, as defined in the Introductory Chapter, is to
+ascertain how we come by that portion of our knowledge (much the
+greatest portion) which is not intuitive: and by what criterion we can,
+in matters not self-evident, distinguish between things proved and
+things not proved, between what is worthy and what is unworthy of
+belief. Of the various questions which present themselves to our
+inquiring faculties, some receive an answer from direct consciousness,
+others, if resolved at all, can only be resolved by means of evidence.
+Logic is concerned with these last. But before inquiring into the mode
+of resolving questions, it is necessary to inquire what are those which
+offer themselves; what questions are conceivable; what inquiries are
+there, to which mankind have either obtained, or been able to imagine it
+possible that they should obtain, an answer. This point is best
+ascertained by a survey and analysis of Propositions.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_I_2">� 2.</a> The answer to every question which it is possible to frame, must be
+contained in a Proposition, or Assertion. Whatever can be an object of
+belief, or even of disbelief, must, when put into words, assume the form
+of a proposition. All truth and all error lie in propositions. What, by
+a convenient misapplication of an abstract term, we call a Truth, means
+simply a True Proposition; and errors are false propositions. <span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>To know
+the import of all possible propositions, would be to know all questions
+which can be raised, all matters which are susceptible of being either
+believed or disbelieved. How many kinds of inquiries can be propounded;
+how many kinds of judgments can be made; and how many kinds of
+propositions it is possible to frame with a meaning; are but different
+forms of one and the same question. Since, then, the objects of all
+Belief and of all Inquiry express themselves in propositions; a
+sufficient scrutiny of Propositions and of their varieties will apprize
+us what questions mankind have actually asked of themselves, and what,
+in the nature of answers to those questions, they have actually thought
+they had grounds to believe.</p>
+
+<p>Now the first glance at a proposition shows that it is formed by putting
+together two names. A proposition, according to the common simple
+definition, which is sufficient for our purpose, is, <i>discourse, in
+which something is affirmed or denied of something</i>. Thus, in the
+proposition, Gold is yellow, the quality <i>yellow</i> is affirmed of the
+substance <i>gold</i>. In the proposition, Franklin was not born in England,
+the fact expressed by the words <i>born in England</i> is denied of the man
+Franklin.</p>
+
+<p>Every proposition consists of three parts: the Subject, the Predicate,
+and the Copula. The predicate is the name denoting that which is
+affirmed or denied. The subject is the name denoting the person or thing
+which something is affirmed or denied of. The copula is the sign
+denoting that there is an affirmation or denial; and thereby enabling
+the hearer or reader to distinguish a proposition from any other kind of
+discourse. Thus, in the proposition, The earth is round, the Predicate
+is the word <i>round</i>, which denotes the quality affirmed, or (as the
+phrase is) predicated: <i>the earth</i>, words denoting the object which that
+quality is affirmed of, compose the Subject; the word <i>is</i>, which serves
+as the connecting mark between the subject and predicate, to show that
+one of them is affirmed of the other, is called the Copula.</p>
+
+<p>Dismissing, for the present, the copula, of which more will be said
+hereafter, every proposition, then, consists of at least <span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>two names;
+brings together two names, in a particular manner. This is already a
+first step towards what we are in quest of. It appears from this, that
+for an act of belief, <i>one</i> object is not sufficient; the simplest act
+of belief supposes, and has something to do with, <i>two</i> objects: two
+names, to say the least; and (since the names must be names of
+something) two <i>nameable things</i>. A large class of thinkers would cut
+the matter short by saying, two <i>ideas</i>. They would say, that the
+subject and predicate are both of them names of ideas; the idea of gold,
+for instance, and the idea of yellow; and that what takes place (or part
+of what takes place) in the act of belief, consists in bringing (as it
+is often expressed) one of these ideas under the other. But this we are
+not yet in a condition to say: whether such be the correct mode of
+describing the phenomenon, is an after consideration. The result with
+which for the present we must be contented, is, that in every act of
+belief <i>two</i> objects are in some manner taken cognizance of; that there
+can be no belief claimed, or question propounded, which does not embrace
+two distinct (either material or intellectual) subjects of thought; each
+of them capable, or not, of being conceived by itself, but incapable of
+being believed by itself.</p>
+
+<p>I may say, for instance, "the sun." The word has a meaning, and suggests
+that meaning to the mind of any one who is listening to me. But suppose
+I ask him, Whether it is true: whether he believes it? He can give no
+answer. There is as yet nothing to believe, or to disbelieve. Now,
+however, let me make, of all possible assertions respecting the sun, the
+one which involves the least of reference to any object besides itself;
+let me say, "the sun exists." Here, at once, is something which a person
+can say he believes. But here, instead of only one, we find two distinct
+objects of conception: the sun is one object; existence is another. Let
+it not be said that this second conception, existence, is involved in
+the first; for the sun may be conceived as no longer existing. "The sun"
+does not convey all the meaning that is conveyed by "the sun exists:"
+"my father" does not include all the meaning of "my father exists," for
+he may be dead; "a round <span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span>square" does not include the meaning of "a
+round square exists," for it does not and cannot exist. When I say "the
+sun," "my father," or a "round square," I do not call upon the hearer
+for any belief or disbelief, nor can either the one or the other be
+afforded me; but if I say, "the sun exists," "my father exists," or "a
+round square exists," I call for belief; and should, in the first of the
+three instances, meet with it; in the second, with belief or disbelief,
+as the case might be; in the third, with disbelief.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_I_3">� 3.</a> This first step in the analysis of the object of belief, which,
+though so obvious, will be found to be not unimportant, is the only one
+which we shall find it practicable to make without a preliminary survey
+of language. If we attempt to proceed further in the same path, that is,
+to analyse any further the import of Propositions; we find forced upon
+us, as a subject of previous consideration, the import of Names. For
+every proposition consists of two names; and every proposition affirms
+or denies one of these names, of the other. Now what we do, what passes
+in our mind, when we affirm or deny two names of one another, must
+depend on what they are names of; since it is with reference to that,
+and not to the mere names themselves, that we make the affirmation or
+denial. Here, therefore, we find a new reason why the signification of
+names, and the relation generally between names and the things signified
+by them, must occupy the preliminary stage of the inquiry we are engaged
+in.</p>
+
+<p>It may be objected that the meaning of names can guide us at most only
+to the opinions, possibly the foolish and groundless opinions, which
+mankind have formed concerning things, and that as the object of
+philosophy is truth, not opinion, the philosopher should dismiss words
+and look into things themselves, to ascertain what questions can be
+asked and answered in regard to them. This advice (which no one has it
+in his power to follow) is in reality an exhortation to discard the
+whole fruits of the labours of his predecessors, and conduct himself as
+if he were the first person who had ever turned an inquiring eye upon
+nature. What does any one's <span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>personal knowledge of Things amount to,
+after subtracting all which he has acquired by means of the words of
+other people? Even after he has learned as much as people usually do
+learn from others, will the notions of things contained in his
+individual mind afford as sufficient a basis for a <i>catalogue raisonn�</i>
+as the notions which are in the minds of all mankind?</p>
+
+<p>In any enumeration and classification of Things, which does not set out
+from their names, no varieties of things will of course be comprehended
+but those recognised by the particular inquirer; and it will still
+remain to be established, by a subsequent examination of names, that the
+enumeration has omitted nothing which ought to have been included. But
+if we begin with names, and use them as our clue to the things, we bring
+at once before us all the distinctions which have been recognised, not
+by a single inquirer, but by all inquirers taken together. It doubtless
+may, and I believe it will, be found, that mankind have multiplied the
+varieties unnecessarily, and have imagined distinctions among things,
+where there were only distinctions in the manner of naming them. But we
+are not entitled to assume this in the commencement. We must begin by
+recognising the distinctions made by ordinary language. If some of these
+appear, on a close examination, not to be fundamental, the enumeration
+of the different kinds of realities may be abridged accordingly. But to
+impose upon the facts in the first instance the yoke of a theory, while
+the grounds of the theory are reserved for discussion in a subsequent
+stage, is not a course which a logician can reasonably adopt.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_II" id="BOOK_I_CHAPTER_II"></a>CHAPTER II.<br />
+
+OF NAMES.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_1">� 1.</a> "A name," says Hobbes,<a name="FNanchor_1_7" id="FNanchor_1_7"></a><a href="#Footnote_1_7" class="fnanchor">[1]</a> "is a word taken at pleasure to serve for
+a mark which may raise in our mind a thought like to some thought we had
+before, and which being pronounced to others, may be to them a sign of
+what thought the speaker had<a name="FNanchor_2_8" id="FNanchor_2_8"></a><a href="#Footnote_2_8" class="fnanchor">[2]</a> before in his mind." This simple
+definition of a name, as a word (or set of words) serving the double
+purpose of a mark to recall to ourselves the likeness of a former
+thought, and a sign to make it known to others, appears unexceptionable.
+Names, indeed, do much more than this; but whatever else they do, grows
+out of, and is the result of this: as will appear in its proper place.</p>
+
+<p>Are names more properly said to be the names of things, or of our ideas
+of things? The first is the expression in common use; the last is that
+of some metaphysicians, who conceived that in adopting it they were
+introducing a highly important distinction. The eminent thinker, just
+quoted, seems to countenance the latter opinion. "But seeing," he
+continues, "names ordered in speech (as is defined) are signs of our
+conceptions, it is manifest they are not signs of the things themselves;
+for that the sound of this word <i>stone</i> should be the sign of a stone,
+cannot be understood in any sense but this, that he that hears it
+collects that he that pronounces it thinks of a stone."</p>
+
+<p>If it be merely meant that the conception alone, and not the thing
+itself, is recalled by the name, or imparted to the hearer, this of
+course cannot be denied. Nevertheless, there seems good reason for
+adhering to the common usage, and <span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>calling the word <i>sun</i> the name of
+the sun, and not the name of our idea of the sun. For names are not
+intended only to make the hearer conceive what we conceive, but also to
+inform him what we believe. Now, when I use a name for the purpose of
+expressing a belief, it is a belief concerning the thing itself, not
+concerning my idea of it. When I say, "the sun is the cause of day," I
+do not mean that my idea of the sun causes or excites in me the idea of
+day; or in other words, that thinking of the sun makes me think of day.
+I mean, that a certain physical fact, which is called the sun's presence
+(and which, in the ultimate analysis, resolves itself into sensations,
+not ideas) causes another physical fact, which is called day. It seems
+proper to consider a word as the <i>name</i> of that which we intend to be
+understood by it when we use it; of that which any fact that we assert
+of it is to be understood of; that, in short, concerning which, when we
+employ the word, we intend to give information. Names, therefore, shall
+always be spoken of in this work as the names of things themselves, and
+not merely of our ideas of things.</p>
+
+<p>But the question now arises, of what things? and to answer this it is
+necessary to take into consideration the different kinds of names.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_2">� 2.</a> It is usual, before examining the various classes into which names
+are commonly divided, to begin by distinguishing from names of every
+description, those words which are not names, but only parts of names.
+Among such are reckoned particles, as <i>of</i>, <i>to</i>, <i>truly</i>, <i>often</i>; the
+inflected cases of nouns substantive, as <i>me</i>, <i>him</i>, <i>John's</i>; and even
+adjectives, as <i>large</i>, <i>heavy</i>. These words do not express things of
+which anything can be affirmed or denied. We cannot say, Heavy fell, or
+A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
+room. Unless, indeed, we are speaking of the mere words themselves, as
+when we say, Truly is an English word, or, Heavy is an adjective. In
+that case they are complete names, viz. names of those particular
+sounds, or of those particular collections of written characters. This
+employment of a word to denote the mere letters and syllables of which
+it <span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span>is composed, was termed by the schoolmen the <i>suppositio materialis</i>
+of the word. In any other sense we cannot introduce one of these words
+into the subject of a proposition, unless in combination with other
+words; as, A heavy <i>body</i> fell, A truly <i>important fact</i> was asserted, A
+<i>member</i> of <i>parliament</i> was in the room.</p>
+
+<p>An adjective, however, is capable of standing by itself as the predicate
+of a proposition; as when we say, Snow is white; and occasionally even
+as the subject, for we may say, White is an agreeable colour. The
+adjective is often said to be so used by a grammatical ellipsis: Snow is
+white, instead of Snow is a white object; White is an agreeable colour,
+instead of, A white colour, or, The colour white, is agreeable. The
+Greeks and Romans were allowed, by the rules of their language, to
+employ this ellipsis universally in the subject as well as in the
+predicate of a proposition. In English this cannot, generally speaking,
+be done. We may say, The earth is round; but we cannot say, Round is
+easily moved; we must say, A round object. This distinction, however, is
+rather grammatical than logical. Since there is no difference of meaning
+between <i>round</i>, and <i>a round object</i>, it is only custom which
+prescribes that on any given occasion one shall be used, and not the
+other. We shall, therefore, without scruple, speak of adjectives as
+names, whether in their own right, or as representative of the more
+circuitous forms of expression above exemplified. The other classes of
+subsidiary words have no title whatever to be considered as names. An
+adverb, or an accusative case, cannot under any circumstances (except
+when their mere letters and syllables are spoken of) figure as one of
+the terms of a proposition.</p>
+
+<p>Words which are not capable of being used as names, but only as parts of
+names, were called by some of the schoolmen Syncategorematic terms: from
+<i>&#963;&#8058;&#957;</i>, with, and <i>&#954;&#945;&#964;&#951;&#947;&#959;&#961;&#8051;&#969;</i>, to predicate, because it was
+only <i>with</i> some other word that they could be predicated. A word which
+could be used either as the subject or predicate of a proposition
+without being accompanied by any other word, was termed by the same
+authorities a Categorematic term. A combination of one or more
+Categorematic, <span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>and one or more Syncategorematic words, as A heavy body,
+or A court of justice, they sometimes called a <i>mixed</i> term; but this
+seems a needless multiplication of technical expressions. A mixed term
+is, in the only useful sense of the word, Categorematic. It belongs to
+the class of what have been called many-worded names.</p>
+
+<p>For, as one word is frequently not a name, but only part of a name, so a
+number of words often compose one single name, and no more. These words,
+"the place which the wisdom or policy of antiquity had destined for the
+residence of the Abyssinian princes," form in the estimation of the
+logician only one name; one Categorematic term. A mode of determining
+whether any set of words makes only one name, or more than one, is by
+predicating something of it, and observing whether, by this predication,
+we make only one assertion or several. Thus, when we say, John Nokes,
+who was the mayor of the town, died yesterday&mdash;by this predication we
+make but one assertion; whence it appears that "John Nokes, who was the
+mayor of the town," is no more than one name. It is true that in this
+proposition, besides the assertion that John Nokes died yesterday, there
+is included another assertion, namely, that John Nokes was mayor of the
+town. But this last assertion was already made: we did not make it by
+adding the predicate, "died yesterday." Suppose, however, that the words
+had been, John Nokes <i>and</i> the mayor of the town, they would have formed
+two names instead of one. For when we say, John Nokes and the mayor of
+the town died yesterday, we make two assertions; one, that John Nokes
+died yesterday; the other, that the mayor of the town died yesterday.</p>
+
+<p>It being needless to illustrate at any greater length the subject of
+many-worded names, we proceed to the distinctions which have been
+established among names, not according to the words they are composed
+of, but according to their signification.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_3">� 3.</a> All names are names of something, real or imaginary; but all things
+have not names appropriated to them <span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>individually. For some individual
+objects we require, and consequently have, separate distinguishing
+names; there is a name for every person, and for every remarkable place.
+Other objects, of which we have not occasion to speak so frequently, we
+do not designate by a name of their own; but when the necessity arises
+for naming them, we do so by putting together several words, each of
+which, by itself, might be and is used for an indefinite number of other
+objects; as when I say, <i>this stone</i>: "this" and "stone" being, each of
+them, names that may be used of many other objects besides the
+particular one meant, though the only object of which they can both be
+used at the given moment, consistently with their signification, may be
+the one of which I wish to speak.</p>
+
+<p>Were this the sole purpose for which names, that are common to more
+things than one, could be employed; if they only served, by mutually
+limiting each other, to afford a designation for such individual objects
+as have no names of their own; they could only be ranked among
+contrivances for economizing the use of language. But it is evident that
+this is not their sole function. It is by their means that we are
+enabled to assert <i>general</i> propositions; to affirm or deny any
+predicate of an indefinite number of things at once. The distinction,
+therefore, between <i>general</i> names, and <i>individual</i> or <i>singular</i>
+names, is fundamental; and may be considered as the first grand division
+of names.</p>
+
+<p>A general name is familiarly defined, a name which is capable of being
+truly affirmed, in the same sense, of each of an indefinite number of
+things. An individual or singular name is a name which is only capable
+of being truly affirmed, in the same sense, of one thing.</p>
+
+<p>Thus, <i>man</i> is capable of being truly affirmed of John, George, Mary,
+and other persons without assignable limit; and it is affirmed of all of
+them in the same sense; for the word man expresses certain qualities,
+and when we predicate it of those persons, we assert that they all
+possess those qualities. But <i>John</i> is only capable of being truly
+affirmed of one single person, at least in the same sense. For though
+there are many persons who bear that name, it is not conferred <span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>upon
+them to indicate any qualities, or anything which belongs to them in
+common; and cannot be said to be affirmed of them in any <i>sense</i> at all,
+consequently not in the same sense. "The king who succeeded William the
+Conqueror," is also an individual name. For, that there cannot be more
+than one person of whom it can be truly affirmed, is implied in the
+meaning of the words. Even "<i>the</i> king," when the occasion or the
+context defines the individual of whom it is to be understood, may
+justly be regarded as an individual name.</p>
+
+<p>It is not unusual, by way of explaining what is meant by a general name,
+to say that it is the name of a <i>class</i>. But this, though a convenient
+mode of expression for some purposes, is objectionable as a definition,
+since it explains the clearer of two things by the more obscure. It
+would be more logical to reverse the proposition, and turn it into a
+definition of the word <i>class</i>: "A class is the indefinite multitude of
+individuals denoted by a general name."</p>
+
+<p>It is necessary to distinguish <i>general</i> from <i>collective</i> names. A
+general name is one which can be predicated of <i>each</i> individual of a
+multitude; a collective name cannot be predicated of each separately,
+but only of all taken together. "The 76th regiment of foot in the
+British army," which is a collective name, is not a general but an
+individual name; for though it can be predicated of a multitude of
+individual soldiers taken jointly, it cannot be predicated of them
+severally. We may say, Jones is a soldier, and Thompson is a soldier,
+and Smith is a soldier, but we cannot say, Jones is the 76th regiment,
+and Thompson is the 76th regiment, and Smith is the 76th regiment. We
+can only say, Jones, and Thompson, and Smith, and Brown, and so forth
+(enumerating all the soldiers), are the 76th regiment.</p>
+
+<p>"The 76th regiment" is a collective name, but not a general one: "a
+regiment" is both a collective and a general name. General with respect
+to all individual regiments, of each of which separately it can be
+affirmed; collective with respect to the individual soldiers of whom any
+regiment is composed.</p>
+
+
+<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p><p class="newsection"><a name="BOOK_I_CHAPTER_II_4">� 4.</a> The second general division of names is into <i>concrete</i> and
+<i>abstract</i>. A concrete name is a name which stands for a thing; an
+abstract name is a name which stands for an attribute of a thing. Thus
+<i>John</i>, <i>the sea</i>, <i>this table</i>, are names of things. <i>White</i>, also, is
+a name of a thing, or rather of things. Whiteness, again, is the name of
+a quality or attribute of those things. Man is a name of many things;
+humanity is a name of an attribute of those things. <i>Old</i> is a name of
+things; <i>old age</i> is a name of one of their attributes.</p>
+
+<p>I have used the words concrete and abstract in the sense annexed to them
+by the schoolmen, who, notwithstanding the imperfections of their
+philosophy, were unrivalled in the construction of technical language,
+and whose definitions, in logic at least, though they never went more
+than a little way into the subject, have seldom, I think, been altered
+but to be spoiled. A practice, however, has grown up in more modern
+times, which, if not introduced by Locke, has gained currency chiefly
+from his example, of applying the expression "abstract name" to all
+names which are the result of abstraction or generalization, and
+consequently to all general names, instead of confining it to the names
+of attributes. The metaphysicians of the Condillac school,&mdash;whose
+admiration of Locke, passing over the profoundest speculations of that
+truly original genius, usually fastens with peculiar eagerness upon his
+weakest points,&mdash;have gone on imitating him in this abuse of language,
+until there is now some difficulty in restoring the word to its original
+signification. A more wanton alteration in the meaning of a word is
+rarely to be met with; for the expression <i>general name</i>, the exact
+equivalent of which exists in all languages I am acquainted with, was
+already available for the purpose to which <i>abstract</i> has been
+misappropriated, while the misappropriation leaves that important class
+of words, the names of attributes, without any compact distinctive
+appellation. The old acceptation, however, has not gone so completely
+out of use, as to deprive those who still adhere to it of all chance of
+being understood. By <i>abstract</i>, then, I shall always, in Logic, mean
+the opposite of <i>concrete</i>: by an abstract <span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>name, the name of an
+attribute; by a concrete name, the name of an object.</p>
+
+<p>Do abstract names belong to the class of general, or to that of singular
+names? Some of them are certainly general. I mean those which are names
+not of one single and definite attribute, but of a class of attributes.
+Such is the word <i>colour</i>, which is a name common to whiteness, redness,
+&amp;c. Such is even the word whiteness, in respect of the different shades
+of whiteness to which it is applied in common; the word magnitude, in
+respect of the various degrees of magnitude and the various dimensions
+of space; the word weight, in respect of the various degrees of weight.
+Such also is the word <i>attribute</i> itself, the common name of all
+particular attributes. But when only one attribute, neither variable in
+degree nor in kind, is designated by the name; as visibleness;
+tangibleness; equality; squareness; milkwhiteness; then the name can
+hardly be considered general; for though it denotes an attribute of many
+different objects, the attribute itself is always conceived as one, not
+many.<a name="FNanchor_3_9" id="FNanchor_3_9"></a><a href="#Footnote_3_9" class="fnanchor">[3]</a> To avoid needless logomachies, the best course would probably
+be to consider these names as neither general nor individual, and to
+place them in a class apart.</p>
+
+<p>It may be objected to our definition of an abstract name, that not only
+the names which we have called abstract, but adjectives, which we have
+placed in the concrete class, are names of attributes; that <i>white</i>, for
+example, is as much the name of the colour as <i>whiteness</i> is. But (as
+before remarked) a word ought to be considered as the name of that which
+we intend to be understood by it when we put it to its principal use,
+that is, when we employ it in predication. When we say snow is white,
+milk is white, linen is white, we do not mean it to be understood that
+snow, or linen, or milk, is a colour. We mean that they are things
+having the colour. The reverse is the case with the word whiteness; what
+we affirm to <i>be</i> whiteness is not snow, but the colour of snow.
+Whiteness, therefore, is the name of the colour exclusively: white is a
+<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span>name of all things whatever having the colour; a name, not of the
+quality whiteness, but of every white object. It is true, this name was
+given to all those various objects on account of the quality; and we may
+therefore say, without impropriety, that the quality forms part of its
+signification; but a name can only be said to stand for, or to be a name
+of, the things of which it can be predicated. We shall presently see
+that all names which can be said to have any signification, all names by
+applying which to an individual we give any information respecting that
+individual, may be said to <i>imply</i> an attribute of some sort; but they
+are not names of the attribute; it has its own proper abstract name.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_5">� 5.</a> This leads to the consideration of a third great division of names,
+into <i>connotative</i> and <i>non-connotative</i>, the latter sometimes, but
+improperly, called <i>absolute</i>. This is one of the most important
+distinctions which we shall have occasion to point out, and one of those
+which go deepest into the nature of language.</p>
+
+<p>A non-connotative term is one which signifies a subject only, or an
+attribute only. A connotative term is one which denotes a subject, and
+implies an attribute. By a subject is here meant anything which
+possesses attributes. Thus John, or London, or England, are names which
+signify a subject only. Whiteness, length, virtue, signify an attribute
+only. None of these names, therefore, are connotative. But <i>white</i>,
+<i>long</i>, <i>virtuous</i>, are connotative. The word white, denotes all white
+things, as snow, paper, the foam of the sea, &amp;c., and implies, or as it
+was termed by the schoolmen, <i>connotes</i><a name="FNanchor_4_10" id="FNanchor_4_10"></a><a href="#Footnote_4_10" class="fnanchor">[4]</a>, the attribute <i>whiteness</i>.
+The word white is not predicated of the attribute, but of the subjects,
+snow, &amp;c.; but when we predicate it of them, we imply, or connote, that
+the attribute whiteness belongs to them. The same may be said of the
+other words above cited. Virtuous, for example, is the name of a class,
+which includes Socrates, Howard, the Man of Ross, and <span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>an undefinable
+number of other individuals, past, present, and to come. These
+individuals, collectively and severally, can alone be said with
+propriety to be denoted by the word: of them alone can it properly be
+said to be a name. But it is a name applied to all of them in
+consequence of an attribute which they are supposed to possess in
+common, the attribute which has received the name of virtue. It is
+applied to all beings that are considered to possess this attribute; and
+to none which are not so considered.</p>
+
+<p>All concrete general names are connotative. The word <i>man</i>, for example,
+denotes Peter, Jane, John, and an indefinite number of other
+individuals, of whom, taken as a class, it is the name. But it is
+applied to them, because they possess, and to signify that they possess,
+certain attributes. These seem to be, corporeity, animal life,
+rationality, and a certain external form, which for distinction we call
+the human. Every existing thing, which possessed all these attributes,
+would be called a man; and anything which possessed none of them, or
+only one, or two, or even three of them without the fourth, would not be
+so called. For example, if in the interior of Africa there were to be
+discovered a race of animals possessing reason equal to that of human
+beings, but with the form of an elephant, they would not be called men.
+Swift's Houyhnhnms would not be so called. Or if such newly-discovered
+beings possessed the form of man without any vestige of reason, it is
+probable that some other name than that of man would be found for them.
+How it happens that there can be any doubt about the matter, will appear
+hereafter. The word <i>man</i>, therefore, signifies all these attributes,
+and all subjects which possess these attributes. But it can be
+predicated only of the subjects. What we call men, are the subjects, the
+individual Stiles and Nokes; not the qualities by which their humanity
+is constituted. The name, therefore, is said to signify the subjects
+<i>directly</i>, the attributes <i>indirectly</i>; it <i>denotes</i> the subjects, and
+implies, or involves, or indicates, or as we shall say henceforth
+<i>connotes</i>, the attributes. It is a connotative name.</p>
+
+<p>Connotative names have hence been also called <i>denominative</i>, <span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>because
+the subject which they denote is denominated by, or receives a name
+from, the attribute which they connote. Snow, and other objects, receive
+the name white, because they possess the attribute which is called
+whiteness; Peter, James, and others receive the name man, because they
+possess the attributes which are considered to constitute humanity. The
+attribute, or attributes, may therefore be said to denominate those
+objects, or to give them a common name.<a name="FNanchor_5_11" id="FNanchor_5_11"></a><a href="#Footnote_5_11" class="fnanchor">[5]</a></p>
+
+<p>It has been seen that all concrete general names are connotative. Even
+abstract names, though the names only of attributes, may in some
+instances be justly considered as connotative; for attributes themselves
+may have attributes ascribed to them; and a word which denotes
+attributes may connote an attribute of those attributes. Of this
+description, for example, is such a word as <i>fault</i>; equivalent to <i>bad</i>
+or <i>hurtful quality</i>. This word is a name common to many attributes, and
+connotes hurtfulness, an attribute of those various attributes. When,
+for example, we say that slowness, in a horse, is a fault, we do not
+mean that the slow movement, the actual change of place of the slow
+horse, is a bad thing, but that the property or peculiarity of the
+horse, from which it derives that name, the quality of being a slow
+mover, is an undesirable peculiarity.</p>
+
+<p>In regard to those concrete names which are not general but individual,
+a distinction must be made.</p>
+
+<p>Proper names are not connotative: they denote the individuals who are
+called by them; but they do not indicate or imply any attributes as
+belonging to those individuals. When we name a child by the name Paul,
+or a dog by the name C�sar, these names are simply marks used to enable
+those individuals to be made subjects of discourse. It may be said,
+indeed, that we must have had some reason for giving them <span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>those names
+rather than any others; and this is true; but the name, once given, is
+independent of the reason. A man may have been named John, because that
+was the name of his father; a town may have been named Dartmouth,
+because it is situated at the mouth of the Dart. But it is no part of
+the signification of the word John, that the father of the person so
+called bore the same name; nor even of the word Dartmouth, to be
+situated at the mouth of the Dart. If sand should choke up the mouth of
+the river, or an earthquake change its course, and remove it to a
+distance from the town, the name of the town would not necessarily be
+changed. That fact, therefore, can form no part of the signification of
+the word; for otherwise, when the fact confessedly ceased to be true, no
+one would any longer think of applying the name. Proper names are
+attached to the objects themselves, and are not dependent on the
+continuance of any attribute of the object.</p>
+
+<p>But there is another kind of names, which, although they are individual
+names, that is, predicable only of one object, are really connotative.
+For, though we may give to an individual a name utterly unmeaning, which
+we call a proper name,&mdash;a word which answers the purpose of showing what
+thing it is we are talking about, but not of telling anything about it;
+yet a name peculiar to an individual is not necessarily of this
+description. It may be significant of some attribute, or some union of
+attributes, which, being possessed by no object but one, determines the
+name exclusively to that individual. "The sun" is a name of this
+description; "God," when used by a monotheist, is another. These,
+however, are scarcely examples of what we are now attempting to
+illustrate, being, in strictness of language, general, not individual
+names: for, however they may be <i>in fact</i> predicable only of one object,
+there is nothing in the meaning of the words themselves which implies
+this: and, accordingly, when we are imagining and not affirming, we may
+speak of many suns; and the majority of mankind have believed, and still
+believe, that there are many gods. But it is easy to produce words which
+are real instances of connotative individual names. It may be part of
+the meaning of the connotative name itself, <span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>that there can exist but
+one individual possessing the attribute which it connotes: as, for
+instance, "the <i>only</i> son of John Stiles;" "the <i>first</i> emperor of
+Rome." Or the attribute connoted may be a connexion with some
+determinate event, and the connexion may be of such a kind as only one
+individual could have; or may at least be such as only one individual
+actually had; and this may be implied in the form of the expression.
+"The father of Socrates" is an example of the one kind (since Socrates
+could not have had two fathers); "the author of the Iliad," "the
+murderer of Henri Quatre," of the second. For, though it is conceivable
+that more persons than one might have participated in the authorship of
+the Iliad, or in the murder of Henri Quatre, the employment of the
+article <i>the</i> implies that, in fact, this was not the case. What is here
+done by the word <i>the</i>, is done in other cases by the context: thus,
+"C�sar's army" is an individual name, if it appears from the context
+that the army meant is that which C�sar commanded in a particular
+battle. The still more general expressions, "the Roman army," or "the
+Christian army," may be individualized in a similar manner. Another case
+of frequent occurrence has already been noticed; it is the following.
+The name, being a many-worded one, may consist, in the first place, of a
+<i>general</i> name, capable therefore in itself of being affirmed of more
+things than one, but which is, in the second place, so limited by other
+words joined with it, that the entire expression can only be predicated
+of one object, consistently with the meaning of the general term. This
+is exemplified in such an instance as the following: "the present prime
+minister of England." Prime Minister of England is a general name; the
+attributes which it connotes may be possessed by an indefinite number of
+persons: in succession however, not simultaneously; since the meaning of
+the name itself imports (among other things) that there can be only one
+such person at a time. This being the case, and the application of the
+name being afterwards limited by the article and the word <i>present</i>, to
+such individuals as possess the attributes at one indivisible point of
+time, it becomes applicable only to one individual. And as this appears
+from the meaning <span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>of the name, without any extrinsic proof, it is
+strictly an individual name.</p>
+
+<p>From the preceding observations it will easily be collected, that
+whenever the names given to objects convey any information, that is,
+whenever they have properly any meaning, the meaning resides not in what
+they <i>denote</i>, but in what they <i>connote</i>. The only names of objects
+which connote nothing are <i>proper</i> names; and these have, strictly
+speaking, no signification.<a name="FNanchor_6_12" id="FNanchor_6_12"></a><a href="#Footnote_6_12" class="fnanchor">[6]</a></p>
+
+<p>If, like the robber in the Arabian Nights, we make a mark with chalk on
+a house to enable us to know it again, the mark has a purpose, but it
+has not properly any meaning. The chalk does not declare anything about
+the house; it does not mean, This is such a person's house, or This is a
+house which contains booty. The object of making the mark is merely
+distinction. I say to myself, All these houses are so nearly alike that
+if I lose sight of them I shall not again be able to distinguish that
+which I am now looking at, from any of the others; I must therefore
+contrive to make the appearance of this one house unlike that of the
+others, that I may hereafter know, when I see the mark&mdash;not indeed any
+attribute of the house&mdash;but simply that it is the same house which I am
+now looking at. Morgiana chalked all the other houses in a similar
+manner, and defeated the scheme: how? simply by obliterating the
+difference of appearance between that house and the others. The chalk
+was still there, but it no longer served the purpose of a distinctive
+mark.</p>
+
+<p>When we impose a proper name, we perform an operation <span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>in some degree
+analogous to what the robber intended in chalking the house. We put a
+mark, not indeed upon the object itself, but, so to speak, upon the idea
+of the object. A proper name is but an unmeaning mark which we connect
+in our minds with the idea of the object, in order that whenever the
+mark meets our eyes or occurs to our thoughts, we may think of that
+individual object. Not being attached to the thing itself, it does not,
+like the chalk, enable us to distinguish the object when we see it; but
+it enables us to distinguish it when it is spoken of, either in the
+records of our own experience, or in the discourse of others; to know
+that what we find asserted in any proposition of which it is the
+subject, is asserted of the individual thing with which we were
+previously acquainted.</p>
+
+<p>When we predicate of anything its proper name; when we say, pointing to
+a man, this is Brown or Smith, or pointing to a city, that it is York,
+we do not, merely by so doing, convey to the hearer any information
+about them, except that those are their names. By enabling him to
+identify the individuals, we may connect them with information
+previously possessed by him; by saying, This is York, we may tell him
+that it contains the Minster. But this is in virtue of what he has
+previously heard concerning York; not by anything implied in the name.
+It is otherwise when objects are spoken of by connotative names. When we
+say, The town is built of marble, we give the hearer what may be
+entirely new information, and this merely by the signification of the
+many-worded connotative name, "built of marble." Such names are not
+signs of the mere objects, invented because we have occasion to think
+and speak of those objects individually; but signs which accompany an
+attribute: a kind of livery in which the attribute clothes all objects
+which are recognised as possessing it. They are not mere marks, but
+more, that is to say, significant marks; and the connotation is what
+constitutes their significance.</p>
+
+<p>As a proper name is said to be the name of the one individual which it
+is predicated of, so (as well from the importance of adhering to
+analogy, as for the other reasons formerly assigned) <span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span>a connotative name
+ought to be considered a name of all the various individuals which it is
+predicable of, or in other words <i>denotes</i>, and not of what it connotes.
+But by learning what things it is a name of, we do not learn the meaning
+of the name: for to the same thing we may, with equal propriety, apply
+many names, not equivalent in meaning. Thus, I call a certain man by the
+name Sophroniscus: I call him by another name, The father of Socrates.
+Both these are names of the same individual, but their meaning is
+altogether different; they are applied to that individual for two
+different purposes; the one, merely to distinguish him from other
+persons who are spoken of; the other to indicate a fact relating to him,
+the fact that Socrates was his son. I further apply to him these other
+expressions: a man, a Greek, an Athenian, a sculptor, an old man, an
+honest man, a brave man. All these are, or may be, names of
+Sophroniscus, not indeed of him alone, but of him and each of an
+indefinite number of other human beings. Each of these names is applied
+to Sophroniscus for a different reason, and by each whoever understands
+its meaning is apprised of a distinct fact or number of facts concerning
+him; but those who knew nothing about the names except that they were
+applicable to Sophroniscus, would be altogether ignorant of their
+meaning. It is even possible that I might know every single individual
+of whom a given name could be with truth affirmed, and yet could not be
+said to know the meaning of the name. A child knows who are its brothers
+and sisters, long before it has any definite conception of the nature of
+the facts which are involved in the signification of those words.</p>
+
+<p>In some cases it is not easy to decide precisely how much a particular
+word does or does not connote; that is, we do not exactly know (the case
+not having arisen) what degree of difference in the object would
+occasion a difference in the name. Thus, it is clear that the word man,
+besides animal life and rationality, connotes also a certain external
+form; but it would be impossible to say precisely what form; that is, to
+decide how great a deviation from the form ordinarily found in the
+beings whom we are accustomed to call men, would suffice in <span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>a
+newly-discovered race to make us refuse them the name of man.
+Rationality, also, being a quality which admits of degrees, it has never
+been settled what is the lowest degree of that quality which would
+entitle any creature to be considered a human being. In all such cases,
+the meaning of the general name is so far unsettled and vague; mankind
+have not come to any positive agreement about the matter. When we come
+to treat of Classification, we shall have occasion to show under what
+conditions this vagueness may exist without practical inconvenience; and
+cases will appear in which the ends of language are better promoted by
+it than by complete precision; in order that, in natural history for
+instance, individuals or species of no very marked character may be
+ranged with those more strongly characterized individuals or species to
+which, in all their properties taken together, they bear the nearest
+resemblance.</p>
+
+<p>But this partial uncertainty in the connotation of names can only be
+free from mischief when guarded by strict precautions. One of the chief
+sources, indeed, of lax habits of thought, is the custom of using
+connotative terms without a distinctly ascertained connotation, and with
+no more precise notion of their meaning than can be loosely collected
+from observing what objects they are used to denote. It is in this
+manner that we all acquire, and inevitably so, our first knowledge of
+our vernacular language. A child learns the meaning of the words <i>man</i>,
+or <i>white</i>, by hearing them applied to a variety of individual objects,
+and finding out, by a process of generalization and analysis which he
+could not himself describe, what those different objects have in common.
+In the case of these two words the process is so easy as to require no
+assistance from culture; the objects called human beings, and the
+objects called white, differing from all others by qualities of a
+peculiarly definite and obvious character. But in many other cases,
+objects bear a general resemblance to one another, which leads to their
+being familiarly classed together under a common name, while, without
+more analytic habits than the generality of mankind possess, it is not
+immediately apparent what are the particular attributes, upon the
+possession of which <span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>in common by them all, their general resemblance
+depends. When this is the case, people use the name without any
+recognised connotation, that is, without any precise meaning; they talk,
+and consequently think, vaguely, and remain contented to attach only the
+same degree of significance to their own words, which a child three
+years old attaches to the words brother and sister. The child at least
+is seldom puzzled by the starting up of new individuals, on whom he is
+ignorant whether or not to confer the title; because there is usually an
+authority close at hand competent to solve all doubts. But a similar
+resource does not exist in the generality of cases; and new objects are
+continually presenting themselves to men, women, and children, which
+they are called upon to class <i>proprio motu</i>. They, accordingly, do this
+on no other principle than that of superficial similarity, giving to
+each new object the name of that familiar object, the idea of which it
+most readily recalls, or which, on a cursory inspection, it seems to
+them most to resemble: as an unknown substance found in the ground will
+be called, according to its texture, earth, sand, or a stone. In this
+manner, names creep on from subject to subject, until all traces of a
+common meaning sometimes disappear, and the word comes to denote a
+number of things not only independently of any common attribute, but
+which have actually no attribute in common; or none but what is shared
+by other things to which the name is capriciously refused. Even
+scientific writers have aided in this perversion of general language
+from its purpose; sometimes because, like the vulgar, they knew no
+better; and sometimes in deference to that aversion to admit new words,
+which induces mankind, on all subjects not considered technical, to
+attempt to make the original stock of names serve with but little
+augmentation to express a constantly increasing number of objects and
+distinctions, and, consequently, to express them in a manner
+progressively more and more imperfect.</p>
+
+<p>To what a degree this loose mode of classing and denominating objects
+has rendered the vocabulary of mental and moral philosophy unfit for the
+purposes of accurate thinking, is best known to whoever has most
+meditated on the present condition <span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>of those branches of knowledge.
+Since, however, the introduction of a new technical language as the
+vehicle of speculations on subjects belonging to the domain of daily
+discussion, is extremely difficult to effect, and would not be free from
+inconvenience even if effected, the problem for the philosopher, and one
+of the most difficult which he has to resolve, is, in retaining the
+existing phraseology, how best to alleviate its imperfections. This can
+only be accomplished by giving to every general concrete name which
+there is frequent occasion to predicate, a definite and fixed
+connotation; in order that it may be known what attributes, when we call
+an object by that name, we really mean to predicate of the object. And
+the question of most nicety is, how to give this fixed connotation to a
+name, with the least possible change in the objects which the name is
+habitually employed to denote; with the least possible disarrangement,
+either by adding or subtraction, of the group of objects which, in
+however imperfect a manner, it serves to circumscribe and hold together;
+and with the least vitiation of the truth of any propositions which are
+commonly received as true.</p>
+
+<p>This desirable purpose, of giving a fixed connotation where it is
+wanting, is the end aimed at whenever any one attempts to give a
+definition of a general name already in use; every definition of a
+connotative name being an attempt either merely to declare, or to
+declare and analyse, the connotation of the name. And the fact, that no
+questions which have arisen in the moral sciences have been subjects of
+keener controversy than the definitions of almost all the leading
+expressions, is a proof how great an extent the evil to which we have
+adverted has attained.</p>
+
+<p>Names with indeterminate connotation are not to be confounded with names
+which have more than one connotation, that is to say, ambiguous words. A
+word may have several meanings, but all of them fixed and recognised
+ones; as the word <i>post</i>, for example, or the word <i>box</i>, the various
+senses of which it would be endless to enumerate. And the paucity of
+existing names, in comparison with the demand for them, may often render
+it advisable and even necessary to retain a name <span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>in this multiplicity
+of acceptations, distinguishing these so clearly as to prevent their
+being confounded with one another. Such a word may be considered as two
+or more names, accidentally written and spoken alike.<a name="FNanchor_7_13" id="FNanchor_7_13"></a><a href="#Footnote_7_13" class="fnanchor">[7]</a></p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_6">� 6.</a> The fourth principal division of names, is into <i>positive</i> and
+<i>negative</i>. Positive, as <i>man</i>, <i>tree</i>, <i>good</i>; negative, as <i>not-man</i>,
+<i>not-tree</i>, <i>not-good</i>. To every positive concrete name, a corresponding
+negative one might be framed. After giving a name to any one thing, or
+to any plurality of things, we might create a second name which should
+be a name of all things whatever, except that particular thing or
+things. These negative names are employed whenever we have occasion to
+speak collectively of all things other than some thing or class of
+things. When the positive name is connotative, the corresponding
+negative name is connotative likewise; but in a peculiar way, connoting
+not the presence but the absence of an attribute. Thus, <i>not-white</i>
+denotes all things whatever except white things; and connotes the
+attribute of not possessing <span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span>whiteness. For the non-possession of any
+given attribute is also an attribute, and may receive a name as such;
+and thus negative concrete names may obtain negative abstract names to
+correspond to them.</p>
+
+<p>Names which are positive in form are often negative in reality, and
+others are really positive though their form is negative. The word
+<i>inconvenient</i>, for example, does not express the mere absence of
+convenience; it expresses a positive attribute, that of being the cause
+of discomfort or annoyance. So the word <i>unpleasant</i>, notwithstanding
+its negative form, does not connote the mere absence of pleasantness,
+but a less degree of what is signified by the word <i>painful</i>, which, it
+is hardly necessary to say, is positive. <i>Idle</i>, on the other hand, is a
+word which, though positive in form, expresses nothing but what would be
+signified either by the phrase <i>not working</i>, or by the phrase <i>not
+disposed to work</i>; and <i>sober</i>, either by <i>not drunk</i> or by <i>not
+drunken</i>.</p>
+
+<p>There is a class of names called <i>privative</i>. A privative name is
+equivalent in its signification to a positive and a negative <span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>name taken
+together; being the name of something which has once had a particular
+attribute, or for some other reason might have been expected to have it,
+but which has it not. Such is the word <i>blind</i>, which is not equivalent
+to <i>not seeing</i>, or to <i>not capable of seeing</i>, for it would not, except
+by a poetical or rhetorical figure, be applied to stocks and stones. A
+thing is not usually said to be blind, unless the class to which it is
+most familiarly referred, or to which it is referred on the particular
+occasion, be chiefly composed of things which can see, as in the case of
+a blind man, or a blind horse; or unless it is supposed for any reason
+that it ought to see; as in saying of a man, that he rushed blindly into
+an abyss, or of philosophers or the clergy that the greater part of them
+are blind guides. The names called privative, therefore, connote two
+things: the absence of certain attributes, and the presence of others,
+from which the presence also of the former might naturally have been
+expected.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_7">� 7.</a> The fifth leading division of names is into <i>relative</i> and
+<i>absolute</i>, or let us rather say, <i>relative</i> and <i>non-relative</i>; for the
+word absolute is put upon much too hard duty in metaphysics, not to be
+willingly spared when its services can be dispensed with. It resembles
+the word <i>civil</i> in the language of jurisprudence, which stands for the
+opposite of criminal, the opposite of ecclesiastical, the opposite of
+military, the opposite of political&mdash;in short, the opposite of any
+positive word which wants a negative.</p>
+
+<p>Relative names are such as father, son; ruler, subject; like; equal;
+unlike; unequal; longer, shorter; cause, effect. Their characteristic
+property is, that they are always given in pairs. Every relative name
+which is predicated of an object, supposes another object (or objects),
+of which we may predicate either that same name or another relative name
+which is said to be the <i>correlative</i> of the former. Thus, when we call
+any person a son, we suppose other persons who must be called parents.
+When we call any event a cause, we suppose another event which is an
+effect. When we say of any distance that it is longer, we suppose
+another distance which is shorter. <span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>When we say of any object that it is
+like, we mean that it is like some other object, which is also said to
+be like the first. In this last case both objects receive the same name;
+the relative term is its own correlative.</p>
+
+<p>It is evident that these words, when concrete, are, like other concrete
+general names, connotative; they denote a subject, and connote an
+attribute; and each of them has or might have a corresponding abstract
+name, to denote the attribute connoted by the concrete. Thus the
+concrete <i>like</i> has its abstract <i>likeness</i>; the concretes, father and
+son, have, or might have, the abstracts, paternity, and filiety, or
+sonship. The concrete name connotes an attribute, and the abstract name
+which answers to it denotes that attribute. But of what nature is the
+attribute? Wherein consists the peculiarity in the connotation of a
+relative name?</p>
+
+<p>The attribute signified by a relative name, say some, is a relation; and
+this they give, if not as a sufficient explanation, at least as the only
+one attainable. If they are asked, What then is a relation? they do not
+profess to be able to tell. It is generally regarded as something
+peculiarly recondite and mysterious. I cannot, however, perceive in what
+respect it is more so than any other attribute; indeed, it appears to me
+to be so in a somewhat less degree. I conceive, rather, that it is by
+examining into the signification of relative names, or, in other words,
+into the nature of the attribute which they connote, that a clear
+insight may best be obtained into the nature of all attributes: of all
+that is meant by an attribute.</p>
+
+<p>It is obvious, in fact, that if we take any two correlative names,
+<i>father</i> and <i>son</i> for instance, though the objects <i>de</i>noted by the
+names are different, they both, in a certain sense, connote the same
+thing. They cannot, indeed, be said to connote the same <i>attribute</i>: to
+be a father, is not the same thing as to be a son. But when we call one
+man a father, another a son, what we mean to affirm is a set of facts,
+which are exactly the same in both cases. To predicate of A that he is
+the father of B, and of B that he is the son of A, is to assert one and
+the same fact in different words. The two propositions are exactly
+equivalent: neither of them <span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>asserts more or asserts less than the
+other. The paternity of A and the filiety of B are not two facts, but
+two modes of expressing the same fact. That fact, when analysed,
+consists of a series of physical events or phenomena, in which both A
+and B are parties concerned, and from which they both derive names. What
+those names really connote, is this series of events: that is the
+meaning, and the whole meaning, which either of them is intended to
+convey. The series of events may be said to <i>constitute</i> the relation;
+the schoolmen called it the foundation of the relation, <i>fundamentum
+relationis</i>.</p>
+
+<p>In this manner any fact, or series of facts, in which two different
+objects are implicated, and which is therefore predicable of both of
+them, may be either considered as constituting an attribute of the one,
+or an attribute of the other. According as we consider it in the former,
+or in the latter aspect, it is connoted by the one or the other of the
+two correlative names. <i>Father</i> connotes the fact, regarded as
+constituting an attribute of A: <i>son</i> connotes the same fact, as
+constituting an attribute of B. It may evidently be regarded with equal
+propriety in either light. And all that appears necessary to account for
+the existence of relative names, is, that whenever there is a fact in
+which two individuals are concerned, an attribute grounded on that fact
+may be ascribed to either of these individuals.</p>
+
+<p>A name, therefore, is said to be relative, when, over and above the
+object which it denotes, it implies in its signification the existence
+of another object, also deriving a denomination from the same fact which
+is the ground of the first name. Or (to express the same meaning in
+other words) a name is relative, when, being the name of one thing, its
+signification cannot be explained but by mentioning another. Or we may
+state it thus&mdash;when the name cannot be employed in discourse so as to
+have a meaning, unless the name of some other thing than what it is
+itself the name of, be either expressed or understood. These definitions
+are all, at bottom, equivalent, being modes of variously expressing this
+one distinctive circumstance&mdash;that every other attribute of an object
+might, without any contradiction, be conceived still to exist if no
+object besides <span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>that one had ever existed;<a name="FNanchor_8_14" id="FNanchor_8_14"></a><a href="#Footnote_8_14" class="fnanchor">[8]</a> but those of its
+attributes which are expressed by relative names, would on that
+supposition be swept away.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_II_8">� 8.</a> Names have been further distinguished into <i>univocal</i> and
+<i>�quivocal</i>: these, however, are not two kinds of names, but two
+different modes of employing names. A name is univocal, or applied
+univocally, with respect to all things of which it can be predicated <i>in
+the same sense</i>: it is �quivocal, or applied �quivocally, as respects
+those things of which it is predicated in different senses. It is
+scarcely necessary to give instances of a fact so familiar as the double
+meaning of a word. In reality, as has been already observed, an
+�quivocal or ambiguous word is not one name, but two names, accidentally
+coinciding in sound. <i>File</i> meaning a steel instrument, and <i>file</i>
+meaning a line of soldiers, have no more title to be considered one
+word, because written alike, than <i>grease</i> and <i>Greece</i> have, because
+they are pronounced alike. They are one sound, appropriated to form two
+different words.</p>
+
+<p>An intermediate case is that of a name used <i>analogically</i> or
+metaphorically; that is, a name which is predicated of two things, not
+univocally, or exactly in the same signification, but in significations
+somewhat similar, and which being derived one from the other, one of
+them may be considered the primary, and the other a secondary
+signification. As when we speak of a brilliant light and a brilliant
+achievement. The word is not applied in the same sense to the light and
+to the achievement; but having been applied to the light in its original
+sense, that of brightness to the eye, it is transferred to the
+achievement in a derivative signification, supposed to be somewhat like
+the primitive one. The word, however, is <span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span>just as properly two names
+instead of one, in this case, as in that of the most perfect ambiguity.
+And one of the commonest forms of fallacious reasoning arising from
+ambiguity, is that of arguing from a metaphorical expression as if it
+were literal; that is, as if a word, when applied metaphorically, were
+the same name as when taken in its original sense: which will be seen
+more particularly in its place.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_III" id="BOOK_I_CHAPTER_III"></a>CHAPTER III.<br />
+
+OF THE THINGS DENOTED BY NAMES.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_1">� 1.</a> Looking back now to the commencement of our inquiry, let us attempt
+to measure how far it has advanced. Logic, we found, is the Theory of
+Proof. But proof supposes something provable, which must be a
+Proposition or Assertion; since nothing but a Proposition can be an
+object of belief, or therefore of proof. A Proposition is, discourse
+which affirms or denies something of some other thing. This is one step:
+there must, it seems, be two things concerned in every act of belief.
+But what are these Things? They can be no other than those signified by
+the two names, which being joined together by a copula constitute the
+Proposition. If, therefore, we knew what all names signify, we should
+know everything which in the existing state of human knowledge, is
+capable either of being made a subject of affirmation or denial, or of
+being itself affirmed or denied of a subject. We have accordingly, in
+the preceding chapter, reviewed the various kinds of Names, in order to
+ascertain what is signified by each of them. And we have now carried
+this survey far enough to be able to take an account of its results, and
+to exhibit an enumeration of all kinds of Things which are capable of
+being made predicates, or of having anything predicated of them: after
+which to determine the import of Predication, that is, of Propositions,
+can be no arduous task.</p>
+
+<p>The necessity of an enumeration of Existences, as the basis of Logic,
+did not escape the attention of the schoolmen, and of their master
+Aristotle, the most comprehensive, if not also the most sagacious, of
+the ancient philosophers. The Categories, or Predicaments&mdash;the former a
+Greek word, the latter its literal translation in the Latin
+language&mdash;were intended by him and his followers as an enumeration of
+all things capable <span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span>of being named; an enumeration by the <i>summa
+genera</i>, <i>i.e.</i> the most extensive classes into which things could be
+distributed; which, therefore, were so many highest Predicates, one or
+other of which was supposed capable of being affirmed with truth of
+every nameable thing whatsoever. The following are the classes into
+which, according to this school of philosophy, Things in general might
+be reduced:&mdash;</p>
+
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">&#927;&#8016;&#963;&#8055;&#945;,</td><td align="left">Substantia.</td></tr>
+<tr><td align="left">&#928;&#959;&#963;&#8056;&#957;,</td><td align="left">Quantitas.</td></tr>
+<tr><td align="left">&#928;&#959;&#953;&#8057;&#957;,</td><td align="left">Qualitas.</td></tr>
+<tr><td align="left">&#928;&#961;&#8057;&#962; &#964;&#953;,</td><td align="left">Relatio.</td></tr>
+<tr><td align="left">&#928;&#959;&#953;&#949;&#8150;&#957;,</td><td align="left">Actio.</td></tr>
+<tr><td align="left">&#928;&#8049;&#963;&#967;&#949;&#953;&#957;,</td><td align="left">Passio.</td></tr>
+<tr><td align="left">&#928;&#959;&#8166;,</td><td align="left">Ubi.</td></tr>
+<tr><td align="left">&#928;&#8057;&#964;&#949;,</td><td align="left">Quando.</td></tr>
+<tr><td align="left">&#922;&#949;&#8150;&#963;&#952;&#945;&#953;,</td><td align="left">Situs.</td></tr>
+<tr><td align="left">&#7964;&#967;&#949;&#953;&#957;,</td><td align="left">Habitus.</td></tr>
+</table></div>
+
+<p>The imperfections of this classification are too obvious to require, and
+its merits are not sufficient to reward, a minute examination. It is a
+mere catalogue of the distinctions rudely marked out by the language of
+familiar life, with little or no attempt to penetrate, by philosophic
+analysis, to the <i>rationale</i> even of those common distinctions. Such an
+analysis, however superficially conducted, would have shown the
+enumeration to be both redundant and defective. Some objects are
+omitted, and others repeated several times under different heads. It is
+like a division of animals into men, quadrupeds, horses, asses, and
+ponies. That, for instance, could not be a very comprehensive view of
+the nature of Relation which could exclude action, passivity, and local
+situation from that category. The same observation applies to the
+categories Quando (or position in time), and Ubi (or position in space);
+while the distinction between the latter and Situs is merely verbal. The
+incongruity of erecting into a <i>summum genus</i> the class which forms the
+tenth category is manifest. On the other hand, the enumeration takes no
+notice of anything besides substances and attributes. In what category
+are we to place sensations, or any other feelings and states of mind; as
+hope, joy, fear; sound, smell, taste; pain, pleasure; thought, judgment,
+<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>conception, and the like? Probably all these would have been placed by
+the Aristotelian school in the categories of <i>actio</i> and <i>passio</i>; and
+the relation of such of them as are active, to their objects, and of
+such of them as are passive, to their causes, would rightly be so
+placed; but the things themselves, the feelings or states of mind,
+wrongly. Feelings, or states of consciousness, are assuredly to be
+counted among realities, but they cannot be reckoned either among
+substances or attributes.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_2">� 2.</a> Before recommencing, under better auspices, the attempt made with
+such imperfect success by the great founder of the science of logic, we
+must take notice of an unfortunate ambiguity in all the concrete names
+which correspond to the most general of all abstract terms, the word
+Existence. When we have occasion for a name which shall be capable of
+denoting whatever exists, as contradistinguished from non-entity or
+Nothing, there is hardly a word applicable to the purpose which is not
+also, and even more familiarly, taken in a sense in which it denotes
+only substances. But substances are not all that exists; attributes, if
+such things are to be spoken of, must be said to exist; feelings
+certainly exist. Yet when we speak of an <i>object</i>, or of a <i>thing</i>, we
+are almost always supposed to mean a substance. There seems a kind of
+contradiction in using such an expression as that one <i>thing</i> is merely
+an attribute of another thing. And the announcement of a Classification
+of Things would, I believe, prepare most readers for an enumeration like
+those in natural history, beginning with the great divisions of animal,
+vegetable, and mineral, and subdividing them into classes and orders.
+If, rejecting the word Thing, we endeavour to find another of a more
+general import, or at least more exclusively confined to that general
+import, a word denoting all that exists, and connoting only simple
+existence; no word might be presumed fitter for such a purpose than
+<i>being</i>: originally the present participle of a verb which in one of its
+meanings is exactly equivalent to the verb <i>exists</i>; and therefore
+suitable, even by its grammatical formation, to be the concrete of the
+abstract <i>existence</i>. But this <span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>word, strange as the fact may appear, is
+still more completely spoiled for the purpose which it seemed expressly
+made for, than the word Thing. <i>Being</i> is, by custom, exactly synonymous
+with substance; except that it is free from a slight taint of a second
+ambiguity; being applied impartially to matter and to mind, while
+substance, though originally and in strictness applicable to both, is
+apt to suggest in preference the idea of matter. Attributes are never
+called Beings; nor are feelings. A Being is that which excites feelings,
+and which possesses attributes. The soul is called a Being; God and
+angels are called Beings; but if we were to say, extension, colour,
+wisdom, virtue, are beings, we should perhaps be suspected of thinking
+with some of the ancients, that the cardinal virtues are animals; or, at
+the least, of holding with the Platonic school the doctrine of
+self-existent Ideas, or with the followers of Epicurus that of Sensible
+Forms, which detach themselves in every direction from bodies, and by
+coming in contact with our organs, cause our perceptions. We should be
+supposed, in short, to believe that Attributes are Substances.</p>
+
+<p>In consequence of this perversion of the word Being, philosophers
+looking about for something to supply its place, laid their hands upon
+the word Entity, a piece of barbarous Latin, invented by the schoolmen
+to be used as an abstract name, in which class its grammatical form
+would seem to place it; but being seized by logicians in distress to
+stop a leak in their terminology, it has ever since been used as a
+concrete name. The kindred word <i>essence</i>, born at the same time and of
+the same parents, scarcely underwent a more complete transformation
+when, from being the abstract of the verb <i>to be</i>, it came to denote
+something sufficiently concrete to be enclosed in a glass bottle. The
+word Entity, since it settled down into a concrete name, has retained
+its universality of signification somewhat less impaired than any of the
+names before mentioned. Yet the same gradual decay to which, after a
+certain age, all the language of psychology seems liable, has been at
+work even here. If you call virtue an <i>entity</i>, you are indeed somewhat
+less strongly suspected of believing it to be a substance than if you
+called it a <i>being</i>; but you are by no means <span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>free from the suspicion.
+Every word which was originally intended to connote mere existence,
+seems, after a long time, to enlarge its connotation to <i>separate</i>
+existence, or existence freed from the condition of belonging to a
+substance; which condition being precisely what constitutes an
+attribute, attributes are gradually shut out; and along with them
+feelings, which in ninety-nine cases out of a hundred have no other name
+than that of the attribute which is grounded on them. Strange that when
+the greatest embarrassment felt by all who have any considerable number
+of thoughts to express, is to find a sufficient variety of precise words
+fitted to express them, there should be no practice to which even
+scientific thinkers are more addicted than that of taking valuable words
+to express ideas which are sufficiently expressed by other words already
+appropriated to them.</p>
+
+<p>When it is impossible to obtain good tools, the next best thing is to
+understand thoroughly the defects of those we have. I have therefore
+warned the reader of the ambiguity of the names which, for want of
+better, I am necessitated to employ. It must now be the writer's
+endeavour so to employ them as in no case to leave the meaning doubtful
+or obscure. No one of the above terms being altogether unambiguous, I
+shall not confine myself to any one, but shall employ on each occasion
+the word which seems least likely in the particular case to lead to
+misunderstanding; nor do I pretend to use either these or any other
+words with a rigorous adherence to one single sense. To do so would
+often leave us without a word to express what is signified by a known
+word in some one or other of its senses: unless authors had an unlimited
+licence to coin new words, together with (what it would be more
+difficult to assume) unlimited power of making readers understand them.
+Nor would it be wise in a writer, on a subject involving so much of
+abstraction, to deny himself the advantage derived from even an improper
+use of a term, when, by means of it, some familiar association is called
+up which brings the meaning home to the mind, as it were by a flash.</p>
+
+<p>The difficulty both to the writer and reader, of the attempt <span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span>which must
+be made to use vague words so as to convey a precise meaning, is not
+wholly a matter of regret. It is not unfitting that logical treatises
+should afford an example of that, to facilitate which is among the most
+important uses of logic. Philosophical language will for a long time,
+and popular language still longer, retain so much of vagueness and
+ambiguity, that logic would be of little value if it did not, among its
+other advantages, exercise the understanding in doing its work neatly
+and correctly with these imperfect tools.</p>
+
+<p>After this preamble it is time to proceed to our enumeration. We shall
+commence with Feelings, the simplest class of nameable things; the term
+Feeling being of course understood in its most enlarged sense.</p>
+
+
+<p class="center" style="margin-top:1.5em;">I. <span class="smcap">Feelings, or States of Consciousness.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_3">� 3.</a> A Feeling and a State of Consciousness are, in the language of
+philosophy, equivalent expressions: everything is a feeling of which the
+mind is conscious; everything which it <i>feels</i>, or, in other words,
+which forms a part of its own sentient existence. In popular language
+Feeling is not always synonymous with State of Consciousness; being
+often taken more peculiarly for those states which are conceived as
+belonging to the sensitive, or to the emotional, phasis of our nature,
+and sometimes, with a still narrower restriction, to the emotional
+alone, as distinguished from what are conceived as belonging to the
+percipient or to the intellectual phasis. But this is an admitted
+departure from correctness of language; just as, by a popular perversion
+the exact converse of this, the word Mind is withdrawn from its rightful
+generality of signification, and restricted to the intellect. The still
+greater perversion by which Feeling is sometimes confined not only to
+bodily sensations, but to the sensations of a single sense, that of
+touch, needs not be more particularly adverted to.</p>
+
+<p>Feeling, in the proper sense of the term, is a genus, of which
+Sensation, Emotion, and Thought, are subordinate species. Under the word
+Thought is here to be included whatever <span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span>we are internally conscious of
+when we are said to think; from the consciousness we have when we think
+of a red colour without having it before our eyes, to the most recondite
+thoughts of a philosopher or poet. Be it remembered, however, that by a
+thought is to be understood what passes in the mind itself, and not any
+object external to the mind, which the person is commonly said to be
+thinking of. He may be thinking of the sun, or of God, but the sun and
+God are not thoughts; his mental image, however, of the sun, and his
+idea of God, are thoughts; states of his mind, not of the objects
+themselves; and so also is his belief of the existence of the sun, or of
+God; or his disbelief, if the case be so. Even imaginary objects (which
+are said to exist only in our ideas) are to be distinguished from our
+ideas of them. I may think of a hobgoblin, as I may think of the loaf
+which was eaten yesterday, or of the flower which will bloom to-morrow.
+But the hobgoblin which never existed is not the same thing with my idea
+of a hobgoblin, any more than the loaf which once existed is the same
+thing with my idea of a loaf, or the flower which does not yet exist,
+but which will exist, is the same with my idea of a flower. They are
+all, not thoughts, but objects of thought; though at the present time
+all the objects are alike non-existent.</p>
+
+<p>In like manner, a Sensation is to be carefully distinguished from the
+object which causes the sensation; our sensation of white from a white
+object: nor is it less to be distinguished from the attribute whiteness,
+which we ascribe to the object in consequence of its exciting the
+sensation. Unfortunately for clearness and due discrimination in
+considering these subjects, our sensations seldom receive separate
+names. We have a name for the objects which produce in us a certain
+sensation: the word <i>white</i>. We have a name for the quality in those
+objects, to which we ascribe the sensation: the name <i>whiteness</i>. But
+when we speak of the sensation itself (as we have not occasion to do
+this often except in our scientific speculations), language, which
+adapts itself for the most part only to the common uses of life, has
+provided us with no single-worded or immediate designation; we must
+employ a circumlocution, and say, The <span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>sensation of white, or The
+sensation of whiteness; we must denominate the sensation either from the
+object, or from the attribute, by which it is excited. Yet the
+sensation, though it never <i>does</i>, might very well be <i>conceived</i> to
+exist, without anything whatever to excite it. We can conceive it as
+arising spontaneously in the mind. But if it so arose, we should have no
+name to denote it which would not be a misnomer. In the case of our
+sensations of hearing we are better provided; we have the word Sound,
+and a whole vocabulary of words to denote the various kinds of sounds.
+For as we are often conscious of these sensations in the absence of any
+perceptible object, we can more easily conceive having them in the
+absence of any object whatever. We need only shut our eyes and listen to
+music, to have a conception of an universe with nothing in it except
+sounds, and ourselves hearing them: and what is easily conceived
+separately, easily obtains a separate name. But in general our names of
+sensations denote indiscriminately the sensation and the attribute.
+Thus, <i>colour</i> stands for the sensations of white, red, &amp;c., but also
+for the quality in the coloured object. We talk of the colours of things
+as among their <i>properties</i>.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_4">� 4.</a> In the case of sensations, another distinction has also to be kept
+in view, which is often confounded, and never without mischievous
+consequences. This is, the distinction between the sensation itself, and
+the state of the bodily organs which precedes the sensation, and which
+constitutes the physical agency by which it is produced. One of the
+sources of confusion on this subject is the division commonly made of
+feelings into Bodily and Mental. Philosophically speaking, there is no
+foundation at all for this distinction: even sensations are states of
+the sentient mind, not states of the body, as distinguished from it.
+What I am conscious of when I see the colour blue, is a feeling of blue
+colour, which is one thing; the picture on my retina, or the phenomenon
+of hitherto mysterious nature which takes place in my optic nerve or in
+my brain, is another thing, of which I am not at all conscious, and
+which scientific investigation alone could have apprised me of. These
+are states of my body; but the sensation of blue, which is the
+consequence <span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>of these states of body, is not a state of body: that which
+perceives and is conscious is called Mind. When sensations are called
+bodily feelings, it is only as being the class of feelings which are
+immediately occasioned by bodily states; whereas the other kinds of
+feelings, thoughts, for instance, or emotions, are immediately excited
+not by anything acting upon the bodily organs, but by sensations, or by
+previous thoughts. This, however, is a distinction not in our feelings,
+but in the agency which produces our feelings: all of them when actually
+produced are states of mind.</p>
+
+<p>Besides the affection of our bodily organs from without, and the
+sensation thereby produced in our minds, many writers admit a third link
+in the chain of phenomena, which they call a Perception, and which
+consists in the recognition of an external object as the exciting cause
+of the sensation. This perception, they say, is an <i>act</i> of the mind,
+proceeding from its own spontaneous activity; while in a sensation the
+mind is passive, being merely acted upon by the outward object. And
+according to some metaphysicians, it is by an act of the mind, similar
+to perception, except in not being preceded by any sensation, that the
+existence of God, the soul, and other hyper-physical objects is
+recognised.</p>
+
+<p>These acts of what is termed perception, whatever be the conclusion
+ultimately come to respecting their nature, must, I conceive, take their
+place among the varieties of feelings or states of mind. In so classing
+them, I have not the smallest intention of declaring or insinuating any
+theory as to the law of mind in which these mental processes may be
+supposed to originate, or the conditions under which they may be
+legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
+suppose must be meant in an analogous case<a name="FNanchor_9_15" id="FNanchor_9_15"></a><a href="#Footnote_9_15" class="fnanchor">[9]</a>) to indicate that as they
+are "<i>merely</i> states of mind," it is superfluous to inquire into their
+distinguishing peculiarities. I abstain from the inquiry as irrelevant
+to the science of logic. In these so-called perceptions, or direct
+recognitions by the mind, of objects, whether physical or spiritual,
+which are external <span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>to itself, I can see only cases of belief; but of
+belief which claims to be intuitive, or independent of external
+evidence. When a stone lies before me, I am conscious of certain
+sensations which I receive from it; but if I say that these sensations
+come to me from an external object which I <i>perceive</i>, the meaning of
+these words is, that receiving the sensations, I intuitively <i>believe</i>
+that an external cause of those sensations exists. The laws of intuitive
+belief, and the conditions under which it is legitimate, are a subject
+which, as we have already so often remarked, belongs not to logic, but
+to the science of the ultimate laws of the human mind.</p>
+
+<p>To the same region of speculation belongs all that can be said
+respecting the distinction which the German metaphysicians and their
+French and English followers so elaborately draw between the <i>acts</i> of
+the mind and its merely passive <i>states</i>; between what it receives from,
+and what it gives to, the crude materials of its experience. I am aware
+that with reference to the view which those writers take of the primary
+elements of thought and knowledge, this distinction is fundamental. But
+for the present purpose, which is to examine, not the original
+groundwork of our knowledge, but how we come by that portion of it which
+is not original; the difference between active and passive states of
+mind is of secondary importance. For us, they all are states of mind,
+they all are feelings; by which, let it be said once more, I mean to
+imply nothing of passivity, but simply that they are psychological
+facts, facts which take place in the mind, and are to be carefully
+distinguished from the external or physical facts with which they may be
+connected either as effects or as causes.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_5">� 5.</a> Among active states of mind, there is, however, one species which
+merits particular attention, because it forms a principal part of the
+connotation of some important classes of names. I mean <i>volitions</i>, or
+acts of the will. When we speak of sentient beings by relative names, a
+large portion of the connotation of the name usually consists of the
+actions of those beings; actions past, present, and possible or probable
+future. Take, for instance, the words Sovereign and Subject. What
+<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>meaning do these words convey, but that of innumerable actions, done or
+to be done by the sovereign and the subjects, to or in regard to one
+another reciprocally? So with the words physician and patient, leader
+and follower, tutor and pupil. In many cases the words also connote
+actions which would be done under certain contingencies by persons other
+than those denoted: as the words mortgagor and mortgagee, obligor and
+obligee, and many other words expressive of legal relation, which
+connote what a court of justice would do to enforce the legal obligation
+if not fulfilled. There are also words which connote actions previously
+done by persons other than those denoted either by the name itself or by
+its correlative; as the word brother. From these instances, it may be
+seen how large a portion of the connotation of names consists of
+actions. Now what is an action? Not one thing, but a series of two
+things: the state of mind called a volition, followed by an effect. The
+volition or intention to produce the effect, is one thing; the effect
+produced in consequence of the intention, is another thing; the two
+together constitute the action. I form the purpose of instantly moving
+my arm; that is a state of my mind: my arm (not being tied or paralytic)
+moves in obedience to my purpose; that is a physical fact, consequent on
+a state of mind. The intention, followed by the fact, or (if we prefer
+the expression) the fact when preceded and caused by the intention, is
+called the action of moving my arm.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_6">� 6.</a> Of the first leading division of nameable things, viz. Feelings or
+States of Consciousness, we began by recognising three subdivisions;
+Sensations, Thoughts, and Emotions. The first two of these we have
+illustrated at considerable length; the third, Emotions, not being
+perplexed by similar ambiguities, does not require similar
+exemplification. And, finally, we have found it necessary to add to
+these three a fourth species, commonly known by the name Volitions.
+Without seeking to prejudge the metaphysical question whether any mental
+state or phenomenon can be found which is not included in one or other
+of these four species, it appears <span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>to me that the amount of illustration
+bestowed upon these may, so far as we are concerned, suffice for the
+whole genus. We shall, therefore, proceed to the two remaining classes
+of nameable things; all things which are external to the mind being
+considered as belonging either to the class of Substances or to that of
+Attributes.</p>
+
+<p class="center" style="margin-top:1.5em;">II. <span class="smcap">Substances.</span></p>
+
+<p class="newsection">Logicians have endeavoured to define Substance and Attribute; but their
+definitions are not so much attempts to draw a distinction between the
+things themselves, as instructions what difference it is customary to
+make in the grammatical structure of the sentence, according as we are
+speaking of substances or of attributes. Such definitions are rather
+lessons of English, or of Greek, Latin, or German, than of mental
+philosophy. An attribute, say the school logicians, must be the
+attribute <i>of</i> something; colour, for example, must be the colour <i>of</i>
+something; goodness must be the goodness <i>of</i> something: and if this
+something should cease to exist, or should cease to be connected with
+the attribute, the existence of the attribute would be at an end. A
+substance, on the contrary, is self-existent; in speaking about it, we
+need not put <i>of</i> after its name. A stone is not the stone <i>of</i>
+anything; the moon is not the moon <i>of</i> anything, but simply the moon.
+Unless, indeed, the name which we choose to give to the substance be a
+relative name; if so, it must be followed either by <i>of</i>, or by some
+other particle, implying, as that preposition does, a reference to
+something else: but then the other characteristic peculiarity of an
+attribute would fail; the <i>something</i> might be destroyed, and the
+substance might still subsist. Thus, a father must be the father <i>of</i>
+something, and so far resembles an attribute, in being referred to
+something besides himself: if there were no child, there would be no
+father: but this, when we look into the matter, only means that we
+should not call him father. The man called father might still exist
+though there were no child, as he existed before there was a child: and
+there would be no contradiction in supposing him to exist, though the
+<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>whole universe except himself were destroyed. But destroy all white
+substances, and where would be the attribute whiteness? Whiteness,
+without any white thing, is a contradiction in terms.</p>
+
+<p>This is the nearest approach to a solution of the difficulty, that will
+be found in the common treatises on logic. It will scarcely be thought
+to be a satisfactory one. If an attribute is distinguished from a
+substance by being the attribute <i>of</i> something, it seems highly
+necessary to understand what is meant by <i>of</i>; a particle which needs
+explanation too much itself, to be placed in front of the explanation of
+anything else. And as for the self-existence of substance, it is very
+true that a substance may be conceived to exist without any other
+substance, but so also may an attribute without any other attribute: and
+we can no more imagine a substance without attributes than we can
+imagine attributes without a substance.</p>
+
+<p>Metaphysicians, however, have probed the question deeper, and given an
+account of Substance considerably more satisfactory than this.
+Substances are usually distinguished as Bodies or Minds. Of each of
+these, philosophers have at length provided us with a definition which
+seems unexceptionable.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_7">� 7.</a> A Body, according to the received doctrine of modern
+metaphysicians, may be defined, the external cause to which we ascribe
+our sensations. When I see and touch a piece of gold, I am conscious of
+a sensation of yellow colour, and sensations of hardness and weight; and
+by varying the mode of handling, I may add to these sensations many
+others completely distinct from them. The sensations are all of which I
+am directly conscious; but I consider them as produced by something not
+only existing independently of my will, but external to my bodily organs
+and to my mind. This external something I call a body.</p>
+
+<p>It may be asked, how come we to ascribe our sensations to any external
+cause? And is there sufficient ground for so ascribing them? It is
+known, that there are metaphysicians <span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>who have raised a controversy on
+the point; maintaining that we are not warranted in referring our
+sensations to a cause such as we understand by the word Body, or to any
+external cause whatever. Though we have no concern here with this
+controversy, nor with the metaphysical niceties on which it turns, one
+of the best ways of showing what is meant by Substance is, to consider
+what position it is necessary to take up, in order to maintain its
+existence against opponents.</p>
+
+<p>It is certain, then, that a part of our notion of a body consists of the
+notion of a number of sensations of our own, or of other sentient
+beings, habitually occurring simultaneously. My conception of the table
+at which I am writing is compounded of its visible form and size, which
+are complex sensations of sight; its tangible form and size, which are
+complex sensations of our organs of touch and of our muscles; its
+weight, which is also a sensation of touch and of the muscles; its
+colour, which is a sensation of sight; its hardness, which is a
+sensation of the muscles; its composition, which is another word for all
+the varieties of sensation which we receive under various circumstances
+from the wood of which it is made, and so forth. All or most of these
+various sensations frequently are, and, as we learn by experience,
+always might be, experienced simultaneously, or in many different orders
+of succession, at our own choice: and hence the thought of any one of
+them makes us think of the others, and the whole becomes mentally
+amalgamated into one mixed state of consciousness, which, in the
+language of the school of Locke and Hartley, is termed a Complex Idea.</p>
+
+<p>Now, there are philosophers who have argued as follows. If we conceive
+an orange to be divested of its natural colour without acquiring any new
+one; to lose its softness without becoming hard, its roundness without
+becoming square or pentagonal, or of any other regular or irregular
+figure whatever; to be deprived of size, of weight, of taste, of smell;
+to lose all its mechanical and all its chemical properties, and acquire
+no new ones; to become, in short, invisible, intangible, imperceptible
+not only by all our senses, but by the senses of all other sentient
+beings, real or possible; nothing, say these <span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>thinkers, would remain.
+For of what nature, they ask, could be the residuum? and by what token
+could it manifest its presence? To the unreflecting its existence seems
+to rest on the evidence of the senses. But to the senses nothing is
+apparent except the sensations. We know, indeed, that these sensations
+are bound together by some law; they do not come together at random, but
+according to a systematic order, which is part of the order established
+in the universe. When we experience one of these sensations, we usually
+experience the others also, or know that we have it in our power to
+experience them. But a fixed law of connexion, making the sensations
+occur together, does not, say these philosophers, necessarily require
+what is called a substratum to support them. The conception of a
+substratum is but one of many possible forms in which that connexion
+presents itself to our imagination; a mode of, as it were, realizing the
+idea. If there be such a substratum, suppose it this instant
+miraculously annihilated, and let the sensations continue to occur in
+the same order, and how would the substratum be missed? By what signs
+should we be able to discover that its existence had terminated? Should
+we not have as much reason to believe that it still existed as we now
+have? And if we should not then be warranted in believing it, how can we
+be so now? A body, therefore, according to these metaphysicians, is not
+anything intrinsically different from the sensations which the body is
+said to produce in us; it is, in short, a set of sensations, or rather,
+of possibilities of sensation, joined together according to a fixed law.</p>
+
+<p>The controversies to which these speculations have given rise, and the
+doctrines which have been developed in the attempt to find a conclusive
+answer to them, have been fruitful of important consequences to the
+Science of Mind. The sensations (it was answered) which we are conscious
+of, and which we receive, not at random, but joined together in a
+certain uniform manner, imply not only a law or laws of connexion, but a
+cause external to our mind, which cause, by its own laws, determines the
+laws according to which the sensations are connected and experienced.
+The schoolmen used to call this external cause by the name we have
+already employed, a <span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span><i>substratum</i>; and its attributes (as they expressed
+themselves) <i>inhered</i>, literally <i>stuck</i>, in it. To this substratum the
+name Matter is usually given in philosophical discussions. It was soon,
+however, acknowledged by all who reflected on the subject, that the
+existence of matter cannot be proved by extrinsic evidence. The answer,
+therefore, now usually made to Berkeley and his followers, is, that the
+belief is intuitive; that mankind, in all ages, have felt themselves
+compelled, by a necessity of their nature, to refer their sensations to
+an external cause: that even those who deny it in theory, yield to the
+necessity in practice, and both in speech, thought, and feeling, do,
+equally with the vulgar, acknowledge their sensations to be the effects
+of something external to them: this knowledge, therefore, it is
+affirmed, is as evidently intuitive as our knowledge of our sensations
+themselves is intuitive. And here the question merges in the fundamental
+problem of metaphysics properly so called; to which science we leave it.</p>
+
+<p>But although the extreme doctrine of the Idealist metaphysicians, that
+objects are nothing but our sensations and the laws which connect them,
+has not been generally adopted by subsequent thinkers; the point of most
+real importance is one on which those metaphysicians are now very
+generally considered to have made out their case: viz., that <i>all we
+know</i> of objects is the sensations which they give us, and the order of
+the occurrence of those sensations. Kant himself, on this point, is as
+explicit as Berkeley or Locke. However firmly convinced that there
+exists an universe of "Things in themselves," totally distinct from the
+universe of phenomena, or of things as they appear to our senses; and
+even when bringing into use a technical expression (<i>Noumenon</i>) to
+denote what the thing is in itself, as contrasted with the
+<i>representation</i> of it in our minds; he allows that this representation
+(the matter of which, he says, consists of our sensations, though the
+form is given by the laws of the mind itself) is all we know of the
+object: and that the real nature of the Thing is, and by the
+constitution of our faculties ever must remain, at least in the present
+state of existence, an impenetrable mystery to us. "Of things absolutely
+or in themselves," says Sir William <span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span>Hamilton,<a name="FNanchor_10_16" id="FNanchor_10_16"></a><a href="#Footnote_10_16" class="fnanchor">[10]</a> "be they external, be
+they internal, we know nothing, or know them only as incognisable; and
+become aware of their incomprehensible existence, only as this is
+indirectly and accidentally revealed to us, through certain qualities
+related to our faculties of knowledge, and which qualities, again, we
+cannot think as unconditioned, irrelative, existent in and of
+themselves. All that we know is therefore ph�nomenal,&mdash;ph�nomenal of the
+unknown."<a name="FNanchor_11_17" id="FNanchor_11_17"></a><a href="#Footnote_11_17" class="fnanchor">[11]</a> The same doctrine is laid down in the clearest and
+strongest terms by M. Cousin, whose observations on the subject are the
+more worthy of attention, as, in consequence of the ultra-German and
+ontological character of his philosophy in other respects, they may be
+regarded as the admissions of an opponent.<a name="FNanchor_12_18" id="FNanchor_12_18"></a><a href="#Footnote_12_18" class="fnanchor">[12]</a></p>
+
+<p>There is not the slightest reason for believing that what we call the
+sensible qualities of the object are a type of anything <span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span>inherent in
+itself, or bear any affinity to its own nature. A cause does not, as
+such, resemble its effects; an east wind is not like the feeling of
+cold, nor heat like the steam of boiling water. Why then should matter
+resemble our sensations? Why should the inmost nature of fire or water
+resemble the impressions made by those objects upon our senses?<a name="FNanchor_13_19" id="FNanchor_13_19"></a><a href="#Footnote_13_19" class="fnanchor">[13]</a> Or
+on what principle are we authorized to deduce from the effects, anything
+concerning the cause, except that it is a cause adequate to produce
+those effects? It may, therefore, safely be laid down as a truth both
+obvious in itself, and admitted by all whom it is at present necessary
+to take into consideration, that, of the outward world, we know and can
+know absolutely nothing, except the sensations which we experience from
+it.<a name="FNanchor_14_20" id="FNanchor_14_20"></a><a href="#Footnote_14_20" class="fnanchor">[14]</a></p>
+
+
+<p><span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span></p><p class="newsection"><a name="BOOK_I_CHAPTER_III_8">� 8.</a> Body having now been defined the external cause, and (according to
+the more reasonable opinion) the unknown external cause, to which we
+refer our sensations; it remains to frame a definition of Mind. Nor,
+after the preceding observations, will this be difficult. For, as our
+conception of a body is that of an unknown exciting cause of sensations,
+so our conception of a mind is that of an unknown recipient, or
+percipient, of them; and not of them alone, but of all our other
+feelings. As body is understood to be the mysterious something which
+excites the mind to feel, so mind is the mysterious something which
+feels and thinks. It is unnecessary to give in the case of mind, as we
+gave in the case of matter, <span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span>a particular statement of the sceptical
+system by which its existence as a Thing in itself, distinct from the
+series of what are denominated its states, is called in question. But it
+is necessary to remark, that on the inmost nature (whatever be meant by
+inmost nature) of the thinking principle, as well as on the inmost
+nature of matter, we are, and with our faculties must always remain,
+entirely in the dark. All which we are aware of, even in our own minds,
+is (in the words of Mr. James Mill) a certain "thread of consciousness;"
+a series of feelings, that is, of sensations, thoughts, emotions, and
+volitions, more or less numerous and complicated. There is a something I
+call Myself, or, by another form of expression, my mind, which I
+consider as distinct from these sensations, thoughts, &amp;c.; a something
+which I conceive to be not the thoughts, but the being that has the
+thoughts, and which I can conceive as existing for ever in a state of
+quiescence, without any thoughts at all. But what this being is, though
+it is myself, I have no knowledge, other than the series of its states
+of consciousness. As bodies manifest themselves to me only through the
+sensations of which I regard them as the causes, so the thinking
+principle, or mind, in my own nature, makes itself known to me only by
+the feelings of which it is conscious. I know nothing about myself, save
+my capacities of feeling or being conscious (including, of course,
+thinking and willing): and were I to learn anything new concerning my
+own nature, I cannot with my present faculties conceive this new
+information to be anything else, than that I have some additional
+capacities, as yet unknown to me, of feeling, thinking, or willing.</p>
+
+<p>Thus, then, as body is the unsentient cause to which we are naturally
+prompted to refer a certain portion of our feelings, so mind may be
+described as the sentient <i>subject</i> (in the scholastic sense of the
+term) of all feelings; that which has or feels them. But of the nature
+of either body or mind, further than the feelings which the former
+excites, and which the latter experiences, we do not, according to the
+best existing doctrine, know anything; and if anything, logic has
+nothing to do with it, or with the manner in which the knowledge is
+acquired. With this result we may conclude this portion of <span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>our subject,
+and pass to the third and only remaining class or division of Nameable
+Things.</p>
+
+
+<p class="center" style="margin-top:1.5em;">III. <span class="smcap">Attributes: and, first, Qualities.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_9">� 9.</a> From what has already been said of Substance, what is to be said of
+Attribute is easily deducible. For if we know not, and cannot know,
+anything of bodies but the sensations which they excite in us or in
+others, those sensations must be all that we can, at bottom, mean by
+their attributes; and the distinction which we verbally make between the
+properties of things and the sensations we receive from them, must
+originate in the convenience of discourse rather than in the nature of
+what is signified by the terms.</p>
+
+<p>Attributes are usually distributed under the three heads of Quality,
+Quantity, and Relation. We shall come to the two latter presently: in
+the first place we shall confine ourselves to the former.</p>
+
+<p>Let us take, then, as our example, one of what are termed the sensible
+qualities of objects, and let that example be whiteness. When we ascribe
+whiteness to any substance, as, for instance, snow; when we say that
+snow has the quality whiteness, what do we really assert? Simply, that
+when snow is present to our organs, we have a particular sensation,
+which we are accustomed to call the sensation of white. But how do I
+know that snow is present? Obviously by the sensations which I derive
+from it, and not otherwise. I infer that the object is present, because
+it gives me a certain assemblage or series of sensations. And when I
+ascribe to it the attribute whiteness, my meaning is only, that, of the
+sensations composing this group or series, that which I call the
+sensation of white colour is one.</p>
+
+<p>This is one view which may be taken of the subject. But there is also
+another and a different view. It may be said, that it is true we <i>know</i>
+nothing of sensible objects, except the sensations they excite in us;
+that the fact of our receiving from snow the particular sensation which
+is called a sensation of <span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>white, is the <i>ground</i> on which we ascribe to
+that substance the quality whiteness; the sole proof of its possessing
+that quality. But because one thing may be the sole evidence of the
+existence of another thing, it does not follow that the two are one and
+the same. The attribute whiteness (it may be said) is not the fact of
+receiving the sensation, but something in the object itself; a <i>power</i>
+inherent in it; something <i>in virtue</i> of which the object produces the
+sensation. And when we affirm that snow possesses the attribute
+whiteness, we do not merely assert that the presence of snow produces in
+us that sensation, but that it does so through, and by reason of, that
+power or quality.</p>
+
+<p>For the purposes of logic it is not of material importance which of
+these opinions we adopt. The full discussion of the subject belongs to
+the other department of scientific inquiry, so often alluded to under
+the name of metaphysics; but it may be said here, that for the doctrine
+of the existence of a peculiar species of entities called qualities, I
+can see no foundation except in a tendency of the human mind which is
+the cause of many delusions. I mean, the disposition, wherever we meet
+with two names which are not precisely synonymous, to suppose that they
+must be the names of two different things; whereas in reality they may
+be names of the same thing viewed in two different lights, or under
+different suppositions as to surrounding circumstances. Because
+<i>quality</i> and <i>sensation</i> cannot be put indiscriminately one for the
+other, it is supposed that they cannot both signify the same thing,
+namely, the impression or feeling with which we are affected through our
+senses by the presence of an object; though there is at least no
+absurdity in supposing that this identical impression or feeling may be
+called a sensation when considered merely in itself, and a quality when
+looked at in relation to any one of the numerous objects, the presence
+of which to our organs excites in our minds that among various other
+sensations or feelings. And if this be admissible as a supposition, it
+rests with those who contend for an entity <i>per se</i> called a quality, to
+show that their opinion is preferable, or is anything in fact but a
+lingering remnant of the scholastic doctrine of occult <span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>causes; the very
+absurdity which Moli�re so happily ridiculed when he made one of his
+pedantic physicians account for the fact that "l'opium endormit," by the
+maxim "parcequ'il a une vertu soporifique."</p>
+
+<p>It is evident that when the physician stated that opium had "une vertu
+soporifique," he did not account for, but merely asserted over again,
+the fact that it <i>endormit</i>. In like manner, when we say that snow is
+white because it has the quality of whiteness, we are only re-asserting
+in more technical language the fact that it excites in us the sensation
+of white. If it be said that the sensation must have some cause, I
+answer, its cause is the presence of the assemblage of phenomena which
+is termed the object. When we have asserted that as often as the object
+is present, and our organs in their normal state, the sensation takes
+place, we have stated all that we know about the matter. There is no
+need, after assigning a certain and intelligible cause, to suppose an
+occult cause besides, for the purpose of enabling the real cause to
+produce its effect. If I am asked, why does the presence of the object
+cause this sensation in me, I cannot tell: I can only say that such is
+my nature, and the nature of the object; that the fact forms a part of
+the constitution of things. And to this we must at last come, even after
+interpolating the imaginary entity. Whatever number of links the chain
+of causes and effects may consist of, how any one link produces the one
+which is next to it, remains equally inexplicable to us. It is as easy
+to comprehend that the object should produce the sensation directly and
+at once, as that it should produce the same sensation by the aid of
+something else called the <i>power</i> of producing it.</p>
+
+<p>But, as the difficulties which may be felt in adopting this view of the
+subject cannot be removed without discussions transcending the bounds of
+our science, I content myself with a passing indication, and shall, for
+the purposes of logic, adopt a language compatible with either view of
+the nature of qualities. I shall say,&mdash;what at least admits of no
+dispute,&mdash;that the quality of whiteness ascribed to the object snow, is
+<i>grounded</i> on its exciting in us the sensation of white; and adopting
+the language already used by the school logicians in the case of the
+<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>kind of attributes called Relations, I shall term the sensation of
+white the foundation of the quality whiteness. For logical purposes the
+sensation is the only essential part of what is meant by the word; the
+only part which we ever can be concerned in proving. When that is
+proved, the quality is proved; if an object excites a sensation, it has,
+of course, the power of exciting it.</p>
+
+
+<p class="center" style="margin-top:1.5em;">IV. <span class="smcap">Relations.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_10">� 10.</a> The <i>qualities</i> of a body, we have said, are the attributes
+grounded on the sensations which the presence of that particular body to
+our organs excites in our minds. But when we ascribe to any object the
+kind of attribute called a Relation, the foundation of the attribute
+must be something in which other objects are concerned besides itself
+and the percipient.</p>
+
+<p>As there may with propriety be said to be a relation between any two
+things to which two correlative names are or may be given, we may expect
+to discover what constitutes a relation in general, if we enumerate the
+principal cases in which mankind have imposed correlative names, and
+observe what these cases have in common.</p>
+
+<p>What, then, is the character which is possessed in common by states of
+circumstances so heterogeneous and discordant as these: one thing <i>like</i>
+another; one thing <i>unlike</i> another; one thing <i>near</i> another; one thing
+<i>far from</i> another; one thing <i>before</i>, <i>after</i>, <i>along with</i> another;
+one thing <i>greater</i>, <i>equal</i>, <i>less</i>, than another; one thing the
+<i>cause</i> of another, the <i>effect</i> of another; one person the <i>master</i>,
+<i>servant</i>, <i>child</i>, <i>parent</i>, <i>debtor</i>, <i>creditor</i>, <i>sovereign</i>,
+<i>subject</i>, <i>attorney</i>, <i>client</i>, of another, and so on?</p>
+
+<p>Omitting, for the present, the case of Resemblance, (a relation which
+requires to be considered separately,) there seems to be one thing
+common to all these cases, and only one; that in each of them there
+exists or occurs, or has existed or occurred, or may be expected to
+exist or occur, some fact or phenomenon, into which the two things which
+are said to be <span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>related to each other, both enter as parties concerned.
+This fact, or phenomenon, is what the Aristotelian logicians called the
+<i>fundamentum relationis</i>. Thus in the relation of greater and less
+between two magnitudes, the <i>fundamentum relationis</i> is the fact that
+one of the two magnitudes could, under certain conditions, be included
+in, without entirely filling, the space occupied by the other magnitude.
+In the relation of master and servant, the <i>fundamentum relationis</i> is
+the fact that the one has undertaken, or is compelled, to perform
+certain services for the benefit and at the bidding of the other.
+Examples might be indefinitely multiplied; but it is already obvious
+that whenever two things are said to be related, there is some fact, or
+series of facts, into which they both enter; and that whenever any two
+things are involved in some one fact, or series of facts, we may ascribe
+to those two things a mutual relation grounded on the fact. Even if they
+have nothing in common but what is common to all things, that they are
+members of the universe, we call that a relation, and denominate them
+fellow-creatures, fellow-beings, or fellow-denizens of the universe. But
+in proportion as the fact into which the two objects enter as parts is
+of a more special and peculiar, or of a more complicated nature, so also
+is the relation grounded upon it. And there are as many conceivable
+relations as there are conceivable kinds of fact in which two things can
+be jointly concerned.</p>
+
+<p>In the same manner, therefore, as a quality is an attribute grounded on
+the fact that a certain sensation or sensations are produced in us by
+the object, so an attribute grounded on some fact into which the object
+enters jointly with another object, is a relation between it and that
+other object. But the fact in the latter case consists of the very same
+kind of elements as the fact in the former; namely, states of
+consciousness. In the case, for example, of any legal relation, as
+debtor and creditor, principal and agent, guardian and ward, the
+<i>fundamentum relationis</i> consists entirely of thoughts, feelings, and
+volitions (actual or contingent), either of the persons themselves or of
+other persons concerned in the same series of transactions; as, for
+instance, the intentions which would be formed <span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>by a judge, in case a
+complaint were made to his tribunal of the infringement of any of the
+legal obligations imposed by the relation; and the acts which the judge
+would perform in consequence; acts being (as we have already seen)
+another word for intentions followed by an effect, and that effect being
+but another word for sensations, or some other feelings, occasioned
+either to the agent himself or to somebody else. There is no part of
+what the names expressive of the relation imply, that is not resolvable
+into states of consciousness; outward objects being, no doubt, supposed
+throughout as the causes by which some of those states of consciousness
+are excited, and minds as the subjects by which all of them are
+experienced, but neither the external objects nor the minds making their
+existence known otherwise than by the states of consciousness.</p>
+
+<p>Cases of relation are not always so complicated as those to which we
+last alluded. The simplest of all cases of relation are those expressed
+by the words antecedent and consequent, and by the word simultaneous. If
+we say, for instance, that dawn preceded sunrise, the fact in which the
+two things, dawn and sunrise, were jointly concerned, consisted only of
+the two things themselves; no third thing entered into the fact or
+phenomenon at all. Unless, indeed, we choose to call the succession of
+the two objects a third thing; but their succession is not something
+added to the things themselves; it is something involved in them. Dawn
+and sunrise announce themselves to our consciousness by two successive
+sensations. Our consciousness of the succession of these sensations is
+not a third sensation or feeling added to them; we have not first the
+two feelings, and then a feeling of their succession. To have two
+feelings at all, implies having them either successively, or else
+simultaneously. Sensations, or other feelings, being given, succession
+and simultaneousness are the two conditions, to the alternative of which
+they are subjected by the nature of our faculties; and no one has been
+able, or needs expect, to analyse the matter any farther.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_11">� 11.</a> In a somewhat similar position are two other sorts of relations,
+Likeness and Unlikeness. I have two sensations; <span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span>we will suppose them to
+be simple ones; two sensations of white, or one sensation of white and
+another of black. I call the first two sensations <i>like</i>; the last two
+<i>unlike</i>. What is the fact or phenomenon constituting the <i>fundamentum</i>
+of this relation? The two sensations first, and then what we call a
+feeling of resemblance, or of want of resemblance. Let us confine
+ourselves to the former case. Resemblance is evidently a feeling; a
+state of the consciousness of the observer. Whether the feeling of the
+resemblance of the two colours be a third state of consciousness, which
+I have <i>after</i> having the two sensations of colour, or whether (like the
+feeling of their succession) it is involved in the sensations
+themselves, may be a matter of discussion. But in either case, these
+feelings of resemblance, and of its opposite dissimilarity, are parts of
+our nature; and parts so far from being capable of analysis, that they
+are presupposed in every attempt to analyse any of our other feelings.
+Likeness and unlikeness, therefore, as well as antecedence, sequence,
+and simultaneousness, must stand apart among relations, as things <i>sui
+generis</i>. They are attributes grounded on facts, that is, on states of
+consciousness, but on states which are peculiar, unresolvable, and
+inexplicable.</p>
+
+<p>But, though likeness or unlikeness cannot be resolved into anything
+else, complex cases of likeness or unlikeness can be resolved into
+simpler ones. When we say of two things which consist of parts, that
+they are like one another, the likeness of the wholes does admit of
+analysis; it is compounded of likenesses between the various parts
+respectively, and of likeness in their arrangement. Of how vast a
+variety of resemblances of parts must that resemblance be composed,
+which induces us to say that a portrait, or a landscape, is like its
+original. If one person mimics another with any success, of how many
+simple likenesses must the general or complex likeness be compounded:
+likeness in a succession of bodily postures; likeness in voice, or in
+the accents and intonations of the voice; likeness in the choice of
+words, and in the thoughts or sentiments expressed, whether by word,
+countenance, or gesture.</p>
+
+<p><span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span></p><p>All likeness and unlikeness of which we have any cognizance, resolve
+themselves into likeness and unlikeness between states of our own, or
+some other, mind. When we say that one body is like another, (since we
+know nothing of bodies but the sensations which they excite,) we mean
+really that there is a resemblance between the sensations excited by the
+two bodies, or between some portions at least of those sensations. If we
+say that two attributes are like one another, (since we know nothing of
+attributes except the sensations or states of feeling on which they are
+grounded,) we mean really that those sensations, or states of feeling,
+resemble each other. We may also say that two relations are alike. The
+fact of resemblance between relations is sometimes called <i>analogy</i>,
+forming one of the numerous meanings of that word. The relation in which
+Priam stood to Hector, namely, that of father and son, resembles the
+relation in which Philip stood to Alexander; resembles it so closely
+that they are called the same relation. The relation in which Cromwell
+stood to England resembles the relation in which Napoleon stood to
+France, though not so closely as to be called the same relation. The
+meaning in both these instances must be, that a resemblance existed
+between the facts which constituted the <i>fundamentum relationis</i>.</p>
+
+<p>This resemblance may exist in all conceivable gradations, from perfect
+undistinguishableness to something extremely slight. When we say, that a
+thought suggested to the mind of a person of genius is like a seed cast
+into the ground, because the former produces a multitude of other
+thoughts, and the latter a multitude of other seeds, this is saying that
+between the relation of an inventive mind to a thought contained in it,
+and the relation of a fertile soil to a seed contained in it, there
+exists a resemblance: the real resemblance being in the two <i>fundamenta
+relationis</i>, in each of which there occurs a germ, producing by its
+development a multitude of other things similar to itself. And as,
+whenever two objects are jointly concerned in a phenomenon, this
+constitutes a relation between those objects, so, if we suppose a second
+pair of objects concerned in a second phenomenon, the slightest
+resemblance between the <span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span>two phenomena is sufficient to admit of its
+being said that the two relations resemble; provided, of course, the
+points of resemblance are found in those portions of the two phenomena
+respectively which are connoted by the relative names.</p>
+
+<p>While speaking of resemblance, it is necessary to take notice of an
+ambiguity of language, against which scarcely any one is sufficiently on
+his guard. Resemblance, when it exists in the highest degree of all,
+amounting to undistinguishableness, is often called identity, and the
+two similar things are said to be the same. I say often, not always; for
+we do not say that two visible objects, two persons for instance, are
+the same, because they are so much alike that one might be mistaken for
+the other: but we constantly use this mode of expression when speaking
+of feelings; as when I say that the sight of any object gives me the
+<i>same</i> sensation or emotion to-day that it did yesterday, or the <i>same</i>
+which it gives to some other person. This is evidently an incorrect
+application of the word <i>same</i>; for the feeling which I had yesterday is
+gone, never to return; what I have to-day is another feeling, exactly
+like the former perhaps, but distinct from it; and it is evident that
+two different persons cannot be experiencing the same feeling, in the
+sense in which we say that they are both sitting at the same table. By a
+similar ambiguity we say, that two persons are ill of the <i>same</i>
+disease; that two persons hold the <i>same</i> office; not in the sense in
+which we say that they are engaged in the same adventure, or sailing in
+the same ship, but in the sense that they fill offices exactly similar,
+though, perhaps, in distant places. Great confusion of ideas is often
+produced, and many fallacies engendered, in otherwise enlightened
+understandings, by not being sufficiently alive to the fact (in itself
+not always to be avoided), that they use the same name to express ideas
+so different as those of identity and undistinguishable resemblance.
+Among modern writers, Archbishop Whately stands almost alone in having
+drawn attention to this distinction, and to the ambiguity connected with
+it.</p>
+
+<p>Several relations, generally called by other names, are really <span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span>cases of
+resemblance. As, for example, equality; which is but another word for
+the exact resemblance commonly called identity, considered as subsisting
+between things in respect of their <i>quantity</i>. And this example forms a
+suitable transition to the third and last of the three heads under
+which, as already remarked, Attributes are commonly arranged.</p>
+
+
+<p class="center" style="margin-top:1.5em;">V. <span class="smcap">Quantity.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_12">� 12.</a> Let us imagine two things, between which there is no difference
+(that is, no dissimilarity), except in quantity alone: for instance, a
+gallon of water, and more than a gallon of water. A gallon of water,
+like any other external object, makes its presence known to us by a set
+of sensations which it excites. Ten gallons of water are also an
+external object, making its presence known to us in a similar manner;
+and as we do not mistake ten gallons of water for a gallon of water, it
+is plain that the set of sensations is more or less different in the two
+cases. In like manner, a gallon of water, and a gallon of wine, are two
+external objects, making their presence known by two sets of sensations,
+which sensations are different from each other. In the first case,
+however, we say that the difference is in quantity; in the last there is
+a difference in quality, while the quantity of the water and of the wine
+is the same. What is the real distinction between the two cases? It is
+not the province of Logic to analyse it; nor to decide whether it is
+susceptible of analysis or not. For us the following considerations are
+sufficient. It is evident that the sensations I receive from the gallon
+of water, and those I receive from the gallon of wine, are not the same,
+that is, not precisely alike; neither are they altogether unlike: they
+are partly similar, partly dissimilar; and that in which they resemble
+is precisely that in which alone the gallon of water and the ten gallons
+do not resemble. That in which the gallon of water and the gallon of
+wine are like each other, and in which the gallon and the ten gallons of
+water are unlike each other, is called their quantity. This <span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span>likeness
+and unlikeness I do not pretend to explain, no more than any other kind
+of likeness or unlikeness. But my object is to show, that when we say of
+two things that they differ in quantity, just as when we say that they
+differ in quality, the assertion is always grounded on a difference in
+the sensations which they excite. Nobody, I presume, will say, that to
+see, or to lift, or to drink, ten gallons of water, does not include in
+itself a different set of sensations from those of seeing, lifting, or
+drinking one gallon; or that to see or handle a foot-rule, and to see or
+handle a yard-measure made exactly like it, are the same sensations. I
+do not undertake to say what the difference in the sensations is.
+Everybody knows, and nobody can tell; no more than any one could tell
+what white is to a person who had never had the sensation. But the
+difference, so far as cognizable by our faculties, lies in the
+sensations. Whatever difference we say there is in the things
+themselves, is, in this as in all other cases, grounded, and grounded
+exclusively, on a difference in the sensations excited by them.</p>
+
+
+<p class="center" style="margin-top:1.5em;">VI. <span class="smcap">Attributes Concluded.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_13">� 13.</a> Thus, then, all the attributes of bodies which are classed under
+Quality or Quantity, are grounded on the sensations which we receive
+from those bodies, and may be defined, the powers which the bodies have
+of exciting those sensations. And the same general explanation has been
+found to apply to most of the attributes usually classed under the head
+of Relation. They, too, are grounded on some fact or phenomenon into
+which the related objects enter as parts; that fact or phenomenon having
+no meaning and no existence to us, except the series of sensations or
+other states of consciousness by which it makes itself known; and the
+relation being simply the power or capacity which the object possesses
+of taking part along with the correlated object in the production of
+that series of sensations or states of consciousness. We have been
+obliged, indeed, to recognise a somewhat different character in certain
+peculiar relations, those of succession <span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>and simultaneity, of likeness
+and unlikeness. These, not being grounded on any fact or phenomenon
+distinct from the related objects themselves, do not admit of the same
+kind of analysis. But these relations, though not, like other relations,
+grounded on states of consciousness, are themselves states of
+consciousness: resemblance is nothing but our feeling of resemblance;
+succession is nothing but our feeling of succession. Or, if this be
+disputed (and we cannot, without transgressing the bounds of our
+science, discuss it here), at least our knowledge of these relations,
+and even our possibility of knowledge, is confined to those which
+subsist between sensations, or other states of consciousness; for,
+though we ascribe resemblance, or succession, or simultaneity, to
+objects and to attributes, it is always in virtue of resemblance or
+succession or simultaneity in the sensations or states of consciousness
+which those objects excite, and on which those attributes are grounded.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_14">� 14.</a> In the preceding investigation we have, for the sake of
+simplicity, considered bodies only, and omitted minds. But what we have
+said, is applicable, <i>mutatis mutandis</i>, to the latter. The attributes
+of minds, as well as those of bodies, are grounded on states of feeling
+or consciousness. But in the case of a mind, we have to consider its own
+states, as well as those which it produces in other minds. Every
+attribute of a mind consists either in being itself affected in a
+certain way, or affecting other minds in a certain way. Considered in
+itself, we can predicate nothing of it but the series of its own
+feelings. When we say of any mind, that it is devout, or superstitious,
+or meditative, or cheerful, we mean that the ideas, emotions, or
+volitions implied in those words, form a frequently recurring part of
+the series of feelings, or states of consciousness, which fill up the
+sentient existence of that mind.</p>
+
+<p>In addition, however, to those attributes of a mind which are grounded
+on its own states of feeling, attributes may also be ascribed to it, in
+the same manner as to a body, grounded on the feelings which it excites
+in other minds. A mind does <span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span>not, indeed, like a body, excite
+sensations, but it may excite thoughts or emotions. The most important
+example of attributes ascribed on this ground, is the employment of
+terms expressive of approbation or blame. When, for example, we say of
+any character, or (in other words) of any mind, that it is admirable, we
+mean that the contemplation of it excites the sentiment of admiration;
+and indeed somewhat more, for the word implies that we not only feel
+admiration, but approve that sentiment in ourselves. In some cases,
+under the semblance of a single attribute, two are really predicated:
+one of them, a state of the mind itself; the other, a state with which
+other minds are affected by thinking of it. As when we say of any one
+that he is generous. The word generosity expresses a certain state of
+mind, but being a term of praise, it also expresses that this state of
+mind excites in us another mental state, called approbation. The
+assertion made, therefore, is twofold, and of the following purport:
+Certain feelings form habitually a part of this person's sentient
+existence; and the idea of those feelings of his, excites the sentiment
+of approbation in ourselves or others.</p>
+
+<p>As we thus ascribe attributes to minds on the ground of ideas and
+emotions, so may we to bodies on similar grounds, and not solely on the
+ground of sensations: as in speaking of the beauty of a statue; since
+this attribute is grounded on the peculiar feeling of pleasure which the
+statue produces in our minds; which is not a sensation, but an emotion.</p>
+
+
+<p class="center" style="margin-top:1.5em;">VII. <span class="smcap">General Results.</span></p>
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_III_15">� 15.</a> Our survey of the varieties of Things which have been, or which
+are capable of being, named&mdash;which have been, or are capable of being,
+either predicated of other Things, or themselves made the subject of
+predications&mdash;is now concluded.</p>
+
+<p>Our enumeration commenced with Feelings. These we scrupulously
+distinguished from the objects which excite them, and from the organs by
+which they are, or may be supposed <span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span>to be, conveyed. Feelings are of
+four sorts: Sensations, Thoughts, Emotions, and Volitions. What are
+called Perceptions are merely a particular case of Belief, and belief is
+a kind of thought. Actions are merely volitions followed by an effect.
+If there be any other kind of mental state not included under these
+subdivisions, we did not think it necessary or proper in this place to
+discuss its existence, or the rank which ought to be assigned to it.</p>
+
+<p>After Feelings we proceeded to Substances. These are either Bodies or
+Minds. Without entering into the grounds of the metaphysical doubts
+which have been raised concerning the existence of Matter and Mind as
+objective realities, we stated as sufficient for us the conclusion in
+which the best thinkers are now for the most part agreed, that all we
+can know of Matter is the sensations which it gives us, and the order of
+occurrence of those sensations; and that while the substance Body is the
+unknown cause of our sensations, the substance Mind is the unknown
+recipient.</p>
+
+<p>The only remaining class of Nameable Things is Attributes; and these are
+of three kinds, Quality, Relation, and Quantity. Qualities, like
+substances, are known to us no otherwise than by the sensations or other
+states of consciousness which they excite: and while, in compliance with
+common usage, we have continued to speak of them as a distinct class of
+Things, we showed that in predicating them no one means to predicate
+anything but those sensations or states of consciousness, on which they
+may be said to be grounded, and by which alone they can be defined or
+described. Relations, except the simple cases of likeness and
+unlikeness, succession and simultaneity, are similarly grounded on some
+fact or phenomenon, that is, on some series of sensations or states of
+consciousness, more or less complicated. The third species of Attribute,
+Quantity, is also manifestly grounded on something in our sensations or
+states of feeling, since there is an indubitable difference in the
+sensations excited by a larger and a smaller bulk, or by a greater or a
+less degree of intensity, in any object of sense or of consciousness.
+All attributes, therefore, are to us nothing but either our sensations
+and other states of feeling, or something <span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span>inextricably involved
+therein; and to this even the peculiar and simple relations just
+adverted to are not exceptions. Those peculiar relations, however, are
+so important, and, even if they might in strictness be classed among
+states of consciousness, are so fundamentally distinct from any other of
+those states, that it would be a vain subtlety to bring them under that
+common description, and it is necessary that they should be classed
+apart.</p>
+
+<p>As the result, therefore, of our analysis, we obtain the following as an
+enumeration and classification of all Nameable Things:&mdash;</p>
+
+<p>1st. Feelings, or States of Consciousness.</p>
+
+<p>2nd. The Minds which experience those feelings.</p>
+
+<p>3rd. The Bodies, or external objects, which excite certain of those
+feelings, together with the powers or properties whereby they excite
+them; these last being included rather in compliance with common
+opinion, and because their existence is taken for granted in the common
+language from which I cannot prudently deviate, than because the
+recognition of such powers or properties as real existences appears to
+be warranted by a sound philosophy.</p>
+
+<p>4th, and last. The Successions and Co-existences, the Likenesses and
+Unlikenesses, between feelings or states of consciousness. Those
+relations, when considered as subsisting between other things, exist in
+reality only between the states of consciousness which those things, if
+bodies, excite, if minds, either excite or experience.</p>
+
+<p>This, until a better can be suggested, may serve as a substitute for the
+abortive Classification of Existences, termed the Categories of
+Aristotle. The practical application of it will appear when we commence
+the inquiry into the Import of Propositions; in other words, when we
+inquire what it is which the mind actually believes, when it gives what
+is called its assent to a proposition.</p>
+
+<p>These four classes comprising, if the classification be correct, all
+Nameable Things, these or some of them must of course compose the
+signification of all names; and of these, or some of them, is made up
+whatever we call a fact.</p>
+
+<p><span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span></p><p>For distinction's sake, every fact which is solely composed of feelings
+or states of consciousness considered as such, is often called a
+Psychological or Subjective fact; while every fact which is composed,
+either wholly or in part, of something different from these, that is, of
+substances and attributes, is called an Objective fact. We may say,
+then, that every objective fact is grounded on a corresponding
+subjective one; and has no meaning to us, (apart from the subjective
+fact which corresponds to it,) except as a name for the unknown and
+inscrutable process by which that subjective or psychological fact is
+brought to pass.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_IV" id="BOOK_I_CHAPTER_IV"></a>CHAPTER IV.<br />
+
+OF PROPOSITIONS.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_IV_1">� 1.</a> In treating of Propositions, as already in treating of Names, some
+considerations of a comparatively elementary nature respecting their
+form and varieties must be premised, before entering upon that analysis
+of the import conveyed by them, which is the real subject and purpose of
+this preliminary book.</p>
+
+<p>A proposition, we have before said, is a portion of discourse in which a
+predicate is affirmed or denied of a subject. A predicate and a subject
+are all that is necessarily required to make up a proposition: but as we
+cannot conclude from merely seeing two names put together, that they are
+a predicate and a subject, that is, that one of them is intended to be
+affirmed or denied of the other, it is necessary that there should be
+some mode or form of indicating that such is the intention; some sign to
+distinguish a predication from any other kind of discourse. This is
+sometimes done by a slight alteration of one of the words, called an
+<i>inflection</i>; as when we say, Fire burns; the change of the second word
+from <i>burn</i> to <i>burns</i> showing that we mean to affirm the predicate burn
+of the subject fire. But this function is more commonly fulfilled by the
+word <i>is</i>, when an affirmation is intended, <i>is not</i>, when a negation;
+or by some other part of the verb <i>to be</i>. The word which thus serves
+the purpose of a sign of predication is called, as we formerly observed,
+the <i>copula</i>. It is important that there should be no indistinctness in
+our conception of the nature and office of the copula; for confused
+notions respecting it are among the causes which have spread mysticism
+over the field of logic, and perverted its speculations into
+logomachies.</p>
+
+<p>It is apt to be supposed that the copula is something more <span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span>than a mere
+sign of predication; that it also signifies existence. In the
+proposition, Socrates is just, it may seem to be implied not only that
+the quality <i>just</i> can be affirmed of Socrates, but moreover that
+Socrates <i>is</i>, that is to say, exists. This, however, only shows that
+there is an ambiguity in the word <i>is</i>; a word which not only performs
+the function of the copula in affirmations, but has also a meaning of
+its own, in virtue of which it may itself be made the predicate of a
+proposition. That the employment of it as a copula does not necessarily
+include the affirmation of existence, appears from such a proposition as
+this, A centaur is a fiction of the poets; where it cannot possibly be
+implied that a centaur exists, since the proposition itself expressly
+asserts that the thing has no real existence.</p>
+
+<p>Many volumes might be filled with the frivolous speculations concerning
+the nature of Being, (<i>&#964;&#959; &#8004;&#957;</i>, <i>&#959;&#8016;&#963;&#8055;&#945;</i>, Ens, Entitas, Essentia, and
+the like) which have arisen from overlooking this double meaning of the
+word <i>to be</i>; from supposing that when it signifies <i>to exist</i>, and when
+it signifies to <i>be</i> some specified thing, as to <i>be</i> a man, to <i>be</i>
+Socrates, to <i>be</i> seen or spoken of, to <i>be</i> a phantom, even to <i>be</i> a
+nonentity, it must still, at bottom, answer to the same idea; and that a
+meaning must be found for it which shall suit all these cases. The fog
+which rose from this narrow spot diffused itself at an early period over
+the whole surface of metaphysics. Yet it becomes us not to triumph over
+the great intellects of Plato and Aristotle because we are now able to
+preserve ourselves from many errors into which they, perhaps inevitably,
+fell. The fire-teazer of a modern steam-engine produces by his exertions
+far greater effects than Milo of Crotona could, but he is not therefore
+a stronger man. The Greeks seldom knew any language but their own. This
+rendered it far more difficult for them than it is for us, to acquire a
+readiness in detecting ambiguities. One of the advantages of having
+accurately studied a plurality of languages, especially of those
+languages which eminent thinkers have used as the vehicle of their
+thoughts, is the practical lesson we learn respecting the ambiguities of
+words, by finding that the same word in one language <span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span>corresponds, on
+different occasions, to different words in another. When not thus
+exercised, even the strongest understandings find it difficult to
+believe that things which have a common name, have not in some respect
+or other a common nature; and often expend much labour very unprofitably
+(as was frequently done by the two philosophers just mentioned) in vain
+attempts to discover in what this common nature consists. But, the habit
+once formed, intellects much inferior are capable of detecting even
+ambiguities which are common to many languages: and it is surprising
+that the one now under consideration, though it exists in the modern
+languages as well as in the ancient, should have been overlooked by
+almost all authors. The quantity of futile speculation which had been
+caused by a misapprehension of the nature of the copula, was hinted at
+by Hobbes; but Mr. James Mill<a name="FNanchor_15_21" id="FNanchor_15_21"></a><a href="#Footnote_15_21" class="fnanchor">[15]</a> was, I believe, the first who
+distinctly characterized the ambiguity, and pointed out how many errors
+in the received systems of philosophy it has had to answer for. It has
+indeed misled the moderns scarcely less than the ancients, though their
+mistakes, because our understandings are not yet so completely
+emancipated from their influence, do not appear equally irrational.</p>
+
+<p>We shall now briefly review the principal distinctions which exist among
+propositions, and the technical terms most commonly in use to express
+those distinctions.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_IV_2">� 2.</a> A proposition being a portion of discourse in which something is
+affirmed or denied of something, the first division of propositions is
+into affirmative and negative. An affirmative proposition is that in
+which the predicate is <i>affirmed</i> of the subject; as, C�sar is dead. A
+negative proposition is that in which the predicate is <i>denied</i> of the
+subject; as, C�sar is not dead. The copula, in this last species of
+proposition, consists of the words <i>is not</i>, which are the sign of
+negation; <i>is</i> being the sign of affirmation.</p>
+
+<p>Some logicians, among whom may be mentioned Hobbes, <span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span>state this
+distinction differently; they recognise only one form of copula, <i>is</i>,
+and attach the negative sign to the predicate. "C�sar is dead," and
+"C�sar is not dead," according to these writers, are propositions
+agreeing not in the subject and predicate, but in the subject only. They
+do not consider "dead," but "not dead," to be the predicate of the
+second proposition, and they accordingly define a negative proposition
+to be one in which the predicate is a negative name. The point, though
+not of much practical moment, deserves notice as an example (not
+unfrequent in logic) where by means of an apparent simplification, but
+which is merely verbal, matters are made more complex than before. The
+notion of these writers was, that they could get rid of the distinction
+between affirming and denying, by treating every case of denying as the
+affirming of a negative name. But what is meant by a negative name? A
+name expressive of the <i>absence</i> of an attribute. So that when we affirm
+a negative name, what we are really predicating is absence and not
+presence; we are asserting not that anything is, but that something is
+not; to express which operation no word seems so proper as the word
+denying. The fundamental distinction is between a fact and the
+non-existence of that fact; between seeing something and not seeing it,
+between C�sar's being dead and his not being dead; and if this were a
+merely verbal distinction, the generalization which brings both within
+the same form of assertion would be a real simplification: the
+distinction, however, being real, and in the facts, it is the
+generalization confounding the distinction that is merely verbal; and
+tends to obscure the subject, by treating the difference between two
+kinds of truths as if it were only a difference between two kinds of
+words. To put things together, and to put them or keep them asunder,
+will remain different operations, whatever tricks we may play with
+language.</p>
+
+<p>A remark of a similar nature may be applied to most of those
+distinctions among propositions which are said to have reference to
+their <i>modality</i>; as, difference of tense or time; the sun <i>did</i> rise,
+the sun <i>is</i> rising, the sun <i>will</i> rise. These <span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span>differences, like that
+between affirmation and negation, might be glossed over by considering
+the incident of time as a mere modification of the predicate: thus, The
+sun is <i>an object having risen</i>, The sun is <i>an object now rising</i>, The
+sun is <i>an object to rise hereafter</i>. But the simplification would be
+merely verbal. Past, present, and future, do not constitute so many
+different kinds of rising; they are designations belonging to the event
+asserted, to the <i>sun's</i> rising to-day. They affect, not the predicate,
+but the applicability of the predicate to the particular subject. That
+which we affirm to be past, present, or future, is not what the subject
+signifies, nor what the predicate signifies, but specifically and
+expressly what the predication signifies; what is expressed only by the
+proposition as such, and not by either or both of the terms. Therefore
+the circumstance of time is properly considered as attaching to the
+copula, which is the sign of predication, and not to the predicate. If
+the same cannot be said of such modifications as these, C�sar <i>may</i> be
+dead; C�sar is <i>perhaps</i> dead; it is <i>possible</i> that C�sar is dead; it
+is only because these fall altogether under another head, being properly
+assertions not of anything relating to the fact itself, but of the state
+of our own mind in regard to it; namely, our absence of disbelief of it.
+Thus "C�sar may be dead" means "I am not sure that C�sar is alive."</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_IV_3">� 3.</a> The next division of propositions is into Simple and Complex. A
+simple proposition is that in which one predicate is affirmed or denied
+of one subject. A complex proposition is that in which there is more
+than one predicate, or more than one subject, or both.</p>
+
+<p>At first sight this division has the air of an absurdity; a solemn
+distinction of things into one and more than one; as if we were to
+divide horses into single horses and teams of horses. And it is true
+that what is called a complex proposition is often not a proposition at
+all, but several propositions, held together by a conjunction. Such, for
+example, is this: C�sar is dead, and Brutus is alive: or even this,
+C�sar is dead, <i>but</i> Brutus is alive. There are here two distinct
+<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span>assertions; and we might as well call a street a complex house, as
+these two propositions a complex proposition. It is true that the
+syncategorematic words <i>and</i> and <i>but</i> have a meaning; but that meaning
+is so far from making the two propositions one, that it adds a third
+proposition to them. All particles are abbreviations, and generally
+abbreviations of propositions; a kind of short-hand, whereby something
+which, to be expressed fully, would have required a proposition or a
+series of propositions, is suggested to the mind at once. Thus the
+words, C�sar is dead and Brutus is alive, are equivalent to these: C�sar
+is dead; Brutus is alive; it is desired that the two preceding
+propositions should be thought of together. If the words were, C�sar is
+dead <i>but</i> Brutus is alive, the sense would be equivalent to the same
+three propositions together with a fourth; "between the two preceding
+propositions there exists a contrast:" viz. either between the two facts
+themselves, or between the feelings with which it is desired that they
+should be regarded.</p>
+
+<p>In the instances cited the two propositions are kept visibly distinct,
+each subject having its separate predicate, and each predicate its
+separate subject. For brevity, however, and to avoid repetition, the
+propositions are often blended together: as in this, "Peter and James
+preached at Jerusalem and in Galilee," which contains four propositions:
+Peter preached at Jerusalem, Peter preached in Galilee, James preached
+at Jerusalem, James preached in Galilee.</p>
+
+<p>We have seen that when the two or more propositions comprised in what is
+called a complex proposition are stated absolutely, and not under any
+condition or proviso, it is not a proposition at all, but a plurality of
+propositions; since what it expresses is not a single assertion, but
+several assertions, which, if true when joined, are true also when
+separated. But there is a kind of proposition which, though it contains
+a plurality of subjects and of predicates, and may be said in one sense
+of the word to consist of several propositions, contains but one
+assertion; and its truth does not at all imply that of the simple
+propositions which compose it. An example of this is, when the simple
+propositions are connected <span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span>by the particle <i>or</i>; as, Either A is B or C
+is D; or by the particle <i>if</i>; as, A is B if C is D. In the former case,
+the proposition is called <i>disjunctive</i>, in the latter, <i>conditional</i>:
+the name <i>hypothetical</i> was originally common to both. As has been well
+remarked by Archbishop Whately and others, the disjunctive form is
+resolvable into the conditional; every disjunctive proposition being
+equivalent to two or more conditional ones. "Either A is B or C is D,"
+means, "if A is not B, C is D; and if C is not D, A is B." All
+hypothetical propositions, therefore, though disjunctive in form, are
+conditional in meaning; and the words hypothetical and conditional may
+be, as indeed they generally are, used synonymously. Propositions in
+which the assertion is not dependent on a condition, are said, in the
+language of logicians, to be <i>categorical</i>.</p>
+
+<p>An hypothetical proposition is not, like the pretended complex
+propositions which we previously considered, a mere aggregation of
+simple propositions. The simple propositions which form part of the
+words in which it is couched, form no part of the assertion which it
+conveys. When we say, If the Koran comes from God, Mahomet is the
+prophet of God, we do not intend to affirm either that the Koran does
+come from God, or that Mahomet is really his prophet. Neither of these
+simple propositions may be true, and yet the truth of the hypothetical
+proposition may be indisputable. What is asserted is not the truth of
+either of the propositions, but the inferribility of the one from the
+other. What, then, is the subject, and what the predicate of the
+hypothetical proposition? "The Koran" is not the subject of it, nor is
+"Mahomet:" for nothing is affirmed or denied either of the Koran or of
+Mahomet. The real subject of the predication is the entire proposition,
+"Mahomet is the prophet of God;" and the affirmation is, that this is a
+legitimate inference from the proposition, "The Koran comes from God."
+The subject and predicate, therefore, of an hypothetical proposition are
+names of propositions. The subject is some one proposition. The
+predicate is a general relative name applicable to propositions; of this
+form&mdash;"an inference from so and so." A fresh instance <span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span>is here afforded
+of the remark, that particles are abbreviations; since "<i>If</i> A is B, C
+is D," is found to be an abbreviation of the following: "The proposition
+C is D, is a legitimate inference from the proposition A is B."</p>
+
+<p>The distinction, therefore, between hypothetical and categorical
+propositions, is not so great as it at first appears. In the
+conditional, as well as in the categorical form, one predicate is
+affirmed of one subject, and no more: but a conditional proposition is a
+proposition concerning a proposition; the subject of the assertion is
+itself an assertion. Nor is this a property peculiar to hypothetical
+propositions. There are other classes of assertions concerning
+propositions. Like other things, a proposition has attributes which may
+be predicated of it. The attribute predicated of it in an hypothetical
+proposition, is that of being an inference from a certain other
+proposition. But this is only one of many attributes that might be
+predicated. We may say, That the whole is greater than its part, is an
+axiom in mathematics: That the Holy Ghost proceeds from the Father
+alone, is a tenet of the Greek Church: The doctrine of the divine right
+of kings was renounced by Parliament at the Revolution: The
+infallibility of the Pope has no countenance from Scripture. In all
+these cases the subject of the predication is an entire proposition.
+That which these different predicates are affirmed of, is <i>the
+proposition</i>, "the whole is greater than its part;" <i>the proposition</i>,
+"the Holy Ghost proceeds from the Father alone;" <i>the proposition</i>,
+"kings have a divine right;" <i>the proposition</i>, "the Pope is
+infallible."</p>
+
+<p>Seeing, then, that there is much less difference between hypothetical
+propositions and any others, than one might be led to imagine from their
+form, we should be at a loss to account for the conspicuous position
+which they have been selected to fill in treatises on logic, if we did
+not remember that what they predicate of a proposition, namely, its
+being an inference from something else, is precisely that one of its
+attributes with which most of all a logician is concerned.</p>
+
+
+<p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p><p class="newsection"><a name="BOOK_I_CHAPTER_IV_4">� 4.</a> The next of the common divisions of Propositions is into
+Universal, Particular, Indefinite, and Singular: a distinction founded
+on the degree of generality in which the name, which is the subject of
+the proposition, is to be understood. The following are examples:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"><i>All men</i> are mortal&mdash;</td><td align="left">Universal.</td></tr>
+<tr><td align="left"><i>Some men</i> are mortal&mdash;</td><td align="left">Particular.</td></tr>
+<tr><td align="left"><i>Man</i> is mortal&mdash;</td><td align="left">Indefinite.</td></tr>
+<tr><td align="left"><i>Julius C�sar</i> is mortal&mdash;</td><td align="left">Singular.</td></tr>
+</table></div>
+
+
+<p>The proposition is Singular, when the subject is an individual name. The
+individual name needs not be a proper name. "The Founder of Christianity
+was crucified," is as much a singular proposition as "Christ was
+crucified."</p>
+
+<p>When the name which is the subject of the proposition is a general name,
+we may intend to affirm or deny the predicate, either of all the things
+that the subject denotes, or only of some. When the predicate is
+affirmed or denied of all and each of the things denoted by the subject,
+the proposition is universal; when of some undefined portion of them
+only, it is particular. Thus, All men are mortal; Every man is mortal;
+are universal propositions. No man is immortal, is also an universal
+proposition, since the predicate, immortal, is denied of each and every
+individual denoted by the term man; the negative proposition being
+exactly equivalent to the following, Every man is not-immortal. But
+"some men are wise," "some men are not wise," are particular
+propositions; the predicate <i>wise</i> being in the one case affirmed and in
+the other denied not of each and every individual denoted by the term
+man, but only of each and every one of some portion of those
+individuals, without specifying what portion; for if this were
+specified, the proposition would be changed either into a singular
+proposition, or into an universal proposition with a different subject;
+as, for instance, "all <i>properly instructed</i> men are wise." There are
+other forms of particular propositions; as, "<i>Most</i> men are imperfectly
+educated:" it being immaterial how large a portion of the subject the
+predicate is asserted of, as long as it is left uncertain how that
+portion is to be distinguished from the rest.</p>
+
+<p><span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p><p>When the form of the expression does not clearly show whether the
+general name which is the subject of the proposition is meant to stand
+for all the individuals denoted by it, or only for some of them, the
+proposition is, by some logicians, called Indefinite; but this, as
+Archbishop Whately observes, is a solecism, of the same nature as that
+committed by some grammarians when in their list of genders they
+enumerate the <i>doubtful</i> gender. The speaker must mean to assert the
+proposition either as an universal or as a particular proposition,
+though he has failed to declare which: and it often happens that though
+the words do not show which of the two he intends, the context, or the
+custom of speech, supplies the deficiency. Thus, when it is affirmed
+that "Man is mortal," nobody doubts that the assertion is intended of
+all human beings; and the word indicative of universality is commonly
+omitted, only because the meaning is evident without it. In the
+proposition, "Wine is good," it is understood with equal readiness,
+though for somewhat different reasons, that the assertion is not
+intended to be universal, but particular.<a name="FNanchor_16_22" id="FNanchor_16_22"></a><a href="#Footnote_16_22" class="fnanchor">[16]</a></p>
+
+<p>When a general name stands for each and every individual which it is a
+name of, or in other words, which it denotes, it is said by logicians to
+be <i>distributed</i>, or taken distributively. Thus, in the proposition, All
+men are mortal, the subject, Man, is distributed, because mortality is
+affirmed of each and every man. The predicate, Mortal, is not
+distributed, because the only mortals who are spoken of in the
+proposition are those who happen to be men; while the word may, for
+aught that appears, and in fact does, comprehend within it an indefinite
+number of objects besides men. In the proposition, Some men are mortal,
+both the predicate and the subject are undistributed. In the following,
+No men have wings, both the predicate and the subject are distributed.
+Not only is the attribute of having wings denied of the entire class
+Man, but that class is severed and cast out from the whole of the class
+Winged, and not merely from some part of that class.</p>
+
+<p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p><p>This phraseology, which is of great service in stating and
+demonstrating the rules of the syllogism, enables us to express very
+concisely the definitions of an universal and a particular proposition.
+An universal proposition is that of which the subject is distributed; a
+particular proposition is that of which the subject is undistributed.</p>
+
+<p>There are many more distinctions among propositions than those we have
+here stated, some of them of considerable importance. But, for
+explaining and illustrating these, more suitable opportunities will
+occur in the sequel.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_V" id="BOOK_I_CHAPTER_V"></a>CHAPTER V.<br />
+
+OF THE IMPORT OF PROPOSITIONS.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_1">� 1.</a> An inquiry into the nature of propositions must have one of two
+objects: to analyse the state of mind called Belief, or to analyse what
+is believed. All language recognises a difference between a doctrine or
+opinion, and the fact of entertaining the opinion; between assent, and
+what is assented to.</p>
+
+<p>Logic, according to the conception here formed of it, has no concern
+with the nature of the act of judging or believing; the consideration of
+that act, as a phenomenon of the mind, belongs to another science.
+Philosophers, however, from Descartes downwards, and especially from the
+era of Leibnitz and Locke, have by no means observed this distinction;
+and would have treated with great disrespect any attempt to analyse the
+import of Propositions, unless founded on an analysis of the act of
+Judgment. A proposition, they would have said, is but the expression in
+words of a Judgment. The thing expressed, not the mere verbal
+expression, is the important matter. When the mind assents to a
+proposition, it judges. Let us find out what the mind does when it
+judges, and we shall know what propositions mean, and not otherwise.</p>
+
+<p>Conformably to these views, almost all the writers on Logic in the last
+two centuries, whether English, German, or French, have made their
+theory of Propositions, from one end to the other, a theory of
+Judgments. They considered a Proposition, or a Judgment, for they used
+the two words indiscriminately, to consist in affirming or denying one
+<i>idea</i> of another. To judge, was to put two ideas together, or to bring
+one idea under another, or to compare two ideas, or to perceive the
+agreement or disagreement between two ideas: <span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span>and the whole doctrine of
+Propositions, together with the theory of Reasoning, (always necessarily
+founded on the theory of Propositions,) was stated as if Ideas, or
+Conceptions, or whatever other term the writer preferred as a name for
+mental representations generally, constituted essentially the subject
+matter and substance of those operations.</p>
+
+<p>It is, of course, true, that in any case of judgment, as for instance
+when we judge that gold is yellow, a process takes place in our minds,
+of which some one or other of these theories is a partially correct
+account. We must have the idea of gold and the idea of yellow, and these
+two ideas must be brought together in our mind. But in the first place,
+it is evident that this is only a part of what takes place; for we may
+put two ideas together without any act of belief; as when we merely
+imagine something, such as a golden mountain; or when we actually
+disbelieve: for in order even to disbelieve that Mahomet was an apostle
+of God, we must put the idea of Mahomet and that of an apostle of God
+together. To determine what it is that happens in the case of assent or
+dissent besides putting two ideas together, is one of the most intricate
+of metaphysical problems. But whatever the solution may be, we may
+venture to assert that it can have nothing whatever to do with the
+import of propositions; for this reason, that propositions (except
+sometimes when the mind itself is the subject treated of) are not
+assertions respecting our ideas of things, but assertions respecting the
+things themselves. In order to believe that gold is yellow, I must,
+indeed, have the idea of gold, and the idea of yellow, and something
+having reference to those ideas must take place in my mind; but my
+belief has not reference to the ideas, it has reference to the things.
+What I believe, is a fact relating to the outward thing, gold, and to
+the impression made by that outward thing upon the human organs; not a
+fact relating to my conception of gold, which would be a fact in my
+mental history, not a fact of external nature. It is true, that in order
+to believe this fact in external nature, another fact must take place in
+my mind, a process must be performed upon my ideas; but so it must in
+everything else that I do. I cannot dig the <span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span>ground unless I have the
+idea of the ground, and of a spade, and of all the other things I am
+operating upon, and unless I put those ideas together.<a name="FNanchor_17_23" id="FNanchor_17_23"></a><a href="#Footnote_17_23" class="fnanchor">[17]</a> But it would
+be a very ridiculous description of digging the ground to say that it is
+putting one idea into another. Digging is an operation which is
+performed upon the things themselves, though it cannot be performed
+unless I have in my mind the ideas of them. And in like manner,
+believing is an act which has for its subject the facts themselves,
+though a previous mental conception of the facts is an indispensable
+condition. When I say that fire causes heat, do I mean that my idea of
+fire causes my idea of heat? No: I mean that the natural phenomenon,
+fire, causes the natural phenomenon, heat. When I mean to assert
+anything respecting the ideas, I give them their proper name, I call
+them ideas: as when I say, that a child's idea of a battle is unlike the
+reality, or that the ideas entertained of the Deity have a great effect
+on the characters of mankind.</p>
+
+<p>The notion that what is of primary importance to the logician in a
+proposition, is the relation between the two <i>ideas</i> corresponding to
+the subject and predicate, (instead of the relation between the two
+<i>phenomena</i> which they respectively express,) seems to me one of the
+most fatal errors ever introduced into the philosophy of Logic; and the
+principal cause why the theory of the science has made such
+inconsiderable progress during the last two centuries. The treatises on
+Logic, and on the branches of Mental Philosophy connected with Logic,
+which have been produced since the intrusion of this cardinal error,
+though sometimes written by men of extraordinary abilities and
+attainments, almost always tacitly imply a theory that the investigation
+of truth consists in contemplating <span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span>and handling our ideas, or
+conceptions of things, instead of the things themselves: a doctrine
+tantamount to the assertion, that the only mode of acquiring knowledge
+of nature is to study it at second hand, as represented in our own
+minds. Meanwhile, inquiries into every kind of natural phenomena were
+incessantly establishing great and fruitful truths on most important
+subjects, by processes upon which these views of the nature of Judgment
+and Reasoning threw no light, and in which they afforded no assistance
+whatever. No wonder that those who knew by practical experience how
+truths are arrived at, should deem a science futile, which consisted
+chiefly of such speculations. What has been done for the advancement of
+Logic since these doctrines came into vogue, has been done not by
+professed logicians, but by discoverers in the other sciences; in whose
+methods of investigation many principles of logic, not previously
+thought of, have successively come forth into light, but who have
+generally committed the error of supposing that nothing whatever was
+known of the art of philosophizing by the old logicians, because their
+modern interpreters have written to so little purpose respecting it.</p>
+
+<p>We have to inquire, then, on the present occasion, not into Judgment,
+but judgments; not into the act of believing, but into the thing
+believed. What is the immediate object of belief in a Proposition? What
+is the matter of fact signified by it? What is it to which, when I
+assert the proposition, I give my assent, and call upon others to give
+theirs? What is that which is expressed by the form of discourse called
+a Proposition, and the conformity of which to fact constitutes the truth
+of the proposition?</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_2">� 2.</a> One of the clearest and most consecutive thinkers whom this country
+or the world has produced, I mean Hobbes, has given the following answer
+to this question. In every proposition (says he) what is signified is,
+the belief of the speaker that the predicate is a name of the same thing
+of which the subject is a name; and if it really is so, the proposition
+is true. Thus the proposition, All men are living beings (he <span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span>would say)
+is true, because <i>living being</i> is a name of everything of which <i>man</i>
+is a name. All men are six feet high, is not true, because <i>six feet
+high</i> is not a name of everything (though it is of some things) of which
+<i>man</i> is a name.</p>
+
+<p>What is stated in this theory as the definition of a true proposition,
+must be allowed to be a property which all true propositions possess.
+The subject and predicate being both of them names of things, if they
+were names of quite different things the one name could not,
+consistently with its signification, be predicated of the other. If it
+be true that some men are copper-coloured, it must be true&mdash;and the
+proposition does really assert&mdash;that among the individuals denoted by
+the name man, there are some who are also among those denoted by the
+name copper-coloured. If it be true that all oxen ruminate, it must be
+true that all the individuals denoted by the name ox are also among
+those denoted by the name ruminating; and whoever asserts that all oxen
+ruminate, undoubtedly does assert that this relation subsists between
+the two names.</p>
+
+<p>The assertion, therefore, which, according to Hobbes, is the only one
+made in any proposition, really is made in every proposition: and his
+analysis has consequently one of the requisites for being the true one.
+We may go a step farther; it is the only analysis that is rigorously
+true of all propositions without exception. What he gives as the meaning
+of propositions, is part of the meaning of all propositions, and the
+whole meaning of some. This, however, only shows what an extremely
+minute fragment of meaning it is quite possible to include within the
+logical formula of a proposition. It does not show that no proposition
+means more. To warrant us in putting together two words with a copula
+between them, it is really enough that the thing or things denoted by
+one of the names should be capable, without violation of usage, of being
+called by the other name also. If, then, this be all the meaning
+necessarily implied in the form of discourse called a Proposition, why
+do I object to it as the scientific definition of what a proposition
+means? Because, though the mere collocation which makes the proposition
+a proposition, conveys no more than this scanty amount of meaning, that
+same collocation <span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span>combined with other circumstances, that <i>form</i>
+combined with other <i>matter</i>, does convey more, and much more.</p>
+
+<p>The only propositions of which Hobbes' principle is a sufficient
+account, are that limited and unimportant class in which both the
+predicate and the subject are proper names. For, as has already been
+remarked, proper names have strictly no meaning; they are mere marks for
+individual objects: and when a proper name is predicated of another
+proper name, all the signification conveyed is, that both the names are
+marks for the same object. But this is precisely what Hobbes produces as
+a theory of predication in general. His doctrine is a full explanation
+of such predications as these: Hyde was Clarendon, or, Tully is Cicero.
+It exhausts the meaning of those propositions. But it is a sadly
+inadequate theory of any others. That it should ever have been thought
+of as such, can be accounted for only by the fact, that Hobbes, in
+common with the other Nominalists, bestowed little or no attention upon
+the <i>connotation</i> of words; and sought for their meaning exclusively in
+what they <i>denote</i>: as if all names had been (what none but proper names
+really are) marks put upon individuals; and as if there were no
+difference between a proper and a general name, except that the first
+denotes only one individual, and the last a greater number.</p>
+
+<p>It has been seen, however, that the meaning of all names, except proper
+names and that portion of the class of abstract names which are not
+connotative, resides in the connotation. When, therefore, we are
+analysing the meaning of any proposition in which the predicate and the
+subject, or either of them, are connotative names, it is to the
+connotation of those terms that we must exclusively look, and not to
+what they <i>denote</i>, or in the language of Hobbes (language so far
+correct) are names of.</p>
+
+<p>In asserting that the truth of a proposition depends on the conformity
+of import between its terms, as, for instance, that the proposition,
+Socrates is wise, is a true proposition, because Socrates and wise are
+names applicable to, or, as he expresses it, names of, the same person;
+it is very remarkable that so powerful a thinker should not have asked
+himself the question, <span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span>But how came they to be names of the same person?
+Surely not because such was the intention of those who invented the
+words. When mankind fixed the meaning of the word wise, they were not
+thinking of Socrates, nor, when his parents gave him the name of
+Socrates, were they thinking of wisdom. The names <i>happen</i> to fit the
+same person because of a certain <i>fact</i>, which fact was not known, nor
+in being, when the names were invented. If we want to know what the fact
+is, we shall find the clue to it in the <i>connotation</i> of the names.</p>
+
+<p>A bird or a stone, a man, or a wise man, means simply, an object having
+such and such attributes. The real meaning of the word man, is those
+attributes, and not Smith, Brown, and the remainder of the individuals.
+The word <i>mortal</i>, in like manner connotes a certain attribute or
+attributes; and when we say, All men are mortal, the meaning of the
+proposition is, that all beings which possess the one set of attributes,
+possess also the other. If, in our experience, the attributes connoted
+by <i>man</i> are always accompanied by the attribute connoted by <i>mortal</i>,
+it will follow as a consequence, that the class <i>man</i> will be wholly
+included in the class <i>mortal</i>, and that <i>mortal</i> will be a name of all
+things of which <i>man</i> is a name: but why? Those objects are brought
+under the name, by possessing the attributes connoted by it: but their
+possession of the attributes is the real condition on which the truth of
+the proposition depends; not their being called by the name. Connotative
+names do not precede, but follow, the attributes which they connote. If
+one attribute happens to be always found in conjunction with another
+attribute, the concrete names which answer to those attributes will of
+course be predicable of the same subjects, and may be said, in Hobbes'
+language, (in the propriety of which on this occasion I fully concur,)
+to be two names for the same things. But the possibility of a concurrent
+application of the two names, is a mere consequence of the conjunction
+between the two attributes, and was, in most cases, never thought of
+when the names were introduced and their signification fixed. That the
+diamond is combustible, was a proposition certainly not dreamt of when
+the words <span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span>Diamond and Combustible first received their meaning; and
+could not have been discovered by the most ingenious and refined
+analysis of the signification of those words. It was found out by a very
+different process, namely, by exerting the senses, and learning from
+them, that the attribute of combustibility existed in the diamonds upon
+which the experiment was tried; the number or character of the
+experiments being such, that what was true of those individuals might be
+concluded to be true of all substances "called by the name," that is, of
+all substances possessing the attributes which the name connotes. The
+assertion, therefore, when analysed, is, that wherever we find certain
+attributes, there will be found a certain other attribute: which is not
+a question of the signification of names, but of laws of nature; the
+order existing among phenomena.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_3">� 3.</a> Although Hobbes' theory of Predication has not, in the terms in
+which he stated it, met with a very favourable reception from subsequent
+thinkers, a theory virtually identical with it, and not by any means so
+perspicuously expressed, may almost be said to have taken the rank of an
+established opinion. The most generally received notion of Predication
+decidedly is that it consists in referring something to a class, <i>i.e.</i>,
+either placing an individual under a class, or placing one class under
+another class. Thus, the proposition, Man is mortal, asserts, according
+to this view of it, that the class man is included in the class mortal.
+"Plato is a philosopher," asserts that the individual Plato is one of
+those who compose the class philosopher. If the proposition is negative,
+then instead of placing something in a class, it is said to exclude
+something from a class. Thus, if the following be the proposition, The
+elephant is not carnivorous; what is asserted (according to this theory)
+is, that the elephant is excluded, from the class carnivorous, or is not
+numbered among the things comprising that class. There is no real
+difference, except in language, between this theory of Predication and
+the theory of Hobbes. For a class <i>is</i> absolutely nothing but an
+indefinite number of individuals denoted by a general <span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>name. The name
+given to them in common, is what makes them a class. To refer anything
+to a class, therefore, is to look upon it as one of the things which are
+to be called by that common name. To exclude it from a class, is to say
+that the common name is not applicable to it.</p>
+
+<p>How widely these views of predication have prevailed, is evident from
+this, that they are the basis of the celebrated <i>dictum de omni et
+nullo</i>. When the syllogism is resolved, by all who treat of it, into an
+inference that what is true of a class is true of all things whatever
+that belong to the class; and when this is laid down by almost all
+professed logicians as the ultimate principle to which all reasoning
+owes its validity; it is clear that in the general estimation of
+logicians, the propositions of which reasonings are composed can be the
+expression of nothing but the process of dividing things into classes,
+and referring everything to its proper class.</p>
+
+<p>This theory appears to me a signal example of a logical error very often
+committed in logic, that of <i>&#8021;&#963;&#964;&#949;&#961;&#959;&#957; &#960;&#961;&#959;&#964;&#8051;&#961;&#959;&#957;</i>, or explaining a
+thing by something which presupposes it. When I say that snow is white,
+I may and ought to be thinking of snow as a class, because I am
+asserting a proposition as true of all snow: but I am certainly not
+thinking of white objects as a class; I am thinking of no white object
+whatever except snow, but only of that, and of the sensation of white
+which it gives me. When, indeed, I have judged, or assented to the
+propositions, that snow is white, and that several other things are also
+white, I gradually begin to think of white objects as a class, including
+snow and those other things. But this is a conception which followed,
+not preceded, those judgments, and therefore cannot be given as an
+explanation of them. Instead of explaining the effect by the cause, this
+doctrine explains the cause by the effect, and is, I conceive, founded
+on a latent misconception of the nature of classification.</p>
+
+<p>There is a sort of language very generally prevalent in these
+discussions, which seems to suppose that classification is an
+arrangement and grouping of definite and known individuals: <span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span>that when
+names were imposed, mankind took into consideration all the individual
+objects in the universe, distributed them into parcels or lists, and
+gave to the objects of each list a common name, repeating this operation
+<i>toties quoties</i> until they had invented all the general names of which
+language consists; which having been once done, if a question
+subsequently arises whether a certain general name can be truly
+predicated of a certain particular object, we have only (as it were) to
+read the roll of the objects upon which that name was conferred, and see
+whether the object about which the question arises is to be found among
+them. The framers of language (it would seem to be supposed) have
+predetermined all the objects that are to compose each class, and we
+have only to refer to the record of an antecedent decision.</p>
+
+<p>So absurd a doctrine will be owned by nobody when thus nakedly stated;
+but if the commonly received explanations of classification and naming
+do not imply this theory, it requires to be shown how they admit of
+being reconciled with any other.</p>
+
+<p>General names are not marks put upon definite objects; classes are not
+made by drawing a line round a given number of assignable individuals.
+The objects which compose any given class are perpetually fluctuating.
+We may frame a class without knowing the individuals, or even any of the
+individuals, of which it may be composed; we may do so while believing
+that no such individuals exist. If by the <i>meaning</i> of a general name
+are to be understood the things which it is the name of, no general
+name, except by accident, has a fixed meaning at all, or ever long
+retains the same meaning. The only mode in which any general name has a
+definite meaning, is by being a name of an indefinite variety of things;
+namely, of all things, known or unknown, past, present, or future, which
+possess certain definite attributes. When, by studying not the meaning
+of words, but the phenomena of nature, we discover that these attributes
+are possessed by some object not previously known to possess them, (as
+when chemists found that the diamond was combustible), we include this
+new object in the class; but it did not already belong to the class. We
+<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span>place the individual in the class because the proposition is true; the
+proposition is not true because the object is placed in the class.</p>
+
+<p>It will appear hereafter, in treating of reasoning, how much the theory
+of that intellectual process has been vitiated by the influence of these
+erroneous notions, and by the habit which they exemplify of assimilating
+all the operations of the human understanding which have truth for their
+object, to processes of mere classification and naming. Unfortunately,
+the minds which have been entangled in this net are precisely those
+which have escaped the other cardinal error commented upon in the
+beginning of the present chapter. Since the revolution which dislodged
+Aristotle from the schools, logicians may almost be divided into those
+who have looked upon reasoning as essentially an affair of Ideas, and
+those who have looked upon it as essentially an affair of Names.</p>
+
+<p>Although, however, Hobbes' theory of Predication, according to the
+well-known remark of Leibnitz, and the avowal of Hobbes himself,<a name="FNanchor_18_24" id="FNanchor_18_24"></a><a href="#Footnote_18_24" class="fnanchor">[18]</a>
+renders truth and falsity completely arbitrary, with no standard but the
+will of men, it must not be concluded that either Hobbes, or any of the
+other thinkers who have in the main agreed with him, did in fact
+consider the distinction between truth and error as less real, or
+attached less importance to it, than other people. To suppose that they
+did so would argue total unacquaintance with their other speculations.
+But this shows how little hold their doctrine possessed over their own
+minds. No person, at bottom, ever imagined that there was nothing more
+in truth than propriety of expression; than using language in conformity
+to a previous convention. When the inquiry was brought down from
+generals to a particular case, it has always been acknowledged that
+there is a distinction between verbal and real questions; that some
+false propositions are uttered from ignorance of the meaning of <span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span>words,
+but that in others the source of the error is a misapprehension of
+things; that a person who has not the use of language at all may form
+propositions mentally, and that they may be untrue, that is, he may
+believe as matters of fact what are not really so. This last admission
+cannot be made in stronger terms than it is by Hobbes himself;<a name="FNanchor_19_25" id="FNanchor_19_25"></a><a href="#Footnote_19_25" class="fnanchor">[19]</a>
+though he will not allow such erroneous belief to be called falsity, but
+only error. And he has himself laid down, in other places, doctrines in
+which the true theory of predication is by implication contained. He
+distinctly says that general names are given to things on account of
+their attributes, and that abstract names are the names of those
+attributes. "Abstract is that which in any subject denotes the cause of
+the concrete name.... And these causes of names are the same with the
+causes of our conceptions, namely, some power of action, or affection,
+of the thing conceived, which some call the manner by which anything
+works upon our senses, but by most men they are called <i>accidents</i>."<a name="FNanchor_20_26" id="FNanchor_20_26"></a><a href="#Footnote_20_26" class="fnanchor">[20]</a>
+It is strange that having gone so far, he should not have gone one step
+farther, and seen that what he calls the cause of the concrete name, is
+in reality the meaning of it; and that when we predicate of any subject
+a name which is given <i>because</i> of an attribute (or, as he calls it, an
+accident), our object is not to affirm the name, but, by means of the
+name, to affirm the attribute.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_4">� 4.</a> Let the predicate be, as we have said, a connotative term; and to
+take the simplest case first, let the subject be a proper name: "The
+summit of Chimborazo is white." The <span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>word white connotes an attribute
+which is possessed by the individual object designated by the words
+"summit of Chimborazo;" which attribute consists in the physical fact,
+of its exciting in human beings the sensation which we call a sensation
+of white. It will be admitted that, by asserting the proposition, we
+wish to communicate information of that physical fact, and are not
+thinking of the names, except as the necessary means of making that
+communication. The meaning of the proposition, therefore, is, that the
+individual thing denoted by the subject, has the attributes connoted by
+the predicate.</p>
+
+<p>If we now suppose the subject also to be a connotative name, the meaning
+expressed by the proposition has advanced a step farther in
+complication. Let us first suppose the proposition to be universal, as
+well as affirmative: "All men are mortal." In this case, as in the last,
+what the proposition asserts (or expresses a belief of) is, of course,
+that the objects denoted by the subject (man) possess the attributes
+connoted by the predicate (mortal). But the characteristic of this case
+is, that the objects are no longer <i>individually</i> designated. They are
+pointed out only by some of their attributes: they are the objects
+called men, that is, possessing the attributes connoted by the name man;
+and the only thing known of them may be those attributes: indeed, as the
+proposition is general, and the objects denoted by the subject are
+therefore indefinite in number, most of them are not known individually
+at all. The assertion, therefore, is not, as before, that the attributes
+which the predicate connotes are possessed by any given individual, or
+by any number of individuals previously known as John, Thomas, &amp;c., but
+that those attributes are possessed by each and every individual
+possessing certain other attributes; that whatever has the attributes
+connoted by the subject, has also those connoted by the predicate; that
+the latter set of attributes <i>constantly accompany</i> the former set.
+Whatever has the attributes of man has the attribute of mortality;
+mortality constantly accompanies the attributes of man.<a name="FNanchor_21_27" id="FNanchor_21_27"></a><a href="#Footnote_21_27" class="fnanchor">[21]</a></p>
+
+<p><span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span></p><p>If it be remembered that every attribute is <i>grounded</i> on some fact or
+phenomenon, either of outward sense or of inward consciousness, and that
+to <i>possess</i> an attribute is another phrase for being the cause of, or
+forming part of, the fact or phenomenon upon which the attribute is
+grounded; we may add one more step to complete the analysis. The
+proposition which asserts that one attribute always accompanies another
+attribute, really asserts thereby no other thing than this, that one
+phenomenon always accompanies another phenomenon; insomuch that where we
+find the one, we have assurance of the existence of the other. Thus, in
+the proposition, All men are mortal, the word man connotes the
+attributes which we ascribe to a certain kind of living creatures, on
+the ground of certain phenomena which they exhibit, and which are partly
+physical phenomena, namely the impressions made on our senses by their
+bodily form and structure, and partly mental phenomena, namely the
+sentient and intellectual life which they have of their own. All this is
+understood when we utter the word man, by any one to whom the meaning of
+the word is known. Now, when we say, Man is mortal, we mean that
+wherever these various physical and mental phenomena are all found,
+there we have assurance that the other physical and mental phenomenon,
+called death, will not fail to take place. The proposition does not
+affirm <i>when</i>; for the connotation of the word <i>mortal</i> goes no farther
+than to the occurrence of the phenomenon at some time or other, leaving
+the precise time undecided.</p>
+
+
+<p><span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span></p><p class="newsection"><a name="BOOK_I_CHAPTER_V_5">� 5.</a> We have already proceeded far enough, not only to demonstrate the
+error of Hobbes, but to ascertain the real import of by far the most
+numerous class of propositions. The object of belief in a proposition,
+when it asserts anything more than the meaning of words, is generally,
+as in the cases which we have examined, either the co-existence or the
+sequence of two phenomena. At the very commencement of our inquiry, we
+found that every act of belief implied two Things: we have now
+ascertained what, in the most frequent case, these two things are,
+namely two Phenomena, in other words, two states of consciousness; and
+what it is which the proposition affirms (or denies) to subsist between
+them, namely either succession or co-existence. And this case includes
+innumerable instances which no one, previous to reflection, would think
+of referring to it. Take the following example: A generous person is
+worthy of honour. Who would expect to recognise here a case of
+co-existence between phenomena? But so it is. The attribute which causes
+a person to be termed generous, is ascribed to him on the ground of
+states of his mind, and particulars of his conduct: both are phenomena:
+the former are facts of internal consciousness; the latter, so far as
+distinct from the former, are physical facts, or perceptions of the
+senses. Worthy of honour admits of a similar analysis. Honour, as here
+used, means a state of approving and admiring emotion, followed on
+occasion by corresponding outward acts. "Worthy of honour" connotes all
+this, together with our approval of the act of showing honour. All these
+are phenomena; states of internal consciousness, accompanied or followed
+by physical facts. When we say, A generous person is worthy of honour,
+we affirm co-existence between the two complicated phenomena connoted by
+the two terms respectively. We affirm, that wherever and whenever the
+inward feelings and outward facts implied in the word generosity have
+place, then and there the existence and manifestation of an inward
+feeling, honour, would be followed in our minds by another inward
+feeling, approval.</p>
+
+<p>After the analysis, in a former chapter, of the import of names, many
+examples are not needed to illustrate the import <span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span>of propositions. When
+there is any obscurity, or difficulty, it does not lie in the meaning of
+the proposition, but in the meaning of the names which compose it; in
+the extremely complicated connotation of many words; the immense
+multitude and prolonged series of facts which often constitute the
+phenomenon connoted by a name. But where it is seen what the phenomenon
+is, there is seldom any difficulty in seeing that the assertion conveyed
+by the proposition is, the co-existence of one such phenomenon with
+another; or the succession of one such phenomenon to another: their
+<i>conjunction</i>, in short, so that where the one is found, we may
+calculate on finding both.</p>
+
+<p>This, however, though the most common, is not the only meaning which
+propositions are ever intended to convey. In the first place, sequences
+and co-existences are not only asserted respecting Phenomena; we make
+propositions also respecting those hidden causes of phenomena, which are
+named substances and attributes. A substance, however, being to us
+nothing but either that which causes, or that which is conscious of,
+phenomena; and the same being true, <i>mutatis mutandis</i>, of attributes;
+no assertion can be made, at least with a meaning, concerning these
+unknown and unknowable entities, except in virtue of the Phenomena by
+which alone they manifest themselves to our faculties. When we say,
+Socrates was cotemporary with the Peloponnesian war, the foundation of
+this assertion, as of all assertions concerning substances, is an
+assertion concerning the phenomena which they exhibit,&mdash;namely, that the
+series of facts by which Socrates manifested himself to mankind, and the
+series of mental states which constituted his sentient existence, went
+on simultaneously with the series of facts known by the name of the
+Peloponnesian war. Still, the proposition does not assert that alone; it
+asserts that the Thing in itself, the <i>noumenon</i> Socrates, was existing,
+and doing or experiencing those various facts during the same time.
+Co-existence and sequence, therefore, may be affirmed or denied not only
+between phenomena, but between noumena, or between a noumenon and
+phenomena. And both of noumena and of phenomena <span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>we may affirm simple
+existence. But what is a noumenon? An unknown cause. In affirming,
+therefore, the existence of a noumenon, we affirm causation. Here,
+therefore, are two additional kinds of fact, capable of being asserted
+in a proposition. Besides the propositions which assert Sequence or
+Coexistence, there are some which assert simple Existence; and others
+assert Causation, which, subject to the explanations which will follow
+in the Third Book, must be considered provisionally as a distinct and
+peculiar kind of assertion.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_6">� 6.</a> To these four kinds of matter-of-fact or assertion, must be added a
+fifth, Resemblance. This was a species of attribute which we found it
+impossible to analyse; for which no <i>fundamentum</i>, distinct from the
+objects themselves, could be assigned. Besides propositions which assert
+a sequence or co-existence between two phenomena, there are therefore
+also propositions which assert resemblance between them: as, This colour
+is like that colour;&mdash;The heat of to-day is <i>equal</i> to the heat of
+yesterday. It is true that such an assertion might with some
+plausibility be brought within the description of an affirmation of
+sequence, by considering it as an assertion that the simultaneous
+contemplation of the two colours is <i>followed</i> by a specific feeling
+termed the feeling of resemblance. But there would be nothing gained by
+encumbering ourselves, especially in this place, with a generalization
+which may be looked upon as strained. Logic does not undertake to
+analyse mental facts into their ultimate elements. Resemblance between
+two phenomena is more intelligible in itself than any explanation could
+make it, and under any classification must remain specifically distinct
+from the ordinary cases of sequence and co-existence.</p>
+
+<p>It is sometimes said, that all propositions whatever, of which the
+predicate is a general name, do, in point of fact, affirm or deny
+resemblance. All such propositions affirm that a thing belongs to a
+class; but things being classed together according to their resemblance,
+everything is of course classed with the things which it is supposed to
+resemble most; and thence, it may be said, when we affirm that Gold is a
+metal, or that <span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span>Socrates is a man, the affirmation intended is, that
+gold resembles other metals, and Socrates other men, more nearly than
+they resemble the objects contained in any other of the classes
+co-ordinate with these.</p>
+
+<p>There is some slight degree of foundation for this remark, but no more
+than a slight degree. The arrangement of things into classes, such as
+the class <i>metal</i>, or the class <i>man</i>, is grounded indeed on a
+resemblance among the things which are placed in the same class, but not
+on a mere general resemblance: the resemblance it is grounded on
+consists in the possession by all those things, of certain common
+peculiarities; and those peculiarities it is which the terms connote,
+and which the propositions consequently assert; not the resemblance: for
+though when I say, Gold is a metal, I say by implication that if there
+be any other metals it must resemble them, yet if there were no other
+metals I might still assert the proposition with the same meaning as at
+present, namely, that gold has the various properties implied in the
+word metal; just as it might be said, Christians are men, even if there
+were no men who were not Christians. Propositions, therefore, in which
+objects are referred to a class because they possess the attributes
+constituting the class, are so far from asserting nothing but
+resemblance, that they do not, properly speaking, assert resemblance at
+all.</p>
+
+<p>But we remarked some time ago (and the reasons of the remark will be
+more fully entered into in a subsequent Book<a name="FNanchor_22_28" id="FNanchor_22_28"></a><a href="#Footnote_22_28" class="fnanchor">[22]</a>) that there is
+sometimes a convenience in extending the boundaries of a class so as to
+include things which possess in a very inferior degree, if in any, some
+of the characteristic properties of the class,&mdash;provided they resemble
+that class more than any other, insomuch that the general propositions
+which are true of the class, will be nearer to being true of those
+things than any other equally general propositions. For instance, there
+are substances called metals which have very few of the properties by
+which metals are commonly recognised; and almost every great family of
+plants or animals <span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>has a few anomalous genera or species on its borders,
+which are admitted into it by a sort of courtesy, and concerning which
+it has been matter of discussion to what family they properly belonged.
+Now when the class-name is predicated of any object of this description,
+we do, by so predicating it, affirm resemblance and nothing more. And in
+order to be scrupulously correct it ought to be said, that in every case
+in which we predicate a general name, we affirm, not absolutely that the
+object possesses the properties designated by the name, but that it
+<i>either</i> possesses those properties, or if it does not, at any rate
+resembles the things which do so, more than it resembles any other
+things. In most cases, however, it is unnecessary to suppose any such
+alternative, the latter of the two grounds being very seldom that on
+which the assertion is made: and when it is, there is generally some
+slight difference in the form of the expression, as, This species (or
+genus) is <i>considered</i>, or <i>may be ranked</i>, as belonging to such and
+such a family: we should hardly say positively that it does belong to
+it, unless it possessed unequivocally the properties of which the
+class-name is scientifically significant.</p>
+
+<p>There is still another exceptional case, in which, though the predicate
+is the name of a class, yet in predicating it we affirm nothing but
+resemblance, the class being founded not on resemblance in any given
+particular, but on general unanalysable resemblance. The classes in
+question are those into which our simple sensations, or other simple
+feelings, are divided. Sensations of white, for instance, are classed
+together, not because we can take them to pieces, and say they are alike
+in this, and not alike in that, but because we feel them to be alike
+altogether, though in different degrees. When, therefore, I say, The
+colour I saw yesterday was a white colour, or, The sensation I feel is
+one of tightness, in both cases the attribute I affirm of the colour or
+of the other sensation is mere resemblance&mdash;simple <i>likeness</i> to
+sensations which I have had before, and which have had those names
+bestowed upon them. The names of feelings, like other concrete general
+names, are connotative; but they connote a mere resemblance. When
+predicated of any individual feeling, <span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span>the information they convey is
+that of its likeness to the other feelings which we have been accustomed
+to call by the same name. Thus much may suffice in illustration of the
+kind of propositions in which the matter-of-fact asserted (or denied) is
+simple Resemblance.</p>
+
+<p>Existence, Coexistence, Sequence, Causation, Resemblance: one or other
+of these is asserted (or denied) in every proposition which is not
+merely verbal. This five-fold division is an exhaustive classification
+of matters-of-fact; of all things that can be believed, or tendered for
+belief; of all questions that can be propounded, and all answers that
+can be returned to them. Instead of Coexistence and Sequence, we shall
+sometimes say, for greater particularity, Order in Place, and Order in
+Time: Order in Place being the specific mode of coexistence, not
+necessary to be more particularly analysed here; while the mere fact of
+coexistence, or simultaneousness, may be classed, together with
+Sequence, under the head of Order in Time.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_V_7">� 7.</a> In the foregoing inquiry into the import of Propositions, we have
+thought it necessary to analyse directly those alone, in which the terms
+of the proposition (or the predicate at least) are concrete terms. But,
+in doing so, we have indirectly analysed those in which the terms are
+abstract. The distinction between an abstract term and its corresponding
+concrete, does not turn upon any difference in what they are appointed
+to signify; for the real signification of a concrete general name is, as
+we have so often said, its connotation; and what the concrete term
+connotes, forms the entire meaning of the abstract name. Since there is
+nothing in the import of an abstract name which is not in the import of
+the corresponding concrete, it is natural to suppose that neither can
+there be anything in the import of a proposition of which the terms are
+abstract, but what there is in some proposition which can be framed of
+concrete terms.</p>
+
+<p>And this presumption a closer examination will confirm. An abstract name
+is the name of an attribute, or combination of attributes. The
+corresponding concrete is a name given to <span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>things, because of, and in
+order to express, their possessing that attribute, or that combination
+of attributes. When, therefore, we predicate of anything a concrete
+name, the attribute is what we in reality predicate of it. But it has
+now been shown that in all propositions of which the predicate is a
+concrete name, what is really predicated is one of five things:
+Existence, Coexistence, Causation, Sequence, or Resemblance. An
+attribute, therefore, is necessarily either an existence, a coexistence,
+a causation, a sequence, or a resemblance. When a proposition consists
+of a subject and predicate which are abstract terms, it consists of
+terms which must necessarily signify one or other of these things. When
+we predicate of anything an abstract name, we affirm of the thing that
+it is one or other of these five things; that it is a case of Existence,
+or of Coexistence, or of Causation, or of Sequence, or of Resemblance.</p>
+
+<p>It is impossible to imagine any proposition expressed in abstract terms,
+which cannot be transformed into a precisely equivalent proposition in
+which the terms are concrete; namely, either the concrete names which
+connote the attributes themselves, or the names of the <i>fundamenta</i> of
+those attributes; the facts or phenomena on which they are grounded. To
+illustrate the latter case, let us take this proposition, of which the
+subject only is an abstract name, "Thoughtlessness is dangerous."
+Thoughtlessness is an attribute, grounded on the facts which we call
+thoughtless actions; and the proposition is equivalent to this,
+Thoughtless actions are dangerous. In the next example the predicate as
+well as the subject are abstract names: "Whiteness is a colour;" or "The
+colour of snow is a whiteness." These attributes being grounded on
+sensations, the equivalent propositions in the concrete would be, The
+sensation of white is one of the sensations called those of colour,&mdash;The
+sensation of sight, caused by looking at snow, is one of the sensations
+called sensations of white. In these propositions, as we have before
+seen, the matter-of-fact asserted is a Resemblance. In the following
+examples, the concrete terms are those which directly correspond to the
+abstract names; connoting <span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span>the attribute which these denote. "Prudence
+is a virtue:" this may be rendered, "All prudent persons, <i>in so far as</i>
+prudent, are virtuous:" "Courage is deserving of honour," thus, "All
+courageous persons are deserving of honour <i>in so far</i> as they are
+courageous:" which is equivalent to this&mdash;"All courageous persons
+deserve an addition to the honour, or a diminution of the disgrace,
+which would attach to them on other grounds."</p>
+
+<p>In order to throw still further light upon the import of propositions of
+which the terms are abstract, we will subject one of the examples given
+above to a minuter analysis. The proposition we shall select is the
+following:&mdash;"Prudence is a virtue." Let us substitute for the word
+virtue an equivalent but more definite expression, such as "a mental
+quality beneficial to society," or "a mental quality pleasing to God,"
+or whatever else we adopt as the definition of virtue. What the
+proposition asserts is a sequence, accompanied with causation; namely,
+that benefit to society, or that the approval of God, is consequent on,
+and caused by, prudence. Here is a sequence; but between what? We
+understand the consequent of the sequence, but we have yet to analyse
+the antecedent. Prudence is an attribute; and, in connexion with it, two
+things besides itself are to be considered; prudent persons, who are the
+<i>subjects</i> of the attribute, and prudential conduct, which may be called
+the <i>foundation</i> of it. Now is either of these the antecedent? and,
+first, is it meant, that the approval of God, or benefit to society, is
+attendant upon all prudent <i>persons</i>? No; except <i>in so far</i> as they are
+prudent; for prudent persons who are scoundrels can seldom on the whole
+be beneficial to society, nor can they be acceptable to a good being. Is
+it upon prudential <i>conduct</i>, then, that divine approbation and benefit
+to mankind are supposed to be invariably consequent? Neither is this the
+assertion meant, when it is said that prudence is a virtue; except with
+the same reservation as before, and for the same reason, namely, that
+prudential conduct, although in <i>so far as</i> it is prudential it is
+beneficial to society, may yet, by reason of some other of its
+qualities, be productive of an injury outweighing the benefit, and
+deserve a displeasure <span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>exceeding the approbation which would be due to
+the prudence. Neither the substance, therefore, (viz. the person,) nor
+the phenomenon, (the conduct,) is an antecedent on which the other term
+of the sequence is universally consequent. But the proposition,
+"Prudence is a virtue," is an universal proposition. What is it, then,
+upon which the proposition affirms the effects in question to be
+universally consequent? Upon that in the person, and in the conduct,
+which causes them to be called prudent, and which is equally in them
+when the action, though prudent, is wicked; namely, a correct foresight
+of consequences, a just estimation of their importance to the object in
+view, and repression of any unreflecting impulse at variance with the
+deliberate purpose. These, which are states of the person's mind, are
+the real antecedent in the sequence, the real cause in the causation,
+asserted by the proposition. But these are also the real ground, or
+foundation, of the attribute Prudence; since wherever these states of
+mind exist we may predicate prudence, even before we know whether any
+conduct has followed. And in this manner every assertion respecting an
+attribute, may be transformed into an assertion exactly equivalent
+respecting the fact or phenomenon which is the ground of the attribute.
+And no case can be assigned, where that which is predicated of the fact
+or phenomenon, does not belong to one or other of the five species
+formerly enumerated: it is either simple Existence, or it is some
+Sequence, Coexistence, Causation, or Resemblance.</p>
+
+<p>And as these five are the only things which can be affirmed, so are they
+the only things which can be denied. "No horses are web-footed" denies
+that the attributes of a horse ever coexist with web-feet. It is
+scarcely necessary to apply the same analysis to Particular affirmations
+and negations. "Some birds are web-footed," affirms that, with the
+attributes connoted by <i>bird</i>, the phenomenon web-feet is sometimes
+co-existent: "Some birds are not web-footed," asserts that there are
+other instances in which this coexistence does not have place. Any
+further explanation of a thing which, if the previous exposition has
+been assented to, is so obvious, may here be spared.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_VI" id="BOOK_I_CHAPTER_VI"></a>CHAPTER VI.<br />
+
+OF PROPOSITIONS MERELY VERBAL.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VI_1">� 1.</a> As a preparation for the inquiry which is the proper object of
+Logic, namely, in what manner propositions are to be proved, we have
+found it necessary to inquire what they contain which requires, or is
+susceptible of, proof; or (which is the same thing) what they assert. In
+the course of this preliminary investigation into the import of
+Propositions, we examined the opinion of the Conceptualists, that a
+proposition is the expression of a relation between two ideas; and the
+doctrine of the Nominalists, that it is the expression of an agreement
+or disagreement between the meanings of two names. We decided that, as
+general theories, both of these are erroneous; and that, though
+propositions may be made both respecting names and respecting ideas,
+neither the one nor the other are the subject-matter of Propositions
+considered generally. We then examined the different kinds of
+Propositions, and found that, with the exception of those which are
+merely verbal, they assert five different kinds of matters of fact,
+namely, Existence, Order in Place, Order in Time, Causation, and
+Resemblance; that in every proposition one of these five is either
+affirmed, or denied, of some fact or phenomenon, or of some object the
+unknown source of a fact or phenomenon.</p>
+
+<p>In distinguishing, however, the different kinds of matters of fact
+asserted in propositions, we reserved one class of propositions, which
+do not relate to any matter of fact, in the proper sense of the term, at
+all, but to the meaning of names. Since names and their signification
+are entirely arbitrary, such propositions are not, strictly speaking,
+susceptible of truth or falsity, but only of conformity or disconformity
+to usage or convention; and all the proof they are capable of, is proof
+of usage; proof that the words have been employed by others in <span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span>the
+acceptation in which the speaker or writer desires to use them. These
+propositions occupy, however, a conspicuous place in philosophy; and
+their nature and characteristics are of as much importance in logic, as
+those of any of the other classes of propositions previously adverted
+to.</p>
+
+<p>If all propositions respecting the signification of words were as simple
+and unimportant as those which served us for examples when examining
+Hobbes' theory of predication, viz. those of which the subject and
+predicate are proper names, and which assert only that those names have,
+or that they have not, been conventionally assigned to the same
+individual, there would be little to attract to such propositions the
+attention of philosophers. But the class of merely verbal propositions
+embraces not only much more than these, but much more than any
+propositions which at first sight present themselves as verbal;
+comprehending a kind of assertions which have been regarded not only as
+relating to things, but as having actually a more intimate relation with
+them than any other propositions whatever. The student in philosophy
+will perceive that I allude to the distinction on which so much stress
+was laid by the schoolmen, and which has been retained either under the
+same or under other names by most metaphysicians to the present day,
+viz. between what were called <i>essential</i>, and what were called
+<i>accidental</i>, propositions, and between essential and accidental
+properties or attributes.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VI_2">� 2.</a> Almost all metaphysicians prior to Locke, as well as many since his
+time, have made a great mystery of Essential Predication, and of
+predicates which are said to be of the <i>essence</i> of the subject. The
+essence of a thing, they said, was that without which the thing could
+neither be, nor be conceived to be. Thus, rationality was of the essence
+of man, because without rationality, man could not be conceived to
+exist. The different attributes which made up the essence of the thing
+were called its essential properties; and a proposition in which any of
+these were predicated of it was called an Essential Proposition, and was
+considered to go deeper into the nature of the thing, and to convey more
+important information <span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span>respecting it, than any other proposition could
+do. All properties, not of the essence of the thing, were called its
+accidents; were supposed to have nothing at all, or nothing
+comparatively, to do with its inmost nature; and the propositions in
+which any of these were predicated of it were called Accidental
+Propositions. A connexion may be traced between this distinction, which
+originated with the schoolmen, and the well-known dogmas of <i>substanti�
+secund�</i> or general substances, and <i>substantial forms</i>, doctrines which
+under varieties of language pervaded alike the Aristotelian and the
+Platonic schools, and of which more of the spirit has come down to
+modern times than might be conjectured from the disuse of the
+phraseology. The false views of the nature of classification and
+generalization which prevailed among the schoolmen, and of which these
+dogmas were the technical expression, afford the only explanation which
+can be given of their having misunderstood the real nature of those
+Essences which held so conspicuous a place in their philosophy. They
+said, truly, that <i>man</i> cannot be conceived without rationality. But
+though <i>man</i> cannot, a being may be conceived exactly like a man in all
+points except that one quality, and those others which are the
+conditions or consequences of it. All therefore which is really true in
+the assertion that man cannot be conceived without rationality, is only,
+that if he had not rationality, he would not be reputed a man. There is
+no impossibility in conceiving the <i>thing</i>, nor, for aught we know, in
+its existing: the impossibility is in the conventions of language, which
+will not allow the thing, even if it exist, to be called by the name
+which is reserved for rational beings. Rationality, in short, is
+involved in the meaning of the word man: is one of the attributes
+connoted by the name. The essence of man, simply means the whole of the
+attributes connoted by the word; and any one of those attributes taken
+singly, is an essential property of man.</p>
+
+<p>But these reflections, so easy to us, would have been difficult to
+persons who thought, as most of the later Aristotelians did, that
+objects were made what they were called, that gold (for instance) was
+made gold, not by the possession of certain properties to which mankind
+have chosen to attach that name, but <span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span>by participation in the nature of
+a certain general substance, called gold in general, which substance,
+together with all the properties that belonged to it, <i>inhered</i> in every
+individual piece of gold.<a name="FNanchor_23_29" id="FNanchor_23_29"></a><a href="#Footnote_23_29" class="fnanchor">[23]</a> As they did not consider these universal
+substances to be attached to all general names, but only to some, they
+thought that an object borrowed only a part of its properties from an
+universal substance, and that the rest belonged to it individually: the
+former they called its essence, and the latter its accidents. The
+scholastic doctrine of essences long survived the theory on which it
+rested, that of the existence of real entities corresponding to general
+terms; and it was reserved for Locke at the end of the seventeenth
+century, to convince philosophers that the supposed essences of classes
+were merely the signification of their names; nor, among the signal
+services which his writings rendered to philosophy, was there one more
+needful or more valuable.</p>
+
+<p>Now, as the most familiar of the general names by which an object is
+designated usually connotes not one only, but several attributes of the
+object, each of which attributes separately forms also the bond of union
+of some class, and the meaning of some general name; we may predicate of
+a name which connotes a variety of attributes, another name which
+connotes only one of these attributes, or some smaller number of them
+than all. In such cases, the universal affirmative proposition will be
+true; since whatever possesses the whole of any set of attributes, must
+possess any part of that same set. A proposition of this sort, however,
+conveys no information to any one who previously understood the whole
+meaning of the terms. The propositions, Every man is a corporeal being,
+Every man is a living creature, Every man is rational, convey no
+knowledge to any one who was already aware of the entire meaning of the
+word <i>man</i>, for the meaning of the word <span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span>includes all this: and that
+every <i>man</i> has the attributes connoted by all these predicates, is
+already asserted when he is called a man. Now, of this nature are all
+the propositions which have been called essential. They are, in fact,
+identical propositions.</p>
+
+<p>It is true that a proposition which predicates any attribute, even
+though it be one implied in the name, is in most cases understood to
+involve a tacit assertion that there <i>exists</i> a thing corresponding to
+the name, and possessing the attributes connoted by it; and this implied
+assertion may convey information, even to those who understood the
+meaning of the name. But all information of this sort, conveyed by all
+the essential propositions of which man can be made the subject, is
+included in the assertion, Men exist. And this assumption of real
+existence is, after all, the result of an imperfection of language. It
+arises from the ambiguity of the copula, which, in addition to its
+proper office of a mark to show that an assertion is made, is also, as
+formerly remarked, a concrete word connoting existence. The actual
+existence of the subject of the proposition is therefore only
+apparently, not really, implied in the predication, if an essential one:
+we may say, A ghost is a disembodied spirit, without believing in
+ghosts. But an accidental, or non-essential, affirmation, does imply the
+real existence of the subject, because in the case of a non-existent
+subject there is nothing for the proposition to assert. Such a
+proposition as, The ghost of a murdered person haunts the couch of the
+murderer, can only have a meaning if understood as implying a belief in
+ghosts; for since the signification of the word ghost implies nothing of
+the kind, the speaker either means nothing, or means to assert a thing
+which he wishes to be believed to have really taken place.</p>
+
+<p>It will be hereafter seen that when any important consequences seem to
+follow, as in mathematics, from an essential proposition, or, in other
+words, from a proposition involved in the meaning of a name, what they
+really flow from is the tacit assumption of the real existence of the
+objects so named. Apart from this assumption of real existence, the
+class of propositions in which the predicate is of the essence of the
+subject <span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span>(that is, in which the predicate connotes the whole or part of
+what the subject connotes, but nothing besides) answer no purpose but
+that of unfolding the whole or some part of the meaning of the name, to
+those who did not previously know it. Accordingly, the most useful, and
+in strictness the only useful kind of essential propositions, are
+Definitions: which, to be complete, should unfold the whole of what is
+involved in the meaning of the word defined; that is, (when it is a
+connotative word,) the whole of what it connotes. In defining a name,
+however, it is not usual to specify its entire connotation, but so much
+only as is sufficient to mark out the objects usually denoted by it from
+all other known objects. And sometimes a merely accidental property, not
+involved in the meaning of the name, answers this purpose equally well.
+The various kinds of definition which these distinctions give rise to,
+and the purposes to which they are respectively subservient, will be
+minutely considered in the proper place.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VI_3">� 3.</a> According to the above view of essential propositions, no
+proposition can be reckoned such which relates to an individual by name,
+that is, in which the subject is a proper name. Individuals have no
+essences. When the schoolmen talked of the essence of an individual,
+they did not mean the properties implied in its name, for the names of
+individuals imply no properties. They regarded as of the essence of an
+individual, whatever was of the essence of the species in which they
+were accustomed to place that individual; <i>i.e.</i> of the class to which
+it was most familiarly referred, and to which, therefore, they conceived
+that it by nature belonged. Thus, because the proposition Man is a
+rational being, was an essential proposition, they affirmed the same
+thing of the proposition, Julius C�sar is a rational being. This
+followed very naturally if genera and species were to be considered as
+entities, distinct from, but <i>inhering</i> in, the individuals composing
+them. If <i>man</i> was a substance inhering in each individual man, the
+<i>essence</i> of man (whatever that might mean) was naturally supposed to
+accompany it; to inhere in John Thompson, and to form the <i>common
+essence</i> of Thompson and Julius C�sar. It might then be <span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>fairly said,
+that rationality, being of the essence of Man, was of the essence also
+of Thompson. But if Man altogether be only the individual men and a name
+bestowed upon them in consequence of certain common properties, what
+becomes of John Thompson's essence?</p>
+
+<p>A fundamental error is seldom expelled from philosophy by a single
+victory. It retreats slowly, defends every inch of ground, and often,
+after it has been driven from the open country, retains a footing in
+some remote fastness. The essences of individuals were an unmeaning
+figment arising from a misapprehension of the essences of classes, yet
+even Locke, when he extirpated the parent error, could not shake himself
+free from that which was its fruit. He distinguished two sorts of
+essences, Real and Nominal. His nominal essences were the essences of
+classes, explained nearly as we have now explained them. Nor is anything
+wanting to render the third book of Locke's Essay a nearly
+unexceptionable treatise on the connotation of names, except to free its
+language from the assumption of what are called Abstract Ideas, which
+unfortunately is involved in the phraseology, though not necessarily
+connected with the thoughts contained in that immortal Third Book.<a name="FNanchor_24_30" id="FNanchor_24_30"></a><a href="#Footnote_24_30" class="fnanchor">[24]</a>
+But, besides nominal essences, he admitted real essences, or essences of
+individual objects, which he supposed to be the causes of the sensible
+properties of those objects. We know not (said he) what these are; (and
+this acknowledgment rendered the fiction comparatively innocuous;) but
+if we did, we could, from them alone, demonstrate the sensible
+properties of the object, as the properties of the triangle are
+<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>demonstrated from the definition of the triangle. I shall have occasion
+to revert to this theory in treating of Demonstration, and of the
+conditions under which one property of a thing admits of being
+demonstrated from another property. It is enough here to remark that,
+according to this definition, the real essence of an object has, in the
+progress of physics, come to be conceived as nearly equivalent, in the
+case of bodies, to their corpuscular structure: what it is now supposed
+to mean in the case of any other entities, I would not take upon myself
+to define.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VI_4">� 4.</a> An essential proposition, then, is one which is purely verbal;
+which asserts of a thing under a particular name, only what is asserted
+of it in the fact of calling it by that name; and which therefore either
+gives no information, or gives it respecting the name, not the thing.
+Non-essential, or accidental propositions, on the contrary, may be
+called Real Propositions, in opposition to Verbal. They predicate of a
+thing some fact not involved in the signification of the name by which
+the proposition speaks of it; some attribute not connoted by that name.
+Such are all propositions concerning things individually designated, and
+all general or particular propositions in which the predicate connotes
+any attribute not connoted by the subject. All these, if true, add to
+our knowledge: they convey information, not already involved in the
+names employed. When I am told that all, or even that some objects,
+which have certain qualities, or which stand in certain relations, have
+also certain other qualities, or stand in certain other relations, I
+learn from this proposition a new fact; a fact not included in my
+knowledge of the meaning of the words, nor even of the existence of
+Things answering to the signification of those words. It is this class
+of propositions only which are in themselves instructive, or from which
+any instructive propositions can be inferred.<a name="FNanchor_25_31" id="FNanchor_25_31"></a><a href="#Footnote_25_31" class="fnanchor">[25]</a></p>
+
+<p><span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span></p><p>Nothing has probably contributed more to the opinion so long prevalent
+of the futility of the school logic, than the circumstance that almost
+all the examples used in the common school books to illustrate the
+doctrine of predication and that of the syllogism, consist of essential
+propositions. They were usually taken either from the branches or from
+the main trunk of the Predicamental Tree, which included nothing but
+what was of the <i>essence</i> of the species: <i>Omne corpus est substantia</i>,
+<i>Omne animal est corpus</i>, <i>Omnis homo est corpus</i>, <i>Omnis homo est
+animal</i>, <i>Omnis homo est rationalis</i>, and so forth. It is far from
+wonderful that the syllogistic art should have been thought to be of no
+use in assisting correct reasoning, when almost the only propositions
+which, in the hands of its professed teachers, it was employed to prove,
+were such as every one assented to without proof the moment he
+comprehended the meaning of the words; and stood exactly on a level, in
+point of evidence, with the premises from which they were drawn. I have,
+therefore, throughout this work, avoided the employment of essential
+propositions as examples, except where the nature of the principle to be
+illustrated specifically required them.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VI_5">� 5.</a> With respect to propositions which do convey information&mdash;which
+assert something of a Thing, under a name that does not already
+presuppose what is about to be asserted; there are two different aspects
+in which these, or rather such of them as are general propositions, may
+be considered: we may either look at them as portions of speculative
+truth, or as memoranda for practical use. According as we consider
+propositions in one or the other of these lights, their import may be
+conveniently expressed in one or in the other of two formulas.</p>
+
+<p>According to the formula which we have hitherto employed, and which is
+best adapted to express the import of the proposition as a portion of
+our theoretical knowledge, All men are mortal, means that the attributes
+of man are always accompanied by the attribute mortality: No men are
+gods, means that the attributes of man are never accompanied by <span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span>the
+attributes, or at least never by all the attributes, signified by the
+word god. But when the proposition is considered as a memorandum for
+practical use, we shall find a different mode of expressing the same
+meaning better adapted to indicate the office which the proposition
+performs. The practical use of a proposition is, to apprise or remind us
+what we have to expect, in any individual case which comes within the
+assertion contained in the proposition. In reference to this purpose,
+the proposition, All men are mortal, means that the attributes of man
+are <i>evidence of</i>, are a <i>mark</i> of, mortality; an indication by which
+the presence of that attribute is made manifest. No men are gods, means
+that the attributes of man are a mark or evidence that some or all of
+the attributes understood to belong to a god are not there; that where
+the former are, we need not expect to find the latter.</p>
+
+<p>These two forms of expression are at bottom equivalent; but the one
+points the attention more directly to what a proposition means, the
+latter to the manner in which it is to be used.</p>
+
+<p>Now it is to be observed that Reasoning (the subject to which we are
+next to proceed) is a process into which propositions enter not as
+ultimate results, but as means to the establishment of other
+propositions. We may expect, therefore, that the mode of exhibiting the
+import of a general proposition which shows it in its application to
+practical use, will best express the function which propositions perform
+in Reasoning. And accordingly, in the theory of Reasoning, the mode of
+viewing the subject which considers a Proposition as asserting that one
+fact or phenomenon is a <i>mark</i> or <i>evidence</i> of another fact or
+phenomenon, will be found almost indispensable. For the purposes of that
+Theory, the best mode of defining the import of a proposition is not the
+mode which shows most clearly what it is in itself, but that which most
+distinctly suggests the manner in which it may be made available for
+advancing from it to other propositions.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_VII" id="BOOK_I_CHAPTER_VII"></a>CHAPTER VII.<br />
+
+OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_1">� 1.</a> In examining into the nature of general propositions, we have
+adverted much less than is usual with logicians to the ideas of a Class,
+and Classification; ideas which, since the Realist doctrine of General
+Substances went out of vogue, have formed the basis of almost every
+attempt at a philosophical theory of general terms and general
+propositions. We have considered general names as having a meaning,
+quite independently of their being the names of classes. That
+circumstance is in truth accidental, it being wholly immaterial to the
+signification of the name whether there are many objects, or only one,
+to which it happens to be applicable, or whether there be any at all.
+God is as much a general term to the Christian or Jew as to the
+Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much
+so as if real objects existed, corresponding to those names. Every name
+the signification of which is constituted by attributes, is potentially
+a name of an indefinite number of objects; but it needs not be actually
+the name of any; and if of any, it may be the name of only one. As soon
+as we employ a name to connote attributes, the things, be they more or
+fewer, which happen to possess those attributes, are constituted <i>ipso
+facto</i> a class. But in predicating the name we predicate only the
+attributes; and the fact of belonging to a class does not, in many
+cases, come into view at all.</p>
+
+<p>Although, however, Predication does not presuppose Classification, and
+though the theory of Names and of Propositions is not cleared up, but
+only encumbered, by intruding the idea of classification into it, there
+is nevertheless a close connexion between Classification and the
+employment of General Names. <span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span>By every general name which we introduce,
+we create a class, if there be any things, real or imaginary, to compose
+it; that is, any Things corresponding to the signification of the name.
+Classes, therefore, mostly owe their existence to general language. But
+general language, also, though that is not the most common case,
+sometimes owes its existence to classes. A general, which is as much as
+to say a significant, name, is indeed mostly introduced because we have
+a signification to express by it; because we need a word by means of
+which to predicate the attributes which it connotes. But it is also true
+that a name is sometimes introduced because we have found it convenient
+to create a class; because we have thought it useful for the regulation
+of our mental operations, that a certain group of objects should be
+thought of together. A naturalist, for purposes connected with his
+particular science, sees reason to distribute the animal or vegetable
+creation into certain groups rather than into any others, and he
+requires a name to bind, as it were, each of his groups together. It
+must not however be supposed that such names, when introduced, differ in
+any respect, as to their mode of signification, from other connotative
+names. The classes which they denote are, as much as any other classes,
+constituted by certain common attributes, and their names are
+significant of those attributes, and of nothing else. The names of
+Cuvier's classes and orders, <i>Plantigrades</i>, <i>Digitigrades</i>, &amp;c., are as
+much the expression of attributes as if those names had preceded,
+instead of grown out of, his classification of animals. The only
+peculiarity of the case is, that the convenience of classification was
+here the primary motive for introducing the names; while in other cases
+the name is introduced as a means of predication, and the formation of a
+class denoted by it is only an indirect consequence.</p>
+
+<p>The principles which ought to regulate Classification as a logical
+process subservient to the investigation of truth, cannot be discussed
+to any purpose until a much later stage of our inquiry. But, of
+Classification as resulting from, and implied in, the fact of employing
+general language, we cannot forbear to treat here, without leaving the
+theory of general names <span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span>and of their employment in predication,
+mutilated and formless.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_2">� 2.</a> This portion of the theory of general language is the subject of
+what is termed the doctrine of the Predicables; a set of distinctions
+handed down from Aristotle, and his follower Porphyry, many of which
+have taken a firm root in scientific, and some of them even in popular,
+phraseology. The predicables are a five-fold division of General Names,
+not grounded as usual on a difference in their meaning, that is, in the
+attribute which they connote, but on a difference in the kind of class
+which they denote. We may predicate of a thing five different varieties
+of class-name:&mdash;</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">A <i>genus</i> of the thing</td><td align="left">(<i>&#947;&#8050;&#957;&#959;&#962;</i>).</td></tr>
+<tr><td align="left">A <i>species</i></td><td align="left">(<i>&#949;&#7990;&#948;&#959;&#962;</i>).</td></tr>
+<tr><td align="left">A <i>differentia</i></td><td align="left">(<i>&#948;&#953;&#945;&#966;&#959;&#961;&#8048;</i>).</td></tr>
+<tr><td align="left">A <i>proprium</i></td><td align="left">(<i>&#7988;&#948;&#953;&#8057;&#957;</i>).</td></tr>
+<tr><td align="left">An <i>accidens</i></td><td align="left">(<i>&#963;&#965;&#956;&#946;&#949;&#946;&#951;&#954;&#8057;&#962;</i>).</td></tr>
+</table></div>
+
+<p>It is to be remarked of these distinctions, that they express, not what
+the predicate is in its own meaning, but what relation it bears to the
+subject of which it happens on the particular occasion to be predicated.
+There are not some names which are exclusively genera, and others which
+are exclusively species, or differenti�; but the same name is referred
+to one or another predicable, according to the subject of which it is
+predicated on the particular occasion. <i>Animal</i>, for instance, is a
+genus with respect to man, or John; a species with respect to Substance,
+or Being. <i>Rectangular</i> is one of the Differenti� of a geometrical
+square; it is merely one of the Accidentia of the table at which I am
+writing. The words genus, species, &amp;c. are therefore relative terms;
+they are names applied to certain predicates, to express the relation
+between them and some given subject: a relation grounded, as we shall
+see, not on what the predicate connotes, but on the class which it
+denotes, and on the place which, in some given classification, that
+class occupies relatively to the particular subject.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_3">� 3.</a> Of these five names, two, Genus and Species, are <span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span>not only used by
+naturalists in a technical acceptation not precisely agreeing with their
+philosophical meaning, but have also acquired a popular acceptation,
+much more general than either. In this popular sense any two classes,
+one of which includes the whole of the other and more, may be called a
+Genus and a Species. Such, for instance, are Animal and Man; Man and
+Mathematician. Animal is a Genus; Man and Brute are its two species; or
+we may divide it into a greater number of species, as man, horse, dog,
+&amp;c. <i>Biped</i>, or <i>two-footed animal</i>, may also be considered a genus, of
+which man and bird are two species. <i>Taste</i> is a genus, of which sweet
+taste, sour taste, salt taste, &amp;c. are species. <i>Virtue</i> is a genus;
+justice, prudence, courage, fortitude, generosity, &amp;c. are its species.</p>
+
+<p>The same class which is a genus with reference to the sub-classes or
+species included in it, may be itself a species with reference to a more
+comprehensive, or, as it is often called, a superior genus. Man is a
+species with reference to animal, but a genus with reference to the
+species Mathematician. Animal is a genus, divided into two species, man
+and brute; but animal is also a species, which, with another species,
+vegetable, makes up the genus, organized being. Biped is a genus with
+reference to man and bird, but a species with respect to the superior
+genus, animal. Taste is a genus divided into species, but also a species
+of the genus sensation. Virtue, a genus with reference to justice,
+temperance, &amp;c., is one of the species of the genus, mental quality.</p>
+
+<p>In this popular sense the words Genus and Species have passed into
+common discourse. And it should be observed that in ordinary parlance,
+not the name of the class, but the class itself, is said to be the genus
+or species; not, of course, the class in the sense of each individual of
+the class, but the individuals collectively, considered as an aggregate
+whole; the name by which the class is designated being then called not
+the genus or species, but the generic or specific name. And this is an
+admissible form of expression; nor is it of any importance which of the
+two modes of speaking we adopt, provided <span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span>the rest of our language is
+consistent with it; but, if we call the class itself the genus, we must
+not talk of predicating the genus. We predicate of man the <i>name</i>
+mortal; and by predicating the name, we may be said, in an intelligible
+sense, to predicate what the name expresses, the <i>attribute</i> mortality;
+but in no allowable sense of the word predication do we predicate of man
+the <i>class</i> mortal. We predicate of him the fact of belonging to the
+class.</p>
+
+<p>By the Aristotelian logicians, the terms genus and species were used in
+a more restricted sense. They did not admit every class which could be
+divided into other classes to be a genus, or every class which could be
+included in a larger class to be a species. Animal was by them
+considered a genus; man and brute co-ordinate species under that genus:
+<i>biped</i>, however, would not have been admitted to be a genus with
+reference to man, but a <i>proprium</i> or <i>accidens</i> only. It was requisite,
+according to their theory, that genus and species should be of the
+<i>essence</i> of the subject. Animal was of the essence of man; biped was
+not. And in every classification they considered some one class as the
+lowest or <i>infima</i> species. Man, for instance, was a lowest species. Any
+further divisions into which the class might be capable of being broken
+down, as man into white, black, and red man, or into priest and layman,
+they did not admit to be species.</p>
+
+<p>It has been seen, however, in the preceding chapter, that the
+distinction between the essence of a class, and the attributes or
+properties which are not of its essence&mdash;a distinction which has given
+occasion to so much abstruse speculation, and to which so mysterious a
+character was formerly, and by many writers is still, attached,&mdash;amounts
+to nothing more than the difference between those attributes of the
+class which are, and those which are not, involved in the signification
+of the class-name. As applied to individuals, the word Essence, we
+found, has no meaning, except in connexion with the exploded tenets of
+the Realists; and what the schoolmen chose to call the essence of an
+individual, was simply the essence of the class to which that individual
+was most familiarly referred.</p>
+
+<p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span></p><p>Is there no difference, then, save this merely verbal one, between the
+classes which the schoolmen admitted to be genera or species, and those
+to which they refused the title? Is it an error to regard some of the
+differences which exist among objects as differences <i>in kind</i> (<i>genere</i>
+or <i>specie</i>), and others only as differences in the accidents? Were the
+schoolmen right or wrong in giving to some of the classes into which
+things may be divided, the name of <i>kinds</i>, and considering others as
+secondary divisions, grounded on differences of a comparatively
+superficial nature? Examination will show that the Aristotelians did
+mean something by this distinction, and something important; but which,
+being but indistinctly conceived, was inadequately expressed by the
+phraseology of essences, and the various other modes of speech to which
+they had recourse.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_4">� 4.</a> It is a fundamental principle in logic, that the power of framing
+classes is unlimited, as long as there is any (even the smallest)
+difference to found a distinction upon. Take any attribute whatever, and
+if some things have it, and others have not, we may ground on the
+attribute a division of all things into two classes; and we actually do
+so, the moment we create a name which connotes the attribute. The number
+of possible classes, therefore, is boundless; and there are as many
+actual classes (either of real or of imaginary things) as there are
+general names, positive and negative together.</p>
+
+<p>But if we contemplate any one of the classes so formed, such as the
+class animal or plant, or the class sulphur or phosphorus, or the class
+white or red, and consider in what particulars the individuals included
+in the class differ from those which do not come within it, we find a
+very remarkable diversity in this respect between some classes and
+others. There are some classes, the things contained in which differ
+from other things only in certain particulars which may be numbered,
+while others differ in more than can be numbered, more even than we need
+ever expect to know. Some classes have little or nothing in common to
+characterize them by, except <span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span>precisely what is connoted by the name:
+white things, for example, are not distinguished by any common
+properties, except whiteness; or if they are, it is only by such as are
+in some way dependent on, or connected with, whiteness. But a hundred
+generations have not exhausted the common properties of animals or of
+plants, of sulphur or of phosphorus; nor do we suppose them to be
+exhaustible, but proceed to new observations and experiments, in the
+full confidence of discovering new properties which were by no means
+implied in those we previously knew. While, if any one were to propose
+for investigation the common properties of all things which are of the
+same colour, the same shape, or the same specific gravity, the absurdity
+would be palpable. We have no ground to believe that any such common
+properties exist, except such as may be shown to be involved in the
+supposition itself, or to be derivable from it by some law of causation.
+It appears, therefore, that the properties, on which we ground our
+classes, sometimes exhaust all that the class has in common, or contain
+it all by some mode of implication; but in other instances we make a
+selection of a few properties from among not only a greater number, but
+a number inexhaustible by us, and to which as we know no bounds, they
+may, so far as we are concerned, be regarded as infinite.</p>
+
+<p>There is no impropriety in saying that, of these two classifications,
+the one answers to a much more radical distinction in the things
+themselves, than the other does. And if any one even chooses to say that
+the one classification is made by nature, the other by us for our
+convenience, he will be right; provided he means no more than this:
+Where a certain apparent difference between things (though perhaps in
+itself of little moment) answers to we know not what number of other
+differences, pervading not only their known properties, but properties
+yet undiscovered, it is not optional but imperative to recognise this
+difference as the foundation of a specific distinction; while, on the
+contrary, differences that are merely finite and determinate, like those
+designated by the words white, black, or red, may be disregarded if the
+purpose for which the classification is made does not require attention
+<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>to those particular properties. The differences, however, are made by
+nature, in both cases; while the recognition of those differences as
+grounds of classification and of naming, is, equally in both cases, the
+act of man: only in the one case, the ends of language and of
+classification would be subverted if no notice were taken of the
+difference, while in the other case, the necessity of taking notice of
+it depends on the importance or unimportance of the particular qualities
+in which the difference happens to consist.</p>
+
+<p>Now, these classes, distinguished by unknown multitudes of properties,
+and not solely by a few determinate ones&mdash;which are parted off from one
+another by an unfathomable chasm, instead of a mere ordinary ditch with
+a visible bottom&mdash;are the only classes which, by the Aristotelian
+logicians, were considered as genera or species. Differences which
+extended only to a certain property or properties, and there terminated,
+they considered as differences only in the <i>accidents</i> of things; but
+where any class differed from other things by an infinite series of
+differences, known and unknown, they considered the distinction as one
+of <i>kind</i>, and spoke of it as being an <i>essential</i> difference, which is
+also one of the current meanings of that vague expression at the present
+day.</p>
+
+<p>Conceiving the schoolmen to have been justified in drawing a broad line
+of separation between these two kinds of classes and of
+class-distinctions, I shall not only retain the division itself, but
+continue to express it in their language. According to that language,
+the proximate (or lowest) Kind to which any individual is referrible, is
+called its species. Conformably to this, Sir Isaac Newton would be said
+to be of the species man. There are indeed numerous sub-classes included
+in the class man, to which Newton also belongs; for example, Christian,
+and Englishman, and Mathematician. But these, though distinct classes,
+are not, in our sense of the term, distinct Kinds of men. A Christian,
+for example, differs from other human beings; but he differs only in the
+attribute which the word expresses, namely, belief in Christianity, and
+whatever else that implies, either as involved in the fact itself, or
+connected with it through some law of cause and effect. We <span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span>should never
+think of inquiring what properties, unconnected with Christianity either
+as cause or effect, are common to all Christians and peculiar to them;
+while in regard to all Men, physiologists are perpetually carrying on
+such an inquiry; nor is the answer ever likely to be completed. Man,
+therefore, we may call a species; Christian, or Mathematician, we
+cannot.</p>
+
+<p>Note here, that it is by no means intended to imply that there may not
+be different Kinds, or logical species, of man. The various races and
+temperaments, the two sexes, and even the various ages, may be
+differences of kind, within our meaning of the term. I do not say that
+they are so. For in the progress of physiology it may almost be said to
+be made out, that the differences which really exist between different
+races, sexes, &amp;c., follow as consequences, under laws of nature, from a
+small number of primary differences which can be precisely determined,
+and which, as the phrase is, <i>account for</i> all the rest. If this be so,
+these are not distinctions in kind; no more than Christian, Jew,
+Mussulman, and Pagan, a difference which also carries many consequences
+along with it. And in this way classes are often mistaken for real
+Kinds, which are afterwards proved not to be so. But if it turned out
+that the differences were not capable of being thus accounted for, then
+Caucasian, Mongolian, Negro, &amp;c. would be really different Kinds of
+human beings, and entitled to be ranked as species by the logician;
+though not by the naturalist. For (as already noticed) the word species
+is used in a different signification in logic and in natural history. By
+the naturalist, organized beings are not usually said to be of different
+species, if it is supposed that they could possibly have descended from
+the same stock. That, however, is a sense artificially given to the
+word, for the technical purposes of a particular science. To the
+logician, if a negro and a white man differ in the same manner (however
+less in degree) as a horse and a camel do, that is, if their differences
+are inexhaustible, and not referrible to any common cause, they are
+different species, whether they are descended from common ancestors or
+not. But if their differences can all be traced to climate and habits,
+or to some <span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span>one or a few special differences in structure, they are not,
+in the logician's view, specially distinct.</p>
+
+<p>When the <i>infima species</i>, or proximate Kind, to which an individual
+belongs, has been ascertained, the properties common to that Kind
+include necessarily the whole of the common properties of every other
+real Kind to which the individual can be referrible. Let the individual,
+for example, be Socrates, and the proximate Kind, man. Animal, or living
+creature, is also a real Kind, and includes Socrates; but, since it
+likewise includes man, or in other words, since all men are animals, the
+properties common to animals form a portion of the common properties of
+the sub-class, man. And if there be any class which includes Socrates
+without including man, that class is not a real Kind. Let the class for
+example, be <i>flat-nosed</i>; that being a class which includes Socrates,
+without including all men. To determine whether it is a real Kind, we
+must ask ourselves this question: Have all flat-nosed animals, in
+addition to whatever is implied in their flat noses, any common
+properties, other than those which are common to all animals whatever?
+If they had; if a flat nose were a mark or index to an indefinite number
+of other peculiarities, not deducible from the former by an
+ascertainable law, then out of the class man we might cut another class,
+flat-nosed man, which according to our definition, would be a Kind. But
+if we could do this, man would not be, as it was assumed to be, the
+proximate Kind. Therefore, the properties of the proximate Kind do
+comprehend those (whether known or unknown) of all other Kinds to which
+the individual belongs; which was the point we undertook to prove. And
+hence, every other Kind which is predicable of the individual, will be
+to the proximate Kind in the relation of a genus, according to even the
+popular acceptation of the terms genus and species; that is, it will be
+a larger class, including it and more.</p>
+
+<p>We are now able to fix the logical meaning of these terms. Every class
+which is a real Kind, that is, which is distinguished from all other
+classes by an indeterminate multitude of properties not derivable from
+one another, is either a genus or a species. A Kind which is not
+divisible into other Kinds, <span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>cannot be a genus, because it has no
+species under it; but it is itself a species, both with reference to the
+individuals below and to the genera above (Species Pr�dicabilis and
+Species Subjicibilis.) But every Kind which admits of division into real
+Kinds (as animal into mammal, bird, fish, &amp;c., or bird into various
+species of birds) is a genus to all below it, a species to all genera in
+which it is itself included. And here we may close this part of the
+discussion, and pass to the three remaining predicables, Differentia,
+Proprium, and Accidens.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_5">� 5.</a> To begin with Differentia. This word is correlative with the words
+genus and species, and as all admit, it signifies the attribute which
+distinguishes a given species from every other species of the same
+genus. This is so far clear: but we may still ask, which of the
+distinguishing attributes it signifies. For we have seen that every Kind
+(and a species must be a Kind) is distinguished from other Kinds not by
+any one attribute, but by an indefinite number. Man, for instance, is a
+species of the genus animal: Rational (or rationality, for it is of no
+consequence here whether we use the concrete or the abstract form) is
+generally assigned by logicians as the Differentia; and doubtless this
+attribute serves the purpose of distinction: but it has also been
+remarked of man, that he is a cooking animal; the only animal that
+dresses its food. This, therefore, is another of the attributes by which
+the species man is distinguished from other species of the same genus:
+would this attribute serve equally well for a differentia? The
+Aristotelians say No; having laid it down that the differentia must,
+like the genus and species, be of the <i>essence</i> of the subject.</p>
+
+<p>And here we lose even that vestige of a meaning grounded in the nature
+of the things themselves, which may be supposed to be attached to the
+word essence when it is said that genus and species must be of the
+essence of the thing. There can be no doubt that when the schoolmen
+talked of the essences of things as opposed to their accidents, they had
+confusedly in view the distinction between differences of kind, <span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>and the
+differences which are not of kind; they meant to intimate that genera
+and species must be Kinds. Their notion of the essence of a thing was a
+vague notion of a something which makes it what it is, <i>i. e.</i> which
+makes it the Kind of thing that it is&mdash;which causes it to have all that
+variety of properties which distinguish its Kind. But when the matter
+came to be looked at more closely, nobody could discover what caused the
+thing to have all those properties, nor even that there was anything
+which caused it to have them. Logicians, however, not liking to admit
+this, and being unable to detect what made the thing to be what it was,
+satisfied themselves with what made it to be what it was called. Of the
+innumerable properties, known and unknown, that are common to the class
+man, a portion only, and of course a very small portion, are connoted by
+its name; these few, however, will naturally have been thus
+distinguished from the rest either for their greater obviousness, or for
+greater supposed importance. These properties, then, which were connoted
+by the name, logicians seized upon, and called them the essence of the
+species; and not stopping there, they affirmed them, in the case of the
+<i>infima species</i>, to be the essence of the individual too; for it was
+their maxim, that the species contained the "whole essence" of the
+thing. Metaphysics, that fertile field of delusion propagated by
+language, does not afford a more signal instance of such delusion. On
+this account it was that rationality, being connoted by the name man,
+was allowed to be a differentia of the class; but the peculiarity of
+cooking their food, not being connoted, was relegated to the class of
+accidental properties.</p>
+
+<p>The distinction, therefore, between Differentia, Proprium, and Accidens,
+is not grounded in the nature of things, but in the connotation of
+names; and we must seek it there, if we wish to find what it is.</p>
+
+<p>From the fact that the genus includes the species, in other words
+<i>de</i>notes more than the species, or is predicable of a greater number of
+individuals, it follows that the species must connote more than the
+genus. It must connote all the attributes which the genus connotes, or
+there would be nothing <span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span>to prevent it from denoting individuals not
+included in the genus. And it must connote something besides, otherwise
+it would include the whole genus. Animal denotes all the individuals
+denoted by man, and many more. Man, therefore, must connote all that
+animal connotes, otherwise there might be men who are not animals; and
+it must connote something more than animal connotes, otherwise all
+animals would be men. This surplus of connotation&mdash;this which the
+species connotes over and above the connotation of the genus&mdash;is the
+Differentia, or specific difference; or, to state the same proposition
+in other words, the Differentia is that which must be added to the
+connotation of the genus, to complete the connotation of the species.</p>
+
+<p>The word man, for instance, exclusively of what it connotes in common
+with animal, also connotes rationality, and at least some approximation
+to that external form which we all know, but which as we have no name
+for it considered in itself, we are content to call the human. The
+Differentia, or specific difference, therefore, of man, as referred to
+the genus animal, is that outward form and the possession of reason. The
+Aristotelians said, the possession of reason, without the outward form.
+But if they adhered to this, they would have been obliged to call the
+Houyhnhnms men. The question never arose, and they were never called
+upon to decide how such a case would have affected their notion of
+essentiality. However this may be, they were satisfied with taking such
+a portion of the differentia as sufficed to distinguish the species from
+all other <i>existing</i> things, though by so doing they might not exhaust
+the connotation of the name.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_6">� 6.</a> And here, to prevent the notion of differentia from being
+restricted within too narrow limits, it is necessary to remark, that a
+species, even as referred to the same genus, will not always have the
+same differentia, but a different one, according to the principle and
+purpose which preside over the particular classification. For example, a
+naturalist surveys the various kinds of animals, and looks out for the
+classification of them most in accordance with the order in which, for
+<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span>zoological purposes, he considers it desirable that we should think of
+them. With this view he finds it advisable that one of his fundamental
+divisions should be into warm-blooded and cold-blooded animals; or into
+animals which breathe with lungs and those which breathe with gills; or
+into carnivorous, and frugivorous or graminivorous; or into those which
+walk on the flat part and those which walk on the extremity of the foot,
+a distinction on which two of Cuvier's families are founded. In doing
+this, the naturalist creates as many new classes; which are by no means
+those to which the individual animal is familiarly and spontaneously
+referred; nor should we ever think of assigning to them so prominent a
+position in our arrangement of the animal kingdom, unless for a
+preconceived purpose of scientific convenience. And to the liberty of
+doing this there is no limit. In the examples we have given, most of the
+classes are real Kinds, since each of the peculiarities is an index to a
+multitude of properties belonging to the class which it characterizes:
+but even if the case were otherwise&mdash;if the other properties of those
+classes could all be derived, by any process known to us, from the one
+peculiarity on which the class is founded&mdash;even then, if these
+derivative properties were of primary importance for the purposes of the
+naturalist, he would be warranted in founding his primary divisions on
+them.</p>
+
+<p>If, however, practical convenience is a sufficient warrant for making
+the main demarcations in our arrangement of objects run in lines not
+coinciding with any distinction of Kind, and so creating genera and
+species in the popular sense which are not genera or species in the
+rigorous sense at all, <i>� fortiori</i> must we be warranted, when our
+genera and species <i>are</i> real genera and species, in marking the
+distinction between them by those of their properties which
+considerations of practical convenience most strongly recommend. If we
+cut a species out of a given genus&mdash;the species man, for instance, out
+of the genus animal&mdash;with an intention on our part that the peculiarity
+by which we are to be guided in the application of the name man should
+be rationality, then rationality is the differentia of the species <span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>man.
+Suppose, however, that being naturalists, we, for the purposes of our
+particular study, cut out of the genus animal the same species man, but
+with an intention that the distinction between man and all other species
+of animal should be, not rationality, but the possession of "four
+incisors in each jaw, tusks solitary, and erect posture." It is evident
+that the word man, when used by us as naturalists, no longer connotes
+rationality, but connotes the three other properties specified; for that
+which we have expressly in view when we impose a name, assuredly forms
+part of the meaning of that name. We may, therefore, lay it down as a
+maxim, that wherever there is a Genus, and a Species marked out from
+that genus by an assignable differentia, the name of the species must be
+connotative, and must connote the differentia; but the connotation may
+be special&mdash;not involved in the signification of the term as ordinarily
+used, but given to it when employed as a term of art or science. The
+word Man in common use, connotes rationality and a certain form, but
+does not connote the number or character of the teeth; in the Linn�an
+system it connotes the number of incisor and canine teeth, but does not
+connote rationality nor any particular form. The word <i>man</i> has,
+therefore, two different meanings; though not commonly considered as
+ambiguous, because it happens in both cases to <i>de</i>note the same
+individual objects. But a case is conceivable in which the ambiguity
+would become evident: we have only to imagine that some new kind of
+animal were discovered, having Linn�us's three characteristics of
+humanity, but not rational, or not of the human form. In ordinary
+parlance, these animals would not be called men; but in natural history
+they must still be called so by those, if any there be, who adhere to
+the Linn�an classification; and the question would arise, whether the
+word should continue to be used in two senses, or the classification be
+given up, and the technical sense of the term be abandoned along with
+it.</p>
+
+<p>Words not otherwise connotative may, in the mode just adverted to,
+acquire a special or technical connotation. Thus the word whiteness, as
+we have so often remarked, connotes <span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span>nothing; it merely denotes the
+attribute corresponding to a certain sensation: but if we are making a
+classification of colours, and desire to justify, or even merely to
+point out, the particular place assigned to whiteness in our
+arrangement, we may define it "the colour produced by the mixture of all
+the simple rays;" and this fact, though by no means implied in the
+meaning of the word whiteness as ordinarily used, but only known by
+subsequent scientific investigation, is part of its meaning in the
+particular essay or treatise, and becomes the differentia of the
+species.<a name="FNanchor_26_32" id="FNanchor_26_32"></a><a href="#Footnote_26_32" class="fnanchor">[26]</a></p>
+
+<p>The differentia, therefore, of a species may be defined to be, that part
+of the connotation of the specific name, whether ordinary or special and
+technical, which distinguishes the species in question from all other
+species of the genus to which on the particular occasion we are
+referring it.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_7">� 7.</a> Having disposed of Genus, Species, and Differentia, we shall not
+find much difficulty in attaining a clear conception of the distinction
+between the other two predicables, as well as between them and the first
+three.</p>
+
+<p>In the Aristotelian phraseology, Genus and Differentia are of the
+<i>essence</i> of the subject; by which, as we have seen, is really meant
+that the properties signified by the genus and those signified by the
+differentia, form part of the connotation of the name denoting the
+species. Proprium and Accidens, on the other hand, form no part of the
+essence, but are predicated of the species only <i>accidentally</i>. Both are
+Accidents, in the wider sense in which the accidents of a thing are
+opposed to its essence; though, in the doctrine of the Predicables,
+Accidens is used for one sort of accident only, Proprium being another
+sort. Proprium, continue the schoolmen, is predicated <i>accidentally</i>,
+indeed, but <i>necessarily</i>; <span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span>or, as they further explain it, signifies an
+attribute which is not indeed part of the essence, but which flows from,
+or is a consequence of, the essence, and is, therefore, inseparably
+attached to the species; <i>e. g.</i> the various properties of a triangle,
+which, though no part of its definition, must necessarily be possessed
+by whatever comes under that definition. Accidens, on the contrary, has
+no connexion whatever with the essence, but may come and go, and the
+species still remain what it was before. If a species could exist
+without its Propria, it must be capable of existing without that on
+which its Propria are necessarily consequent, and therefore without its
+essence, without that which constitutes it a species. But an Accidens,
+whether separable or inseparable from the species in actual experience,
+may be supposed separated, without the necessity of supposing any other
+alteration; or at least, without supposing any of the essential
+properties of the species to be altered, since with them an Accidens has
+no connexion.</p>
+
+<p>A Proprium, therefore, of the species, may be defined, any attribute
+which belongs to all the individuals included in the species, and which,
+though not connoted by the specific name, (either ordinarily if the
+classification we are considering be for ordinary purposes, or specially
+if it be for a special purpose,) yet follows from some attribute which
+the name either ordinarily or specially connotes.</p>
+
+<p>One attribute may follow from another in two ways; and there are
+consequently two kinds of Proprium. It may follow as a conclusion
+follows premises, or it may follow as an effect follows a cause. Thus,
+the attribute of having the opposite sides equal, which is not one of
+those connoted by the word Parallelogram, nevertheless follows from
+those connoted by it, namely, from having the opposite sides straight
+lines and parallel, and the number of sides four. The attribute,
+therefore, of having the opposite sides equal, is a Proprium of the
+class parallelogram; and a Proprium of the first kind, which follows
+from the connoted attributes by way of <i>demonstration</i>. The attribute of
+being capable of understanding language, is a Proprium of the species
+man, since <span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span>without being connoted by the word, it follows from an
+attribute which the word does connote, viz. from the attribute of
+rationality. But this is a Proprium of the second kind, which follows by
+way of <i>causation</i>. How it is that one property of a thing follows, or
+can be inferred, from another; under what conditions this is possible,
+and what is the exact meaning of the phrase; are among the questions
+which will occupy us in the two succeeding Books. At present it needs
+only be said, that whether a Proprium follows by demonstration or by
+causation, it follows <i>necessarily</i>; that is to say, its not following
+would be inconsistent with some law which we regard as a part of the
+constitution either of our thinking faculty or of the universe.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VII_8">� 8.</a> Under the remaining predicable, Accidens, are included all
+attributes of a thing which are neither involved in the signification of
+the name (whether ordinarily or as a term of art), nor have, so far as
+we know, any necessary connexion with attributes which are so involved.
+They are commonly divided into Separable and Inseparable Accidents.
+Inseparable accidents are those which&mdash;although we know of no connexion
+between them and the attributes constitutive of the species, and
+although, therefore, so far as we are aware, they might be absent
+without making the name inapplicable and the species a different
+species&mdash;are yet never in fact known to be absent. A concise mode of
+expressing the same meaning is, that inseparable accidents are
+properties which are universal to the species, but not necessary to it.
+Thus, blackness is an attribute of a crow, and, as far as we know, an
+universal one. But if we were to discover a race of white birds, in
+other respects resembling crows, we should not say, These are not crows;
+we should say, These are white crows. Crow, therefore, does not connote
+blackness; nor, from any of the attributes which it does connote,
+whether as a word in popular use or as a term of art, could blackness be
+inferred. Not only, therefore, can we conceive a white crow, but we know
+of no reason why such an animal should not exist. Since, however, none
+but black crows are known to exist, blackness, in the present state of
+our <span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>knowledge, ranks as an accident, but an inseparable accident, of
+the species crow.</p>
+
+<p>Separable Accidents are those which are found, in point of fact, to be
+sometimes absent from the species; which are not only not necessary, but
+not even universal. They are such as do not belong to every individual
+of the species, but only to some individuals; or if to all, not at all
+times. Thus the colour of an European is one of the separable accidents
+of the species man, because it is not an attribute of all human
+creatures. Being born, is also (speaking in the logical sense) a
+separable accident of the species man, because, though an attribute of
+all human beings, it is so only at one particular time. <i>� fortiori</i>
+those attributes which are not constant even in the same individual, as,
+to be in one or in another place, to be hot or cold, sitting or walking,
+must be ranked as separable accidents.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span></p>
+<h3><a name="BOOK_I_CHAPTER_VIII" id="BOOK_I_CHAPTER_VIII"></a>CHAPTER VIII.<br />
+
+OF DEFINITION.</h3>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_1">� 1.</a> One necessary part of the theory of Names and of Propositions
+remains to be treated of in this place: the theory of Definitions. As
+being the most important of the class of propositions which we have
+characterized as purely verbal, they have already received some notice
+in the chapter preceding the last. But their fuller treatment was at
+that time postponed, because definition is so closely connected with
+classification, that, until the nature of the latter process is in some
+measure understood, the former cannot be discussed to much purpose.</p>
+
+<p>The simplest and most correct notion of a Definition is, a proposition
+declaratory of the meaning of a word; namely, either the meaning which
+it bears in common acceptation, or that which the speaker or writer, for
+the particular purposes of his discourse, intends to annex to it.</p>
+
+<p>The definition of a word being the proposition which enunciates its
+meaning, words which have no meaning are unsusceptible of definition.
+Proper names, therefore, cannot be defined. A proper name being a mere
+mark put upon an individual, and of which it is the characteristic
+property to be destitute of meaning, its meaning cannot of course be
+declared; though we may indicate by language, as we might indicate still
+more conveniently by pointing with the finger, upon what individual that
+particular mark has been, or is intended to be, put. It is no definition
+of "John Thomson" to say he is "the son of General Thomson;" for the
+name John Thomson does not express this. Neither is it any definition of
+"John Thomson" to say he is "the man now crossing the street." These
+propositions may serve to make known who is the particular man to whom
+the name belongs, but that may be done still more unambiguously by
+pointing to <span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span>him, which, however, has not been esteemed one of the modes
+of definition.</p>
+
+<p>In the case of connotative names, the meaning, as has been so often
+observed, is the connotation; and the definition of a connotative name,
+is the proposition which declares its connotation. This might be done
+either directly or indirectly. The direct mode would be by a proposition
+in this form: "Man" (or whatsoever the word may be) "is a name connoting
+such and such attributes," or "is a name which, when predicated of
+anything, signifies the possession of such and such attributes by that
+thing." Or thus: Man is everything which possesses such and such
+attributes: Man is everything which possesses corporeity, organization,
+life, rationality, and certain peculiarities of external form.</p>
+
+<p>This form of definition is the most precise and least equivocal of any;
+but it is not brief enough, and is besides too technical for common
+discourse. The more usual mode of declaring the connotation of a name,
+is to predicate of it another name or names of known signification,
+which connote the same aggregation of attributes. This may be done
+either by predicating of the name intended to be defined, another
+connotative name exactly synonymous, as, "Man is a human being," which
+is not commonly accounted a definition at all; or by predicating two or
+more connotative names, which make up among them the whole connotation
+of the name to be defined. In this last case, again, we may either
+compose our definition of as many connotative names as there are
+attributes, each attribute being connoted by one, as, Man is a
+corporeal, organized, animated, rational being, shaped so and so; or we
+may employ names which connote several of the attributes at once, as,
+Man is a rational <i>animal</i>, shaped so and so.</p>
+
+<p>The definition of a name, according to this view of it, is the sum total
+of all the <i>essential</i> propositions which can be framed with that name
+for their subject. All propositions the truth of which is implied in the
+name, all those which we are made aware of by merely hearing the name,
+are included in the definition, if complete, and may be evolved from it
+<span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span>without the aid of any other premises; whether the definition expresses
+them in two or three words, or in a larger number. It is, therefore, not
+without reason that Condillac and other writers have affirmed a
+definition to be an <i>analysis</i>. To resolve any complex whole into the
+elements of which it is compounded, is the meaning of analysis: and this
+we do when we replace one word which connotes a set of attributes
+collectively, by two or more which connote the same attributes singly,
+or in smaller groups.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_2">� 2.</a> From this, however, the question naturally arises, in what manner
+are we to define a name which connotes only a single attribute: for
+instance, "white," which connotes nothing but whiteness; "rational,"
+which connotes nothing but the possession of reason. It might seem that
+the meaning of such names could only be declared in two ways; by a
+synonymous term, if any such can be found; or in the direct way already
+alluded to: "White is a name connoting the attribute whiteness." Let us
+see, however, whether the analysis of the meaning of the name, that is,
+the breaking down of that meaning into several parts, admits of being
+carried farther. Without at present deciding this question as to the
+word <i>white</i>, it is obvious that in the case of <i>rational</i> some further
+explanation may be given of its meaning than is contained in the
+proposition, "Rational is that which possesses the attribute of reason;"
+since the attribute reason itself admits of being defined. And here we
+must turn our attention to the definitions of attributes, or rather of
+the names of attributes, that is, of abstract names.</p>
+
+<p>In regard to such names of attributes as are connotative, and express
+attributes of those attributes, there is no difficulty: like other
+connotative names they are defined by declaring their connotation. Thus,
+the word <i>fault</i> may be defined, "a quality productive of evil or
+inconvenience." Sometimes, again, the attribute to be defined is not one
+attribute, but an union of several: we have only, therefore, to put
+together the names of all the attributes taken separately, and we obtain
+the definition of the name which belongs <span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>to them all taken together; a
+definition which will correspond exactly to that of the corresponding
+concrete name. For, as we define a concrete name by enumerating the
+attributes which it connotes, and as the attributes connoted by a
+concrete name form the entire signification of the corresponding
+abstract name, the same enumeration will serve for the definition of
+both. Thus, if the definition of <i>a human being</i> be this, "a being,
+corporeal, animated, rational, shaped so and so," the definition of
+<i>humanity</i> will be corporeity and animal life, combined with
+rationality, and with such and such a shape.</p>
+
+<p>When, on the other hand, the abstract name does not express a
+complication of attributes, but a single attribute, we must remember
+that every attribute is grounded on some fact or phenomenon, from which,
+and which alone, it derives its meaning. To that fact or phenomenon,
+called in a former chapter the foundation of the attribute, we must,
+therefore, have recourse for its definition. Now, the foundation of the
+attribute may be a phenomenon of any degree of complexity, consisting of
+many different parts, either coexistent or in succession. To obtain a
+definition of the attribute, we must analyse the phenomenon into these
+parts. Eloquence, for example, is the name of one attribute only; but
+this attribute is grounded on external effects of a complicated nature,
+flowing from acts of the person to whom we ascribed the attribute; and
+by resolving this phenomenon of causation into its two parts, the cause
+and the effect, we obtain a definition of eloquence, viz. the power of
+influencing the feelings by speech or writing.</p>
+
+<p>A name, therefore, whether concrete or abstract, admits of definition,
+provided we are able to analyse, that is, to distinguish into parts, the
+attribute or set of attributes which constitute the meaning both of the
+concrete name and of the corresponding abstract: if a set of attributes,
+by enumerating them; if a single attribute, by dissecting the fact or
+phenomenon (whether of perception or of internal consciousness) which is
+the foundation of the attribute. But, further, even when the fact is one
+of our simple feelings or states of consciousness, and therefore
+unsusceptible of analysis, the names both of the object and of the
+attribute still admit of definition: or rather, <span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span>would do so if all our
+simple feelings had names. Whiteness may be defined, the property or
+power of exciting the sensation of white. A white object may be defined,
+an object which excites the sensation of white. The only names which are
+unsusceptible of definition, because their meaning is unsusceptible of
+analysis, are the names of the simple feelings themselves. These are in
+the same condition as proper names. They are not indeed, like proper
+names, unmeaning; for the words <i>sensation of white</i> signify, that the
+sensation which I so denominate resembles other sensations which I
+remember to have had before, and to have called by that name. But as we
+have no words by which to recal those former sensations, except the very
+word which we seek to define, or some other which, being exactly
+synonymous with it, requires definition as much, words cannot unfold the
+signification of this class of names; and we are obliged to make a
+direct appeal to the personal experience of the individual whom we
+address.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_3">� 3.</a> Having stated what seems to be the true idea of a Definition, we
+proceed to examine some opinions of philosophers, and some popular
+conceptions on the subject, which conflict more or less with that idea.</p>
+
+<p>The only adequate definition of a name is, as already remarked, one
+which declares the facts, and the whole of the facts, which the name
+involves in its signification. But with most persons the object of a
+definition does not embrace so much; they look for nothing more, in a
+definition, than a guide to the correct use of the term&mdash;a protection
+against applying it in a manner inconsistent with custom and convention.
+Anything, therefore, is to them a sufficient definition of a term, which
+will serve as a correct index to what the term denotes; though not
+embracing the whole, and sometimes, perhaps, not even any part, of what
+it connotes. This gives rise to two sorts of imperfect, or unscientific
+definition; Essential but incomplete Definitions, and Accidental
+Definitions, or Descriptions. In the former, a connotative name is
+defined by a part only of its connotation; in the latter, by something
+which forms no part of the connotation at all.</p>
+
+<p><span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span></p><p>An example of the first kind of imperfect definitions is the
+following:&mdash;Man is a rational animal. It is impossible to consider this
+as a complete definition of the word Man, since (as before remarked) if
+we adhered to it we should be obliged to call the Houyhnhnms men; but as
+there happen to be no Houyhnhnms, this imperfect definition is
+sufficient to mark out and distinguish from all other things, the
+objects at present denoted by "man;" all the beings actually known to
+exist, of whom the name is predicable. Though the word is defined by
+some only among the attributes which it connotes, not by all, it happens
+that all known objects which possess the enumerated attributes, possess
+also those which are omitted; so that the field of predication which the
+word covers, and the employment of it which is conformable to usage, are
+as well indicated by the inadequate definition as by an adequate one.
+Such definitions, however, are always liable to be overthrown by the
+discovery of new objects in nature.</p>
+
+<p>Definitions of this kind are what logicians have had in view, when they
+laid down the rule, that the definition of a species should be <i>per
+genus et differentiam</i>. Differentia being seldom taken to mean the whole
+of the peculiarities constitutive of the species, but some one of those
+peculiarities only, a complete definition would be <i>per genus et
+differentias</i>, rather than <i>differentiam</i>. It would include, with the
+name of the superior genus, not merely <i>some</i> attribute which
+distinguishes the species intended to be defined from all other species
+of the same genus, but <i>all</i> the attributes implied in the name of the
+species, which the name of the superior genus has not already implied.
+The assertion, however, that a definition must of necessity consist of a
+genus and differenti�, is not tenable. It was early remarked by
+logicians, that the <i>summum genus</i> in any classification, having no
+genus superior to itself, could not be defined in this manner. Yet we
+have seen that all names, except those of our elementary feelings, are
+susceptible of definition in the strictest sense; by setting forth in
+words the constituent parts of the fact or phenomenon, of which the
+connotation of every word is ultimately composed.</p>
+
+
+<p><span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span></p><p class="newsection"><a name="BOOK_I_CHAPTER_VIII_4">� 4.</a> Although the first kind of imperfect definition, (which defines a
+connotative term by a part only of what it connotes, but a part
+sufficient to mark out correctly the boundaries of its denotation,) has
+been considered by the ancients, and by logicians in general, as a
+complete definition; it has always been deemed necessary that the
+attributes employed should really form part of the connotation; for the
+rule was that the definition must be drawn from the <i>essence</i> of the
+class; and this would not have been the case if it had been in any
+degree made up of attributes not connoted by the name. The second kind
+of imperfect definition, therefore, in which the name of a class is
+defined by any of its accidents,&mdash;that is, by attributes which are not
+included in its connotation,&mdash;has been rejected from the rank of genuine
+Definition by all logicians, and has been termed Description.</p>
+
+<p>This kind of imperfect definition, however, takes its rise from the same
+cause as the other, namely, the willingness to accept as a definition
+anything which, whether it expounds the meaning of the name or not,
+enables us to discriminate the things denoted by the name from all other
+things, and consequently to employ the term in predication without
+deviating from established usage. This purpose is duly answered by
+stating any (no matter what) of the attributes which are common to the
+whole of the class, and peculiar to it; or any combination of attributes
+which happens to be peculiar to it, though separately each of those
+attributes may be common to it with some other things. It is only
+necessary that the definition (or description) thus formed, should be
+<i>convertible</i> with the name which it professes to define; that is,
+should be exactly co-extensive with it, being predicable of everything
+of which it is predicable, and of nothing of which it is not predicable;
+though the attributes specified may have no connexion with those which
+mankind had in view when they formed or recognised the class, and gave
+it a name. The following are correct definitions of Man, according to
+this test: Man is a mammiferous animal, having (by nature) two hands
+(for the human species answers to this description, and no <span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span>other animal
+does): Man is an animal who cooks his food: Man is a featherless biped.</p>
+
+<p>What would otherwise be a mere description, may be raised to the rank of
+a real definition by the peculiar purpose which the speaker or writer
+has in view. As was seen in the preceding chapter, it may, for the ends
+of a particular art or science, or for the more convenient statement of
+an author's particular doctrines, be advisable to give to some general
+name, without altering its denotation, a special connotation, different
+from its ordinary one. When this is done, a definition of the name by
+means of the attributes which make up the special connotation, though in
+general a mere accidental definition or description, becomes on the
+particular occasion and for the particular purpose a complete and
+genuine definition. This actually occurs with respect to one of the
+preceding examples, "Man is a mammiferous animal having two hands,"
+which is the scientific definition of man, considered as one of the
+species in Cuvier's distribution of the animal kingdom.</p>
+
+<p>In cases of this sort, though the definition is still a declaration of
+the meaning which in the particular instance the name is appointed to
+convey, it cannot be said that to state the meaning of the word is the
+purpose of the definition. The purpose is not to expound a name, but a
+classification. The special meaning which Cuvier assigned to the word
+Man, (quite foreign to its ordinary meaning, though involving no change
+in the denotation of the word,) was incidental to a plan of arranging
+animals into classes on a certain principle, that is, according to a
+certain set of distinctions. And since the definition of Man according
+to the ordinary connotation of the word, though it would have answered
+every other purpose of a definition, would not have pointed out the
+place which the species ought to occupy in that particular
+classification; he gave the word a special connotation, that he might be
+able to define it by the kind of attributes on which, for reasons of
+scientific convenience, he had resolved to found his division of
+animated nature.</p>
+
+<p>Scientific definitions, whether they are definitions of scientific
+terms, or of common terms used in a scientific sense, are <span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>almost always
+of the kind last spoken of: their main purpose is to serve as the
+landmarks of scientific classification. And since the classifications in
+any science are continually modified as scientific knowledge advances,
+the definitions in the sciences are also constantly varying. A striking
+instance is afforded by the words Acid and Alkali, especially the
+former. As experimental discovery advanced, the substances classed with
+acids have been constantly multiplying, and by a natural consequence the
+attributes connoted by the word have receded and become fewer. At first
+it connoted the attributes, of combining with an alkali to form a
+neutral substance (called a salt); being compounded of a base and
+oxygen; causticity to the taste and touch; fluidity, &amp;c. The true
+analysis of muriatic acid, into chlorine and hydrogen, caused the second
+property, composition from a base and oxygen, to be excluded from the
+connotation. The same discovery fixed the attention of chemists upon
+hydrogen as an important element in acids; and more recent discoveries
+having led to the recognition of its presence in sulphuric, nitric, and
+many other acids, where its existence was not previously suspected,
+there is now a tendency to include the presence of this element in the
+connotation of the word. But carbonic acid, silica, sulphurous acid,
+have no hydrogen in their composition; that property cannot therefore be
+connoted by the term, unless those substances are no longer to be
+considered acids. Causticity and fluidity have long since been excluded
+from the characteristics of the class, by the inclusion of silica and
+many other substances in it; and the formation of neutral bodies by
+combination with alkalis, together with such electro-chemical
+peculiarities as this is supposed to imply, are now the only
+<i>differenti�</i> which form the fixed connotation of the word Acid, as a
+term of chemical science.</p>
+
+<p>What is true of the definition of any term of science, is of course true
+of the definition of a science itself: and accordingly, (as observed in
+the Introductory Chapter of this work,) the definition of a science must
+necessarily be progressive and provisional. Any extension of knowledge
+or alteration in the current opinions respecting the subject matter, may
+lead to a <span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>change more or less extensive in the particulars included in
+the science; and its composition being thus altered, it may easily
+happen that a different set of characteristics will be found better
+adapted as differenti� for defining its name.</p>
+
+<p>In the same manner in which a special or technical definition has for
+its object to expound the artificial classification out of which it
+grows; the Aristotelian logicians seem to have imagined that it was also
+the business of ordinary definition to expound the ordinary, and what
+they deemed the natural, classification of things, namely, the division
+of them into Kinds; and to show the place which each Kind occupies, as
+superior, collateral, or subordinate, among other Kinds. This notion
+would account for the rule that all definition must necessarily be <i>per
+genus et differentiam</i>, and would also explain why a single differentia
+was deemed sufficient. But to expound, or express in words, a
+distinction of Kind, has already been shown to be an impossibility: the
+very meaning of a Kind is, that the properties which distinguish it do
+not grow out of one another, and cannot therefore be set forth in words,
+even by implication, otherwise than by enumerating them all: and all are
+not known, nor are ever likely to be so. It is idle, therefore, to look
+to this as one of the purposes of a definition: while, if it be only
+required that the definition of a Kind should indicate what Kinds
+include it or are included by it, any definitions which expound the
+connotation of the names will do this: for the name of each class must
+necessarily connote enough of its properties to fix the boundaries of
+the class. If the definition, therefore, be a full statement of the
+connotation, it is all that a definition can be required to be.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_5">� 5.</a> Of the two incomplete and popular modes of definition, and in what
+they differ from the complete or philosophical mode, enough has now been
+said. We shall next examine an ancient doctrine, once generally
+prevalent and still by no means exploded, which I regard as the source
+of a great part of the obscurity hanging over some of the most important
+processes of the understanding in the pursuit of truth. According to
+this, the definitions of which we have now <span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span>treated are only one of two
+sorts into which definitions may be divided, viz. definitions of names,
+and definitions of things. The former are intended to explain the
+meaning of a term; the latter, the nature of a thing; the last being
+incomparably the most important.</p>
+
+<p>This opinion was held by the ancient philosophers, and by their
+followers, with the exception of the Nominalists; but as the spirit of
+modern metaphysics, until a recent period, has been on the whole a
+Nominalist spirit, the notion of definitions of things has been to a
+certain extent in abeyance, still continuing, however, to breed
+confusion in logic, by its consequences indeed rather than by itself.
+Yet the doctrine in its own proper form now and then breaks out, and has
+appeared (among other places) where it was scarcely to be expected, in a
+justly admired work, Archbishop Whately's <i>Logic</i>.<a name="FNanchor_27_33" id="FNanchor_27_33"></a><a href="#Footnote_27_33" class="fnanchor">[27]</a> In a review of
+that work published by me in the <i>Westminster <span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>Review</i> for January 1828,
+and containing some opinions which I no longer entertain, I find the
+following observations on the question now before us; observations with
+which my present view of that question is still sufficiently in
+accordance.</p>
+
+<p>"The distinction between nominal and real definitions, between
+definitions of words and what are called definitions of things, though
+conformable to the ideas of most of the Aristotelian logicians, cannot,
+as it appears to us, be maintained. We apprehend that no definition is
+ever intended to 'explain and unfold the nature of a thing.' It is some
+confirmation of our opinion, that none of those writers who have thought
+that there were definitions of things, have ever succeeded in
+discovering any criterion by which the definition of a thing can be
+distinguished from any other proposition relating to the thing. The
+definition, they say, unfolds the nature of the thing: but no definition
+can unfold its whole nature; and every proposition in which any quality
+whatever is predicated of the thing, unfolds some part of its nature.
+The true state of the case we take to be this. All definitions are of
+names, and of names only; but, in some definitions, it is clearly
+apparent, that nothing is intended except to explain the meaning of the
+word; while in others, besides explaining the meaning of the word, it is
+intended to be implied that there exists a thing, corresponding to the
+word. Whether this be or be not implied in any given case, cannot be
+collected from the mere form of the expression. 'A centaur is an animal
+with the upper parts of a man and the lower parts of a horse,' and 'A
+triangle is a rectilineal figure with three sides,' are, in form,
+expressions precisely similar; although in the former it is not implied
+that any <i>thing</i>, conformable to the term, really exists, while in the
+latter it is; as may be seen by substituting, in both definitions, the
+word <i>means</i> for <i>is</i>. In the first expression, 'A centaur means an
+animal,' &amp;c., the sense would remain unchanged: in the second, 'A
+triangle means,' &amp;c., the meaning would be altered, since it would be
+obviously impossible to deduce any of the truths of geometry from a
+proposition expressive only of the manner in which we intend to employ a
+particular sign.</p>
+
+<p><span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span></p><p>"There are, therefore, expressions, commonly passing for definitions,
+which include in themselves more than the mere explanation of the
+meaning of a term. But it is not correct to call an expression of this
+sort a peculiar kind of definition. Its difference from the other kind
+consists in this, that it is not a definition, but a definition and
+something more. The definition above given of a triangle, obviously
+comprises not one, but two propositions, perfectly distinguishable. The
+one is, 'There may exist a figure, bounded by three straight lines;' the
+other, 'And this figure may be termed a triangle.' The former of these
+propositions is not a definition at all: the latter is a mere nominal
+definition, or explanation of the use and application of a term. The
+first is susceptible of truth or falsehood, and may therefore be made
+the foundation of a train of reasoning. The latter can neither be true
+nor false; the only character it is susceptible of is that of conformity
+or disconformity to the ordinary usage of language."</p>
+
+<p>There is a real distinction, then, between definitions of names, and
+what are erroneously called definitions of things; but it is, that the
+latter, along with the meaning of a name, covertly asserts a matter of
+fact. This covert assertion is not a definition, but a postulate. The
+definition is a mere identical proposition, which gives information only
+about the use of language, and from which no conclusions affecting
+matters of fact can possibly be drawn. The accompanying postulate, on
+the other hand, affirms a fact, which may lead to consequences of every
+degree of importance. It affirms the actual or possible existence of
+Things possessing the combination of attributes set forth in the
+definition; and this, if true, may be foundation sufficient on which to
+build a whole fabric of scientific truth.</p>
+
+<p>We have already made, and shall often have to repeat, the remark, that
+the philosophers who overthrew Realism by no means got rid of the
+consequences of Realism, but retained long afterwards, in their own
+philosophy, numerous propositions which could only have a rational
+meaning as part of a Realistic system. It had been handed down from
+Aristotle, and probably from earlier times, as an obvious truth, that
+the <span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span>science of Geometry is deduced from definitions. This, so long as a
+definition was considered to be a proposition "unfolding the nature of
+the thing," did well enough. But Hobbes followed, and rejected utterly
+the notion that a definition declares the nature of the thing, or does
+anything but state the meaning of a name; yet he continued to affirm as
+broadly as any of his predecessors, that the <i>&#7936;&#961;&#967;&#945;&#8054;</i>,
+<i>principia</i>, or original premises of mathematics, and even of all
+science, are definitions; producing the singular paradox, that systems
+of scientific truth, nay, all truths whatever at which we arrive by
+reasoning, are deduced from the arbitrary conventions of mankind
+concerning the signification of words.</p>
+
+<p>To save the credit of the doctrine that definitions are the premises of
+scientific knowledge, the proviso is sometimes added, that they are so
+only under a certain condition, namely, that they be framed conformably
+to the phenomena of nature; that is, that they ascribe such meanings to
+terms as shall suit objects actually existing. But this is only an
+instance of the attempt so often made, to escape from the necessity of
+abandoning old language after the ideas which it expresses have been
+exchanged for contrary ones. From the meaning of a name (we are told) it
+is possible to infer physical facts, provided the name has corresponding
+to it an existing thing. But if this proviso be necessary, from which of
+the two is the inference really drawn? From the existence of a thing
+having the properties, or from the existence of a name meaning them?</p>
+
+<p>Take, for instance, any of the definitions laid down as premises in
+Euclid's Elements; the definition, let us say, of a circle. This, being
+analysed, consists of two propositions; the one an assumption with
+respect to a matter of fact, the other a genuine definition. "A figure
+may exist, having all the points in the line which bounds it equally
+distant from a single point within it:" "Any figure possessing this
+property is called a circle." Let us look at one of the demonstrations
+which are said to depend on this definition, and observe to which of the
+two propositions contained in it the demonstration really appeals.
+"About the centre A, describe the circle <span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>B C D." Here is an assumption
+that a figure, such as the definition expresses, <i>may</i> be described;
+which is no other than the postulate, or covert assumption, involved in
+the so-called definition. But whether that figure be called a circle or
+not is quite immaterial. The purpose would be as well answered, in all
+respects except brevity, were we to say, "Through the point B, draw a
+line returning into itself, of which every point shall be at an equal
+distance from the point A." By this the definition of a circle would be
+got rid of, and rendered needless; but not the postulate implied in it;
+without that the demonstration could not stand. The circle being now
+described, let us proceed to the consequence. "Since B C D is a circle,
+the radius B A is equal to the radius C A." B A is equal to C A, not
+because B C D is a circle, but because B C D is a figure with the radii
+equal. Our warrant for assuming that such a figure about the centre A,
+with the radius B A, may be made to exist, is the postulate. Whether the
+admissibility of these postulates rests on intuition, or on proof, may
+be a matter of dispute; but in either case they are the premises on
+which the theorems depend; and while these are retained it would make no
+difference in the certainty of geometrical truths, though every
+definition in Euclid, and every technical term therein defined, were
+laid aside.</p>
+
+<p>It is, perhaps, superfluous to dwell at so much length on what is so
+nearly self-evident; but when a distinction, obvious as it may appear,
+has been confounded, and by powerful intellects, it is better to say too
+much than too little for the purpose of rendering such mistakes
+impossible in future. I will, therefore, detain the reader while I point
+out one of the absurd consequences flowing from the supposition that
+definitions, as such, are the premises in any of our reasonings, except
+such as relate to words only. If this supposition were true, we might
+argue correctly from true premises, and arrive at a false conclusion. We
+should only have to assume as a premise the definition of a nonentity;
+or rather of a name which has no entity corresponding to it. Let this,
+for instance, be our definition:</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a serpent breathing flame.</div>
+
+<p><span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span></p><p>This proposition, considered only as a definition, is indisputably
+correct. A dragon <i>is</i> a serpent breathing flame: the word <i>means</i> that.
+The tacit assumption, indeed, (if there were any such understood
+assertion), of the existence of an object with properties corresponding
+to the definition, would, in the present instance, be false. Out of this
+definition we may carve the premises of the following syllogism:</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a thing which breathes flame:</div>
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a serpent:</div>
+
+<p>From which the conclusion is,</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">Therefore some serpent or serpents breathe flame:&mdash;</div>
+
+<p>an unexceptionable syllogism in the first mode of the third figure, in
+which both premises are true and yet the conclusion false; which every
+logician knows to be an absurdity. The conclusion being false and the
+syllogism correct, the premises cannot be true. But the premises,
+considered as parts of a definition, are true. Therefore, the premises
+considered as parts of a definition cannot be the real ones. The real
+premises must be&mdash;</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a <i>really existing</i> thing which breathes flame:</div>
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a <i>really existing</i> serpent:</div>
+
+<p>which implied premises being false, the falsity of the conclusion
+presents no absurdity.</p>
+
+<p>If we would determine what conclusion follows from the same ostensible
+premises when the tacit assumption of real existence is left out, let
+us, according to the recommendation in a previous page, substitute
+<i>means</i> for <i>is</i>. We then have&mdash;</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">Dragon is <i>a word meaning</i> a thing which breathes flame:</div>
+<div style="margin-left: 2em;text-indent:-1em;">Dragon is <i>a word meaning</i> a serpent:</div>
+
+
+<p>From which the conclusion is,</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">Some <i>word or words which mean</i> a serpent, also mean a thing which breathes flame:</div>
+
+<p>where the conclusion (as well as the premises) is true, and is the only
+kind of conclusion which can ever follow from a definition, namely, a
+proposition relating to the meaning of words.</p>
+
+<p>There is still another shape into which we may transform this syllogism.
+We may suppose the middle term to be the <span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span>designation neither of a thing
+nor of a name, but of an idea. We then have&mdash;</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">The <i>idea of</i> a dragon is <i>an idea of</i> a thing which breathes flame:</div>
+<div style="margin-left: 2em;text-indent:-1em;">The <i>idea of</i> a dragon is <i>an idea of</i> a serpent:</div>
+<div style="margin-left: 2em;text-indent:-1em;">Therefore, there is <i>an idea of</i> a serpent, which is <i>an idea of</i> a thing breathing flame.</div>
+
+<p>Here the conclusion is true, and also the premises; but the premises are
+not definitions. They are propositions affirming that an idea existing
+in the mind, includes certain ideal elements. The truth of the
+conclusion follows from the existence of the psychological phenomenon
+called the idea of a dragon; and therefore still from the tacit
+assumption of a matter of fact.<a name="FNanchor_28_34" id="FNanchor_28_34"></a><a href="#Footnote_28_34" class="fnanchor">[28]</a></p>
+
+<p>When, as in this last syllogism, the conclusion is a proposition
+<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span>respecting an idea, the assumption on which it depends may be merely
+that of the existence of an idea. But when the conclusion is a
+proposition concerning a Thing, the postulate involved in the definition
+which stands as the apparent premise, is the existence of a thing
+conformable to the definition, and not merely of an idea conformable to
+it. This assumption of real existence will always convey the impression
+that we intend to make, when we profess to define any name which is
+already known to be a name of really existing objects. On this account
+it is, that the assumption was not necessarily implied in the definition
+of a dragon, while there was no doubt of its being included in the
+definition of a circle.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_6">� 6.</a> One of the circumstances which have contributed to keep up the
+notion, that demonstrative truths follow from definitions rather than
+from the postulates implied in those definitions, is, that the
+postulates, even in those sciences which are considered to surpass all
+others in demonstrative certainty, are not always exactly true. It is
+not true that a circle exists, or can be described, which has all its
+radii <i>exactly</i> equal. Such accuracy is ideal only; it is not found in
+nature, still less can it be realized by art. People had a difficulty,
+therefore, in conceiving that the most certain of all conclusions could
+rest on premises which, instead of being certainly true, are certainly
+not true to the full extent asserted. This apparent paradox will be
+examined when we come to treat of Demonstration; where we shall be able
+to show that as much of the postulate is true, as is required to support
+as much as is true of the conclusion. Philosophers, however, to whom
+this view had not occurred, or whom it did not satisfy, have thought it
+indispensable that there should be found in definitions something <i>more</i>
+certain, or at least more accurately true, than the implied postulate of
+the real existence of a corresponding object. And this something they
+flattered themselves they had found, when they laid it down that a
+definition is a statement and analysis not of the mere meaning of a
+word, nor yet of the nature of a thing, but of an idea. Thus, the
+proposition, "A circle is a plane figure bounded <span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span>by a line all the
+points of which are at an equal distance from a given point within it,"
+was considered by them, not as an assertion that any real circle has
+that property, (which would not be exactly true,) but that we <i>conceive</i>
+a circle as having it; that our abstract idea of a circle is an idea of
+a figure with its radii exactly equal.</p>
+
+<p>Conformably to this it is said, that the subject-matter of mathematics,
+and of every other demonstrative science, is not things as they really
+exist, but abstractions of the mind. A geometrical line is a line
+without breadth; but no such line exists in nature; it is a notion
+merely suggested to the mind by its experience of nature. The definition
+(it is said) is a definition of this mental line, not of any actual
+line: and it is only of the mental line, not of any line existing in
+nature, that the theorems of geometry are accurately true.</p>
+
+<p>Allowing this doctrine respecting the nature of demonstrative truth to
+be correct (which, in a subsequent place, I shall endeavour to prove
+that it is not;) even on that supposition, the conclusions which seem to
+follow from a definition, do not follow from the definition as such, but
+from an implied postulate. Even if it be true that there is no object in
+nature answering to the definition of a line, and that the geometrical
+properties of lines are not true of any lines in nature, but only of the
+idea of a line; the definition, at all events, postulates the real
+existence of such an idea: it assumes that the mind can frame, or rather
+has framed, the notion of length without breadth, and without any other
+sensible property whatever. To me, indeed, it appears that the mind
+cannot form any such notion; it cannot conceive length without breadth;
+it can only, in contemplating objects, attend to their length,
+exclusively of their other sensible qualities, and so determine what
+properties may be predicated of them in virtue of their length alone. If
+this be true, the postulate involved in the geometrical definition of a
+line, is the real existence, not of length without breadth, but merely
+of length, that is, of long objects. This is quite enough to support all
+the truths of geometry, since every property of a geometrical line is
+really a property <span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span>of all physical objects in so far as possessing
+length. But even what I hold to be the false doctrine on the subject,
+leaves the conclusion that our reasonings are grounded on the matters of
+fact postulated in definitions, and not on the definitions themselves,
+entirely unaffected; and accordingly this conclusion is one which I have
+in common with Dr. Whewell, in his <i>Philosophy of the Inductive
+Sciences</i>: though, on the nature of demonstrative truth, Dr. Whewell's
+opinions are greatly at variance with mine. And here, as in many other
+instances, I gladly acknowledge that his writings are eminently
+serviceable in clearing from confusion the initial steps in the analysis
+of the mental processes, even where his views respecting the ultimate
+analysis are such as (though with unfeigned respect) I cannot but regard
+as fundamentally erroneous.</p>
+
+
+<p class="newsection"><a name="BOOK_I_CHAPTER_VIII_7">� 7.</a> Although, according to the opinion here presented, Definitions are
+properly of names only, and not of things, it does not follow from this
+that definitions are arbitrary. How to define a name, may not only be an
+inquiry of considerable difficulty and intricacy, but may involve
+considerations going deep into the nature of the things which are
+denoted by the name. Such, for instance, are the inquiries which form
+the subjects of the most important of Plato's Dialogues; as, "What is
+rhetoric?" the topic of the Gorgias, or "What is justice?" that of the
+Republic. Such, also, is the question scornfully asked by Pilate, "What
+is truth?" and the fundamental question with speculative moralists in
+all ages, "What is virtue?"</p>
+
+<p>It would be a mistake to represent these difficult and noble inquiries
+as having nothing in view beyond ascertaining the conventional meaning
+of a name. They are inquiries not so much to determine what is, as what
+should be, the meaning of a name; which, like other practical questions
+of terminology, requires for its solution that we should enter, and
+sometimes enter very deeply, into the properties not merely of names but
+of the things named.</p>
+
+<p>Although the meaning of every concrete general name resides in the
+attributes which it connotes, the objects were <span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>named before the
+attributes; as appears from the fact that in all languages, abstract
+names are mostly compounds or other derivatives of the concrete names
+which correspond to them. Connotative names, therefore, were, after
+proper names, the first which were used: and in the simpler cases, no
+doubt, a distinct connotation was present to the minds of those who
+first used the name, and was distinctly intended by them to be conveyed
+by it. The first person who used the word white, as applied to snow or
+to any other object, knew, no doubt, very well what quality he intended
+to predicate, and had a perfectly distinct conception in his mind of the
+attribute signified by the name.</p>
+
+<p>But where the resemblances and differences on which our classifications
+are founded are not of this palpable and easily determinable kind;
+especially where they consist not in any one quality but in a number of
+qualities, the effects of which being blended together are not very
+easily discriminated, and referred each to its true source; it often
+happens that names are applied to nameable objects, with no distinct
+connotation present to the minds of those who apply them. They are only
+influenced by a general resemblance between the new object and all or
+some of the old familiar objects which they have been accustomed to call
+by that name. This, as we have seen, is the law which even the mind of
+the philosopher must follow, in giving names to the simple elementary
+feelings of our nature: but, where the things to be named are complex
+wholes, a philosopher is not content with noticing a general
+resemblance; he examines what the resemblance consists in: and he only
+gives the same name to things which resemble one another in the same
+definite particulars. The philosopher, therefore, habitually employs his
+general names with a definite connotation. But language was not made,
+and can only in some small degree be mended, by philosophers. In the
+minds of the real arbiters of language, general names, especially where
+the classes they denote cannot be brought before the tribunal of the
+outward senses to be identified and discriminated, connote little more
+than a vague gross resemblance <span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span>to the things which they were earliest,
+or have been most, accustomed to call by those names. When, for
+instance, ordinary persons predicate the words <i>just</i> or <i>unjust</i> of any
+action, <i>noble</i> or <i>mean</i> of any sentiment, expression, or demeanour,
+<i>statesman</i> or <i>charlatan</i> of any personage figuring in politics, do
+they mean to affirm of those various subjects any determinate
+attributes, of whatever kind? No: they merely recognise, as they think,
+some likeness, more or less vague and loose, between these and some
+other things which they have been accustomed to denominate or to hear
+denominated by those appellations.</p>
+
+<p>Language, as Sir James Mackintosh used to say of governments, "is not
+made, but grows." A name is not imposed at once and by previous purpose
+upon a <i>class</i> of objects, but is first applied to one thing, and then
+extended by a series of transitions to another and another. By this
+process (as has been remarked by several writers, and illustrated with
+great force and clearness by Dugald Stewart in his Philosophical Essays)
+a name not unfrequently passes by successive links of resemblance from
+one object to another, until it becomes applied to things having nothing
+in common with the first things to which the name was given; which,
+however, do not, for that reason, drop the name; so that it at last
+denotes a confused huddle of objects, having nothing whatever in common;
+and connotes nothing, not even a vague and general resemblance. When a
+name has fallen into this state, in which by predicating it of any
+object we assert literally nothing about the object, it has become unfit
+for the purposes either of thought or of the communication of thought;
+and can only be made serviceable by stripping it of some part of its
+multifarious denotation, and confining it to objects possessed of some
+attributes in common, which it may be made to connote. Such are the
+inconveniences of a language which "is not made, but grows." Like the
+governments which are in a similar case, it may be compared to a road
+which is not made but has made itself: it requires continual mending in
+order to be passable.</p>
+
+<p>From this it is already evident, why the question respecting <span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>the
+definition of an abstract name is often one of so much difficulty. The
+question, What is justice? is, in other words, What is the attribute
+which mankind mean to predicate when they call an action just? To which
+the first answer is, that having come to no precise agreement on the
+point, they do not mean to predicate distinctly any attribute at all.
+Nevertheless, all believe that there is some common attribute belonging
+to all the actions which they are in the habit of calling just. The
+question then must be, whether there is any such common attribute? and,
+in the first place, whether mankind agree sufficiently with one another
+as to the particular actions which they do or do not call just, to
+render the inquiry, what quality those actions have in common, a
+possible one: if so, whether the actions really have any quality in
+common; and if they have, what it is. Of these three, the first alone is
+an inquiry into usage and convention; the other two are inquiries into
+matters of fact. And if the second question (whether the actions form a
+class at all) has been answered negatively, there remains a fourth,
+often more arduous than all the rest, namely, how best to form a class
+artificially, which the name may denote.</p>
+
+<p>And here it is fitting to remark, that the study of the spontaneous
+growth of languages is of the utmost importance to those who would
+logically remodel them. The classifications rudely made by established
+language, when retouched, as they almost all require to be, by the hands
+of the logician, are often in themselves excellently suited to his
+purposes. As compared with the classifications of a philosopher, they
+are like the customary law of a country, which has grown up as it were
+spontaneously, compared with laws methodized and digested into a code:
+the former are a far less perfect instrument than the latter; but being
+the result of a long, though unscientific, course of experience, they
+contain a mass of materials which may be made very usefully available in
+the formation of the systematic body of written law. In like manner, the
+established grouping of objects under a common name, even when founded
+only on a gross and general resemblance, is evidence, in the first
+place, that the resemblance is <span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span>obvious, and therefore considerable;
+and, in the next place, that it is a resemblance which has struck great
+numbers of persons during a series of years and ages. Even when a name,
+by successive extensions, has come to be applied to things among which
+there does not exist this gross resemblance common to them all, still at
+every step in its progress we shall find such a resemblance. And these
+transitions of the meaning of words are often an index to real
+connexions between the things denoted by them, which might otherwise
+escape the notice of thinkers; of those at least who, from using a
+different language, or from any difference in their habitual
+associations, have fixed their attention in preference on some other
+aspect of the things. The history of philosophy abounds in examples of
+such oversights, committed for want of perceiving the hidden link that
+connected together the seemingly disparate meanings of some ambiguous
+word.<a name="FNanchor_29_35" id="FNanchor_29_35"></a><a href="#Footnote_29_35" class="fnanchor">[29]</a></p>
+
+<p>Whenever the inquiry into the definition of the name of any real object
+consists of anything else than a mere comparison of authorities, we
+tacitly assume that a meaning must be found for the name, compatible
+with its continuing to denote, if possible all, but at any rate the
+greater or the more important part, of the things of which it is
+commonly predicated. The inquiry, therefore, into the definition, is an
+inquiry into the resemblances and differences among those things:
+whether there be any resemblance running through them all; if not,
+through what portion of them such a general resemblance can <span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span>be traced:
+and finally, what are the common attributes, the possession of which
+gives to them all, or to that portion of them, the character of
+resemblance which has led to their being classed together. When these
+common attributes have been ascertained and specified, the name which
+belongs in common to the resembling objects acquires a distinct instead
+of a vague connotation; and by possessing this distinct connotation,
+becomes susceptible of definition.</p>
+
+<p>In giving a distinct connotation to the general name, the philosopher
+will endeavour to fix upon such attributes as, while they are common to
+all the things usually denoted by the name, are also of greatest
+importance in themselves; either directly, or from the number, the
+conspicuousness, or the interesting character, of the consequences to
+which they lead. He will select, as far as possible, such <i>differenti�</i>
+as lead to the greatest number of interesting <i>propria</i>. For these,
+rather than the more obscure and recondite qualities on which they often
+depend, give that general character and aspect to a set of objects,
+which determine the groups into which they naturally fall. But to
+penetrate to the more hidden agreement on which these obvious and
+superficial agreements depend, is often one of the most difficult of
+scientific problems. As it is among the most difficult, so it seldom
+fails to be among the most important. And since upon the result of this
+inquiry respecting the causes of the properties of a class of things,
+there incidentally depends the question what shall be the meaning of a
+word; some of the most profound and most valuable investigations which
+philosophy presents to us, have been introduced by, and have offered
+themselves under the guise of, inquiries into the definition of a name.</p>
+
+<div class="footnotes"><h3>FOOTNOTES:</h3>
+
+<div class="footnote"><p><a name="Footnote_1_7" id="Footnote_1_7"></a><a href="#FNanchor_1_7"><span class="label">[1]</span></a> <i>Computation or Logic</i>, chap. ii.</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_8" id="Footnote_2_8"></a><a href="#FNanchor_2_8"><span class="label">[2]</span></a> In the original "had, <i>or had not</i>." These last words, as
+involving a subtlety foreign to our present purpose, I have forborne to
+quote.</p></div>
+
+<div class="footnote"><p><a name="Footnote_3_9" id="Footnote_3_9"></a><a href="#FNanchor_3_9"><span class="label">[3]</span></a> Vide infra, <a href="#Footnote_5_40">note at the end of � 3, book ii. ch. ii.</a></p></div>
+
+<div class="footnote"><p><a name="Footnote_4_10" id="Footnote_4_10"></a><a href="#FNanchor_4_10"><span class="label">[4]</span></a> <i>Notare</i>, to mark; <i>con</i>notare, to mark <i>along with</i>; to
+mark one thing <i>with</i> or <i>in addition to</i> another.</p></div>
+
+<div class="footnote"><p><a name="Footnote_5_11" id="Footnote_5_11"></a><a href="#FNanchor_5_11"><span class="label">[5]</span></a> Archbishop Whately, who, in the later editions of his
+<i>Elements of Logic</i>, aided in reviving the important distinction treated
+of in the text, proposes the term "Attributive" as a substitute for
+"Connotative" (p. 22, 9th ed.) The expression is, in itself,
+appropriate; but as it has not the advantage of being connected with any
+verb, of so markedly distinctive a character as "to connote," it is not,
+I think, fitted to supply the place of the word Connotative in
+scientific use.</p></div>
+
+<div class="footnote"><p><a name="Footnote_6_12" id="Footnote_6_12"></a><a href="#FNanchor_6_12"><span class="label">[6]</span></a> A writer who entitles his book <i>Philosophy; or, the Science
+of Truth</i>, charges me in his very first page (referring at the foot of
+it to this passage) with asserting that <i>general</i> names have properly no
+signification. And he repeats this statement many times in the course of
+his volume, with comments, not at all flattering, thereon. It is well to
+be now and then reminded to how great a length perverse misquotation
+(for, strange as it appears, I do not believe that the writer is
+dishonest) can sometimes go. It is a warning to readers, when they see
+an author accused, with volume and page referred to, and the apparent
+guarantee of inverted commas, of maintaining something more than
+commonly absurd, not to give implicit credence to the assertion without
+verifying the reference.</p></div>
+
+<div class="footnote"><p><a name="Footnote_7_13" id="Footnote_7_13"></a><a href="#FNanchor_7_13"><span class="label">[7]</span></a> Before quitting the subject of connotative names, it is
+proper to observe, that the first writer who, in our times, has adopted
+from the schoolmen the word <i>to connote</i>, Mr. James Mill, in his
+<i>Analysis of the Phenomena of the Human Mind</i>, employs it in a
+signification different from that in which it is here used. He uses the
+word in a sense coextensive with its etymology, applying it to every
+case in which a name, while pointing directly to one thing, (which is
+consequently termed its signification,) includes also a tacit reference
+to some other thing. In the case considered in the text, that of
+concrete general names, his language and mine are the converse of one
+another. Considering (very justly) the signification of the name to lie
+in the attribute, he speaks of the word as <i>noting</i> the attribute, and
+<i>connoting</i> the things possessing the attribute. And he describes
+abstract names as being properly concrete names with their connotation
+dropped: whereas, in my view, it is the <i>de</i>notation which would be said
+to be dropped, what was previously connoted becoming the whole
+signification.
+</p><p>
+In adopting a phraseology at variance with that which so high an
+authority, and one which I am less likely than any other person to
+undervalue, has deliberately sanctioned, I have been influenced by the
+urgent necessity for a term exclusively appropriated to express the
+manner in which a concrete general name serves to mark the attributes
+which are involved in its signification. This necessity can scarcely be
+felt in its full force by any one who has not found by experience how
+vain is the attempt to communicate clear ideas on the philosophy of
+language without such a word. It is hardly an exaggeration to say, that
+some of the most prevalent of the errors with which logic has been
+infected, and a large part of the cloudiness and confusion of ideas
+which have enveloped it, would, in all probability, have been avoided,
+if a term had been in common use to express exactly what I have
+signified by the term to connote. And the schoolmen, to whom we are
+indebted for the greater part of our logical language, gave us this
+also, and in this very sense. For though some of their general
+expressions countenance the use of the word in the more extensive and
+vague acceptation in which it is taken by Mr. Mill, yet when they had to
+define it specifically as a technical term, and to fix its meaning as
+such, with that admirable precision which always characterizes their
+definitions, they clearly explained that nothing was said to be connoted
+except <i>forms</i>, which word may generally, in their writings, be
+understood as synonymous with <i>attributes</i>.
+</p><p>
+Now, if the word <i>to connote</i>, so well suited to the purpose to which
+they applied it, be diverted from that purpose by being taken to fulfil
+another, for which it does not seem to me to be at all required; I am
+unable to find any expression to replace it, but such as are commonly
+employed in a sense so much more general, that it would be useless
+attempting to associate them peculiarly with this precise idea. Such are
+the words, to involve, to imply, &amp;c. By employing these, I should fail
+of attaining the object for which alone the name is needed, namely, to
+distinguish this particular kind of involving and implying from all
+other kinds, and to assure to it the degree of habitual attention which
+its importance demands.</p></div>
+
+<div class="footnote"><p><a name="Footnote_8_14" id="Footnote_8_14"></a><a href="#FNanchor_8_14"><span class="label">[8]</span></a> Or rather, all objects except itself and the percipient
+mind; for, as we shall see hereafter, to ascribe any attribute to an
+object, necessarily implies a mind to perceive it.
+</p><p>
+The simple and clear explanation given in the text, of relation and
+relative names, a subject so long the opprobrium of metaphysics, was
+given (as far as I know) for the first time, by Mr. James Mill, in his
+Analysis of the Phenomena of the Human Mind.</p></div>
+
+<div class="footnote"><p><a name="Footnote_9_15" id="Footnote_9_15"></a><a href="#FNanchor_9_15"><span class="label">[9]</span></a> <i>Philosophy of the Inductive Sciences</i>, vol. i. p. 40.</p></div>
+
+<div class="footnote"><p><a name="Footnote_10_16" id="Footnote_10_16"></a><a href="#FNanchor_10_16"><span class="label">[10]</span></a> <i>Discussions on Philosophy</i>, &amp;c. Appendix I. pp. 643-4.</p></div>
+
+<div class="footnote"><p><a name="Footnote_11_17" id="Footnote_11_17"></a><a href="#FNanchor_11_17"><span class="label">[11]</span></a> It is to be regretted that Sir William Hamilton, though he
+often strenuously insists on this doctrine, and though, in the passage
+quoted, he states it with a comprehensiveness and force which leave
+nothing to be desired, did not consistently adhere to his own doctrine,
+but maintained along with it opinions with which it is utterly
+irreconcileable. See the third and other chapters of <i>An Examination of
+Sir William Hamilton's Philosophy</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_12_18" id="Footnote_12_18"></a><a href="#FNanchor_12_18"><span class="label">[12]</span></a> "Nous savons qu'il existe quelque chose hors de nous,
+parceque nous ne pouvons expliquer nos perceptions sans les rattacher �
+des causes distinctes de nous-m�mes; nous savons de plus que ces causes,
+dont nous ne connaissons pas d'ailleurs l'essence, produisent les effets
+les plus variables, les plus divers, et m�me les plus contraires, selon
+qu'elles rencontrent telle nature ou telle disposition du sujet. Mais
+savons-nous quelque chose de plus? et m�me, vu le caract�re ind�termin�
+des causes que nous concevons dans les corps, y a-t-il quelque chose de
+plus � savoir? Y a-t-il lieu de nous enqu�rir si nous percevons les
+choses telles qu'elles sont? Non �videmment.... Je ne dis pas que le
+probl�me est insoluble, <i>je dis qu'il est absurde et enferme une
+contradiction</i>. Nous <i>ne savons pas ce que ces causes sont en
+elles-m�mes</i>, et la raison nous d�fend de chercher � le conna�tre: mais
+il est bien �vident <i>� priori</i>, qu'<i>elles ne sont pas en elles-m�mes ce
+qu'elles sont par rapport � nous</i>, puisque la pr�sence du sujet modifie
+n�cessairement leur action. Supprimez tout sujet sentant, il est certain
+que ces causes agiraient encore puisqu'elles continueraient d'exister;
+mais elles agiraient autrement; elles seraient encore des qualit�s et
+des propri�t�s, mais qui ne ressembleraient � rien de ce que nous
+connaissons. Le feu ne manifesterait plus aucune des propri�t�s que nous
+lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.
+<i>C'est d'ailleurs peut-�tre un probl�me qui ne r�pugne pas seulement �
+la nature de notre esprit, mais � l'essence m�me des choses.</i> Quand m�me
+en effet on supprimerait par la pens�e tous les sujets sentants, il
+faudrait encore admettre que nul corps ne manifesterait ses propri�t�s
+autrement qu'en relation avec un sujet quelconque, et dans ce cas <i>ses
+propri�t�s ne seraient encore que relatives</i>: en sorte qu'il me para�t
+fort raisonnable d'admettre que les propri�t�s d�termin�es des corps
+n'existent pas ind�pendamment d'un sujet quelconque, et que quand on
+demande si les propri�t�s de la mati�re sont telles que nous les
+percevons, il faudrait voir auparavant si elles sont en tant que
+d�termin�es, et dans quel sens il est vrai de dire qu'elles
+sont."&mdash;<i>Cours d'Histoire de la Philosophie Morale au 18me si�cle</i>, 8me
+le�on.</p></div>
+
+<div class="footnote"><p><a name="Footnote_13_19" id="Footnote_13_19"></a><a href="#FNanchor_13_19"><span class="label">[13]</span></a> An attempt, indeed, has been made by Reid and others, to
+establish that although some of the properties we ascribe to objects
+exist only in our sensations, others exist in the things themselves,
+being such as cannot possibly be copies of any impression upon the
+senses; and they ask, from what sensations our notions of extension and
+figure have been derived? The gauntlet thrown down by Reid was taken up
+by Brown, who, applying greater powers of analysis than had previously
+been applied to the notions of extension and figure, pointed out that
+the sensations from which those notions are derived, are sensations of
+touch, combined with sensations of a class previously too little
+adverted to by metaphysicians, those which have their seat in our
+muscular frame. His analysis, which was adopted and followed up by James
+Mill, has been further and greatly improved upon in Professor Bain's
+profound work, <i>The Senses and the Intellect</i>, and in the chapters on
+"Perception" of a work of eminent analytic power, Mr. Herbert Spencer's
+<i>Principles of Psychology</i>.
+</p><p>
+On this point M. Cousin may again be cited in favour of the better
+doctrine. M. Cousin recognises, in opposition to Reid, the essential
+subjectivity of our conceptions of what are called the primary qualities
+of matter, as extension, solidity, &amp;c., equally with those of colour,
+heat, and the remainder of the so-called secondary qualities.&mdash;<i>Cours</i>,
+ut supra, 9me le�on.</p></div>
+
+<div class="footnote"><p><a name="Footnote_14_20" id="Footnote_14_20"></a><a href="#FNanchor_14_20"><span class="label">[14]</span></a> This doctrine, which is the most complete form of the
+philosophical theory known as the Relativity of Human Knowledge, has,
+since the recent revival in this country of an active interest in
+metaphysical speculation, been the subject of a greatly increased amount
+of discussion and controversy; and dissentients have manifested
+themselves in considerably greater number than I had any knowledge of
+when the passage in the text was written. The doctrine has been attacked
+from two sides. Some thinkers, among whom are the late Professor
+Ferrier, in his <i>Institutes of Metaphysic</i>, and Professor John Grote in
+his <i>Exploratio Philosophica</i>, appear to deny altogether the reality of
+Noumena, or Things in themselves&mdash;of an unknowable substratum or support
+for the sensations which we experience, and which, according to the
+theory, constitute all our knowledge of an external world. It seems to
+me, however, that in Professor Grote's case at least, the denial of
+Noumena is only apparent, and that he does not essentially differ from
+the other class of objectors, including Mr. Bailey in his valuable
+<i>Letters on the Philosophy of the Human Mind</i>, and (in spite of the
+striking passage quoted in the text) also Sir William Hamilton, who
+contend for a direct knowledge by the human mind of more than the
+sensations&mdash;of certain attributes or properties as they exist not in us,
+but in the Things themselves.
+</p><p>
+With the first of these opinions, that which denies Noumena, I have, as
+a metaphysician, no quarrel; but, whether it be true or false, it is
+irrelevant to Logic. And since all the forms of language are in
+contradiction to it, nothing but confusion could result from its
+unnecessary introduction into a treatise, every essential doctrine of
+which could stand equally well with the opposite and accredited opinion.
+The other and rival doctrine, that of a direct perception or intuitive
+knowledge of the outward object as it is in itself, considered as
+distinct from the sensations we receive from it, is of far greater
+practical moment. But even this question, depending on the nature and
+laws of Intuitive Knowledge, is not within the province of Logic. For
+the grounds of my own opinion concerning it, I must content myself with
+referring to a work already mentioned&mdash;<i>An Examination of Sir William
+Hamilton's Philosophy</i>; several chapters of which are devoted to a full
+discussion of the questions and theories relating to the supposed direct
+perception of external objects.</p></div>
+
+<div class="footnote"><p><a name="Footnote_15_21" id="Footnote_15_21"></a><a href="#FNanchor_15_21"><span class="label">[15]</span></a> <i>Analysis of the Human Mind</i>, i. 126 et seq.</p></div>
+
+<div class="footnote"><p><a name="Footnote_16_22" id="Footnote_16_22"></a><a href="#FNanchor_16_22"><span class="label">[16]</span></a> It may, however, be considered as equivalent to an
+universal proposition with a different predicate, viz. "All wine is good
+<i>qu�</i> wine," or "is good in respect of the qualities which constitute it
+wine."</p></div>
+
+<div class="footnote"><p><a name="Footnote_17_23" id="Footnote_17_23"></a><a href="#FNanchor_17_23"><span class="label">[17]</span></a> Dr. Whewell (<i>Philosophy of Discovery</i>, p. 242) questions
+this statement, and asks, "Are we to say that a mole cannot dig the
+ground, except he has an idea of the ground, and of the snout and paws
+with which he digs it?" I do not know what passes in a mole's mind, nor
+what amount of mental apprehension may or may not accompany his
+instinctive actions. But a human being does not use a spade by instinct;
+and he certainly could not use it unless he had knowledge of a spade,
+and of the earth which he uses it upon.</p></div>
+
+<div class="footnote"><p><a name="Footnote_18_24" id="Footnote_18_24"></a><a href="#FNanchor_18_24"><span class="label">[18]</span></a> "From hence also this may be deduced, that the first
+truths were arbitrarily made by those that first of all imposed names
+upon things, or received them from the imposition of others. For it is
+true (for example) that <i>man is a living creature</i>, but it is for this
+reason, that it pleased men to impose both these names on the same
+thing."&mdash;<i>Computation or Logic</i>, ch. iii. sect. 8.</p></div>
+
+<div class="footnote"><p><a name="Footnote_19_25" id="Footnote_19_25"></a><a href="#FNanchor_19_25"><span class="label">[19]</span></a> "Men are subject to err not only in affirming and denying,
+but also in perception, and in silent cogitation.... Tacit errors, or
+the errors of sense and cogitation, are made by passing from one
+imagination to the imagination of another different thing; or by
+feigning that to be past, or future, which never was, nor ever shall be;
+as when by seeing the image of the sun in water, we imagine the sun
+itself to be there; or by seeing swords, that there has been, or shall
+be, fighting, because it uses to be so for the most part; or when from
+promises we feign the mind of the promiser to be such and such; or,
+lastly, when from any sign we vainly imagine something to be signified
+which is not. And errors of this sort are common to all things that have
+sense."&mdash;<i>Computation or Logic</i>, ch. v. sect. 1.</p></div>
+
+<div class="footnote"><p><a name="Footnote_20_26" id="Footnote_20_26"></a><a href="#FNanchor_20_26"><span class="label">[20]</span></a> Ch. iii. sect. 3.</p></div>
+
+<div class="footnote"><p><a name="Footnote_21_27" id="Footnote_21_27"></a><a href="#FNanchor_21_27"><span class="label">[21]</span></a> To the preceding statement it has been objected, that "we
+naturally construe the subject of a proposition in its extension, and
+the predicate (which therefore may be an adjective) in its intension,
+(connotation): and that consequently coexistence of attributes does not,
+any more than the opposite theory of equation of groups, correspond with
+the living processes of thought and language." I acknowledge the
+distinction here drawn, which, indeed, I had myself laid down and
+exemplified a few pages back (<a href="#Page_104">p. 104</a>). But though it is true that we
+naturally "construe the subject of a proposition in its extension," this
+extension, or in other words, the extent of the class denoted by the
+name, is not apprehended or indicated directly. It is both apprehended
+and indicated solely through the attributes. In the "living processes of
+thought and language" the extension, though in this case really thought
+of (which in the case of the predicate it is not), is thought of only
+through the medium of what my acute and courteous critic terms the
+"intension."
+</p><p>
+For further illustrations of this subject, see <i>Examination of Sir
+William Hamilton's Philosophy</i>, ch. xxii.</p></div>
+
+<div class="footnote"><p><a name="Footnote_22_28" id="Footnote_22_28"></a><a href="#FNanchor_22_28"><span class="label">[22]</span></a> <span title="See Vol. II.">Book iv. ch. vii.</span></p></div>
+
+<div class="footnote"><p><a name="Footnote_23_29" id="Footnote_23_29"></a><a href="#FNanchor_23_29"><span class="label">[23]</span></a> The doctrines which prevented the real meaning of Essences
+from being understood, had not assumed so settled a shape in the time of
+Aristotle and his immediate followers, as was afterwards given to them
+by the Realists of the middle ages. Aristotle himself (in his Treatise
+on the Categories) expressly denies that the <i>&#948;&#949;&#8059;&#964;&#949;&#961;&#945;&#953; &#959;&#8020;&#963;&#953;&#945;&#953;</i>,
+or Substanti� Secund�, inhere in a subject. They are only, he says,
+predicated of it.</p></div>
+
+<div class="footnote"><p><a name="Footnote_24_30" id="Footnote_24_30"></a><a href="#FNanchor_24_30"><span class="label">[24]</span></a> The always acute and often profound author of <i>An Outline
+of Sematology</i> (Mr. B. H. Smart) justly says, "Locke will be much more
+intelligible if, in the majority of places, we substitute 'the knowledge
+of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms
+on Locke's use of the word Idea, this is the one which, as it appears to
+me, most nearly hits the mark; and I quote it for the additional reason
+that it precisely expresses the point of difference respecting the
+import of Propositions, between my view and what I have spoken of as the
+Conceptualist view of them. Where a Conceptualist says that a name or a
+proposition expresses our Idea of a thing, I should generally say
+(instead of our Idea) our Knowledge, or Belief, concerning the thing
+itself.</p></div>
+
+<div class="footnote"><p><a name="Footnote_25_31" id="Footnote_25_31"></a><a href="#FNanchor_25_31"><span class="label">[25]</span></a> This distinction corresponds to that which is drawn by
+Kant and other metaphysicians between what they term <i>analytic</i>, and
+<i>synthetic</i>, judgments; the former being those which can be evolved from
+the meaning of the terms used.</p></div>
+
+<div class="footnote"><p><a name="Footnote_26_32" id="Footnote_26_32"></a><a href="#FNanchor_26_32"><span class="label">[26]</span></a> If we allow a differentia to what is not really a species.
+For the distinction of Kinds, in the sense explained by us, not being in
+any way applicable to attributes, it of course follows that although
+attributes may be put into classes, those classes can be admitted to be
+genera or species only by courtesy.</p></div>
+
+<div class="footnote"><p><a name="Footnote_27_33" id="Footnote_27_33"></a><a href="#FNanchor_27_33"><span class="label">[27]</span></a> In the fuller discussion which Archbishop Whately has
+given to this subject in his later editions, he almost ceases to regard
+the definitions of names and those of things as, in any important sense,
+distinct. He seems (9th ed. p. 145) to limit the notion of a Real
+Definition to one which "explains anything <i>more</i> of the nature of the
+thing than is implied in the name;" (including under the word "implied,"
+not only what the name connotes, but everything which can be deduced by
+reasoning from the attributes connoted). Even this, as he adds, is
+usually called, not a Definition, but a Description; and (as it seems to
+me) rightly so called. A Description, I conceive, can only be ranked
+among Definitions, when taken (as in the case of the zoological
+definition of man) to fulfil the true office of a Definition, by
+declaring the connotation given to a word in some special use, as a term
+of science or art: which special connotation of course would not be
+expressed by the proper definition of the word in its ordinary
+employment.
+</p><p>
+Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
+understands by a Real Definition one which contains <i>less</i> than the
+Nominal Definition, provided only that what it contains is sufficient
+for distinction. "By <i>real</i> definition I mean such an explanation of the
+word, be it the whole of the meaning or only part, as will be sufficient
+to separate the things contained under that word from all others. Thus
+the following, I believe, is a complete definition of an elephant: An
+animal which naturally drinks by drawing the water into its nose, and
+then spurting it into its mouth."&mdash;<i>Formal Logic</i>, p. 36. Mr. De
+Morgan's general proposition and his example are at variance; for the
+peculiar mode of drinking of the elephant certainly forms no part of the
+meaning of the word elephant. It could not be said, because a person
+happened to be ignorant of this property, that he did not know what an
+elephant means.</p></div>
+
+<div class="footnote"><p><a name="Footnote_28_34" id="Footnote_28_34"></a><a href="#FNanchor_28_34"><span class="label">[28]</span></a> In the only attempt which, so far as I know, has been made
+to refute the preceding argumentation, it is maintained that in the
+first form of the syllogism,
+</p>
+
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a thing which breathes flame,</div>
+<div style="margin-left: 2em;text-indent:-1em;">A dragon is a serpent,</div>
+<div style="margin-left: 2em;text-indent:-1em;">Therefore some serpent or serpents breathe flame,</div>
+
+<p>
+"there is just as much truth in the conclusion as there is in the
+premises, or rather, no more in the latter than in the former. If the
+general name serpent includes both real and imaginary serpents, there is
+no falsity in the conclusion; if not, there is falsity in the minor
+premise."
+</p><p>
+Let us, then, try to set out the syllogism on the hypothesis that the
+name serpent includes imaginary serpents. We shall find that it is now
+necessary to alter the predicates; for it cannot be asserted that an
+imaginary creature breathes flame: in predicating of it such a fact, we
+assert by the most positive implication that it is real and not
+imaginary. The conclusion must run thus, "Some serpent or serpents
+either do or are <i>imagined</i> to breathe flame." And to prove this
+conclusion by the instance of dragons, the premises must be, A dragon is
+<i>imagined</i> as breathing flame, A dragon is a (real or imaginary)
+serpent: from which it undoubtedly follows, that there are serpents
+which are imagined to breathe flame; but the major premise is not a
+definition, nor part of a definition; which is all that I am concerned
+to prove.
+</p><p>
+Let us now examine the other assertion&mdash;that if the word serpent stands
+for none but real serpents, the minor premise (a dragon is a serpent) is
+false. This is exactly what I have myself said of the premise,
+considered as a statement of fact: but it is not false as part of the
+definition of a dragon; and since the premises, or one of them, must be
+false, (the conclusion being so,) the real premise cannot be the
+definition, which is true, but the statement of fact, which is false.</p></div>
+
+<div class="footnote"><p><a name="Footnote_29_35" id="Footnote_29_35"></a><a href="#FNanchor_29_35"><span class="label">[29]</span></a> "Few people" (I have said in another place) "have
+reflected how great a knowledge of Things is required to enable a man to
+affirm that any given argument turns wholly upon words. There is,
+perhaps, not one of the leading terms of philosophy which is not used in
+almost innumerable shades of meaning, to express ideas more or less
+widely different from one another. Between two of these ideas a
+sagacious and penetrating mind will discern, as it were intuitively, an
+unobvious link of connexion, upon which, though perhaps unable to give a
+logical account of it, he will found a perfectly valid argument, which
+his critic, not having so keen an insight into the Things, will mistake
+for a fallacy turning on the double meaning of a term. And the greater
+the genius of him who thus safely leaps over the chasm, the greater will
+probably be the crowing and vain-glory of the mere logician, who,
+hobbling after him, evinces his own superior wisdom by pausing on its
+brink, and giving up as desperate his proper business of bridging it
+over."</p></div>
+</div>
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span></p>
+<h2><a name="BOOK_II" id="BOOK_II"></a>BOOK II.<br />
+
+OF REASONING.</h2>
+
+
+<blockquote><p><span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span></p><p>&#916;&#953;&#969;&#961;&#953;&#963;&#956;&#8051;&#957;&#969;&#957;
+&#948;&#949; &#964;&#959;&#8059;&#964;&#969;&#957; &#955;&#8051;&#947;&#969;&#956;&#949;&#957;
+&#7972;&#948;&#951;, &#948;&#953;&#8048; &#964;&#8055;&#957;&#969;&#957;,
+&#954;&#945;&#8054; &#960;&#8057;&#964;&#949;,
+&#954;&#945;&#8054; &#960;&#8182;&#962; &#947;&#8055;&#957;&#949;&#964;&#945;&#953;
+&#960;&#8118;&#962; &#963;&#965;&#955;&#955;&#959;&#947;&#953;&#963;&#956;&#8057;&#962;
+&#8021;&#963;&#964;&#949;&#961;&#959;&#957; &#948;&#8050; &#955;&#949;&#954;&#964;&#8051;&#959;&#957;
+&#960;&#949;&#961;&#8054;
+&#7936;&#960;&#959;&#948;&#949;&#8055;&#958;&#949;&#969;&#962;.
+&#928;&#961;&#8057;&#964;&#949;&#961;&#959;&#957; &#947;&#8048;&#961; &#960;&#949;&#961;&#8054;
+&#963;&#965;&#955;&#955;&#959;&#947;&#953;&#963;&#956;&#959;&#8166; &#955;&#949;&#954;&#964;&#8051;&#959;&#957;,
+&#7970; &#960;&#949;&#961;&#8054;
+&#7936;&#960;&#959;&#948;&#949;&#8055;&#958;&#949;&#969;&#962;,
+&#948;&#953;&#8048; &#964;&#8056; &#954;&#945;&#952;&#8057;&#955;&#959;&#965;
+&#956;&#8118;&#955;&#955;&#959;&#957; &#949;&#7984;&#957;&#945;&#8054; &#964;&#8056;&#957;
+&#963;&#965;&#955;&#955;&#959;&#947;&#953;&#963;&#956;&#8057;&#957;.
+&#7977; &#956;&#8050;&#957; &#947;&#8048;&#961; &#7936;&#960;&#8057;&#948;&#949;&#953;&#958;&#953;&#962;,
+&#963;&#965;&#955;&#955;&#959;&#947;&#953;&#963;&#956;&#8057;&#962; &#964;&#953;&#962;;
+&#8001; &#963;&#965;&#955;&#955;&#959;&#947;&#953;&#963;&#956;&#8057;&#962; &#948;&#8050; &#959;&#8016;
+&#960;&#8118;&#962;, &#7936;&#960;&#8057;&#948;&#949;&#953;&#958;&#953;&#962;.
+</p></blockquote>
+
+<p>
+<span style="margin-left: 50%;"><span class="smcap">Arist.</span> <i>Analyt. Prior.</i> l. i. cap. 4.</span><br />
+</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_I" id="BOOK_II_CHAPTER_I"></a>CHAPTER I.<br />
+
+OF INFERENCE, OR REASONING, IN GENERAL.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_I_1">� 1.</a> In the preceding Book, we have been occupied not with the nature of
+Proof, but with the nature of Assertion: the import conveyed by a
+Proposition, whether that Proposition be true or false; not the means by
+which to discriminate true from false Propositions. The proper subject,
+however, of Logic is Proof. Before we could understand what Proof is, it
+was necessary to understand what that is to which proof is applicable;
+what that is which can be a subject of belief or disbelief, of
+affirmation or denial; what, in short, the different kinds of
+Propositions assert.</p>
+
+<p>This preliminary inquiry we have prosecuted to a definite result.
+Assertion, in the first place, relates either to the meaning of words,
+or to some property of the things which words signify. Assertions
+respecting the meaning of words, among which definitions are the most
+important, hold a place, and an indispensable one, in philosophy; but as
+the meaning of words is essentially arbitrary, this class of assertions
+are not susceptible of truth or falsity, nor therefore of proof or
+disproof. Assertions respecting Things, or what may be called Real
+Propositions, in contradistinction to verbal ones, are of various sorts.
+We have analysed the import of each sort, and have ascertained the
+nature of the things they relate to, and the nature of what they
+severally assert respecting those things. We found that whatever be the
+form of the proposition, and whatever its nominal subject or predicate,
+the real subject of every proposition is some one or more facts or
+phenomena of consciousness, or some one or more of the hidden causes or
+powers to which we ascribe those facts; and that what is predicated or
+asserted, either in the affirmative or <span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>negative, of those phenomena or
+those powers, is always either Existence, Order in Place, Order in Time,
+Causation, or Resemblance. This, then, is the theory of the Import of
+Propositions, reduced to its ultimate elements: but there is another and
+a less abstruse expression for it, which, though stopping short in an
+earlier stage of the analysis, is sufficiently scientific for many of
+the purposes for which such a general expression is required. This
+expression recognises the commonly received distinction between Subject
+and Attribute, and gives the following as the analysis of the meaning of
+propositions:&mdash;Every Proposition asserts, that some given subject does
+or does not possess some attribute; or that some attribute is or is not
+(either in all or in some portion of the subjects in which it is met
+with) conjoined with some other attribute.</p>
+
+<p>We shall now for the present take our leave of this portion of our
+inquiry, and proceed to the peculiar problem of the Science of Logic,
+namely, how the assertions, of which we have analysed the import, are
+proved or disproved; such of them, at least, as, not being amenable to
+direct consciousness or intuition, are appropriate subjects of proof.</p>
+
+<p>We say of a fact or statement, that it is proved, when we believe its
+truth by reason of some other fact or statement from which it is said to
+<i>follow</i>. Most of the propositions, whether affirmative or negative,
+universal, particular, or singular, which we believe, are not believed
+on their own evidence, but on the ground of something previously
+assented to, from which they are said to be <i>inferred</i>. To infer a
+proposition from a previous proposition or propositions; to give
+credence to it, or claim credence for it, as a conclusion from something
+else; is to <i>reason</i>, in the most extensive sense of the term. There is
+a narrower sense, in which the name reasoning is confined to the form of
+inference which is termed ratiocination, and of which the syllogism is
+the general type. The reasons for not conforming to this restricted use
+of the term were stated in an earlier stage of our inquiry, and
+additional motives will be suggested by the considerations on which we
+are now about to enter.</p>
+
+
+<p><span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span></p><p class="newsection"><a name="BOOK_II_CHAPTER_I_2">� 2.</a> In proceeding to take into consideration the cases in which
+inferences can legitimately be drawn, we shall first mention some cases
+in which the inference is apparent, not real; and which require notice
+chiefly that they may not be confounded with cases of inference properly
+so called. This occurs when the proposition ostensibly inferred from
+another, appears on analysis to be merely a repetition of the same, or
+part of the same, assertion, which was contained in the first. All the
+cases mentioned in books of Logic as examples of �quipollency or
+equivalence of propositions, are of this nature. Thus, if we were to
+argue, No man is incapable of reason, for every man is rational; or, All
+men are mortal, for no man is exempt from death; it would be plain that
+we were not proving the proposition, but only appealing to another mode
+of wording it, which may or may not be more readily comprehensible by
+the hearer, or better adapted to suggest the real proof, but which
+contains in itself no shadow of proof.</p>
+
+<p>Another case is where, from an universal proposition, we affect to infer
+another which differs from it only in being particular: as All A is B,
+therefore Some A is B: No A is B, therefore Some A is not B. This, too,
+is not to conclude one proposition from another, but to repeat a second
+time something which had been asserted at first; with the difference,
+that we do not here repeat the whole of the previous assertion, but only
+an indefinite part of it.</p>
+
+<p>A third case is where, the antecedent having affirmed a predicate of a
+given subject, the consequent affirms of the same subject something
+already connoted by the former predicate: as, Socrates is a man,
+therefore Socrates is a living creature; where all that is connoted by
+living creature was affirmed of Socrates when he was asserted to be a
+man. If the propositions are negative, we must invert their order, thus:
+Socrates is not a living creature, therefore he is not a man; for if we
+deny the less, the greater, which includes it, is already denied by
+implication. These, therefore, are not really cases of inference; and
+yet the trivial examples by which, in manuals of Logic, the rules of the
+syllogism are <span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span>illustrated, are often of this ill-chosen kind; formal
+demonstrations of conclusions to which whoever understands the terms
+used in the statement of the data, has already, and consciously,
+assented.</p>
+
+<p>The most complex case of this sort of apparent inference is what is
+called the Conversion of propositions; which consists in turning the
+predicate into a subject, and the subject into a predicate, and framing
+out of the same terms thus reversed, another proposition, which must be
+true if the former is true. Thus, from the particular affirmative
+proposition, Some A is B, we may infer that Some B is A. From the
+universal negative, No A is B, we may conclude that No B is A. From the
+universal affirmative proposition, All A is B, it cannot be inferred
+that all B is A; though all water is liquid, it is not implied that all
+liquid is water; but it is implied that some liquid is so; and hence the
+proposition, All A is B, is legitimately convertible into Some B is A.
+This process, which converts an universal proposition into a particular,
+is termed conversion <i>per accidens</i>. From the proposition, Some A is not
+B, we cannot even infer that some B is not A; though some men are not
+Englishmen, it does not follow that some Englishmen are not men. The
+only mode usually recognised of converting a particular negative
+proposition, is in the form, Some A is not B, therefore, something which
+is not B is A; and this is termed conversion by contraposition. In this
+case, however, the predicate and subject are not merely reversed, but
+one of them is changed. Instead of [A] and [B], the terms of the new
+proposition are [a thing which is not B], and [A]. The original
+proposition, Some A <i>is not</i> B, is first changed into a proposition
+�quipollent with it, Some A <i>is</i> "a thing which is not B;" and the
+proposition, being now no longer a particular negative, but a particular
+affirmative, <i>admits</i> of conversion in the first mode, or as it is
+called, <i>simple</i> conversion.<a name="FNanchor_1_36" id="FNanchor_1_36"></a><a href="#Footnote_1_36" class="fnanchor">[1]</a></p>
+
+<p><span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span></p><p>In all these cases there is not really any inference; there is in the
+conclusion no new truth, nothing but what was already asserted in the
+premises, and obvious to whoever apprehends them. The fact asserted in
+the conclusion is either the very same fact, or part of the fact
+asserted in the original proposition. This follows from our previous
+analysis of the Import of Propositions. When we say, for example, that
+some lawful sovereigns are tyrants, what is the meaning of the
+assertion? That the attributes connoted by the term "lawful sovereign,"
+and the attributes connoted by the term "tyrant," sometimes coexist in
+the same individual. Now this is also precisely what we mean, when we
+say that some tyrants are lawful sovereigns; which, therefore, is not a
+second proposition inferred from the first, any more than the English
+translation of Euclid's Elements is a collection of theorems different
+from, and consequences of, those contained in the Greek original. Again,
+if we assert that no great general is a rash man, we mean that the
+attributes connoted by "great general," and those connoted by "rash,"
+never coexist in the same subject; which is also the exact meaning which
+would be expressed by saying, that no rash man is a great general. When
+we say that all quadrupeds are warm-blooded, we assert, not only that
+the attributes connoted by "quadruped" and those connoted by
+"warm-blooded" sometimes coexist, but that the former never exist
+without the latter: now the proposition, Some warm-blooded creatures are
+quadrupeds, expresses the first half of this meaning, dropping the
+latter half; and therefore has been already affirmed in the antecedent
+proposition, All quadrupeds are warm-blooded. But that <i>all</i>
+warm-blooded creatures are quadrupeds, or, in other words, that the
+attributes connoted by "warm-blooded" never exist without those connoted
+by "quadruped," has not been asserted, and cannot be inferred. In order
+to reassert, in an inverted form, the whole of what was affirmed in the
+proposition, All quadrupeds are warm-blooded, we must convert it by
+contraposition, thus, Nothing which is not warm-blooded is a quadruped.
+This proposition, and the one from which it is derived, are exactly
+equivalent, and either of them may be substituted <span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span>for the other; for,
+to say that when the attributes of a quadruped are present, those of a
+warm-blooded creature are present, is to say that when the latter are
+absent the former are absent.</p>
+
+<p>In a manual for young students, it would be proper to dwell at greater
+length on the conversion and �quipollency of propositions. For, though
+that cannot be called reasoning or inference which is a mere reassertion
+in different words of what had been asserted before, there is no more
+important intellectual habit, nor any the cultivation of which falls
+more strictly within the province of the art of logic, than that of
+discerning rapidly and surely the identity of an assertion when
+disguised under diversity of language. That important chapter in logical
+treatises which relates to the Opposition of Propositions, and the
+excellent technical language which logic provides for distinguishing the
+different kinds or modes of opposition, are of use chiefly for this
+purpose. Such considerations as these, that contrary propositions may
+both be false, but cannot both be true; that subcontrary propositions
+may both be true, but cannot both be false; that of two contradictory
+propositions one must be true and the other false; that of two
+subalternate propositions the truth of the universal proves the truth of
+the particular, and the falsity of the particular proves the falsity of
+the universal, but not <i>vice vers�</i>;<a name="FNanchor_2_37" id="FNanchor_2_37"></a><a href="#Footnote_2_37" class="fnanchor">[2]</a> are apt to appear, at first
+sight, very technical and mysterious, but when explained, seem almost
+too obvious to require so formal a statement, since the same amount of
+explanation which is necessary to make the principles intelligible,
+would enable the truths which they convey to be <span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span>apprehended in any
+particular case which can occur. In this respect, however, these axioms
+of logic are on a level with those of mathematics. That things which are
+equal to the same thing are equal to one another, is as obvious in any
+particular case as it is in the general statement: and if no such
+general maxim had ever been laid down, the demonstrations in Euclid
+would never have halted for any difficulty in stepping across the gap
+which this axiom at present serves to bridge over. Yet no one has ever
+censured writers on geometry, for placing a list of these elementary
+generalizations at the head of their treatises, as a first exercise to
+the learner of the faculty which will be required in him at every step,
+that of apprehending a <i>general</i> truth. And the student of logic, in the
+discussion even of such truths as we have cited above, acquires habits
+of circumspect interpretation of words, and of exactly measuring the
+length and breadth of his assertions, which are among the most
+indispensable conditions of any considerable mental attainment, and
+which it is one of the primary objects of logical discipline to
+cultivate.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_I_3">� 3.</a> Having noticed, in order to exclude from the province of Reasoning
+or Inference properly so called, the cases in which the progression from
+one truth to another is only apparent, the logical consequent being a
+mere repetition of the logical antecedent; we now pass to those which
+are cases of inference in the proper acceptation of the term, those in
+which we set out from known truths, to arrive at others really distinct
+from them.</p>
+
+<p>Reasoning, in the extended sense in which I use the term, and in which
+it is synonymous with Inference, is popularly said to be of two kinds:
+reasoning from particulars to generals, and reasoning from generals to
+particulars; the former being called Induction, the latter Ratiocination
+or Syllogism. It will presently be shown that there is a third species
+of reasoning, which falls under neither of these descriptions, and
+which, nevertheless, is not only valid, but is the foundation of both
+the others.</p>
+
+<p>It is necessary to observe, that the expressions, reasoning <span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span>from
+particulars to generals, and reasoning from generals to particulars, are
+recommended by brevity rather than by precision, and do not adequately
+mark, without the aid of a commentary, the distinction between Induction
+(in the sense now adverted to) and Ratiocination. The meaning intended
+by these expressions is, that Induction is inferring a proposition from
+propositions <i>less general</i> than itself, and Ratiocination is inferring
+a proposition from propositions <i>equally</i> or <i>more</i> general. When, from
+the observation of a number of individual instances, we ascend to a
+general proposition, or when, by combining a number of general
+propositions, we conclude from them another proposition still more
+general, the process, which is substantially the same in both instances,
+is called Induction. When from a general proposition, not alone (for
+from a single proposition nothing can be concluded which is not involved
+in the terms), but by combining it with other propositions, we infer a
+proposition of the same degree of generality with itself, or a less
+general proposition, or a proposition merely individual, the process is
+Ratiocination. When, in short, the conclusion is more general than the
+largest of the premises, the argument is commonly called Induction; when
+less general, or equally general, it is Ratiocination.</p>
+
+<p>As all experience begins with individual cases, and proceeds from them
+to generals, it might seem most conformable to the natural order of
+thought that Induction should be treated of before we touch upon
+Ratiocination. It will, however, be advantageous, in a science which
+aims at tracing our acquired knowledge to its sources, that the inquirer
+should commence with the latter rather than with the earlier stages of
+the process of constructing our knowledge; and should trace derivative
+truths backward to the truths from which they are deduced, and on which
+they depend for their evidence, before attempting to point out the
+original spring from which both ultimately take their rise. The
+advantages of this order of proceeding in the present instance will
+manifest themselves as we advance, in a manner superseding the necessity
+of any further justification or explanation.</p>
+
+<p><span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span></p><p>Of Induction, therefore, we shall say no more at present, than that it
+at least is, without doubt, a process of real inference. The conclusion
+in an induction embraces more than is contained in the premises. The
+principle or law collected from particular instances, the general
+proposition in which we embody the result of our experience, covers a
+much larger extent of ground than the individual experiments which form
+its basis. A principle ascertained by experience, is more than a mere
+summing up of what has been specifically observed in the individual
+cases which have been examined; it is a generalization grounded on those
+cases, and expressive of our belief, that what we there found true is
+true in an indefinite number of cases which we have not examined, and
+are never likely to examine. The nature and grounds of this inference,
+and the conditions necessary to make it legitimate, will be the subject
+of discussion in the Third Book: but that such inference really takes
+place is not susceptible of question. In every induction we proceed from
+truths which we knew, to truths which we did not know; from facts
+certified by observation, to facts which we have not observed, and even
+to facts not capable of being now observed; future facts, for example;
+but which we do not hesitate to believe on the sole evidence of the
+induction itself.</p>
+
+<p>Induction, then, is a real process of Reasoning or Inference. Whether,
+and in what sense, as much can be said of the Syllogism, remains to be
+determined by the examination into which we are about to enter.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_II" id="BOOK_II_CHAPTER_II"></a>CHAPTER II.<br />
+
+OF RATIOCINATION, OR SYLLOGISM.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_II_1">� 1.</a> The analysis of the Syllogism has been so accurately and fully
+performed in the common manuals of Logic, that in the present work,
+which is not designed as a manual, it is sufficient to recapitulate,
+<i>memori� caus�</i>, the leading results of that analysis, as a foundation
+for the remarks to be afterwards made on the functions of the syllogism,
+and the place which it holds in science.</p>
+
+<p>To a legitimate syllogism it is essential that there should be three,
+and no more than three, propositions, namely, the conclusion, or
+proposition to be proved, and two other propositions which together
+prove it, and which are called the premises. It is essential that there
+should be three, and no more than three, terms, namely, the subject and
+predicate of the conclusion, and another called the middleterm, which
+must be found in both premises, since it is by means of it that the
+other two terms are to be connected together. The predicate of the
+conclusion is called the major term of the syllogism; the subject of the
+conclusion is called the minor term. As there can be but three terms,
+the major and minor terms must each be found in one, and only one, of
+the premises, together with the middleterm which is in them both. The
+premise which contains the middleterm and the major term is called the
+major premise; that which contains the middleterm and the minor term is
+called the minor premise.</p>
+
+<p>Syllogisms are divided by some logicians into three <i>figures</i>, by others
+into four, according to the position of the middleterm, which may either
+be the subject in both premises, the predicate in both, or the subject
+in one and the predicate in the other. The most common case is that in
+which the middleterm is the subject of the major premise and the
+predicate of <span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span>the minor. This is reckoned as the first figure. When the
+middleterm is the predicate in both premises, the syllogism belongs to
+the second figure; when it is the subject in both, to the third. In the
+fourth figure the middleterm is the subject of the minor premise and the
+predicate of the major. Those writers who reckon no more than three
+figures, include this case in the first.</p>
+
+<p>Each figure is divided into <i>moods</i>, according to what are called the
+<i>quantity</i> and <i>quality</i> of the propositions, that is, according as they
+are universal or particular, affirmative or negative. The following are
+examples of all the legitimate moods, that is, all those in which the
+conclusion correctly follows from the premises. A is the minor term, C
+the major, B the middleterm.</p>
+
+<p class="center"><span class="smcap">First Figure.</span></p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All B is C</td><td align="left">No B is C</td><td align="left">All B is C</td><td align="left">No B is C</td></tr>
+<tr><td align="left">All A is B</td><td align="left">All A is B</td><td align="left">Some A is B</td><td align="left">Some A is B</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;"> therefore</span></td></tr>
+<tr><td align="left">All A is C</td><td align="left">No A is C</td><td align="left">Some A is C</td><td align="left">Some A is not C</td></tr>
+</table></div>
+
+<p class="center"><span class="smcap">Second Figure.</span></p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">No C is B</td><td align="left">All C is B</td><td align="left">No C is B</td><td align="left">All C is B</td></tr>
+<tr><td align="left">All A is B</td><td align="left">No A is B</td><td align="left">Some A is B</td><td align="left">Some A is not B</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">No A is C</td><td align="left">No A is C</td><td align="left">Some A is not C</td><td align="left">Some A is not C</td></tr>
+</table></div>
+
+<p class="center"><span class="smcap">Third Figure.</span></p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All B is C</td><td align="left">No B is C</td><td align="left">Some B is C</td><td align="left">All B is C</td><td align="left">Some B is not C</td><td align="left">No B is C</td></tr>
+<tr><td align="left">All B is A</td><td align="left">All B is A</td><td align="left">All B is A</td><td align="left">Some B is A</td><td align="left">All B is A</td><td align="left">Some B is A</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Some A is C</td><td align="left">Some A is not C</td><td align="left">Some A is C</td><td align="left">Some A is C</td><td align="left">Some A is not C</td><td align="left">Some A is not C</td></tr>
+</table></div>
+
+<p class="center"><span class="smcap">Fourth Figure.</span></p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All C is B</td><td align="left">All C is B</td><td align="left">Some C is B</td><td align="left">No C is B</td><td align="left">No C is B</td></tr>
+<tr><td align="left">All B is A</td><td align="left">No B is A</td><td align="left">All B is A</td><td align="left">All B is A</td><td align="left">Some B is A</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Some A is C</td><td align="left">Some A is not C</td><td align="left">Some A is C</td><td align="left">Some A is not C</td><td align="left">Some A is not C</td></tr>
+</table></div>
+
+<p>In these exemplars, or blank forms for making syllogisms, no place is
+assigned to <i>singular</i> propositions; not, of course, because such
+propositions are not used in ratiocination, but because, their predicate
+being affirmed or denied of the whole of the subject, they are ranked,
+for the purposes of the syllogism, with universal propositions. Thus,
+these two syllogisms&mdash;</p>
+
+<p><span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span></p>
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All men are mortal,</td><td align="left">All men are mortal</td></tr>
+<tr><td align="left">All kings are men,</td><td align="left">Socrates is a man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">All kings are mortal,</td><td align="left">Socrates is mortal,</td></tr>
+</table></div>
+
+<p>are arguments precisely similar, and are both ranked in the first mood
+of the first figure.</p>
+
+<p>The reasons why syllogisms in any of the above forms are legitimate,
+that is, why, if the premises are true, the conclusion must inevitably
+be so, and why this is not the case in any other possible mood, (that
+is, in any other combination of universal and particular, affirmative
+and negative propositions,) any person taking interest in these
+inquiries may be presumed to have either learned from the common school
+books of the syllogistic logic, or to be capable of discovering for
+himself. The reader may, however, be referred, for every needful
+explanation, to Archbishop Whately's <i>Elements of Logic</i>, where he will
+find stated with philosophical precision, and explained with remarkable
+perspicuity, the whole of the common doctrine of the syllogism.</p>
+
+<p>All valid ratiocination; all reasoning by which, from general
+propositions previously admitted, other propositions equally or less
+general are inferred; may be exhibited in some of the above forms. The
+whole of Euclid, for example, might be thrown without difficulty into a
+series of syllogisms, regular in mood and figure.</p>
+
+<p>Though a syllogism framed according to any of these formul� is a valid
+argument, all correct ratiocination admits of being stated in syllogisms
+of the first figure alone. The rules for throwing an argument in any of
+the other figures into the first figure, are called rules for the
+<i>reduction</i> of syllogisms. It is done by the <i>conversion</i> of one or
+other, or both, of the premises. Thus an argument in the first mood of
+the second figure, as&mdash;</p>
+
+
+<div class="wider" style="margin-left:10%;margin-right:10%">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">No C is B</td></tr>
+<tr><td align="left">All A is B</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">No A is C,</td></tr>
+</table></div>
+
+<p>may be reduced as follows. The proposition, No C is B, <span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span>being an
+universal negative, admits of simple conversion, and may be changed into
+No B is C, which, as we showed, is the very same assertion in other
+words&mdash;the same fact differently expressed. This transformation having
+been effected, the argument assumes the following form:&mdash;</p>
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">No B is C</td></tr>
+<tr><td align="left">All A is B</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">No A is C,</td></tr>
+</table></div>
+
+<p>which is a good syllogism in the second mood of the first figure. Again,
+an argument in the first mood of the third figure must resemble the
+following:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All B is C</td></tr>
+<tr><td align="left">All B is A</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Some A is C,</td></tr>
+</table></div>
+
+<p>where the minor premise, All B is A, conformably to what was laid down
+in the last chapter respecting universal affirmatives, does not admit of
+simple conversion, but may be converted <i>per accidens</i>, thus, Some A is
+B; which, though it does not express the whole of what is asserted in
+the proposition All B is A, expresses, as was formerly shown, part of
+it, and must therefore be true if the whole is true. We have, then, as
+the result of the reduction, the following syllogism in the third mood
+of the first figure:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All B is C</td></tr>
+<tr><td align="left">Some A is B,</td></tr>
+</table></div>
+
+<p>from which it obviously follows, that</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">Some A is C.</td></tr>
+</table></div>
+
+<p>In the same manner, or in a manner on which after these examples it is
+not necessary to enlarge, every mood of the second, third, and fourth
+figures may be reduced to some one of the four moods of the first. In
+other words, every conclusion which can be proved in any of the last
+three figures, may be proved in the first figure from the same premises,
+with a slight alteration in the mere manner of expressing <span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span>them. Every
+valid ratiocination, therefore, may be stated in the first figure, that
+is, in one of the following forms:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left" style="padding-right:1px;" colspan="3">Every B is C</td><td align="left" colspan="3">No B is C</td></tr>
+<tr><td align="left" style="padding-right:1px;">All A</td><td align="left" rowspan="2" style="padding-left:1px;"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-left:1px;">is B,</td><td align="left" style="padding-right:1px;">All A</td><td align="left" rowspan="2" style="padding-left:1px;"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-left:1px;">is B,</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some A</td><td align="left">Some A</td></tr>
+<tr><td align="left" style="padding-right:1px;"><span style="margin-left: 1em;">therefore</span></td><td align="left"></td><td align="left"></td><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left" style="padding-right:1px;">All A</td><td align="left" rowspan="2" style="padding-left:1px;"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-left:1px;">is C.</td><td align="left" style="padding-right:1px;">No A is</td><td align="left" rowspan="2" style="padding-left:1px;"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-left:1px;">C.</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some A</td><td align="left" style="padding-right:1px;">Some A is not</td></tr>
+</table></div>
+
+<p>Or if more significant symbols are preferred:&mdash;</p>
+
+<p>To prove an affirmative, the argument must admit of being stated in this
+form:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left" style="padding-right:1px;" colspan="3">All animals are mortal;</td></tr>
+<tr><td align="left" style="padding-right:1px;">All men</td><td align="left" rowspan="3" style="padding-left:1px;"><span style="font-size:300%;">}</span></td><td align="left" rowspan="3" style="padding-left:1px;">are animals;</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some men</td></tr>
+<tr><td align="left" style="padding-right:1px;">Socrates</td></tr>
+<tr><td align="left" style="padding-right:1px;"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left" style="padding-right:1px;">All men</td><td align="left" rowspan="3" style="padding-left:1px;"><span style="font-size:300%;">}</span></td><td align="left" rowspan="3" style="padding-left:1px;">are mortal.</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some men</td></tr>
+<tr><td align="left" style="padding-right:1px;">Socrates</td></tr>
+</table></div>
+
+<p>To prove a negative, the argument must be capable of being expressed in
+this form:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left" colspan="3" style="padding-right:1px;">No one who is capable of self-control is necessarily vicious;</td></tr>
+<tr><td align="left" style="padding-right:1px;">All negroes</td><td align="left" rowspan="3" style="padding-left:1px;"><span style="font-size:300%;">}</span></td><td align="left" rowspan="3" style="padding-left:1px;">are capable of self-control;</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some negroes</td></tr>
+<tr><td align="left" style="padding-right:1px;">Mr. A's negro</td></tr>
+<tr><td align="left" style="padding-right:1px;"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left" style="padding-right:1px;">No negroes are</td><td align="left" rowspan="3" style="padding-left:1px;"><span style="font-size:300%;">}</span></td><td align="left" rowspan="3" style="padding-left:1px;">necessarily vicious.</td></tr>
+<tr><td align="left" style="padding-right:1px;">Some negroes are not</td></tr>
+<tr><td align="left" style="padding-right:1px;">Mr. A's negro is not</td></tr>
+</table></div>
+
+<p>Though all ratiocination admits of being thrown into one or the other of
+these forms, and sometimes gains considerably by the transformation,
+both in clearness and in the obviousness of its consequence; there are,
+no doubt, cases in which the argument falls more naturally into one of
+the other three figures, and in which its conclusiveness is more
+<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>apparent at the first glance in those figures, than when reduced to the
+first. Thus, if the proposition were that pagans may be virtuous, and
+the evidence to prove it were the example of Aristides; a syllogism in
+the third figure,</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">Aristides was virtuous,</td></tr>
+<tr><td align="left">Aristides was a pagan,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Some pagan was virtuous,</td></tr>
+</table></div>
+
+<p>would be a more natural mode of stating the argument, and would carry
+conviction more instantly home, than the same ratiocination strained
+into the first figure, thus&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">Aristides was virtuous,</td></tr>
+<tr><td align="left">Some pagan was Aristides,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Some pagan was virtuous.</td></tr>
+</table></div>
+
+<p>A German philosopher, Lambert, whose <i>Neues Organon</i> (published in the
+year 1764) contains among other things one of the most elaborate and
+complete expositions which had ever been made of the syllogistic
+doctrine, has expressly examined what sort of arguments fall most
+naturally and suitably into each of the four figures; and his
+investigation is characterized by great ingenuity and clearness of
+thought.<a name="FNanchor_3_38" id="FNanchor_3_38"></a><a href="#Footnote_3_38" class="fnanchor">[3]</a> The argument, however, is one and the same, in whichever
+figure it is expressed; since, as we have already seen, the premises of
+a syllogism in the second, third, or fourth figure, and those of the
+syllogism in the first figure to which it may be reduced, are the same
+premises in everything except language, or, at least, as much of them as
+contributes to the proof of the conclusion <span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>is the same. We are
+therefore at liberty, in conformity with the general opinion of
+logicians, to consider the two elementary forms of the first figure as
+the universal types of all correct ratiocination; the one, when the
+conclusion to be proved is affirmative, the other, when it is negative;
+even though certain arguments may have a tendency to clothe themselves
+in the forms of the second, third, and fourth figures; which, however,
+cannot possibly happen with the only class of arguments which are of
+first-rate scientific importance, those in which the conclusion is an
+universal affirmative, such conclusions being susceptible of proof in
+the first figure alone.<a name="FNanchor_4_39" id="FNanchor_4_39"></a><a href="#Footnote_4_39" class="fnanchor">[4]</a></p>
+
+
+<p><span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span></p><p class="newsection"><a name="BOOK_II_CHAPTER_II_2">� 2.</a> On examining, then, these two general formul�, we find that in
+both of them, one premise, the major, is an universal proposition; and
+according as this is affirmative or negative, the conclusion is so too.
+All ratiocination, therefore, starts from a <i>general</i> proposition,
+principle, or assumption: a <span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>proposition in which a predicate is
+affirmed or denied of an entire class; that is, in which some attribute,
+or the negation of some attribute, is asserted of an indefinite number
+of objects distinguished by a common characteristic, and designated in
+consequence, by a common name.</p>
+
+<p>The other premise is always affirmative, and asserts that something
+(which may be either an individual, a class, or part <span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span>of a class)
+belongs to, or is included in, the class respecting which something was
+affirmed or denied in the major premise. It follows that the attribute
+affirmed or denied of the entire class may (if that affirmation or
+denial was correct) be affirmed or denied of the object or objects
+alleged to be included in the class: and this is precisely the assertion
+made in the conclusion.</p>
+
+<p>Whether or not the foregoing is an adequate account of the constituent
+parts of the syllogism, will be presently considered; but as far as it
+goes it is a true account. It has accordingly been generalized, and
+erected into a logical maxim, on which all ratiocination is said to be
+founded, insomuch that to reason, and to apply the maxim, are supposed
+to be one and the same thing. The maxim is, That whatever can be
+affirmed (or denied) of a class, may be affirmed (or denied) of
+everything included in the class. This axiom, supposed to be the basis
+of the syllogistic theory, is termed by logicians the <i>dictum de omni et
+nullo</i>.</p>
+
+<p>This maxim, however, when considered as a principle of reasoning,
+appears suited to a system of metaphysics once indeed generally
+received, but which for the last two centuries has been considered as
+finally abandoned, though there have not been wanting in our own day
+attempts at its revival. So long as what are termed Universals were
+regarded as a peculiar kind of substances, having an objective existence
+distinct from the individual objects classed under them, the <i>dictum de
+omni</i> conveyed an important meaning; because it expressed the
+intercommunity of nature, which it was necessary <span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span>on that theory that we
+should suppose to exist between those general substances and the
+particular substances which were subordinated to them. That everything
+predicable of the universal was predicable of the various individuals
+contained under it, was then no identical proposition, but a statement
+of what was conceived as a fundamental law of the universe. The
+assertion that the entire nature and properties of the <i>substantia
+secunda</i> formed part of the nature and properties of each of the
+individual substances called by the same name; that the properties of
+Man, for example, were properties of all men; was a proposition of real
+significance when man did not <i>mean</i> all men, but something inherent in
+men, and vastly superior to them in dignity. Now, however, when it is
+known that a class, an universal, a genus or species, is not an entity
+<i>per se</i>, but neither more nor less than the individual substances
+themselves which are placed in the class, and that there is nothing real
+in the matter except those objects, a common name given to them, and
+common attributes indicated by the name; what, I should be glad to know,
+do we learn by being told, that whatever can be affirmed of a class, may
+be affirmed of every object contained in the class? The class is nothing
+but the objects contained in it: and the <i>dictum de omni</i> merely amounts
+to the identical proposition, that whatever is true of certain objects,
+is true of each of those objects. If all ratiocination were no more than
+the application of this maxim to particular cases, the syllogism would
+indeed be, what it has so often been declared to be, solemn trifling.
+The <i>dictum de omni</i> is on a par with another truth, which in its time
+was also reckoned of great importance, "Whatever is, is." To give any
+real meaning to the <i>dictum de omni</i>, we must consider it not as an
+axiom, but as a definition; we must look upon it as intended to explain,
+in a circuitous and paraphrastic manner, the meaning of the word,
+<i>class</i>.</p>
+
+<p>An error which seemed finally refuted and dislodged from thought, often
+needs only put on a new suit of phrases, to be welcomed back to its old
+quarters, and allowed to repose unquestioned for another cycle of ages.
+Modern philosophers <span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>have not been sparing in their contempt for the
+scholastic dogma that genera and species are a peculiar kind of
+substances, which general substances being the only permanent things,
+while the individual substances comprehended under them are in a
+perpetual flux, knowledge, which necessarily imports stability, can only
+have relation to those general substances or universals, and not to the
+facts or particulars included under them. Yet, though nominally
+rejected, this very doctrine, whether disguised under the Abstract Ideas
+of Locke (whose speculations, however, it has less vitiated than those
+of perhaps any other writer who has been infected with it), under the
+ultra-nominalism of Hobbes and Condillac, or the ontology of the later
+Kantians, has never ceased to poison philosophy. Once accustomed to
+consider scientific investigation as essentially consisting in the study
+of universals, men did not drop this habit of thought when they ceased
+to regard universals as possessing an independent existence: and even
+those who went the length of considering them as mere names, could not
+free themselves from the notion that the investigation of truth
+consisted entirely or partly in some kind of conjuration or juggle with
+those names. When a philosopher adopted fully the Nominalist view of the
+signification of general language, retaining along with it the <i>dictum
+de omni</i> as the foundation of all reasoning, two such premises fairly
+put together were likely, if he was a consistent thinker, to land him in
+rather startling conclusions. Accordingly it has been seriously held, by
+writers of deserved celebrity, that the process of arriving at new
+truths by reasoning consists in the mere substitution of one set of
+arbitrary signs for another; a doctrine which they suppose to derive
+irresistible confirmation from the example of algebra. If there were any
+process in sorcery or necromancy more preternatural than this, I should
+be much surprised. The culminating point of this philosophy is the noted
+aphorism of Condillac, that a science is nothing, or scarcely anything,
+but <i>une langue bien faite</i>; in other words, that the one sufficient
+rule for discovering the nature and properties of objects is to name
+them properly: as if the reverse were not the truth, that it is
+impossible to name <span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span>them properly except in proportion as we are already
+acquainted with their nature and properties. Can it be necessary to say,
+that none, not even the most trivial knowledge with respect to Things,
+ever was or could be originally got at by any conceivable manipulation
+of mere names, as such; and that what can be learned from names, is only
+what somebody who used the names knew before? Philosophical analysis
+confirms the indication of common sense, that the function of names is
+but that of enabling us to <i>remember</i> and to <i>communicate</i> our thoughts.
+That they also strengthen, even to an incalculable extent, the power of
+thought itself, is most true: but they do this by no intrinsic and
+peculiar virtue; they do it by the power inherent in an artificial
+memory, an instrument of which few have adequately considered the
+immense potency. As an artificial memory, language truly is, what it has
+so often been called, an instrument of thought; but it is one thing to
+be the instrument, and another to be the exclusive subject upon which
+the instrument is exercised. We think, indeed, to a considerable extent,
+by means of names, but what we think of, are the things called by those
+names; and there cannot be a greater error than to imagine that thought
+can be carried on with nothing in our mind but names, or that we can
+make the names think for us.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_II_3">� 3.</a> Those who considered the <i>dictum de omni</i> as the foundation of the
+syllogism, looked upon arguments in a manner corresponding to the
+erroneous view which Hobbes took of propositions. Because there are some
+propositions which are merely verbal, Hobbes, in order apparently that
+his definition might be rigorously universal, defined a proposition as
+if no propositions declared anything except the meaning of words. If
+Hobbes was right; if no further account than this could be given of the
+import of propositions; no theory could be given but the commonly
+received one, of the combination of propositions in a syllogism. If the
+minor premise asserted nothing more than that something belongs to a
+class, and if the major premise asserted nothing of that class except
+that it is included in another class, the conclusion would only be <span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span>that
+what was included in the lower class is included in the higher, and the
+result, therefore, nothing except that the classification is consistent
+with itself. But we have seen that it is no sufficient account of the
+meaning of a proposition, to say that it refers something to, or
+excludes something from, a class. Every proposition which conveys real
+information asserts a matter of fact, dependent on the laws of nature,
+and not on classification. It asserts that a given object does or does
+not possess a given attribute; or it asserts that two attributes, or
+sets of attributes, do or do not (constantly or occasionally) coexist.
+Since such is the purport of all propositions which convey any real
+knowledge, and since ratiocination is a mode of acquiring real
+knowledge, any theory of ratiocination which does not recognise this
+import of propositions, cannot, we may be sure, be the true one.</p>
+
+<p>Applying this view of propositions to the two premises of a syllogism,
+we obtain the following results. The major premise, which, as already
+remarked, is always universal, asserts, that all things which have a
+certain attribute (or attributes) have or have not along with it, a
+certain other attribute (or attributes). The minor premise asserts that
+the thing or set of things which are the subject of that premise, have
+the first-mentioned attribute; and the conclusion is, that they have (or
+that they have not) the second. Thus in our former example,</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All men are mortal,</td></tr>
+<tr><td align="left">Socrates is a man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Socrates is mortal,</td></tr>
+</table></div>
+
+<p>the subject and predicate of the major premise are connotative terms,
+denoting objects and connoting attributes. The assertion in the major
+premise is, that along with one of the two sets of attributes, we always
+find the other: that the attributes connoted by "man" never exist unless
+conjoined with the attribute called mortality. The assertion in the
+minor premise is that the individual named Socrates possesses the former
+attributes; and it is concluded that he possesses also the <span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>attribute
+mortality. Or if both the premises are general propositions, as</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All men are mortal,</td></tr>
+<tr><td align="left">All kings are men,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">All kings are mortal,</td></tr>
+</table></div>
+
+<p>the minor premise asserts that the attributes denoted by kingship only
+exist in conjunction with those signified by the word man. The major
+asserts as before, that the last-mentioned attributes are never found
+without the attribute of mortality. The conclusion is, that wherever the
+attributes of kingship are found, that of mortality is found also.</p>
+
+<p>If the major premise were negative, as, No men are omnipotent, it would
+assert, not that the attributes connoted by "man" never exist without,
+but that they never exist with, those connoted by "omnipotent:" from
+which, together with the minor premise, it is concluded, that the same
+incompatibility exists between the attribute omnipotence and those
+constituting a king. In a similar manner we might analyse any other
+example of the syllogism.</p>
+
+<p>If we generalize this process, and look out for the principle or law
+involved in every such inference, and presupposed in every syllogism,
+the propositions of which are anything more than merely verbal; we find,
+not the unmeaning <i>dictum de omni et nullo</i>, but a fundamental
+principle, or rather two principles, strikingly resembling the axioms of
+mathematics. The first, which is the principle of affirmative
+syllogisms, is, that things which coexist with the same thing, coexist
+with one another. The second is the principle of negative syllogisms,
+and is to this effect: that a thing which coexists with another thing,
+with which other a third thing does not coexist, is not coexistent with
+that third thing. These axioms manifestly relate to facts, and not to
+conventions; and one or other of them is the ground of the legitimacy of
+every argument in which facts and not conventions are the matter treated
+of.<a name="FNanchor_5_40" id="FNanchor_5_40"></a><a href="#Footnote_5_40" class="fnanchor">[5]</a></p>
+
+
+<p><span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span></p><p class="newsection"><a name="BOOK_II_CHAPTER_II_4">� 4.</a> It remains to translate this exposition of the syllogism from the
+one into the other of the two languages in <span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>which we formerly
+remarked<a name="FNanchor_6_41" id="FNanchor_6_41"></a><a href="#Footnote_6_41" class="fnanchor">[6]</a> that all propositions, and of course therefore all
+combinations of propositions, might be expressed. We observed that a
+proposition might be considered in two different lights; as a portion of
+our knowledge of nature, or as a memorandum for our guidance. Under the
+former, or speculative aspect, an affirmative general proposition is an
+assertion of a speculative truth, viz. that whatever has a certain
+attribute has a certain other attribute. Under the other aspect, it is
+to be regarded not as a part of our knowledge, but as an aid for our
+practical exigencies, by enabling us, when we see or learn that an
+object possesses one of the two attributes, to infer that it possesses
+the other; thus employing the first attribute as a mark or evidence of
+the second. Thus regarded, every syllogism comes within the following
+general formula:&mdash;</p>
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">Attribute A is a mark of attribute B,</td></tr>
+<tr><td align="left">The given object has the mark A,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">The given object has the attribute B.</td></tr>
+</table></div>
+
+<p>Referred to this type, the arguments which we have lately <span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span>cited as
+specimens of the syllogism, will express themselves in the following
+manner:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">The attributes of man are a mark of the attribute mortality,</td></tr>
+<tr><td align="left">Socrates has the attributes of man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Socrates has the attribute mortality.</td></tr>
+</table></div>
+
+<p>And again,</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">The attributes of man are a mark of the attribute mortality,</td></tr>
+<tr><td align="left">The attributes of a king are a mark of the attributes of man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">The attributes of a king are a mark of the attribute mortality.</td></tr>
+</table></div>
+
+<p>And, lastly,</p>
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">The attributes of man are a mark of the absence of the attribute omnipotence,</td></tr>
+<tr><td align="left">The attributes of a king are a mark of the attributes of man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">The attributes of a king are a mark of the absence of the attribute signified by the word omnipotent (or, are evidence of the absence of that attribute).</td></tr>
+</table></div>
+
+<p>To correspond with this alteration in the form of the syllogisms, the
+axioms on which the syllogistic process is founded must undergo a
+corresponding transformation. In this altered phraseology, both those
+axioms may be brought under one general expression; namely, that
+whatever has any mark, has that which it is a mark of. Or, when the
+minor premise as well as the major is universal, we may state it thus:
+Whatever is a mark of any mark, is a mark of that which this last is a
+mark of. To trace the identity of these axioms with those previously
+laid down, may be left to the intelligent reader. We shall find, as we
+proceed, the great convenience of the phraseology into which we have
+last thrown them, and which is better adapted than any I am acquainted
+with, to express with precision and force what is aimed at, and actually
+accomplished, in every case of the ascertainment of a truth by
+ratiocination.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_III" id="BOOK_II_CHAPTER_III"></a>CHAPTER III.<br />
+
+OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_1">� 1.</a> We have shown what is the real nature of the truths with which the
+Syllogism is conversant, in contradistinction to the more superficial
+manner in which their import is conceived in the common theory; and what
+are the fundamental axioms on which its probative force or
+conclusiveness depends. We have now to inquire, whether the syllogistic
+process, that of reasoning from generals to particulars, is, or is not,
+a process of inference; a progress from the known to the unknown: a
+means of coming to a knowledge of something which we did not know
+before.</p>
+
+<p>Logicians have been remarkably unanimous in their mode of answering this
+question. It is universally allowed that a syllogism is vicious if there
+be anything more in the conclusion than was assumed in the premises. But
+this is, in fact, to say, that nothing ever was, or can be, proved by
+syllogism, which was not known, or assumed to be known, before. Is
+ratiocination, then, not a process of inference? And is the syllogism,
+to which the word reasoning has so often been represented to be
+exclusively appropriate, not really entitled to be called reasoning at
+all? This seems an inevitable consequence of the doctrine, admitted by
+all writers on the subject, that a syllogism can prove no more than is
+involved in the premises. Yet the acknowledgment so explicitly made, has
+not prevented one set of writers from continuing to represent the
+syllogism as the correct analysis of what the mind actually performs in
+discovering and proving the larger half of the truths, whether of
+science or of daily life, which we believe; while those who have avoided
+this inconsistency, and followed out the general theorem respecting the
+logical value <span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>of the syllogism to its legitimate corollary, have been
+led to impute uselessness and frivolity to the syllogistic theory
+itself, on the ground of the <i>petitio principii</i> which they allege to be
+inherent in every syllogism. As I believe both these opinions to be
+fundamentally erroneous, I must request the attention of the reader to
+certain considerations, without which any just appreciation of the true
+character of the syllogism, and the functions it performs in philosophy,
+appears to me impossible; but which seem to have been either overlooked,
+or insufficiently adverted to, both by the defenders of the syllogistic
+theory and by its assailants.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_2">� 2.</a> It must be granted that in every syllogism, considered as an
+argument to prove the conclusion, there is a <i>petitio principii</i>. When
+we say,</p>
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All men are mortal,</td></tr>
+<tr><td align="left">Socrates is a man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">Socrates is mortal;</td></tr>
+</table></div>
+
+<p>it is unanswerably urged by the adversaries of the syllogistic theory,
+that the proposition, Socrates is mortal, is presupposed in the more
+general assumption, All men are mortal: that we cannot be assured of the
+mortality of all men, unless we are already certain of the mortality of
+every individual man: that if it be still doubtful whether Socrates, or
+any other individual we choose to name, be mortal or not, the same
+degree of uncertainty must hang over the assertion, All men are mortal:
+that the general principle, instead of being given as evidence of the
+particular case, cannot itself be taken for true without exception,
+until every shadow of doubt which could affect any case comprised with
+it, is dispelled by evidence <i>aliund�</i>; and then what remains for the
+syllogism to prove? That, in short, no reasoning from generals to
+particulars can, as such, prove anything: since from a general principle
+we cannot infer any particulars, but those which the principle itself
+assumes as known.</p>
+
+<p>This doctrine appears to me irrefragable; and if logicians, <span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span>though
+unable to dispute it, have usually exhibited a strong disposition to
+explain it away, this was not because they could discover any flaw in
+the argument itself, but because the contrary opinion seemed to rest on
+arguments equally indisputable. In the syllogism last referred to, for
+example, or in any of those which we previously constructed, is it not
+evident that the conclusion may, to the person to whom the syllogism is
+presented, be actually and <i>bon� fide</i> a new truth? Is it not matter of
+daily experience that truths previously unthought of, facts which have
+not been, and cannot be, directly observed, are arrived at by way of
+general reasoning? We believe that the Duke of Wellington is mortal. We
+do not know this by direct observation, so long as he is not yet dead.
+If we were asked how, this being the case, we know the duke to be
+mortal, we should probably answer, Because all men are so. Here,
+therefore, we arrive at the knowledge of a truth not (as yet)
+susceptible of observation, by a reasoning which admits of being
+exhibited in the following syllogism:&mdash;</p>
+
+
+
+<div class="wider">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All men are mortal,</td></tr>
+<tr><td align="left">The Duke of Wellington is a man,</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">therefore</span></td></tr>
+<tr><td align="left">The Duke of Wellington is mortal.</td></tr>
+</table></div>
+
+<p>And since a large portion of our knowledge is thus acquired, logicians
+have persisted in representing the syllogism as a process of inference
+or proof; though none of them has cleared up the difficulty which arises
+from the inconsistency between that assertion, and the principle, that
+if there be anything in the conclusion which was not already asserted in
+the premises, the argument is vicious. For it is impossible to attach
+any serious scientific value to such a mere salvo, as the distinction
+drawn between being involved <i>by implication</i> in the premises, and being
+directly asserted in them. When Archbishop Whately says<a name="FNanchor_7_42" id="FNanchor_7_42"></a><a href="#Footnote_7_42" class="fnanchor">[7]</a> that the
+object of reasoning is "merely to expand and unfold the assertions wrapt
+up, as it were, and implied in those with which we set out, and to bring
+a person <span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span>to perceive and acknowledge the full force of that which he
+has admitted," he does not, I think, meet the real difficulty requiring
+to be explained, namely, how it happens that a science, like geometry,
+<i>can</i> be all "wrapt up" in a few definitions and axioms. Nor does this
+defence of the syllogism differ much from what its assailants urge
+against it as an accusation, when they charge it with being of no use
+except to those who seek to press the consequences of an admission into
+which a person has been entrapped without having considered and
+understood its full force. When you admitted the major premise, you
+asserted the conclusion; but, says Archbishop Whately, you asserted it
+by implication merely: this, however, can here only mean that you
+asserted it unconsciously; that you did not know you were asserting it;
+but, if so, the difficulty revives in this shape&mdash;Ought you not to have
+known? Were you warranted in asserting the general proposition without
+having satisfied yourself of the truth of everything which it fairly
+includes? And if not, is not the syllogistic art <i>prim� facie</i> what its
+assailants affirm it to be, a contrivance for catching you in a trap,
+and holding you fast in it?<a name="FNanchor_8_43" id="FNanchor_8_43"></a><a href="#Footnote_8_43" class="fnanchor">[8]</a></p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_3">� 3.</a> From this difficulty there appears to be but one issue. The
+proposition that the Duke of Wellington is mortal, is evidently an
+inference; it is got at as a conclusion <span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span>from something else; but do we,
+in reality, conclude it from the proposition, All men are mortal? I
+answer, no.</p>
+
+<p>The error committed is, I conceive, that of overlooking the distinction
+between two parts of the process of philosophizing, the inferring part,
+and the registering part; and ascribing to the latter the functions of
+the former. The mistake is that of referring a person to his own notes
+for the origin of his knowledge. If a person is asked a question, and is
+at the moment unable to answer it, he may refresh his memory by turning
+to a memorandum which he carries about with him. But if he were asked,
+how the fact came to his knowledge, he would scarcely answer, because it
+was set down in his note-book: unless the book was written, like the
+Koran, with a quill from the wing of the angel Gabriel.</p>
+
+<p>Assuming that the proposition, The Duke of Wellington is mortal, is
+immediately an inference from the proposition, All men are mortal;
+whence do we derive our knowledge of that general truth? Of course from
+observation. Now, all which man can observe are individual cases. From
+these all general truths must be drawn, and into these they may be again
+resolved; for a general truth is but an aggregate of particular truths;
+a comprehensive expression, by which an indefinite number of individual
+facts are affirmed or denied at once. But a general proposition is not
+merely a compendious form for recording and preserving in the memory a
+number of particular facts, all of which have been observed.
+Generalization is not a process of mere naming, it is also a process of
+inference. From instances which we have observed, we feel warranted in
+concluding, that what we found true in those instances, holds in all
+similar ones, past, present, and future, however numerous they may be.
+We then, by that valuable contrivance of language which enables us to
+speak of many as if they were one, record all that we have observed,
+together with all that we infer from our observations, in one concise
+expression; and have thus only one proposition, instead of an endless
+number, to remember or to communicate. The results of many observations
+and <span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span>inferences, and instructions for making innumerable inferences in
+unforeseen cases, are compressed into one short sentence.</p>
+
+<p>When, therefore, we conclude from the death of John and Thomas, and
+every other person we ever heard of in whose case the experiment had
+been fairly tried, that the Duke of Wellington is mortal like the rest;
+we may, indeed, pass through the generalization, All men are mortal, as
+an intermediate stage; but it is not in the latter half of the process,
+the descent from all men to the Duke of Wellington, that the <i>inference</i>
+resides. The inference is finished when we have asserted that all men
+are mortal. What remains to be performed afterwards is merely
+decyphering our own notes.</p>
+
+<p>Archbishop Whately has contended that syllogizing, or reasoning from
+generals to particulars, is not, agreeably to the vulgar idea, a
+peculiar <i>mode</i> of reasoning, but the philosophical analysis of <i>the</i>
+mode in which all men reason, and must do so if they reason at all. With
+the deference due to so high an authority, I cannot help thinking that
+the vulgar notion is, in this case, the more correct. If, from our
+experience of John, Thomas, &amp;c., who once were living, but are now dead,
+we are entitled to conclude that all human beings are mortal, we might
+surely without any logical inconsequence have concluded at once from
+those instances, that the Duke of Wellington is mortal. The mortality of
+John, Thomas, and company is, after all, the whole evidence we have for
+the mortality of the Duke of Wellington. Not one iota is added to the
+proof by interpolating a general proposition. Since the individual cases
+are all the evidence we can possess, evidence which no logical form into
+which we choose to throw it can make greater than it is; and since that
+evidence is either sufficient in itself, or, if insufficient for the one
+purpose, cannot be sufficient for the other; I am unable to see why we
+should be forbidden to take the shortest cut from these sufficient
+premises to the conclusion, and constrained to travel the "high priori
+road," by the arbitrary fiat of logicians. I cannot perceive why it
+should be impossible <span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>to journey from one place to another unless we
+"march up a hill, and then march down again." It may be the safest road,
+and there may be a resting-place at the top of the hill, affording a
+commanding view of the surrounding country; but for the mere purpose of
+arriving at our journey's end, our taking that road is perfectly
+optional; it is a question of time, trouble, and danger.</p>
+
+<p>Not only <i>may</i> we reason from particulars to particulars without passing
+through generals, but we perpetually do so reason. All our earliest
+inferences are of this nature. From the first dawn of intelligence we
+draw inferences, but years elapse before we learn the use of general
+language. The child, who, having burnt his fingers, avoids to thrust
+them again into the fire, has reasoned or inferred, though he has never
+thought of the general maxim, Fire burns. He knows from memory that he
+has been burnt, and on this evidence believes, when he sees a candle,
+that if he puts his finger into the flame of it, he will be burnt again.
+He believes this in every case which happens to arise; but without
+looking, in each instance, beyond the present case. He is not
+generalizing; he is inferring a particular from particulars. In the same
+way, also, brutes reason. There is no ground for attributing to any of
+the lower animals the use of signs, of such a nature as to render
+general propositions possible. But those animals profit by experience,
+and avoid what they have found to cause them pain, in the same manner,
+though not always with the same skill, as a human creature. Not only the
+burnt child, but the burnt dog, dreads the fire.</p>
+
+<p>I believe that, in point of fact, when drawing inferences from our
+personal experience, and not from maxims handed down to us by books or
+tradition, we much oftener conclude from particulars to particulars
+directly, than through the intermediate agency of any general
+proposition. We are constantly reasoning from ourselves to other people,
+or from one person to another, without giving ourselves the trouble to
+erect our observations into general maxims of human or external nature.
+When we conclude that some person will, on some given occasion, feel or
+act so and so, we sometimes <span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span>judge from an enlarged consideration of the
+manner in which human beings in general, or persons of some particular
+character, are accustomed to feel and act: but much oftener from merely
+recollecting the feelings and conduct of the same person in some
+previous instance, or from considering how we should feel or act
+ourselves. It is not only the village matron, who, when called to a
+consultation upon the case of a neighbour's child, pronounces on the
+evil and its remedy simply on the recollection and authority of what she
+accounts the similar case of her Lucy. We all, where we have no definite
+maxims to steer by, guide ourselves in the same way: and if we have an
+extensive experience, and retain its impressions strongly, we may
+acquire in this manner a very considerable power of accurate judgment,
+which we may be utterly incapable of justifying or of communicating to
+others. Among the higher order of practical intellects there have been
+many of whom it was remarked how admirably they suited their means to
+their ends, without being able to give any sufficient reasons for what
+they did; and applied, or seemed to apply, recondite principles which
+they were wholly unable to state. This is a natural consequence of
+having a mind stored with appropriate particulars, and having been long
+accustomed to reason at once from these to fresh particulars, without
+practising the habit of stating to oneself or to others the
+corresponding general propositions. An old warrior, on a rapid glance at
+the outlines of the ground, is able at once to give the necessary orders
+for a skilful arrangement of his troops; though if he has received
+little theoretical instruction, and has seldom been called upon to
+answer to other people for his conduct, he may never have had in his
+mind a single general theorem respecting the relation between ground and
+array. But his experience of encampments, in circumstances more or less
+similar, has left a number of vivid, unexpressed, ungeneralized
+analogies in his mind, the most appropriate of which, instantly
+suggesting itself, determines him to a judicious arrangement.</p>
+
+<p>The skill of an uneducated person in the use of weapons, <span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span>or of tools,
+is of a precisely similar nature. The savage who executes unerringly the
+exact throw which brings down his game, or his enemy, in the manner most
+suited to his purpose, under the operation of all the conditions
+necessarily involved, the weight and form of the weapon, the direction
+and distance of the object, the action of the wind, &amp;c., owes this power
+to a long series of previous experiments, the results of which he
+certainly never framed into any verbal theorems or rules. The same thing
+may generally be said of any other extraordinary manual dexterity. Not
+long ago a Scotch manufacturer procured from England, at a high rate of
+wages, a working dyer, famous for producing very fine colours, with the
+view of teaching to his other workmen the same skill. The workman came;
+but his mode of proportioning the ingredients, in which lay the secret
+of the effects he produced, was by taking them up in handfuls, while the
+common method was to weigh them. The manufacturer sought to make him
+turn his handling system into an equivalent weighing system, that the
+general principle of his peculiar mode of proceeding might be
+ascertained. This, however, the man found himself quite unable to do,
+and therefore could impart his skill to nobody. He had, from the
+individual cases of his own experience, established a connexion in his
+mind between fine effects of colour, and tactual perceptions in handling
+his dyeing materials; and from these perceptions he could, in any
+particular case, infer the means to be employed, and the effects which
+would be produced, but could not put others in possession of the grounds
+on which he proceeded, from having never generalized them in his own
+mind, or expressed them in language.</p>
+
+<p>Almost every one knows Lord Mansfield's advice to a man of practical
+good sense, who, being appointed governor of a colony, had to preside in
+its court of justice, without previous judicial practice or legal
+education. The advice was to give his decision boldly, for it would
+probably be right; but never to venture on assigning reasons, for they
+would almost infallibly be wrong. In cases like this, which are of no
+uncommon occurrence, it would be absurd to suppose <span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span>that the bad reason
+was the source of the good decision. Lord Mansfield knew that if any
+reason were assigned it would be necessarily an afterthought, the judge
+being <i>in fact</i> guided by impressions from past experience, without the
+circuitous process of framing general principles from them, and that if
+he attempted to frame any such he would assuredly fail. Lord Mansfield,
+however, would not have doubted that a man of equal experience who had
+also a mind stored with general propositions derived by legitimate
+induction from that experience, would have been greatly preferable as a
+judge, to one, however sagacious, who could not be trusted with the
+explanation and justification of his own judgments. The cases of men of
+talent performing wonderful things they know not how, are examples of
+the rudest and most spontaneous form of the operations of superior
+minds. It is a defect in them, and often a source of errors, not to have
+generalized as they went on; but generalization, though a help, the most
+important indeed of all helps, is not an essential.</p>
+
+<p>Even the scientifically instructed, who possess, in the form of general
+propositions, a systematic record of the results of the experience of
+mankind, need not always revert to those general propositions in order
+to apply that experience to a new case. It is justly remarked by Dugald
+Stewart, that though the reasonings in mathematics depend entirely on
+the axioms, it is by no means necessary to our seeing the conclusiveness
+of the proof, that the axioms should be expressly adverted to. When it
+is inferred that AB is equal to CD because each of them is equal to EF,
+the most uncultivated understanding, as soon as the propositions were
+understood, would assent to the inference, without having ever heard of
+the general truth that "things which are equal to the same thing are
+equal to one another." This remark of Stewart, consistently followed
+out, goes to the root, as I conceive, of the philosophy of
+ratiocination; and it is to be regretted that he himself stopt short at
+a much more limited application of it. He saw that the general
+propositions on which a reasoning is said to depend, may, in certain
+cases, be altogether omitted, without impairing <span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span>its probative force.
+But he imagined this to be a peculiarity belonging to axioms; and argued
+from it, that axioms are not the foundations or first principles of
+geometry, from which all the other truths of the science are
+synthetically deduced (as the laws of motion and of the composition of
+forces in dynamics, the equal mobility of fluids in hydrostatics, the
+laws of reflection and refraction in optics, are the first principles of
+those sciences); but are merely necessary assumptions, self-evident
+indeed, and the denial of which would annihilate all demonstration, but
+from which, as premises, nothing can be demonstrated. In the present, as
+in many other instances, this thoughtful and elegant writer has
+perceived an important truth, but only by halves. Finding, in the case
+of geometrical axioms, that general names have not any talismanic virtue
+for conjuring new truths out of the well where they lie hid, and not
+seeing that this is equally true in every other case of generalization,
+he contended that axioms are in their nature barren of consequences, and
+that the really fruitful truths, the real first principles of geometry,
+are the definitions; that the definition, for example, of the circle is
+to the properties of the circle, what the laws of equilibrium and of the
+pressure of the atmosphere are to the rise of the mercury in the
+Torricellian tube. Yet all that he had asserted respecting the function
+to which the axioms are confined in the demonstrations of geometry,
+holds equally true of the definitions. Every demonstration in Euclid
+might be carried on without them. This is apparent from the ordinary
+process of proving a proposition of geometry by means of a diagram. What
+assumption, in fact, do we set out from, to demonstrate by a diagram any
+of the properties of the circle? Not that in all circles the radii are
+equal, but only that they are so in the circle ABC. As our warrant for
+assuming this, we appeal, it is true, to the definition of a circle in
+general; but it is only necessary that the assumption be granted in the
+case of the particular circle supposed. From this, which is not a
+general but a singular proposition, combined with other propositions of
+a similar kind, some of which <i>when generalized</i> are called definitions,
+and others axioms, we prove that a certain conclusion is true, not of
+all circles, but <span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span>of the particular circle ABC; or at least would be so,
+if the facts precisely accorded with our assumptions. The enunciation,
+as it is called, that is, the general theorem which stands at the head
+of the demonstration, is not the proposition actually demonstrated. One
+instance only is demonstrated: but the process by which this is done, is
+a process which, when we consider its nature, we perceive might be
+exactly copied in an indefinite number of other instances; in every
+instance which conforms to certain conditions. The contrivance of
+general language furnishing us with terms which connote these
+conditions, we are able to assert this indefinite multitude of truths in
+a single expression, and this expression is the general theorem. By
+dropping the use of diagrams, and substituting, in the demonstrations,
+general phrases for the letters of the alphabet, we might prove the
+general theorem directly, that is, we might demonstrate all the cases at
+once; and to do this we must, of course, employ as our premises, the
+axioms and definitions in their general form. But this only means, that
+if we can prove an individual conclusion by assuming an individual fact,
+then in whatever case we are warranted in making an exactly similar
+assumption, we may draw an exactly similar conclusion. The definition is
+a sort of notice to ourselves and others, what assumptions we think
+ourselves entitled to make. And so in all cases, the general
+propositions, whether called definitions, axioms, or laws of nature,
+which we lay down at the beginning of our reasonings, are merely
+abridged statements, in a kind of short-hand, of the particular facts,
+which, as occasion arises, we either think we may proceed on as proved,
+or intend to assume. In any one demonstration it is enough if we assume
+for a particular case suitably selected, what by the statement of the
+definition or principle we announce that we intend to assume in all
+cases which may arise. The definition of the circle, therefore, is to
+one of Euclid's demonstrations, exactly what, according to Stewart, the
+axioms are; that is, the demonstration does not depend on it, but yet if
+we deny it the demonstration fails. The proof does not rest on the
+general assumption, but on a similar assumption confined to the
+particular case: that case, however, <span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span>being chosen as a specimen or
+paradigm of the whole class of cases included in the theorem, there can
+be no ground for making the assumption in that case which does not exist
+in every other; and to deny the assumption as a general truth, is to
+deny the right of making it in the particular instance.</p>
+
+<p>There are, undoubtedly, the most ample reasons for stating both the
+principles and the theorems in their general form, and these will be
+explained presently, so far as explanation is requisite. But, that
+unpractised learners, even in making use of one theorem to demonstrate
+another, reason rather from particular to particular than from the
+general proposition, is manifest from the difficulty they find in
+applying a theorem to a case in which the configuration of the diagram
+is extremely unlike that of the diagram by which the original theorem
+was demonstrated. A difficulty which, except in cases of unusual mental
+power, long practice can alone remove, and removes chiefly by rendering
+us familiar with all the configurations consistent with the general
+conditions of the theorem.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_4">� 4.</a> From the considerations now adduced, the following conclusions seem
+to be established. All inference is from particulars to particulars:
+General propositions are merely registers of such inferences already
+made, and short formul� for making more: The major premise of a
+syllogism, consequently, is a formula of this description: and the
+conclusion is not an inference drawn <i>from</i> the formula, but an
+inference drawn <i>according</i> to the formula: the real logical antecedent,
+or premise, being the particular facts from which the general
+proposition was collected by induction. Those facts, and the individual
+instances which supplied them, may have been forgotten: but a record
+remains, not indeed descriptive of the facts themselves, but showing how
+those cases may be distinguished, respecting which the facts, when
+known, were considered to warrant a given inference. According to the
+indications of this record we draw our conclusion; which is, to all
+intents and purposes, a conclusion from the forgotten facts. <span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span>For this
+it is essential that we should read the record correctly: and the rules
+of the syllogism are a set of precautions to ensure our doing so.</p>
+
+<p>This view of the functions of the syllogism is confirmed by the
+consideration of precisely those cases which might be expected to be
+least favourable to it, namely, those in which ratiocination is
+independent of any previous induction. We have already observed that the
+syllogism, in the ordinary course of our reasoning, is only the latter
+half of the process of travelling from premises to a conclusion. There
+are, however, some peculiar cases in which it is the whole process.
+Particulars alone are capable of being subjected to observation; and all
+knowledge which is derived from observation, begins, therefore, of
+necessity, in particulars; but our knowledge may, in cases of certain
+descriptions, be conceived as coming to us from other sources than
+observation. It may present itself as coming from testimony, which, on
+the occasion and for the purpose in hand, is accepted as of an
+authoritative character: and the information thus communicated, may be
+conceived to comprise not only particular facts but general
+propositions, as when a scientific doctrine is accepted without
+examination on the authority of writers, or a theological doctrine on
+that of Scripture. Or the generalization may not be, in the ordinary
+sense, an assertion at all, but a command; a law, not in the
+philosophical, but in the moral and political sense of the term: an
+expression of the desire of a superior, that we, or any number of other
+persons, shall conform our conduct to certain general instructions. So
+far as this asserts a fact, namely, a volition of the legislator, that
+fact is an individual fact, and the proposition, therefore, is not a
+general proposition. But the description therein contained of the
+conduct which it is the will of the legislator that his subjects should
+observe, is general. The proposition asserts, not that all men <i>are</i>
+anything, but that all men <i>shall</i> do something.</p>
+
+<p>In both these cases the generalities are the original data, and the
+particulars are elicited from them by a process which correctly resolves
+itself into a series of syllogisms. The real nature, however, of the
+supposed deductive process, is evident <span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span>enough. The only point to be
+determined is, whether the authority which declared the general
+proposition, intended to include this case in it; and whether the
+legislator intended his command to apply to the present case among
+others, or not. This is ascertained by examining whether the case
+possesses the marks by which, as those authorities have signified, the
+cases which they meant to certify or to influence may be known. The
+object of the inquiry is to make out the witness's or the legislator's
+intention, through the indication given by their words. This is a
+question, as the Germans express it, of hermeneutics. The operation is
+not a process of inference, but a process of interpretation.</p>
+
+<p>In this last phrase we have obtained an expression which appears to me
+to characterize, more aptly than any other, the functions of the
+syllogism in all cases. When the premises are given by authority, the
+function of Reasoning is to ascertain the testimony of a witness, or the
+will of a legislator, by interpreting the signs in which the one has
+intimated his assertion and the other his command. In like manner, when
+the premises are derived from observation, the function of Reasoning is
+to ascertain what we (or our predecessors) formerly thought might be
+inferred from the observed facts, and to do this by interpreting a
+memorandum of ours, or of theirs. The memorandum reminds us, that from
+evidence, more or less carefully weighed, it formerly appeared that a
+certain attribute might be inferred wherever we perceive a certain mark.
+The proposition, All men are mortal (for instance) shows that we have
+had experience from which we thought it followed that the attributes
+connoted by the term man, are a mark of mortality. But when we conclude
+that the Duke of Wellington is mortal, we do not infer this from the
+memorandum, but from the former experience. All that we infer from the
+memorandum is our own previous belief, (or that of those who transmitted
+to us the proposition), concerning the inferences which that former
+experience would warrant.</p>
+
+<p>This view of the nature of the syllogism renders consistent and
+intelligible what otherwise remains obscure and <span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span>confused in the theory
+of Archbishop Whately and other enlightened defenders of the syllogistic
+doctrine, respecting the limits to which its functions are confined.
+They affirm in as explicit terms as can be used, that the sole office of
+general reasoning is to prevent inconsistency in our opinions; to
+prevent us from assenting to anything, the truth of which would
+contradict something to which we had previously on good grounds given
+our assent. And they tell us, that the sole ground which a syllogism
+affords for assenting to the conclusion, is that the supposition of its
+being false, combined with the supposition that the premises are true,
+would lead to a contradiction in terms. Now this would be but a lame
+account of the real grounds which we have for believing the facts which
+we learn from reasoning, in contradistinction to observation. The true
+reason why we believe that the Duke of Wellington will die, is that his
+fathers, and our fathers, and all other persons who were cotemporary
+with them, have died. Those facts are the real premises of the
+reasoning. But we are not led to infer the conclusion from those
+premises, by the necessity of avoiding any verbal inconsistency. There
+is no contradiction in supposing that all those persons have died, and
+that the Duke of Wellington may, notwithstanding, live for ever. But
+there would be a contradiction if we first, on the ground of those same
+premises, made a general assertion including and covering the case of
+the Duke of Wellington, and then refused to stand to it in the
+individual case. There is an inconsistency to be avoided between the
+memorandum we make of the inferences which may be justly drawn in future
+cases, and the inferences we actually draw in those cases when they
+arise. With this view we interpret our own formula, precisely as a judge
+interprets a law: in order that we may avoid drawing any inferences not
+conformable to our former intention, as a judge avoids giving any
+decision not conformable to the legislator's intention. The rules for
+this interpretation are the rules of the syllogism: and its sole purpose
+is to maintain consistency between the conclusions we draw in every
+particular case, and the previous general directions for drawing them;
+whether those general <span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>directions were framed by ourselves as the result
+of induction, or were received by us from an authority competent to give
+them.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_5">� 5.</a> In the above observations it has, I think, been shown, that, though
+there is always a process of reasoning or inference where a syllogism is
+used, the syllogism is not a correct analysis of that process of
+reasoning or inference; which is, on the contrary, (when not a mere
+inference from testimony) an inference from particulars to particulars;
+authorized by a previous inference from particulars to generals, and
+substantially the same with it; of the nature, therefore, of Induction.
+But while these conclusions appear to me undeniable, I must yet enter a
+protest, as strong as that of Archbishop Whately himself, against the
+doctrine that the syllogistic art is useless for the purposes of
+reasoning. The reasoning lies in the act of generalization, not in
+interpreting the record of that act; but the syllogistic form is an
+indispensable collateral security for the correctness of the
+generalization itself.</p>
+
+<p>It has already been seen, that if we have a collection of particulars
+sufficient for grounding an induction, we need not frame a general
+proposition; we may reason at once from those particulars to other
+particulars. But it is to be remarked withal, that whenever, from a set
+of particular cases, we can legitimately draw any inference, we may
+legitimately make our inference a general one. If, from observation and
+experiment, we can conclude to one new case, so may we to an indefinite
+number. If that which has held true in our past experience will
+therefore hold in time to come, it will hold not merely in some
+individual case, but in all cases of some given description. Every
+induction, therefore, which suffices to prove one fact, proves an
+indefinite multitude of facts: the experience which justifies a single
+prediction must be such as will suffice to bear out a general theorem.
+This theorem it is extremely important to ascertain and declare, in its
+broadest form of generality; and thus to place before our minds, in its
+<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span>full extent, the whole of what our evidence must prove if it proves
+anything.</p>
+
+<p>This throwing of the whole body of possible inferences from a given set
+of particulars, into one general expression, operates as a security for
+their being just inferences, in more ways than one. First, the general
+principle presents a larger object to the imagination than any of the
+singular propositions which it contains. A process of thought which
+leads to a comprehensive generality, is felt as of greater importance
+than one which terminates in an insulated fact; and the mind is, even
+unconsciously, led to bestow greater attention upon the process, and to
+weigh more carefully the sufficiency of the experience appealed to, for
+supporting the inference grounded upon it. There is another, and a more
+important, advantage. In reasoning from a course of individual
+observations to some new and unobserved case, which we are but
+imperfectly acquainted with (or we should not be inquiring into it), and
+in which, since we are inquiring into it, we probably feel a peculiar
+interest; there is very little to prevent us from giving way to
+negligence, or to any bias which may affect our wishes or our
+imagination, and, under that influence, accepting insufficient evidence
+as sufficient. But if, instead of concluding straight to the particular
+case, we place before ourselves an entire class of facts&mdash;the whole
+contents of a general proposition, every tittle of which is legitimately
+inferrible from our premises, if that one particular conclusion is so;
+there is then a considerable likelihood that if the premises are
+insufficient, and the general inference, therefore, groundless, it will
+comprise within it some fact or facts the reverse of which we already
+know to be true; and we shall thus discover the error in our
+generalization by a <i>reductio ad impossibile</i>.</p>
+
+<p>Thus if, during the reign of Marcus Aurelius, a subject of the Roman
+empire, under the bias naturally given to the imagination and
+expectations by the lives and characters of the Antonines, had been
+disposed to expect that Commodus would be a just ruler; supposing him to
+stop there, he might only have been undeceived by sad experience. But if
+he <span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span>reflected that this expectation could not be justifiable unless from
+the same evidence he was warranted in concluding some general
+proposition, as, for instance, that all Roman emperors are just rulers;
+he would immediately have thought of Nero, Domitian, and other
+instances, which, showing the falsity of the general conclusion, and
+therefore the insufficiency of the premises, would have warned him that
+those premises could not prove in the instance of Commodus, what they
+were inadequate to prove in any collection of cases in which his was
+included.</p>
+
+<p>The advantage, in judging whether any controverted inference is
+legitimate, of referring to a parallel case, is universally
+acknowledged. But by ascending to the general proposition, we bring
+under our view not one parallel case only, but all possible parallel
+cases at once; all cases to which the same set of evidentiary
+considerations are applicable.</p>
+
+<p>When, therefore, we argue from a number of known cases to another case
+supposed to be analogous, it is always possible, and generally
+advantageous, to divert our argument into the circuitous channel of an
+induction from those known cases to a general proposition, and a
+subsequent application of that general proposition to the unknown case.
+This second part of the operation, which, as before observed, is
+essentially a process of interpretation, will be resolvable into a
+syllogism or a series of syllogisms, the majors of which will be general
+propositions embracing whole classes of cases; every one of which
+propositions must be true in all its extent, if the argument is
+maintainable. If, therefore, any fact fairly coming within the range of
+one of these general propositions, and consequently asserted by it, is
+known or suspected to be other than the proposition asserts it to be,
+this mode of stating the argument causes us to know or to suspect that
+the original observations, which are the real grounds of our conclusion,
+are not sufficient to support it. And in proportion to the greater
+chance of our detecting the inconclusiveness of our evidence, will be
+the increased reliance we are entitled to place in it if no such
+evidence of defect shall appear.</p>
+
+<p>The value, therefore, of the syllogistic form, and of the <span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span>rules for
+using it correctly, does not consist in their being the form and the
+rules according to which our reasonings are necessarily, or even
+usually, made; but in their furnishing us with a mode in which those
+reasonings may always be represented, and which is admirably calculated,
+if they are inconclusive, to bring their inconclusiveness to light. An
+induction from particulars to generals, followed by a syllogistic
+process from those generals to other particulars, is a form in which we
+may always state our reasonings if we please. It is not a form in which
+we <i>must</i> reason, but it is a form in which we <i>may</i> reason, and into
+which it is indispensable to throw our reasoning, when there is any
+doubt of its validity: though when the case is familiar and little
+complicated, and there is no suspicion of error, we may, and do, reason
+at once from the known particular cases to unknown ones.<a name="FNanchor_9_44" id="FNanchor_9_44"></a><a href="#Footnote_9_44" class="fnanchor">[9]</a></p>
+
+<p>These are the uses of syllogism, as a mode of verifying any given
+argument. Its ulterior uses, as respects the general course of our
+intellectual operations, hardly require illustration, being in fact the
+acknowledged uses of general language. They amount substantially to
+this, that the inductions may be made once for all: a single careful
+interrogation of experience may suffice, and the result may be
+registered in the form of a general proposition, which is committed to
+memory or to writing, and from which afterwards we have only to
+syllogize. The particulars of our experiments may then be dismissed from
+the memory, in which it would be impossible to retain so great a
+multitude of details; while the knowledge which those details afforded
+for future use, and which would otherwise be lost as soon as the
+observations were forgotten, <span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span>or as their record became too bulky for
+reference, is retained in a commodious and immediately available shape
+by means of general language.</p>
+
+<p>Against this advantage is to be set the countervailing inconvenience,
+that inferences originally made on insufficient evidence, become
+consecrated, and, as it were, hardened into general maxims; and the mind
+cleaves to them from habit, after it has outgrown any liability to be
+misled by similar fallacious appearances if they were now for the first
+time presented; but having forgotten the particulars, it does not think
+of revising its own former decision. An inevitable drawback, which,
+however considerable in itself, forms evidently but a small set-off
+against the immense benefits of general language.</p>
+
+<p>The use of the syllogism is in truth no other than the use of general
+propositions in reasoning. We <i>can</i> reason without them; in simple and
+obvious cases we habitually do so; minds of great sagacity can do it in
+cases not simple and obvious, provided their experience supplies them
+with instances essentially similar to every combination of circumstances
+likely to arise. But other minds, and the same minds where they have not
+the same pre-eminent advantages of personal experience, are quite
+helpless without the aid of general propositions, wherever the case
+presents the smallest complication; and if we made no general
+propositions, few persons would get much beyond those simple inferences
+which are drawn by the more intelligent of the brutes. Though not
+necessary to reasoning, general propositions are necessary to any
+considerable progress in reasoning. It is, therefore, natural and
+indispensable to separate the process of investigation into two parts;
+and obtain general formul� for determining what inferences may be drawn,
+before the occasion arises for drawing the inferences. The work of
+drawing them is then that of applying the formul�; and the rules of
+syllogism are a system of securities for the correctness of the
+application.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_6">� 6.</a> To complete the series of considerations connected <span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span>with the
+philosophical character of the syllogism, it is requisite to consider,
+since the syllogism is not the universal type of the reasoning process,
+what is the real type. This resolves itself into the question, what is
+the nature of the minor premise, and in what manner it contributes to
+establish the conclusion: for as to the major, we now fully understand,
+that the place which it nominally occupies in our reasonings, properly
+belongs to the individual facts or observations of which it expresses
+the general result; the major itself being no real part of the argument,
+but an intermediate halting-place for the mind, interposed by an
+artifice of language between the real premises and the conclusion, by
+way of a security, which it is in a most material degree, for the
+correctness of the process. The minor, however, being an indispensable
+part of the syllogistic expression of an argument, without doubt either
+is, or corresponds to, an equally indispensable part of the argument
+itself, and we have only to inquire what part.</p>
+
+<p>It is perhaps worth while to notice here a speculation of a philosopher
+to whom mental science is much indebted, but who, though a very
+penetrating, was a very hasty thinker, and whose want of due
+circumspection rendered him fully as remarkable for what he did not see,
+as for what he saw. I allude to Dr. Thomas Brown, whose theory of
+ratiocination is peculiar. He saw the <i>petitio principii</i> which is
+inherent in every syllogism, if we consider the major to be itself the
+evidence by which the conclusion is proved, instead of being, what in
+fact it is, an assertion of the existence of evidence sufficient to
+prove any conclusion of a given description. Seeing this, Dr. Brown not
+only failed to see the immense advantage, in point of security for
+correctness, which is gained by interposing this step between the real
+evidence and the conclusion; but he thought it incumbent on him to
+strike out the major altogether from the reasoning process, without
+substituting anything else, and maintained that our reasonings consist
+only of the minor premise and the conclusion, Socrates is a man,
+therefore Socrates is mortal: thus actually suppressing, as an
+unnecessary step in the argument, <span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span>the appeal to former experience. The
+absurdity of this was disguised from him by the opinion he adopted, that
+reasoning is merely analysing our own general notions, or abstract
+ideas; and that the proposition, Socrates is mortal, is evolved from the
+proposition, Socrates is a man, simply by recognising the notion of
+mortality as already contained in the notion we form of a man.</p>
+
+<p>After the explanations so fully entered into on the subject of
+propositions, much further discussion cannot be necessary to make the
+radical error of this view of ratiocination apparent. If the word man
+connoted mortality; if the meaning of "mortal" were involved in the
+meaning of "man;" we might, undoubtedly, evolve the conclusion from the
+minor alone, because the minor would have already asserted it. But if,
+as is in fact the case, the word man does not connote mortality, how
+does it appear that in the mind of every person who admits Socrates to
+be a man, the idea of man must include the idea of mortality? Dr. Brown
+could not help seeing this difficulty, and in order to avoid it, was
+led, contrary to his intention, to re-establish, under another name,
+that step in the argument which corresponds to the major, by affirming
+the necessity of <i>previously perceiving</i> the relation between the idea
+of man and the idea of mortal. If the reasoner has not previously
+perceived this relation, he will not, says Dr. Brown, infer because
+Socrates is a man, that Socrates is mortal. But even this admission,
+though amounting to a surrender of the doctrine that an argument
+consists of the minor and the conclusion alone, will not save the
+remainder of Dr. Brown's theory. The failure of assent to the argument
+does not take place merely because the reasoner, for want of due
+analysis, does not perceive that his idea of man includes the idea of
+mortality; it takes place, much more commonly, because in his mind that
+relation between the two ideas has never existed. And in truth it never
+does exist, except as the result of experience. Consenting, for the sake
+of the argument, to discuss the question on a supposition of which we
+have recognised the radical incorrectness, namely, that the meaning of a
+proposition relates to the ideas of the things <span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span>spoken of, and not to
+the things themselves; I must yet observe, that the idea of man, as an
+universal idea, the common property of all rational creatures, cannot
+involve anything but what is strictly implied in the name. If any one
+includes in his own private idea of man, as no doubt is always the case,
+some other attributes, such for instance as mortality, he does so only
+as the consequence of experience, after having satisfied himself that
+all men possess that attribute: so that whatever the idea contains, in
+any person's mind, beyond what is included in the conventional
+signification of the word, has been added to it as the result of assent
+to a proposition; while Dr. Brown's theory requires us to suppose, on
+the contrary, that assent to the proposition is produced by evolving,
+through an analytic process, this very element out of the idea. This
+theory, therefore, may be considered as sufficiently refuted; and the
+minor premise must be regarded as totally insufficient to prove the
+conclusion, except with the assistance of the major, or of that which
+the major represents, namely, the various singular propositions
+expressive of the series of observations, of which the generalization
+called the major premise is the result.</p>
+
+<p>In the argument, then, which proves that Socrates is mortal, one
+indispensable part of the premises will be as follows: "My father, and
+my father's father, A, B, C, and an indefinite number of other persons,
+were mortal;" which is only an expression in different words of the
+observed fact that they have died. This is the major premise divested of
+the <i>petitio principii</i>, and cut down to as much as is really known by
+direct evidence.</p>
+
+<p>In order to connect this proposition with the conclusion Socrates is
+mortal, the additional link necessary is such a proposition as the
+following: "Socrates resembles my father, and my father's father, and
+the other individuals specified." This proposition we assert when we say
+that Socrates is a man. By saying so we likewise assert in what respect
+he resembles them, namely, in the attributes connoted by the word man.
+And we conclude that he further resembles them in the attribute
+mortality.</p>
+
+
+<p><span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span></p><p class="newsection"><a name="BOOK_II_CHAPTER_III_7">� 7.</a> We have thus obtained what we were seeking, an universal type of
+the reasoning process. We find it resolvable in all cases into the
+following elements: Certain individuals have a given attribute; an
+individual or individuals resemble the former in certain other
+attributes; therefore they resemble them also in the given attribute.
+This type of ratiocination does not claim, like the syllogism, to be
+conclusive, from the mere form of the expression; nor can it possibly be
+so. That one proposition does or does not assert the very fact which was
+already asserted in another, may appear from the form of the expression,
+that is, from a comparison of the language; but when the two
+propositions assert facts which are <i>bon� fide</i> different, whether the
+one fact proves the other or not can never appear from the language, but
+must depend on other considerations. Whether, from the attributes in
+which Socrates resembles those men who have heretofore died, it is
+allowable to infer that he resembles them also in being mortal, is a
+question of Induction; and is to be decided by the principles or canons
+which we shall hereafter recognise as tests of the correct performance
+of that great mental operation.</p>
+
+<p>Meanwhile, however, it is certain, as before remarked, that if this
+inference can be drawn as to Socrates, it can be drawn as to all others
+who resemble the observed individuals in the same attributes in which he
+resembles them; that is (to express the thing concisely) of all mankind.
+If, therefore, the argument be admissible in the case of Socrates, we
+are at liberty, once for all, to treat the possession of the attributes
+of man as a mark, or satisfactory evidence, of the attribute of
+mortality. This we do by laying down the universal proposition, All men
+are mortal, and interpreting this, as occasion arises, in its
+application to Socrates and others. By this means we establish a very
+convenient division of the entire logical operation into two steps;
+first, that of ascertaining what attributes are marks of mortality; and,
+secondly, whether any given individuals possess those marks. And it will
+generally be advisable, in our speculations on the reasoning process, to
+consider this double operation as in <span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span>fact taking place, and all
+reasoning as carried on in the form into which it must necessarily be
+thrown to enable us to apply to it any test of its correct performance.</p>
+
+<p>Although, therefore, all processes of thought in which the ultimate
+premises are particulars, whether we conclude from particulars to a
+general formula, or from particulars to other particulars according to
+that formula, are equally Induction: we shall yet, conformably to usage,
+consider the name Induction as more peculiarly belonging to the process
+of establishing the general proposition, and the remaining operation,
+which is substantially that of interpreting the general proposition, we
+shall call by its usual name, Deduction. And we shall consider every
+process by which anything is inferred respecting an unobserved case, as
+consisting of an Induction followed by a Deduction; because, although
+the process needs not necessarily be carried on in this form, it is
+always susceptible of the form, and must be thrown into it when
+assurance of scientific accuracy is needed and desired.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_8">� 8.</a> The theory of the syllogism, laid down in the preceding pages, has
+obtained, among other important adhesions, three of peculiar value;
+those of Sir John Herschel,<a name="FNanchor_10_45" id="FNanchor_10_45"></a><a href="#Footnote_10_45" class="fnanchor">[10]</a> Dr. Whewell<a name="FNanchor_11_46" id="FNanchor_11_46"></a><a href="#Footnote_11_46" class="fnanchor">[11]</a> and Mr. Bailey;<a name="FNanchor_12_47" id="FNanchor_12_47"></a><a href="#Footnote_12_47" class="fnanchor">[12]</a> Sir
+John Herschel considering the doctrine, though not strictly "a
+discovery,"<a name="FNanchor_13_48" id="FNanchor_13_48"></a><a href="#Footnote_13_48" class="fnanchor">[13]</a> to be "one of the greatest steps which have yet been
+made in the philosophy of Logic." "When we consider" (to quote the
+further words of the same authority) "the inveteracy of the habits and
+prejudices which it has cast to the winds," there is no cause for
+misgiving in the fact that other thinkers, no less entitled to
+consideration, have formed a very different estimate <span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span>of it. Their
+principal objection cannot be better or more succinctly stated than by
+borrowing a sentence from Archbishop Whately.<a name="FNanchor_14_49" id="FNanchor_14_49"></a><a href="#Footnote_14_49" class="fnanchor">[14]</a> "In every case where
+an inference is drawn from Induction (unless that name is to be given to
+a mere random guess without any grounds at all) we must form a judgment
+that the instance or instances adduced are <i>sufficient</i> to authorize the
+conclusion; that it is <i>allowable</i> to take these instances as a sample
+warranting an inference respecting the whole class;" and the expression
+of this judgment in words (it has been said by several of my critics)
+<i>is</i> the major premise.</p>
+
+<p>I quite admit that the major is an affirmation of the sufficiency of the
+evidence on which the conclusion rests. That it is so, is the very
+essence of my own theory. And whoever admits that the major premise is
+<i>only</i> this, adopts the theory in its essentials.</p>
+
+<p>But I cannot concede that this recognition of the sufficiency of the
+evidence&mdash;that is, of the correctness of the induction&mdash;is a part of the
+induction itself; unless we ought to say that it is a part of everything
+we do, to satisfy ourselves that it has been done rightly. We conclude
+from known instances to unknown by the impulse of the generalizing
+propensity; and (until after a considerable amount of practice and
+mental discipline) the question of the sufficiency of the evidence is
+only raised by a retrospective act, turning back upon our own footsteps,
+and examining whether we were warranted in doing what we have already
+done. To speak of this reflex operation as part of the original one,
+requiring to be expressed in words in order that the verbal formula may
+correctly represent the psychological process, appears to me false
+psychology.<a name="FNanchor_15_50" id="FNanchor_15_50"></a><a href="#Footnote_15_50" class="fnanchor">[15]</a> We review our syllogistic as well as our inductive
+processes, and recognise that they have been correctly performed; but
+logicians do not add a third premise to the syllogism, to express this
+act of recognition. A careful copyist verifies his transcript by
+collating it with the original; and <span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span>if no error appears, he recognises
+that the transcript has been correctly made. But we do not call the
+examination of the copy a part of the act of copying.</p>
+
+<p>The conclusion in an induction is inferred from the evidence itself, and
+not from a recognition of the sufficiency of the evidence; as I infer
+that my friend is walking towards me because I see him, and not because
+I recognise that my eyes are open, and that eyesight is a means of
+knowledge. In all operations which require care, it is good to assure
+ourselves that the process has been performed accurately; but the
+testing of the process is not the process itself; and, besides, may have
+been omitted altogether, and yet the process be correct. It is precisely
+because that operation is omitted in ordinary unscientific reasoning,
+that there is anything gained in certainty by throwing reasoning into
+the syllogistic form. To make sure, as far as possible, that it shall
+not be omitted, we make the testing operation a part of the reasoning
+process itself. We insist that the inference from particulars to
+particulars shall pass through a general proposition. But this is a
+security for good reasoning, not a condition of all reasoning; and in
+some cases not even a security. Our most familiar inferences are all
+made before we learn the use of general propositions; and a person of
+untutored sagacity will skilfully apply his acquired experience to
+adjacent cases, though he would bungle grievously in fixing the limits
+of the appropriate general theorem. But though he may conclude rightly,
+he never, properly speaking, knows whether he has done so or not; he has
+not tested his reasoning. Now, this is precisely what forms of reasoning
+do for us. We do not need them to enable us to reason, but to enable us
+to know whether we reason correctly.</p>
+
+<p>In still further answer to the objection, it may be added that, even
+when the test has been applied, and the sufficiency of the evidence
+recognised,&mdash;if it is sufficient to support the general proposition, it
+is sufficient also to support an inference from particulars to
+particulars without passing through the general proposition. The
+inquirer who has logically satisfied himself that the conditions of
+legitimate induction were <span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span>realized in the cases A, B, C, would be as
+much justified in concluding directly to the Duke of Wellington as in
+concluding to all men. The general conclusion is never legitimate,
+unless the particular one would be so too; and in no sense, intelligible
+to me, can the particular conclusion be said to be drawn from the
+general one. Whenever there is ground for drawing any conclusion at all
+from particular instances, there is ground for a general conclusion; but
+that this general conclusion should be actually drawn, however useful,
+cannot be an indispensable condition of the validity of the inference in
+the particular case. A man gives away sixpence by the same power by
+which he disposes of his whole fortune; but it is not necessary to the
+legality of the smaller act, that he should make a formal assertion of
+his right to the greater one.</p>
+
+<p>Some additional remarks, in reply to minor objections, are appended.<a name="FNanchor_16_51" id="FNanchor_16_51"></a><a href="#Footnote_16_51" class="fnanchor">[16]</a></p>
+
+
+<p><span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span></p>
+<p class="newsection"><a name="BOOK_II_CHAPTER_III_9">� 9.</a> The preceding considerations enable us to understand the true
+nature of what is termed, by recent writers, Formal Logic, and the
+relation between it and Logic in the widest sense. Logic, as I conceive
+it, is the entire theory of <span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span>the ascertainment of reasoned or inferred
+truth. Formal Logic, therefore, which Sir William Hamilton from his own
+point of view, and Archbishop Whately from his, have represented as the
+whole of Logic properly so called, is really a very subordinate part of
+it, not being directly concerned with the process of Reasoning or
+Inference in the sense in which that process is a part of the
+Investigation of Truth. What, then, is Formal Logic? The name seems to
+be properly applied to all that portion of doctrine which relates to the
+equivalence of different modes of expression; the rules for determining
+when assertions in a given form imply or suppose the truth or falsity of
+other assertions. This includes the theory of the Import of
+Propositions, and of their Conversion, <span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span>�quipollence, and Opposition; of
+those falsely called Inductions (to be hereafter spoken of<a name="FNanchor_17_52" id="FNanchor_17_52"></a><a href="#Footnote_17_52" class="fnanchor">[17]</a>), in
+which the apparent generalization is a mere abridged statement of cases
+known individually; and finally, of the syllogism: while the theory of
+Naming, and of (what is inseparably connected with it) Definition,
+though belonging still more to the other and larger kind of logic than
+to this, is a necessary preliminary to this. The end aimed at by Formal
+Logic, and attained by the observance of its precepts, is not truth, but
+consistency. It has been seen that this is the only direct purpose of
+the rules of the syllogism; the intention and effect of which is simply
+to keep our inferences or conclusions in complete consistency with our
+general formul� or directions for drawing them. The Logic of Consistency
+is a necessary auxiliary to the logic of truth, not only because what is
+inconsistent with itself or with other truths cannot be true, but also
+because truth can only be successfully pursued by drawing inferences
+from experience, which, if warrantable at all, admit of being
+generalized, and, to test their warrantableness, require to be exhibited
+in a generalized form; after which the correctness of their application
+to particular cases is a question which specially concerns the Logic of
+Consistency. This Logic, not requiring any preliminary knowledge of the
+processes or conclusions of the various sciences, may be studied with
+benefit in a much earlier stage of education than the Logic of Truth:
+and the practice which has empirically obtained of teaching it apart,
+through elementary treatises which do not attempt to include anything
+else, though the reasons assigned for the practice are in general very
+far from philosophical, admits of a philosophical justification.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_IV" id="BOOK_II_CHAPTER_IV"></a>CHAPTER IV.<br />
+
+OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_1">� 1.</a> In our analysis of the syllogism, it appeared that the minor
+premise always affirms a resemblance between a new case and some cases
+previously known; while the major premise asserts something which,
+having been found true of those known cases, we consider ourselves
+warranted in holding true of any other case resembling the former in
+certain given particulars.</p>
+
+<p>If all ratiocinations resembled, as to the minor premise, the examples
+which were exclusively employed in the preceding chapter; if the
+resemblance, which that premise asserts, were obvious to the senses, as
+in the proposition "Socrates is a man," or were at once ascertainable by
+direct observation; there would be no necessity for trains of reasoning,
+and Deductive or Ratiocinative Sciences would not exist. Trains of
+reasoning exist only for the sake of extending an induction founded, as
+all inductions must be, on observed cases, to other cases in which we
+not only cannot directly observe what is to be proved, but cannot
+directly observe even the mark which is to prove it.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_2">� 2.</a> Suppose the syllogism to be, All cows ruminate, the animal which is
+before me is a cow, therefore it ruminates. The minor, if true at all,
+is obviously so: the only premise the establishment of which requires
+any anterior process of inquiry, is the major; and provided the
+induction of which that premise is the expression was correctly
+performed, the conclusion respecting the animal now present will be
+instantly drawn; because, as soon as she is compared with the formula,
+she will be identified as being included in it. But suppose the
+syllogism to be the following:&mdash;All arsenic is <span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span>poisonous, the substance
+which is before me is arsenic, therefore it is poisonous. The truth of
+the minor may not here be obvious at first sight; it may not be
+intuitively evident, but may itself be known only by inference. It may
+be the conclusion of another argument, which, thrown into the
+syllogistic form, would stand thus:&mdash;Whatever when lighted produces a
+dark spot on a piece of white porcelain held in the flame, which spot is
+soluble in hypochlorite of calcium, is arsenic; the substance before me
+conforms to this condition; therefore it is arsenic. To establish,
+therefore, the ultimate conclusion, The substance before me is
+poisonous, requires a process, which, in order to be syllogistically
+expressed, stands in need of two syllogisms; and we have a Train of
+Reasoning.</p>
+
+<p>When, however, we thus add syllogism to syllogism, we are really adding
+induction to induction. Two separate inductions must have taken place to
+render this chain of inference possible; inductions founded, probably,
+on different sets of individual instances, but which converge in their
+results, so that the instance which is the subject of inquiry comes
+within the range of them both. The record of these inductions is
+contained in the majors of the two syllogisms. First, we, or others for
+us, have examined various objects which yielded under the given
+circumstances a dark spot with the given property, and found that they
+possessed the properties connoted by the word arsenic; they were
+metallic, volatile, their vapour had a smell of garlic, and so forth.
+Next, we, or others for us, have examined various specimens which
+possessed this metallic and volatile character, whose vapour had this
+smell, &amp;c., and have invariably found that they were poisonous. The
+first observation we judge that we may extend to all substances whatever
+which yield that particular kind of dark spot; the second, to all
+metallic and volatile substances resembling those we examined; and
+consequently, not to those only which are seen to be such, but to those
+which are concluded to be such by the prior induction. The substance
+before us is only seen to come within one of these inductions; but by
+means of this one, it is brought within the other. We are still, as
+before, concluding from particulars to <span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span>particulars; but we are now
+concluding from particulars observed, to other particulars which are
+not, as in the simple case, <i>seen</i> to resemble them in the material
+points, but <i>inferred</i> to do so, because resembling them in something
+else, which we have been led by quite a different set of instances to
+consider as a mark of the former resemblance.</p>
+
+<p>This first example of a train of reasoning is still extremely simple,
+the series consisting of only two syllogisms. The following is somewhat
+more complicated:&mdash;No government, which earnestly seeks the good of its
+subjects, is likely to be overthrown; some particular government
+earnestly seeks the good of its subjects, therefore it is not likely to
+be overthrown. The major premise in this argument we shall suppose not
+to be derived from considerations <i>� priori</i>, but to be a generalization
+from history, which, whether correct or erroneous, must have been
+founded on observation of governments concerning whose desire of the
+good of their subjects there was no doubt. It has been found, or thought
+to be found, that these were not easily overthrown, and it has been
+deemed that those instances warranted an extension of the same predicate
+to any and every government which resembles them in the attribute of
+desiring earnestly the good of its subjects. But <i>does</i> the government
+in question thus resemble them? This may be debated <i>pro</i> and <i>con</i> by
+many arguments, and must, in any case, be proved by another induction;
+for we cannot directly observe the sentiments and desires of the persons
+who carry on the government. To prove the minor, therefore, we require
+an argument in this form: Every government which acts in a certain
+manner, desires the good of its subjects; the supposed government acts
+in that particular manner, therefore it desires the good of its
+subjects. But is it true that the government acts in the manner
+supposed? This minor also may require proof; still another induction, as
+thus:&mdash;What is asserted by intelligent and disinterested witnesses, may
+be believed to be true; that the government acts in this manner, is
+asserted by such witnesses, therefore it may be believed to be true. The
+argument hence consists of three steps. Having the evidence <span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span>of our
+senses that the case of the government under consideration resembles a
+number of former cases, in the circumstance of having something asserted
+respecting it by intelligent and disinterested witnesses, we infer,
+first, that, as in those former instances, so in this instance, the
+assertion is true. Secondly, what was asserted of the government being
+that it acts in a particular manner, and other governments or persons
+having been observed to act in the same manner, the government in
+question is brought into known resemblance with those other governments
+or persons; and since they were known to desire the good of the people,
+it is thereupon, by a second induction, inferred that the particular
+government spoken of, desires the good of the people. This brings that
+government into known resemblance with the other governments which were
+thought likely to escape revolution, and thence, by a third induction,
+it is concluded that this particular government is also likely to
+escape. This is still reasoning from particulars to particulars, but we
+now reason to the new instance from three distinct sets of former
+instances: to one only of those sets of instances do we directly
+perceive the new one to be similar; but from that similarity we
+inductively infer that it has the attribute by which it is assimilated
+to the next set, and brought within the corresponding induction; after
+which by a repetition of the same operation we infer it to be similar to
+the third set, and hence a third induction conducts us to the ultimate
+conclusion.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_3">� 3.</a> Notwithstanding the superior complication of these examples,
+compared with those by which in the preceding chapter we illustrated the
+general theory of reasoning, every doctrine which we then laid down
+holds equally true in these more intricate cases. The successive general
+propositions are not steps in the reasoning, are not intermediate links
+in the chain of inference, between the particulars observed and those to
+which we apply the observation. If we had sufficiently capacious
+memories, and a sufficient power of maintaining order among a huge mass
+of details, the reasoning could go <span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span>on without any general propositions;
+they are mere formul� for inferring particulars from particulars. The
+principle of general reasoning is (as before explained), that if from
+observation of certain known particulars, what was seen to be true of
+them can be inferred to be true of any others, it may be inferred of all
+others which are of a certain description. And in order that we may
+never fail to draw this conclusion in a new case when it can be drawn
+correctly, and may avoid drawing it when it cannot, we determine once
+for all what are the distinguishing marks by which such cases may be
+recognised. The subsequent process is merely that of identifying an
+object, and ascertaining it to have those marks; whether we identify it
+by the very marks themselves, or by others which we have ascertained
+(through another and a similar process) to be marks of those marks. The
+real inference is always from particulars to particulars, from the
+observed instances to an unobserved one: but in drawing this inference,
+we conform to a formula which we have adopted for our guidance in such
+operations, and which is a record of the criteria by which we thought we
+had ascertained that we might distinguish when the inference could, and
+when it could not, be drawn. The real premises are the individual
+observations, even though they may have been forgotten, or, being the
+observations of others and not of ourselves, may, to us, never have been
+known: but we have before us proof that we or others once thought them
+sufficient for an induction, and we have marks to show whether any new
+case is one of those to which, if then known, the induction would have
+been deemed to extend. These marks we either recognise at once, or by
+the aid of other marks, which by another previous induction we collected
+to be marks of the first. Even these marks of marks may only be
+recognised through a third set of marks; and we may have a train of
+reasoning, of any length, to bring a new case within the scope of an
+induction grounded on particulars its similarity to which is only
+ascertained in this indirect manner.</p>
+
+<p>Thus, in the preceding example, the ultimate inductive inference <span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span>was,
+that a certain government was not likely to be overthrown; this
+inference was drawn according to a formula in which desire of the public
+good was set down as a mark of not being likely to be overthrown; a mark
+of this mark was, acting in a particular manner; and a mark of acting in
+that manner was, being asserted to do so by intelligent and
+disinterested witnesses: this mark, the government under discussion was
+recognised by the senses as possessing. Hence that government fell
+within the last induction, and by it was brought within all the others.
+The perceived resemblance of the case to one set of observed particular
+cases, brought it into known resemblance with another set, and that with
+a third.</p>
+
+<p>In the more complex branches of knowledge, the deductions seldom
+consist, as in the examples hitherto exhibited, of a single chain, <i>a</i> a
+mark of <i>b</i>, <i>b</i> of <i>c</i>, <i>c</i> of <i>d</i>, therefore <i>a</i> a mark of <i>d</i>. They
+consist (to carry on the same metaphor) of several chains united at the
+extremity, as thus: <i>a</i> a mark of <i>d</i>, <i>b</i> of <i>e</i>, <i>c</i> of <i>f</i>, <i>d e f</i>
+of <i>n</i>, therefore <i>a b c</i> a mark of <i>n</i>. Suppose, for example, the
+following combination of circumstances; 1st, rays of light impinging on
+a reflecting surface; 2nd, that surface parabolic; 3rd, those rays
+parallel to each other and to the axis of the surface. It is to be
+proved that the concourse of these three circumstances is a mark that
+the reflected rays will pass through the focus of the parabolic surface.
+Now, each of the three circumstances is singly a mark of something
+material to the case. Rays of light impinging on a reflecting surface,
+are a mark that those rays will be reflected at an angle equal to the
+angle of incidence. The parabolic form of the surface is a mark that,
+from any point of it, a line drawn to the focus and a line parallel to
+the axis will make equal angles with the surface. And finally, the
+parallelism of the rays to the axis is a mark that their angle of
+incidence coincides with one of these equal angles. The three marks
+taken together are therefore a mark of all these three things united.
+But the three united are evidently a mark that the angle of reflection
+must coincide with the other of the two equal angles, that formed by a
+line drawn to the focus; and this again, by <span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span>the fundamental axiom
+concerning straight lines, is a mark that the reflected rays pass
+through the focus. Most chains of physical deduction are of this more
+complicated type; and even in mathematics such are abundant, as in all
+propositions where the hypothesis includes numerous conditions: "<i>If</i> a
+circle be taken, and <i>if</i> within that circle a point be taken, not the
+centre, and <i>if</i> straight lines be drawn from that point to the
+circumference, then," &amp;c.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_4">� 4.</a> The considerations now stated remove a serious difficulty from the
+view we have taken of reasoning; which view might otherwise have seemed
+not easily reconcileable with the fact that there are Deductive or
+Ratiocinative Sciences. It might seem to follow, if all reasoning be
+induction, that the difficulties of philosophical investigation must lie
+in the inductions exclusively, and that when these were easy, and
+susceptible of no doubt or hesitation, there could be no science, or, at
+least, no difficulties in science. The existence, for example, of an
+extensive Science of Mathematics, requiring the highest scientific
+genius in those who contributed to its creation, and calling for a most
+continued and vigorous exertion of intellect in order to appropriate it
+when created, may seem hard to be accounted for on the foregoing theory.
+But the considerations more recently adduced remove the mystery, by
+showing, that even when the inductions themselves are obvious, there may
+be much difficulty in finding whether the particular case which is the
+subject of inquiry comes within them; and ample room for scientific
+ingenuity in so combining various inductions, as, by means of one within
+which the case evidently falls, to bring it within others in which it
+cannot be directly seen to be included.</p>
+
+<p>When the more obvious of the inductions which can be made in any science
+from direct observations, have been made, and general formulas have been
+framed, determining the limits within which these inductions are
+applicable; as often as a new case can be at once seen to come within
+one of the formulas, the induction is applied to the new case, and the
+business is ended. But new cases are continually arising, <span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span>which do not
+obviously come within any formula whereby the question we want solved in
+respect of them could be answered. Let us take an instance from
+geometry: and as it is taken only for illustration, let the reader
+concede to us for the present, what we shall endeavour to prove in the
+next chapter, that the first principles of geometry are results of
+induction. Our example shall be the fifth proposition of the first book
+of Euclid. The inquiry is, Are the angles at the base of an isosceles
+triangle equal or unequal? The first thing to be considered is, what
+inductions we have, from which we can infer equality or inequality. For
+inferring equality we have the following formul�:&mdash;Things which being
+applied to each other coincide, are equals. Things which are equal to
+the same thing are equals. A whole and the sum of its parts are equals.
+The sums of equal things are equals. The differences of equal things are
+equals. There are no other original formul� to prove equality. For
+inferring inequality we have the following:&mdash;A whole and its parts are
+unequals. The sums of equal things and unequal things are unequals. The
+differences of equal things and unequal things are unequals. In all,
+eight formul�. The angles at the base of an isosceles triangle do not
+obviously come within any of these. The formul� specify certain marks of
+equality and of inequality, but the angles cannot be perceived
+intuitively to have any of those marks. On examination it appears that
+they have; and we ultimately succeed in bringing them within the
+formula, "The differences of equal things are equal." Whence comes the
+difficulty of recognising these angles as the differences of equal
+things? Because each of them is the difference not of one pair only, but
+of innumerable pairs of angles; and out of these we had to imagine and
+select two, which could either be intuitively perceived to be equals, or
+possessed some of the marks of equality set down in the various formul�.
+By an exercise of ingenuity, which, on the part of the first inventor,
+deserves to be regarded as considerable, two pairs of angles were hit
+upon, which united these requisites. First, it could be perceived
+intuitively that their differences were the angles at the base; and,
+secondly, they possessed one of the marks of <span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span>equality, namely,
+coincidence when applied to one another. This coincidence, however, was
+not perceived intuitively, but inferred, in conformity to another
+formula.</p>
+
+<p>For greater clearness, I subjoin an analysis of the demonstration.
+Euclid, it will be remembered, demonstrates his fifth proposition by
+means of the fourth. This it is not allowable for us to do, because we
+are undertaking to trace deductive truths not to prior deductions, but
+to their original inductive foundation. We must therefore use the
+premises of the fourth proposition instead of its conclusion, and prove
+the fifth directly from first principles. To do so requires six
+formulas. (We must begin, as in Euclid, by prolonging the equal sides
+AB, AC, to equal distances, and joining the extremities BE, DC.)</p>
+
+<div class="figcenter">
+<img src="images/fig.png" alt="" />
+</div>
+
+<p class="center"><span class="smcap">First Formula.</span> <i>The sums of equals are equal.</i></p>
+
+<p>AD and AE are sums of equals by the supposition. Having that mark of
+equality, they are concluded by this formula to be equal.</p>
+
+<p class="center"><span class="smcap">Second Formula.</span> <i>Equal straight lines being applied to one another
+coincide.</i></p>
+
+<p>AC, AB, are within this formula by supposition; AD, AE, have been
+brought within it by the preceding step. Both these pairs of straight
+lines have the property of equality; which, according to the second
+formula, is a mark that, if applied to each other, they will coincide.
+Coinciding altogether means coinciding in every part, and of course at
+their extremities, D, E, and B, C.</p>
+
+<p class="center"><span class="smcap">Third Formula.</span> <i>Straight lines, having their extremities coincident,
+coincide.</i></p>
+
+<p>BE and CD have been brought within this formula by the preceding
+induction; they will, therefore, coincide.</p>
+
+<p><span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span></p><p class="center"><span class="smcap">Fourth Formula.</span> <i>Angles, having their sides coincident, coincide.</i></p>
+
+<p>The third induction having shown that BE and CD coincide, and the second
+that AB, AC, coincide, the angles ABE and ACD are thereby brought within
+the fourth formula, and accordingly coincide.</p>
+
+<p class="center"><span class="smcap">Fifth Formula.</span> <i>Things which coincide are equal.</i></p>
+
+<p>The angles ABE and ACD are brought within this formula by the induction
+immediately preceding. This train of reasoning being also applicable,
+<i>mutatis mutandis</i>, to the angles EBC, DCB, these also are brought
+within the fifth formula. And, finally,</p>
+
+<p class="center"><span class="smcap">Sixth Formula.</span> <i>The differences of equals are equal.</i></p>
+
+<p>The angle ABC being the difference of ABE, CBE, and the angle ACB being
+the difference of ACD, DCB; which have been proved to be equals; ABC and
+ACB are brought within the last formula by the whole of the previous
+process.</p>
+
+<p>The difficulty here encountered is chiefly that of figuring to ourselves
+the two angles at the base of the triangle ABC as remainders made by
+cutting one pair of angles out of another, while each pair shall be
+corresponding angles of triangles which have two sides and the
+intervening angle equal. It is by this happy contrivance that so many
+different inductions are brought to bear upon the same particular case.
+And this not being at all an obvious thought, it may be seen from an
+example so near the threshold of mathematics, how much scope there may
+well be for scientific dexterity in the higher branches of that and
+other sciences, in order so to combine a few simple inductions, as to
+bring within each of them innumerable cases which are not obviously
+included in it; and how long, and numerous, and complicated may be the
+processes necessary for bringing the inductions together, even when each
+induction may itself be very easy and simple. All the inductions
+involved in all geometry are comprised in those simple ones, the formul�
+of which are the Axioms, and a few of the <span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span>so-called Definitions. The
+remainder of the science is made up of the processes employed for
+bringing unforeseen cases within these inductions; or (in syllogistic
+language) for proving the minors necessary to complete the syllogisms;
+the majors being the definitions and axioms. In those definitions and
+axioms are laid down the whole of the marks, by an artful combination of
+which it has been found possible to discover and prove all that is
+proved in geometry. The marks being so few, and the inductions which
+furnish them being so obvious and familiar; the connecting of several of
+them together, which constitutes Deductions, or Trains of Reasoning,
+forms the whole difficulty of the science, and with a trifling
+exception, its whole bulk; and hence Geometry is a Deductive Science.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_5">� 5.</a> It will be seen hereafter<a name="FNanchor_18_53" id="FNanchor_18_53"></a><a href="#Footnote_18_53" class="fnanchor">[18]</a> that there are weighty scientific
+reasons for giving to every science as much of the character of a
+Deductive Science as possible; for endeavouring to construct the science
+from the fewest and the simplest possible inductions, and to make these,
+by any combinations however complicated, suffice for proving even such
+truths, relating to complex cases, as could be proved, if we chose, by
+inductions from specific experience. Every branch of natural philosophy
+was originally experimental; each generalization rested on a special
+induction, and was derived from its own distinct set of observations and
+experiments. From being sciences of pure experiment, as the phrase is,
+or, to speak more correctly, sciences in which the reasonings mostly
+consist of no more than one step, and are expressed by single
+syllogisms, all these sciences have become to some extent, and some of
+them in nearly the whole of their extent, sciences of pure reasoning;
+whereby multitudes of truths, already known by induction from as many
+different sets of experiments, have come to be exhibited as deductions
+or corollaries from inductive propositions of a simpler and more
+universal character. Thus mechanics, hydrostatics, optics, acoustics,
+thermology, <span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span>have successively been rendered mathematical; and astronomy
+was brought by Newton within the laws of general mechanics. Why it is
+that the substitution of this circuitous mode of proceeding for a
+process apparently much easier and more natural, is held, and justly, to
+be the greatest triumph of the investigation of nature, we are not, in
+this stage of our inquiry, prepared to examine. But it is necessary to
+remark, that although, by this progressive transformation, all sciences
+tend to become more and more Deductive, they are not, therefore, the
+less Inductive; every step in the Deduction is still an Induction. The
+opposition is not between the terms Deductive and Inductive, but between
+Deductive and Experimental. A science is experimental, in proportion as
+every new case, which presents any peculiar features, stands in need of
+a new set of observations and experiments&mdash;a fresh induction. It is
+deductive, in proportion as it can draw conclusions, respecting cases of
+a new kind, by processes which bring those cases under old inductions;
+by ascertaining that cases which cannot be observed to have the
+requisite marks, have, however, marks of those marks.</p>
+
+<p>We can now, therefore, perceive what is the generic distinction between
+sciences which can be made Deductive, and those which must as yet remain
+Experimental. The difference consists in our having been able, or not
+yet able, to discover marks of marks. If by our various inductions we
+have been able to proceed no further than to such propositions as these,
+<i>a</i> a mark of <i>b</i>, or <i>a</i> and <i>b</i> marks of one another, <i>c</i> a mark of
+<i>d</i>, or <i>c</i> and <i>d</i> marks of one another, without anything to connect
+<i>a</i> or <i>b</i> with <i>c</i> or <i>d</i>; we have a science of detached and mutually
+independent generalizations, such as these, that acids redden vegetable
+blues, and that alkalies colour them green; from neither of which
+propositions could we, directly or indirectly, infer the other: and a
+science, so far as it is composed of such propositions, is purely
+experimental. Chemistry, in the present state of our knowledge, has not
+yet thrown off this character. There are other sciences, however, of
+which the propositions are of this kind: <i>a</i> a mark of <i>b</i>, <i>b</i> a mark
+of <i>c</i>, <i>c</i> of <i>d</i>, <i>d</i> of <i>e</i>, &amp;c. In these sciences we can mount <span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span>the
+ladder from <i>a</i> to <i>e</i> by a process of ratiocination; we can conclude
+that <i>a</i> is a mark of <i>e</i>, and that every object which has the mark <i>a</i>
+has the property <i>e</i>, although, perhaps, we never were able to observe
+<i>a</i> and <i>e</i> together, and although even <i>d</i>, our only direct mark of
+<i>e</i>, may not be perceptible in those objects, but only inferrible. Or,
+varying the first metaphor, we may be said to get from <i>a</i> to <i>e</i>
+underground: the marks <i>b</i>, <i>c</i>, <i>d</i>, which indicate the route, must all
+be possessed somewhere by the objects concerning which we are inquiring;
+but they are below the surface: <i>a</i> is the only mark that is visible,
+and by it we are able to trace in succession all the rest.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_6">� 6.</a> We can now understand how an experimental may transform itself into
+a deductive science by the mere progress of experiment. In an
+experimental science, the inductions, as we have said, lie detached, as,
+<i>a</i> a mark of <i>b</i>, <i>c</i> a mark of <i>d</i>, <i>e</i> a mark of <i>f</i>, and so on: now,
+a new set of instances, and a consequent new induction, may at any time
+bridge over the interval between two of these unconnected arches; <i>b</i>,
+for example, may be ascertained to be a mark of <i>c</i>, which enables us
+thenceforth to prove deductively that <i>a</i> is a mark of <i>c</i>. Or, as
+sometimes happens, some comprehensive induction may raise an arch high
+in the air, which bridges over hosts of them at once: <i>b</i>, <i>d</i>, <i>f</i>, and
+all the rest, turning out to be marks of some one thing, or of things
+between which a connexion has already been traced. As when Newton
+discovered that the motions, whether regular or apparently anomalous, of
+all the bodies of the solar system, (each of which motions had been
+inferred by a separate logical operation, from separate marks,) were all
+marks of moving round a common centre, with a centripetal force varying
+directly as the mass, and inversely as the square of the distance from
+that centre. This is the greatest example which has yet occurred of the
+transformation, at one stroke, of a science which was still to a great
+degree merely experimental, into a deductive science.</p>
+
+<p>Transformations of the same nature, but on a smaller scale, <span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span>continually
+take place in the less advanced branches of physical knowledge, without
+enabling them to throw off the character of experimental sciences. Thus
+with regard to the two unconnected propositions before cited, namely,
+Acids redden vegetable blues, Alkalies make them green; it is remarked
+by Liebig, that all blue colouring matters which are reddened by acids
+(as well as, reciprocally, all red colouring matters which are rendered
+blue by alkalies) contain nitrogen: and it is quite possible that this
+circumstance may one day furnish a bond of connexion between the two
+propositions in question, by showing that the antagonistic action of
+acids and alkalies in producing or destroying the colour blue, is the
+result of some one, more general, law. Although this connecting of
+detached generalizations is so much gain, it tends but little to give a
+deductive character to any science as a whole; because the new courses
+of observation and experiment, which thus enable us to connect together
+a few general truths, usually make known to us a still greater number of
+unconnected new ones. Hence chemistry, though similar extensions and
+simplifications of its generalizations are continually taking place, is
+still in the main an experimental science; and is likely so to continue
+unless some comprehensive induction should be hereafter arrived at,
+which, like Newton's, shall connect a vast number of the smaller known
+inductions together, and change the whole method of the science at once.
+Chemistry has already one great generalization, which, though relating
+to one of the subordinate aspects of chemical phenomena, possesses
+within its limited sphere this comprehensive character; the principle of
+Dalton, called the atomic theory, or the doctrine of chemical
+equivalents: which by enabling us to a certain extent to foresee the
+proportions in which two substances will combine, before the experiment
+has been tried, constitutes undoubtedly a source of new chemical truths
+obtainable by deduction, as well as a connecting principle for all
+truths of the same description previously obtained by experiment.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_IV_7">� 7.</a> The discoveries which change the method of a science from
+experimental to deductive, mostly consist in <span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span>establishing, either by
+deduction or by direct experiment, that the varieties of a particular
+phenomenon uniformly accompany the varieties of some other phenomenon
+better known. Thus the science of sound, which previously stood in the
+lowest rank of merely experimental science, became deductive when it was
+proved by experiment that every variety of sound was consequent on, and
+therefore a mark of, a distinct and definable variety of oscillatory
+motion among the particles of the transmitting medium. When this was
+ascertained, it followed that every relation of succession or
+coexistence which obtained between phenomena of the more known class,
+obtained also between the phenomena which corresponded to them in the
+other class. Every sound, being a mark of a particular oscillatory
+motion, became a mark of everything which, by the laws of dynamics, was
+known to be inferrible from that motion; and everything which by those
+same laws was a mark of any oscillatory motion among the particles of an
+elastic medium, became a mark of the corresponding sound. And thus many
+truths, not before suspected, concerning sound, become deducible from
+the known laws of the propagation of motion through an elastic medium;
+while facts already empirically known respecting sound, become an
+indication of corresponding properties of vibrating bodies, previously
+undiscovered.</p>
+
+<p>But the grand agent for transforming experimental into deductive
+sciences, is the science of number. The properties of numbers, alone
+among all known phenomena, are, in the most rigorous sense, properties
+of all things whatever. All things are not coloured, or ponderable, or
+even extended; but all things are numerable. And if we consider this
+science in its whole extent, from common arithmetic up to the calculus
+of variations, the truths already ascertained seem all but infinite, and
+admit of indefinite extension.</p>
+
+<p>These truths, though affirmable of all things whatever, of course apply
+to them only in respect of their quantity. But if it comes to be
+discovered that variations of quality in any class of phenomena,
+correspond regularly to variations of quantity either in those same or
+in some other phenomena; <span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span>every formula of mathematics applicable to
+quantities which vary in that particular manner, becomes a mark of a
+corresponding general truth respecting the variations in quality which
+accompany them: and the science of quantity being (as far as any science
+can be) altogether deductive, the theory of that particular kind of
+qualities becomes, to this extent, deductive likewise.</p>
+
+<p>The most striking instance in point which history affords (though not an
+example of an experimental science rendered deductive, but of an
+unparalleled extension given to the deductive process in a science which
+was deductive already), is the revolution in geometry which originated
+with Descartes, and was completed by Clairaut. These great
+mathematicians pointed out the importance of the fact, that to every
+variety of position in points, direction in lines, or form in curves or
+surfaces (all of which are Qualities), there corresponds a peculiar
+relation of quantity between either two or three rectilineal
+co-ordinates; insomuch that if the law were known according to which
+those co-ordinates vary relatively to one another, every other
+geometrical property of the line or surface in question, whether
+relating to quantity or quality, would be capable of being inferred.
+Hence it followed that every geometrical question could be solved, if
+the corresponding algebraical one could; and geometry received an
+accession (actual or potential) of new truths, corresponding to every
+property of numbers which the progress of the calculus had brought, or
+might in future bring, to light. In the same general manner, mechanics,
+astronomy, and in a less degree, every branch of natural philosophy
+commonly so called, have been made algebraical. The varieties of
+physical phenomena with which those sciences are conversant, have been
+found to answer to determinable varieties in the quantity of some
+circumstance or other; or at least to varieties of form or position, for
+which corresponding equations of quantity had already been, or were
+susceptible of being, discovered by geometers.</p>
+
+<p>In these various transformations, the propositions of the science of
+number do but fulfil the function proper to all propositions <span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span>forming a
+train of reasoning, viz. that of enabling us to arrive in an indirect
+method, by marks of marks, at such of the properties of objects as we
+cannot directly ascertain (or not so conveniently) by experiment. We
+travel from a given visible or tangible fact, through the truths of
+numbers, to the facts sought. The given fact is a mark that a certain
+relation subsists between the quantities of some of the elements
+concerned; while the fact sought presupposes a certain relation between
+the quantities of some other elements: now, if these last quantities are
+dependent in some known manner upon the former, or <i>vice vers�</i>, we can
+argue from the numerical relation between the one set of quantities, to
+determine that which subsists between the other set; the theorems of the
+calculus affording the intermediate links. And thus one of the two
+physical facts becomes a mark of the other, by being a mark of a mark of
+a mark of it.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_V" id="BOOK_II_CHAPTER_V"></a>CHAPTER V.<br />
+
+OF DEMONSTRATION, AND NECESSARY TRUTHS.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_V_1">� 1.</a> If, as laid down in the two preceding chapters, the foundation of
+all sciences, even deductive or demonstrative sciences, is Induction; if
+every step in the ratiocinations even of geometry is an act of
+induction; and if a train of reasoning is but bringing many inductions
+to bear upon the same subject of inquiry, and drawing a case within one
+induction by means of another; wherein lies the peculiar certainty
+always ascribed to the sciences which are entirely, or almost entirely,
+deductive? Why are they called the Exact Sciences? Why are mathematical
+certainty, and the evidence of demonstration, common phrases to express
+the very highest degree of assurance attainable by reason? Why are
+mathematics by almost all philosophers, and (by some) even those
+branches of natural philosophy which, through the medium of mathematics,
+have been converted into deductive sciences, considered to be
+independent of the evidence of experience and observation, and
+characterized as systems of Necessary Truth?</p>
+
+<p>The answer I conceive to be, that this character of necessity, ascribed
+to the truths of mathematics, and even (with some reservations to be
+hereafter made) the peculiar certainty attributed to them, is an
+illusion; in order to sustain which, it is necessary to suppose that
+those truths relate to, and express the properties of, purely imaginary
+objects. It is acknowledged that the conclusions of geometry are
+deduced, partly at least, from the so-called Definitions, and that those
+definitions are assumed to be correct representations, as far as they
+go, of the objects with which geometry is conversant. Now we have
+pointed out that, from a definition as such, no proposition, unless it
+be one concerning the meaning of a word, can ever follow; and that what
+apparently follows <span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span>from a definition, follows in reality from an
+implied assumption that there exists a real thing conformable thereto.
+This assumption, in the case of the definitions of geometry, is false:
+there exist no real things exactly conformable to the definitions. There
+exist no points without magnitude; no lines without breadth, nor
+perfectly straight; no circles with all their radii exactly equal, nor
+squares with all their angles perfectly right. It will perhaps be said
+that the assumption does not extend to the actual, but only to the
+possible, existence of such things. I answer that, according to any test
+we have of possibility, they are not even possible. Their existence, so
+far as we can form any judgment, would seem to be inconsistent with the
+physical constitution of our planet at least, if not of the universe. To
+get rid of this difficulty, and at the same time to save the credit of
+the supposed system of necessary truth, it is customary to say that the
+points, lines, circles, and squares which are the subject of geometry,
+exist in our conceptions merely, and are part of our minds; which minds,
+by working on their own materials, construct an <i>� priori</i> science, the
+evidence of which is purely mental, and has nothing whatever to do with
+outward experience. By howsoever high authorities this doctrine may have
+been sanctioned, it appears to me psychologically incorrect. The points,
+lines, circles, and squares, which any one has in his mind, are (I
+apprehend) simply copies of the points, lines, circles, and squares
+which he has known in his experience. Our idea of a point, I apprehend
+to be simply our idea of the <i>minimum visibile</i>, the smallest portion of
+surface which we can see. A line, as defined by geometers, is wholly
+inconceivable. We can reason about a line as if it had no breadth;
+because we have a power, which is the foundation of all the control we
+can exercise over the operations of our minds; the power, when a
+perception is present to our senses, or a conception to our intellects,
+of <i>attending</i> to a part only of that perception or conception, instead
+of the whole. But we cannot <i>conceive</i> a line without breadth; we can
+form no mental picture of such a line: all the lines which we have in
+our minds are lines possessing breadth. If any one doubts this, we may
+refer him to his own <span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span>experience. I much question if any one who fancies
+that he can conceive what is called a mathematical line, thinks so from
+the evidence of his consciousness: I suspect it is rather because he
+supposes that unless such a conception were possible, mathematics could
+not exist as a science: a supposition which there will be no difficulty
+in showing to be entirely groundless.</p>
+
+<p>Since, then, neither in nature, nor in the human mind, do there exist
+any objects exactly corresponding to the definitions of geometry, while
+yet that science cannot be supposed to be conversant about non-entities;
+nothing remains but to consider geometry as conversant with such lines,
+angles, and figures, as really exist; and the definitions, as they are
+called, must be regarded as some of our first and most obvious
+generalizations concerning those natural objects. The correctness of
+those generalizations, as generalizations, is without a flaw: the
+equality of all the radii of a circle is true of all circles, so far as
+it is true of any one: but it is not exactly true of any circle; it is
+only nearly true; so nearly that no error of any importance in practice
+will be incurred by feigning it to be exactly true. When we have
+occasion to extend these inductions, or their consequences, to cases in
+which the error would be appreciable&mdash;to lines of perceptible breadth or
+thickness, parallels which deviate sensibly from equidistance, and the
+like&mdash;we correct our conclusions, by combining with them a fresh set of
+propositions relating to the aberration; just as we also take in
+propositions relating to the physical or chemical properties of the
+material, if those properties happen to introduce any modification into
+the result; which they easily may, even with respect to figure and
+magnitude, as in the case, for instance, of expansion by heat. So long,
+however, as there exists no practical necessity for attending to any of
+the properties of the object except its geometrical properties, or to
+any of the natural irregularities in those, it is convenient to neglect
+the consideration of the other properties and of the irregularities, and
+to reason as if these did not exist: accordingly, we formally announce
+in the definitions, that we intend to proceed on this plan. But it is
+<span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span>an error to suppose, because we resolve to confine our attention to a
+certain number of the properties of an object, that we therefore
+conceive, or have an idea of, the object, denuded of its other
+properties. We are thinking, all the time, of precisely such objects as
+we have seen and touched, and with all the properties which naturally
+belong to them; but, for scientific convenience, we feign them to be
+divested of all properties, except those which are material to our
+purpose, and in regard to which we design to consider them.</p>
+
+<p>The peculiar accuracy, supposed to be characteristic of the first
+principles of geometry, thus appears to be fictitious. The assertions on
+which the reasonings of the science are founded, do not, any more than
+in other sciences, exactly correspond with the fact; but we suppose that
+they do so, for the sake of tracing the consequences which follow from
+the supposition. The opinion of Dugald Stewart respecting the
+foundations of geometry, is, I conceive, substantially correct; that it
+is built on hypotheses; that it owes to this alone the peculiar
+certainty supposed to distinguish it; and that in any science whatever,
+by reasoning from a set of hypotheses, we may obtain a body of
+conclusions as certain as those of geometry, that is, as strictly in
+accordance with the hypotheses, and as irresistibly compelling assent,
+<i>on condition</i> that those hypotheses are true.</p>
+
+<p>When, therefore, it is affirmed that the conclusions of geometry are
+necessary truths, the necessity consists in reality only in this, that
+they correctly follow from the suppositions from which they are deduced.
+Those suppositions are so far from being necessary, that they are not
+even true; they purposely depart, more or less widely, from the truth.
+The only sense in which necessity can be ascribed to the conclusions of
+any scientific investigation, is that of legitimately following from
+some assumption, which, by the conditions of the inquiry, is not to be
+questioned. In this relation, of course, the derivative truths of every
+deductive science must stand to the inductions, or assumptions, on which
+the science is founded, and which, whether true or untrue, certain or
+doubtful in themselves, are always supposed certain for the purposes of
+the <span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span>particular science. And therefore the conclusions of all deductive
+sciences were said by the ancients to be necessary propositions. We have
+observed already that to be predicated necessarily was characteristic of
+the predicable Proprium, and that a proprium was any property of a thing
+which could be deduced from its essence, that is, from the properties
+included in its definition.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_V_2">� 2.</a> The important doctrine of Dugald Stewart, which I have endeavoured
+to enforce, has been contested by Dr. Whewell, both in the dissertation
+appended to his excellent <i>Mechanical Euclid</i>, and in his elaborate work
+on the <i>Philosophy of the Inductive Sciences</i>; in which last he also
+replies to an article in the Edinburgh Review, (ascribed to a writer of
+great scientific eminence), in which Stewart's opinion was defended
+against his former strictures. The supposed refutation of Stewart
+consists in proving against him (as has also been done in this work)
+that the premises of geometry are not definitions, but assumptions of
+the real existence of things corresponding to those definitions. This,
+however, is doing little for Dr. Whewell's purpose; for it is these very
+assumptions which are asserted to be hypotheses, and which he, if he
+denies that geometry is founded on hypotheses, must show to be absolute
+truths. All he does, however, is to observe, that they at any rate, are
+not <i>arbitrary</i> hypotheses; that we should not be at liberty to
+substitute other hypotheses for them; that not only "a definition, to be
+admissible, must necessarily refer to and agree with some conception
+which we can distinctly frame in our thoughts," but that the straight
+lines, for instance, which we define, must be "those by which angles are
+contained, those by which triangles are bounded, those of which
+parallelism may be predicated, and the like."<a name="FNanchor_19_54" id="FNanchor_19_54"></a><a href="#Footnote_19_54" class="fnanchor">[19]</a> And this is true; but
+this has never been contradicted. Those who say that the premises of
+geometry are hypotheses, are not bound to maintain them to be hypotheses
+which have no relation whatever to fact. Since an hypothesis framed for
+the purpose of scientific inquiry must <span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span>relate to something which has
+real existence, (for there can be no science respecting non-entities,)
+it follows that any hypothesis we make respecting an object, to
+facilitate our study of it, must not involve anything which is
+distinctly false, and repugnant to its real nature: we must not ascribe
+to the thing any property which it has not; our liberty extends only to
+slightly exaggerating some of those which it has, (by assuming it to be
+completely what it really is very nearly,) and suppressing others, under
+the indispensable obligation of restoring them whenever, and in as far
+as, their presence or absence would make any material difference in the
+truth of our conclusions. Of this nature, accordingly, are the first
+principles involved in the definitions of geometry. That the hypotheses
+should be of this particular character, is however no further necessary,
+than inasmuch as no others could enable us to deduce conclusions which,
+with due corrections, would be true of real objects: and in fact, when
+our aim is only to illustrate truths, and not to investigate them, we
+are not under any such restriction. We might suppose an imaginary
+animal, and work out by deduction, from the known laws of physiology,
+its natural history; or an imaginary commonwealth, and from the elements
+composing it, might argue what would be its fate. And the conclusions
+which we might thus draw from purely arbitrary hypotheses, might form a
+highly useful intellectual exercise: but as they could only teach us
+what <i>would</i> be the properties of objects which do not really exist,
+they would not constitute any addition to our knowledge of nature: while
+on the contrary, if the hypothesis merely divests a real object of some
+portion of its properties, without clothing it in false ones, the
+conclusions will always express, under known liability to correction,
+actual truth.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_V_3">� 3.</a> But though Dr. Whewell has not shaken Stewart's doctrine as to the
+hypothetical character of that portion of the first principles of
+geometry which are involved in the so-called definitions, he has, I
+conceive, greatly the advantage of Stewart on another important point in
+the theory of geometrical reasoning; the necessity of admitting, among
+those first <span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span>principles, axioms as well as definitions. Some of the
+axioms of Euclid might, no doubt, be exhibited in the form of
+definitions, or might be deduced, by reasoning, from propositions
+similar to what are so called. Thus, if instead of the axiom, Magnitudes
+which can be made to coincide are equal, we introduce a definition,
+"Equal magnitudes are those which may be so applied to one another as to
+coincide;" the three axioms which follow (Magnitudes which are equal to
+the same are equal to one another&mdash;If equals are added to equals the
+sums are equal&mdash;If equals are taken from equals the remainders are
+equal,) may be proved by an imaginary superposition, resembling that by
+which the fourth proposition of the first book of Euclid is
+demonstrated. But though these and several others may be struck out of
+the list of first principles, because, though not requiring
+demonstration, they are susceptible of it; there will be found in the
+list of axioms two or three fundamental truths, not capable of being
+demonstrated: among which must be reckoned the proposition that two
+straight lines cannot inclose a space, (or its equivalent, Straight
+lines which coincide in two points coincide altogether,) and some
+property of parallel lines, other than that which constitutes their
+definition: one of the most suitable for the purpose being that selected
+by Professor Playfair: "Two straight lines which intersect each other
+cannot both of them be parallel to a third straight line."<a name="FNanchor_20_55" id="FNanchor_20_55"></a><a href="#Footnote_20_55" class="fnanchor">[20]</a></p>
+
+<p>The axioms, as well those which are indemonstrable as those which admit
+of being demonstrated, differ from that other class of fundamental
+principles which are involved in the <span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span>definitions, in this, that they
+are true without any mixture of hypothesis. That things which are equal
+to the same thing are equal to one another, is as true of the lines and
+figures in nature, as it would be of the imaginary ones assumed in the
+definitions. In this respect, however, mathematics are only on a par
+with most other sciences. In almost all sciences there are some general
+propositions which are exactly true, while the greater part are only
+more or less distant approximations to the truth. Thus in mechanics, the
+first law of motion (the continuance of a movement once impressed, until
+stopped or slackened by some resisting force) is true without
+qualification or error. The rotation of the earth in twenty-four hours,
+of the same length as in our time, has gone on since the first accurate
+observations, without the increase or diminution of one second in all
+that period. These are inductions which require no fiction to make them
+be received as accurately true: but along with them there are others, as
+for instance the propositions respecting the figure of the earth, which
+are but approximations to the truth; and in order to use them for the
+further advancement of our knowledge, we must feign that they are
+exactly true, though they really want something of being so.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_V_4">� 4.</a> It remains to inquire, what is the ground of our belief in
+axioms&mdash;what is the evidence on which they rest? I answer, they are
+experimental truths; generalizations from observation. The proposition,
+Two straight lines cannot inclose a space&mdash;or in other words, Two
+straight lines which have once met, do not meet again, but continue to
+diverge&mdash;is an induction from the evidence of our senses.</p>
+
+<p>This opinion runs counter to a scientific prejudice of long standing and
+great strength, and there is probably no proposition enunciated in this
+work for which a more unfavourable reception is to be expected. It is,
+however, no new opinion; and even if it were so, would be entitled to be
+judged, not by its novelty, but by the strength of the arguments by
+which it can be supported. I consider it very fortunate that so eminent
+a champion of the contrary opinion as Dr. Whewell, has <span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span>found occasion
+for a most elaborate treatment of the whole theory of axioms, in
+attempting to construct the philosophy of the mathematical and physical
+sciences on the basis of the doctrine against which I now contend.
+Whoever is anxious that a discussion should go to the bottom of the
+subject, must rejoice to see the opposite side of the question worthily
+represented. If what is said by Dr. Whewell, in support of an opinion
+which he has made the foundation of a systematic work, can be shown not
+to be conclusive, enough will have been done, without going further in
+quest of stronger arguments and a more powerful adversary.</p>
+
+<p>It is not necessary to show that the truths which we call axioms are
+originally <i>suggested</i> by observation, and that we should never have
+known that two straight lines cannot inclose a space if we had never
+seen a straight line: thus much being admitted by Dr. Whewell, and by
+all, in recent times, who have taken his view of the subject. But they
+contend, that it is not experience which <i>proves</i> the axiom; but that
+its truth is perceived <i>� priori</i>, by the constitution of the mind
+itself, from the first moment when the meaning of the proposition is
+apprehended; and without any necessity for verifying it by repeated
+trials, as is requisite in the case of truths really ascertained by
+observation.</p>
+
+<p>They cannot, however, but allow that the truth of the axiom, Two
+straight lines cannot inclose a space, even if evident independently of
+experience, is also evident from experience. Whether the axiom needs
+confirmation or not, it receives confirmation in almost every instant of
+our lives; since we cannot look at any two straight lines which
+intersect one another, without seeing that from that point they continue
+to diverge more and more. Experimental proof crowds in upon us in such
+endless profusion, and without one instance in which there can be even a
+suspicion of an exception to the rule, that we should soon have stronger
+ground for believing the axiom, even as an experimental truth, than we
+have for almost any of the general truths which we confessedly learn
+from the evidence of our senses. Independently of <i>� priori</i> evidence,
+we should certainly believe it with an intensity of <span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span>conviction far
+greater than we accord to any ordinary physical truth: and this too at a
+time of life much earlier than that from which we date almost any part
+of our acquired knowledge, and much too early to admit of our retaining
+any recollection of the history of our intellectual operations at that
+period. Where then is the necessity for assuming that our recognition of
+these truths has a different origin from the rest of our knowledge, when
+its existence is perfectly accounted for by supposing its origin to be
+the same? when the causes which produce belief in all other instances,
+exist in this instance, and in a degree of strength as much superior to
+what exists in other cases, as the intensity of the belief itself is
+superior? The burden of proof lies on the advocates of the contrary
+opinion: it is for them to point out some fact, inconsistent with the
+supposition that this part of our knowledge of nature is derived from
+the same sources as every other part.<a name="FNanchor_21_56" id="FNanchor_21_56"></a><a href="#Footnote_21_56" class="fnanchor">[21]</a></p>
+
+<p>This, for instance, they would be able to do, if they could prove
+chronologically that we had the conviction (at least practically) so
+early in infancy as to be anterior to those impressions on the senses,
+upon which, on the other theory, the conviction is founded. This,
+however, cannot be proved: the point being too far back to be within the
+reach of memory, and too obscure for external observation. The advocates
+of the <i>� priori</i> theory are obliged to have recourse to other
+arguments. <span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span>These are reducible to two, which I shall endeavour to state
+as clearly and as forcibly as possible.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_V_5">� 5.</a> In the first place it is said that if our assent to the proposition
+that two straight lines cannot inclose a space, were derived from the
+senses, we could only be convinced of its truth by actual trial, that
+is, by seeing or feeling the straight lines; whereas in fact it is seen
+to be true by merely thinking of them. That a stone thrown into water
+goes to the bottom, may be perceived by our senses, but mere thinking of
+a stone thrown into the water would never have led us to that
+conclusion: not so, however, with the axioms relating to straight lines:
+if I could be made to conceive what a straight line is, without having
+seen one, I should at once recognise that two such lines cannot inclose
+a space. Intuition is "imaginary looking;"<a name="FNanchor_22_57" id="FNanchor_22_57"></a><a href="#Footnote_22_57" class="fnanchor">[22]</a> but experience must be
+real looking: if we see a property of straight lines to be true by
+merely fancying ourselves to be looking at them, the ground of our
+belief cannot be the senses, or experience; it must be something mental.</p>
+
+<p>To this argument it might be added in the case of this particular axiom,
+(for the assertion would not be true of all axioms,) that the evidence
+of it from actual ocular inspection is not only unnecessary, but
+unattainable. What says the axiom? That two straight lines <i>cannot</i>
+inclose a space; that after having once intersected, if they are
+prolonged to infinity they do not meet, but continue to diverge from one
+another. <span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span>How can this, in any single case, be proved by actual
+observation? We may follow the lines to any distance we please; but we
+cannot follow them to infinity: for aught our senses can testify, they
+may, immediately beyond the farthest point to which we have traced them,
+begin to approach, and at last meet. Unless, therefore, we had some
+other proof of the impossibility than observation affords us, we should
+have no ground for believing the axiom at all.</p>
+
+<p>To these arguments, which I trust I cannot be accused of understating, a
+satisfactory answer will, I conceive, be found, if we advert to one of
+the characteristic properties of geometrical forms&mdash;their capacity of
+being painted in the imagination with a distinctness equal to reality:
+in other words, the exact resemblance of our ideas of form to the
+sensations which suggest them. This, in the first place, enables us to
+make (at least with a little practice) mental pictures of all possible
+combinations of lines and angles, which resemble the realities quite as
+well as any which we could make on paper; and in the next place, make
+those pictures just as fit subjects of geometrical experimentation as
+the realities themselves; inasmuch as pictures, if sufficiently
+accurate, exhibit of course all the properties which would be manifested
+by the realities at one given instant, and on simple inspection: and in
+geometry we are concerned only with such properties, and not with that
+which pictures could not exhibit, the mutual action of bodies one upon
+another. The foundations of geometry would therefore be laid in direct
+experience, even if the experiments (which in this case consist merely
+in attentive contemplation) were practised solely upon what we call our
+ideas, that is, upon the diagrams in our minds, and not upon outward
+objects. For in all systems of experimentation we take some objects to
+serve as representatives of all which resemble them; and in the present
+case the conditions which qualify a real object to be the representative
+of its class, are completely fulfilled by an object existing only in our
+fancy. Without denying, therefore, the possibility of satisfying
+ourselves that two straight lines cannot inclose a space, by merely
+thinking of straight lines without actually looking at them; I contend,
+that we do not <span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span>believe this truth on the ground of the imaginary
+intuition simply, but because we know that the imaginary lines exactly
+resemble real ones, and that we may conclude from them to real ones with
+quite as much certainty as we could conclude from one real line to
+another. The conclusion, therefore, is still an induction from
+observation. And we should not be authorized to substitute observation
+of the image in our mind, for observation of the reality, if we had not
+learnt by long-continued experience that the properties of the reality
+are faithfully represented in the image; just as we should be
+scientifically warranted in describing an animal which we have never
+seen, from a picture made of it with a daguerreotype; but not until we
+had learnt by ample experience, that observation of such a picture is
+precisely equivalent to observation of the original.</p>
+
+<p>These considerations also remove the objection arising from the
+impossibility of ocularly following the lines in their prolongation to
+infinity. For though, in order actually to see that two given lines
+never meet, it would be necessary to follow them to infinity; yet
+without doing so we may know that if they ever do meet, or if, after
+diverging from one another, they begin again to approach, this must take
+place not at an infinite, but at a finite distance. Supposing,
+therefore, such to be the case, we can transport ourselves thither in
+imagination, and can frame a mental image of the appearance which one or
+both of the lines must present at that point, which we may rely on as
+being precisely similar to the reality. Now, whether we fix our
+contemplation upon this imaginary picture, or call to mind the
+generalizations we have had occasion to make from former ocular
+observation, we learn by the evidence of experience, that a line which,
+after diverging from another straight line, begins to approach to it,
+produces the impression on our senses which we describe by the
+expression, "a bent line," not by the expression, "a straight line."<a name="FNanchor_23_58" id="FNanchor_23_58"></a><a href="#Footnote_23_58" class="fnanchor">[23]</a></p>
+
+
+<p><span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span></p><p class="newsection"><a name="BOOK_II_CHAPTER_V_6">� 6.</a> The first of the two arguments in support of the theory that
+axioms are <i>� priori</i> truths, having, I think, been sufficiently
+answered; I proceed to the second, which is usually the most relied on.
+Axioms (it is asserted) are conceived by us not only as true, but as
+universally and necessarily true. Now, experience cannot possibly give
+to any proposition this <span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span>character. I may have seen snow a hundred
+times, and may have seen that it was white, but this cannot give me
+entire assurance even that all snow is white; much less that snow <i>must</i>
+be white. "However many instances we may have observed of the truth of a
+proposition, there is nothing to assure us that the next case shall not
+be an exception to the rule. If it be strictly true that every ruminant
+animal yet known has cloven hoofs, we still cannot be sure that some
+creature will not hereafter be discovered which has the first of these
+attributes, without having the other.... Experience must always consist
+of a limited number of observations; and, however numerous these may be,
+they can show nothing with regard to the infinite number of cases in
+which the experiment has not been made." Besides, Axioms are not only
+universal, they are also necessary. Now "experience cannot offer the
+smallest ground for the necessity of a proposition. She can observe and
+record what has happened; but she cannot find, in any case, or in any
+accumulation of cases, any reason for what <i>must</i> happen. She may see
+objects side by side; but she cannot see a reason why they must ever be
+side by side. She finds certain events to occur in succession; but the
+succession supplies, in its occurrence, no reason for its recurrence.
+She contemplates external objects; but she cannot detect any internal
+bond, which indissolubly connects the future with the past, the possible
+with the real. To learn a proposition by experience, and to see it to be
+necessarily true, are two altogether different processes of
+thought."<a name="FNanchor_24_59" id="FNanchor_24_59"></a><a href="#Footnote_24_59" class="fnanchor">[24]</a> And Dr. Whewell adds, "If any one does not clearly
+comprehend this distinction of necessary and contingent truths, he will
+not be able to go along with us in our researches into the foundations
+of human knowledge; nor, indeed, to pursue with success any speculation
+on the subject."<a name="FNanchor_25_60" id="FNanchor_25_60"></a><a href="#Footnote_25_60" class="fnanchor">[25]</a></p>
+
+<p>In the following passage, we are told what the distinction is, the
+non-recognition of which incurs this denunciation. "Necessary truths are
+those in which we not only learn that the proposition is true, but see
+that it <i>must</i> be true; in which <span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span>the negation of the truth is not only
+false, but impossible; in which we cannot, even by an effort of
+imagination, or in a supposition, conceive the reverse of that which is
+asserted. That there are such truths cannot be doubted. We may take, for
+example, all relations of number. Three and Two added together make
+Five. We cannot conceive it to be otherwise. We cannot, by any freak of
+thought, imagine Three and Two to make Seven."<a name="FNanchor_26_61" id="FNanchor_26_61"></a><a href="#Footnote_26_61" class="fnanchor">[26]</a></p>
+
+<p>Although Dr. Whewell has naturally and properly employed a variety of
+phrases to bring his meaning more forcibly home, he would, I presume,
+allow that they are all equivalent; and that what he means by a
+necessary truth, would be sufficiently defined, a proposition the
+negation of which is not only false but inconceivable. I am unable to
+find in any of his expressions, turn them what way you will, a meaning
+beyond this, and I do not believe he would contend that they mean
+anything more.</p>
+
+<p>This, therefore, is the principle asserted: that propositions, the
+negation of which is inconceivable, or in other words, which we cannot
+figure to ourselves as being false, must rest on evidence of a higher
+and more cogent description than any which experience can afford.</p>
+
+<p>Now I cannot but wonder that so much stress should be laid on the
+circumstance of inconceivableness, when there is such ample experience
+to show, that our capacity or incapacity of conceiving a thing has very
+little to do with the possibility of the thing in itself; but is in
+truth very much an affair of accident, and depends on the past history
+and habits of our own minds. There is no more generally acknowledged
+fact in human nature, than the extreme difficulty at first felt in
+conceiving anything as possible, which is in contradiction to long
+established and familiar experience; or even to old familiar habits of
+thought. And this difficulty is a necessary result of the fundamental
+laws of the human mind. When we have often seen and thought of two
+things together, and have never in any one instance either seen or
+thought of them <span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span>separately, there is by the primary law of association
+an increasing difficulty, which may in the end become insuperable, of
+conceiving the two things apart. This is most of all conspicuous in
+uneducated persons, who are in general utterly unable to separate any
+two ideas which have once become firmly associated in their minds; and
+if persons of cultivated intellect have any advantage on the point, it
+is only because, having seen and heard and read more, and being more
+accustomed to exercise their imagination, they have experienced their
+sensations and thoughts in more varied combinations, and have been
+prevented from forming many of these inseparable associations. But this
+advantage has necessarily its limits. The most practised intellect is
+not exempt from the universal laws of our conceptive faculty. If daily
+habit presents to any one for a long period two facts in combination,
+and if he is not led during that period either by accident or by his
+voluntary mental operations to think of them apart, he will probably in
+time become incapable of doing so even by the strongest effort; and the
+supposition that the two facts can be separated in nature, will at last
+present itself to his mind with all the characters of an inconceivable
+phenomenon.<a name="FNanchor_27_62" id="FNanchor_27_62"></a><a href="#Footnote_27_62" class="fnanchor">[27]</a> There are remarkable instances of this in the history of
+science: instances in which the most instructed men rejected as
+impossible, because inconceivable, things which their posterity, by
+earlier practice and longer perseverance in the attempt, found it quite
+easy to conceive, and which everybody now knows to be true. There was a
+time when men of the most cultivated intellects, and the most
+emancipated from the dominion of early prejudice, could not credit the
+existence of antipodes; were unable to conceive, in opposition to old
+association, the force of gravity acting upwards instead of downwards.
+The Cartesians long rejected the Newtonian doctrine of the gravitation
+<span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span>of all bodies towards one another, on the faith of a general
+proposition, the reverse of which seemed to them to be
+inconceivable&mdash;the proposition that a body cannot act where it is not.
+All the cumbrous machinery of imaginary vortices, assumed without the
+smallest particle of evidence, appeared to these philosophers a more
+rational mode of explaining the heavenly motions, than one which
+involved what seemed to them so great an absurdity.<a name="FNanchor_28_63" id="FNanchor_28_63"></a><a href="#Footnote_28_63" class="fnanchor">[28]</a> And they no
+doubt found it as impossible to conceive that a body should act upon the
+earth at the distance of the sun or moon, as we find it to conceive an
+end to space or time, or two straight lines inclosing a space. Newton
+himself had not been able to realize the conception, or we should not
+have had his hypothesis of a subtle ether, the occult cause of
+gravitation; and his writings prove, that though he deemed the
+particular nature of the intermediate agency a matter of conjecture, the
+necessity of <i>some</i> such agency appeared to him indubitable. It would
+seem that even now the majority of scientific men have not completely
+got over this very difficulty; for though they have at last learnt to
+conceive the sun <i>attracting</i> the earth without any intervening fluid,
+they cannot yet conceive the sun <i>illuminating</i> the earth without some
+such medium.</p>
+
+<p>If, then, it be so natural to the human mind, even in a high state of
+culture, to be incapable of conceiving, and on that ground to believe
+impossible, what is afterwards not only found to be conceivable but
+proved to be true; what wonder <span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span>if in cases where the association is
+still older, more confirmed, and more familiar, and in which nothing
+ever occurs to shake our conviction, or even suggest to us any
+conception at variance with the association, the acquired incapacity
+should continue, and be mistaken for a natural incapacity? It is true,
+our experience of the varieties in nature enables us, within certain
+limits, to conceive other varieties analogous to them. We can conceive
+the sun or moon falling; for though we never saw them fall, nor ever
+perhaps imagined them falling, we have seen so many other things fall,
+that we have innumerable familiar analogies to assist the conception;
+which, after all, we should probably have some difficulty in framing,
+were we not well accustomed to see the sun and moon move (or appear to
+move,) so that we are only called upon to conceive a slight change in
+the direction of motion, a circumstance familiar to our experience. But
+when experience affords no model on which to shape the new conception,
+how is it possible for us to form it? How, for example, can we imagine
+an end to space or time? We never saw any object without something
+beyond it, nor experienced any feeling without something following it.
+When, therefore, we attempt to conceive the last point of space, we have
+the idea irresistibly raised of other points beyond it. When we try to
+imagine the last instant of time, we cannot help conceiving another
+instant after it. Nor is there any necessity to assume, as is done by a
+modern school of metaphysicians, a peculiar fundamental law of the mind
+to account for the feeling of infinity inherent in our conceptions of
+space and time; that apparent infinity is sufficiently accounted for by
+simpler and universally acknowledged laws.</p>
+
+<p>Now, in the case of a geometrical axiom, such, for example, as that two
+straight lines cannot inclose a space,&mdash;a truth which is testified to us
+by our very earliest impressions of the external world,&mdash;how is it
+possible (whether those external impressions be or be not the ground of
+our belief) that the reverse of the proposition <i>could</i> be otherwise
+than inconceivable to us? What analogy have we, what similar order of
+facts in any other branch of our experience, to facilitate to us <span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span>the
+conception of two straight lines inclosing a space? Nor is even this
+all. I have already called attention to the peculiar property of our
+impressions of form, that the ideas or mental images exactly resemble
+their prototypes, and adequately represent them for the purposes of
+scientific observation. From this, and from the intuitive character of
+the observation, which in this case reduces itself to simple inspection,
+we cannot so much as call up in our imagination two straight lines, in
+order to attempt to conceive them inclosing a space, without by that
+very act repeating the scientific experiment which establishes the
+contrary. Will it really be contended that the inconceivableness of the
+thing, in such circumstances, proves anything against the experimental
+origin of the conviction? Is it not clear that in whichever mode our
+belief in the proposition may have originated, the impossibility of our
+conceiving the negative of it must, on either hypothesis, be the same?
+As, then, Dr. Whewell exhorts those who have any difficulty in
+recognising the distinction held by him between necessary and contingent
+truths, to study geometry,&mdash;a condition which I can assure him I have
+conscientiously fulfilled,&mdash;I, in return, with equal confidence, exhort
+those who agree with him, to study the general laws of association;
+being convinced that nothing more is requisite than a moderate
+familiarity with those laws, to dispel the illusion which ascribes a
+peculiar necessity to our earliest inductions from experience, and
+measures the possibility of things in themselves, by the human capacity
+of conceiving them.</p>
+
+<p>I hope to be pardoned for adding, that Dr. Whewell himself has both
+confirmed by his testimony the effect of habitual association in giving
+to an experimental truth the appearance of a necessary one, and afforded
+a striking instance of that remarkable law in his own person. In his
+<i>Philosophy of the Inductive Sciences</i> he continually asserts, that
+propositions which not only are not self-evident, but which we know to
+have been discovered gradually, and by great efforts of genius and
+patience, have, when once established, appeared so self-evident that,
+but for historical proof, it would have been impossible to conceive that
+they had not been recognised from the <span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span>first by all persons in a sound
+state of their faculties. "We now despise those who, in the Copernican
+controversy, could not conceive the apparent motion of the sun on the
+heliocentric hypothesis; or those who, in opposition to Galileo, thought
+that a uniform force might be that which generated a velocity
+proportional to the space; or those who held there was something absurd
+in Newton's doctrine of the different refrangibility of differently
+coloured rays; or those who imagined that when elements combine, their
+sensible qualities must be manifest in the compound; or those who were
+reluctant to give up the distinction of vegetables into herbs, shrubs,
+and trees. We cannot help thinking that men must have been singularly
+dull of comprehension, to find a difficulty in admitting what is to us
+so plain and simple. We have a latent persuasion that we in their place
+should have been wiser and more clear-sighted; that we should have taken
+the right side, and given our assent at once to the truth. Yet in
+reality such a persuasion is a mere delusion. The persons who, in such
+instances as the above, were on the losing side, were very far, in most
+cases, from being persons more prejudiced, or stupid, or narrow-minded,
+than the greater part of mankind now are; and the cause for which they
+fought was far from being a manifestly bad one, till it had been so
+decided by the result of the war.... So complete has been the victory of
+truth in most of these instances, that at present we can hardly imagine
+the struggle to have been necessary. <i>The very essence of these triumphs
+is, that they lead us to regard the views we reject as not only false
+but inconceivable.</i>"<a name="FNanchor_29_64" id="FNanchor_29_64"></a><a href="#Footnote_29_64" class="fnanchor">[29]</a></p>
+
+<p>This last proposition is precisely what I contend for; and I ask no
+more, in order to overthrow the whole theory of its author on the nature
+of the evidence of axioms. For what is that theory? That the truth of
+axioms cannot have been learnt from experience, because their falsity is
+inconceivable. But Dr. Whewell himself says, that we are continually
+led, by the natural progress of thought, to regard as inconceivable what
+our forefathers not only conceived but believed, nay even <span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span>(he might
+have added) were unable to conceive the reverse of. He cannot intend to
+justify this mode of thought: he cannot mean to say, that we can be
+right in regarding as inconceivable what others have conceived, and as
+self-evident what to others did not appear evident at all. After so
+complete an admission that inconceivableness is an accidental thing, not
+inherent in the phenomenon itself, but dependent on the mental history
+of the person who tries to conceive it, how can he ever call upon us to
+reject a proposition as impossible on no other ground than its
+inconceivableness? Yet he not only does so, but has unintentionally
+afforded some of the most remarkable examples which can be cited of the
+very illusion which he has himself so clearly pointed out. I select as
+specimens, his remarks on the evidence of the three laws of motion, and
+of the atomic theory.</p>
+
+<p>With respect to the laws of motion, Dr. Whewell says: "No one can doubt
+that, in historical fact, these laws were collected from experience.
+That such is the case, is no matter of conjecture. We know the time, the
+persons, the circumstances, belonging to each step of each
+discovery."<a name="FNanchor_30_65" id="FNanchor_30_65"></a><a href="#Footnote_30_65" class="fnanchor">[30]</a> After this testimony, to adduce evidence of the fact
+would be superfluous. And not only were these laws by no means
+intuitively evident, but some of them were originally paradoxes. The
+first law was especially so. That a body, once in motion, would continue
+for ever to move in the same direction with undiminished velocity unless
+acted upon by some new force, was a proposition which mankind found for
+a long time the greatest difficulty in crediting. It stood opposed to
+apparent experience of the most familiar kind, which taught that it was
+the nature of motion to abate gradually, and at last terminate of
+itself. Yet when once the contrary doctrine was firmly established,
+mathematicians, as Dr. Whewell observes, speedily began to believe that
+laws, thus contradictory to first appearances, and which, even after
+full proof had been obtained, it had required generations to render
+familiar to the minds of the scientific world, were under "a
+demonstrable necessity, compelling them to be such as they are and no
+<span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span>other;" and he himself, though not venturing "absolutely to pronounce"
+that <i>all</i> these laws "can be rigorously traced to an absolute necessity
+in the nature of things,"<a name="FNanchor_31_66" id="FNanchor_31_66"></a><a href="#Footnote_31_66" class="fnanchor">[31]</a> does actually so think of the law just
+mentioned; of which he says: "Though the discovery of the first law of
+motion was made, historically speaking, by means of experiment, we have
+now attained a point of view in which we see that it might have been
+certainly known to be true, independently of experience."<a name="FNanchor_32_67" id="FNanchor_32_67"></a><a href="#Footnote_32_67" class="fnanchor">[32]</a> Can there
+be a more striking exemplification than is here afforded, of the effect
+of association which we have described? Philosophers, for generations,
+have the most extraordinary difficulty in putting certain ideas
+together; they at last succeed in doing so; and after a sufficient
+repetition of the process, they first fancy a natural bond between the
+ideas, then experience a growing difficulty, which at last, by the
+continuation of the same progress, becomes an impossibility, of severing
+them from one another. If such be the progress of an experimental
+conviction of which the date is of yesterday, and which is in opposition
+to first appearances, how must it fare with those which are conformable
+to appearances familiar from the first dawn of intelligence, and of the
+conclusiveness of which, from the earliest records of human thought, no
+sceptic has suggested even a momentary doubt?</p>
+
+<p>The other instance which I shall quote is a truly astonishing one, and
+may be called the <i>reductio ad absurdum</i> of the theory of
+inconceivableness. Speaking of the laws of chemical composition, Dr.
+Whewell says:<a name="FNanchor_33_68" id="FNanchor_33_68"></a><a href="#Footnote_33_68" class="fnanchor">[33]</a> "That they could never have been clearly understood,
+and therefore never firmly established, without laborious and exact
+experiments, is certain; but yet we may venture to say, that being once
+known, they possess an evidence beyond that of mere experiment. <i>For how
+in fact can we conceive combinations, otherwise than as definite in kind
+and quality?</i> If we were to suppose each element ready to combine with
+any other indifferently, and indifferently in any quantity, we should
+have a <span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span>world in which all would be confusion and indefiniteness. There
+would be no fixed kinds of bodies. Salts, and stones, and ores, would
+approach to and graduate into each other by insensible degrees. Instead
+of this, we know that the world consists of bodies distinguishable from
+each other by definite differences, capable of being classified and
+named, and of having general propositions asserted concerning them. And
+as <i>we cannot conceive a world in which this should not be the case</i>, it
+would appear that we cannot conceive a state of things in which the laws
+of the combination of elements should not be of that definite and
+measured kind which we have above asserted."</p>
+
+<p>That a philosopher of Dr. Whewell's eminence should gravely assert that
+we cannot conceive a world in which the simple elements should combine
+in other than definite proportions; that by dint of meditating on a
+scientific truth, the original discoverer of which was still living, he
+should have rendered the association in his own mind between the idea of
+combination and that of constant proportions so familiar and intimate as
+to be unable to conceive the one fact without the other; is so signal an
+instance of the mental law for which I am contending, that one word more
+in illustration must be superfluous.</p>
+
+<p>In the latest and most complete elaboration of his metaphysical system
+(the <i>Philosophy of Discovery</i>), as well as in the earlier discourse on
+the <i>Fundamental Antithesis of Philosophy</i>, reprinted as an appendix to
+that work, Dr. Whewell, while very candidly admitting that his language
+was open to misconception, disclaims having intended to say that mankind
+in general can <i>now</i> perceive the law of definite proportions in
+chemical combination to be a necessary truth. All he meant was that
+philosophical chemists in a future generation may possibly see this.
+"Some truths may be seen by intuition, but yet the intuition of them may
+be a rare and a difficult attainment."<a name="FNanchor_34_69" id="FNanchor_34_69"></a><a href="#Footnote_34_69" class="fnanchor">[34]</a> And he explains that the
+inconceivableness <span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span>which, according to his theory, is the test of
+axioms, "depends entirely upon the clearness of the Ideas which the
+axioms involve. So long as those Ideas are vague and indistinct, the
+contrary of an Axiom may be assented to, though it cannot be distinctly
+conceived. It may be assented to, not because it is possible, but
+because we do not see clearly what is possible. To a person who is only
+beginning to think geometrically, there may appear nothing absurd in the
+assertion, that two straight lines may inclose a space. And in the same
+manner, to a person who is only beginning to think of mechanical truths,
+it may not appear to be absurd, that in mechanical processes, Reaction
+should be greater or less than Action; and so, again, to a person who
+has not thought steadily about Substance, it may not appear
+inconceivable, that by chemical operations, we should generate new
+matter, or destroy matter which already exists."<a name="FNanchor_35_70" id="FNanchor_35_70"></a><a href="#Footnote_35_70" class="fnanchor">[35]</a> Necessary truths,
+therefore, are not those of which we cannot conceive, but "those of
+which we cannot <i>distinctly</i> conceive, the contrary."<a name="FNanchor_36_71" id="FNanchor_36_71"></a><a href="#Footnote_36_71" class="fnanchor">[36]</a> So long as our
+ideas are indistinct altogether, we do not know what is or is not
+capable of being distinctly conceived; but, by the ever increasing
+distinctness with which scientific men apprehend the general conceptions
+of science, they in time come to perceive that there are certain laws of
+nature, which, though historically and as a matter of fact they were
+learnt from experience, we cannot, now that we know them, distinctly
+conceive to be other than they are.</p>
+
+<p>The account which I should give of this progress of the scientific mind
+is somewhat different. After a general law of nature has been
+ascertained, men's minds do not at first acquire a complete facility of
+familiarly representing to themselves the phenomena of nature in the
+character which that law assigns to them. The habit which constitutes
+the scientific cast of mind, that of conceiving facts of all
+descriptions conformably to the laws which regulate them&mdash;phenomena of
+all descriptions according to the relations which have been ascertained
+really to exist between them; this habit, in the case of newly
+<span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span>discovered relations, comes only by degrees. So long as it is not
+thoroughly formed, no necessary character is ascribed to the new truth.
+But in time, the philosopher attains a state of mind in which his mental
+picture of nature spontaneously represents to him all the phenomena with
+which the new theory is concerned, in the exact light in which the
+theory regards them: all images or conceptions derived from any other
+theory, or from the confused view of the facts which is anterior to any
+theory, having entirely disappeared from his mind. The mode of
+representing facts which results from the theory, has now become, to his
+faculties, the only natural mode of conceiving them. It is a known
+truth, that a prolonged habit of arranging phenomena in certain groups,
+and explaining them by means of certain principles, makes any other
+arrangement or explanation of these facts be felt as unnatural: and it
+may at last become as difficult to him to represent the facts to himself
+in any other mode, as it often was, originally, to represent them in
+that mode.</p>
+
+<p>But, further, if the theory is true, as we are supposing it to be, any
+other mode in which he tries, or in which he was formerly accustomed, to
+represent the phenomena, will be seen by him to be inconsistent with the
+facts that suggested the new theory&mdash;facts which now form a part of his
+mental picture of nature. And since a contradiction is always
+inconceivable, his imagination rejects these false theories, and
+declares itself incapable of conceiving them. Their inconceivableness to
+him does not, however, result from anything in the theories themselves,
+intrinsically and <i>� priori</i> repugnant to the human faculties; it
+results from the repugnance between them and a portion of the facts;
+which facts as long as he did not know, or did not distinctly realize in
+his mental representations, the false theory did not appear other than
+conceivable; it becomes inconceivable, merely from the fact that
+contradictory elements cannot be combined in the same conception.
+Although, then, his real reason for rejecting theories at variance with
+the true one, is no other than that they clash with his experience, he
+easily falls into the belief, that he rejects them because they are
+inconceivable, and that he adopts the true theory because <span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span>it is
+self-evident, and does not need the evidence of experience at all.</p>
+
+<p>This I take to be the real and sufficient explanation of the paradoxical
+truth, on which so much stress is laid by Dr. Whewell, that a
+scientifically cultivated mind is actually, in virtue of that
+cultivation, unable to conceive suppositions which a common man
+conceives without the smallest difficulty. For there is nothing
+inconceivable in the suppositions themselves; the impossibility is in
+combining them with facts inconsistent with them, as part of the same
+mental picture; an obstacle of course only felt by those who know the
+facts, and are able to perceive the inconsistency. As far as the
+suppositions themselves are concerned, in the case of many of Dr.
+Whewell's necessary truths the negative of the axiom is, and probably
+will be as long as the human race lasts, as easily conceivable as the
+affirmative. There is no axiom (for example) to which Dr. Whewell
+ascribes a more thorough character of necessity and self-evidence, than
+that of the indestructibility of matter. That this is a true law of
+nature I fully admit; but I imagine there is no human being to whom the
+opposite supposition is inconceivable&mdash;who has any difficulty in
+imagining a portion of matter annihilated: inasmuch as its apparent
+annihilation, in no respect distinguishable from real by our unassisted
+senses, takes place every time that water dries up, or fuel is consumed.
+Again, the law that bodies combine chemically in definite proportions is
+undeniably true; but few besides Dr. Whewell have reached the point
+which he seems personally to have arrived at, (though he only dares
+prophesy similar success to the multitude after the lapse of
+generations,) that of being unable to conceive a world in which the
+elements are ready to combine with one another "indifferently in any
+quantity;" nor is it likely that we shall ever rise to this sublime
+height of inability, so long as all the mechanical mixtures in our
+planet, whether solid, liquid, or a�riform, exhibit to our daily
+observation the very phenomenon declared to be inconceivable.</p>
+
+<p>According to Dr. Whewell, these and similar laws of nature cannot be
+drawn from experience, inasmuch as they are, on <span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span>the contrary, assumed
+in the interpretation of experience. Our inability to "add to or
+diminish the quantity of matter in the world," is a truth which "neither
+is nor can be derived from experience; for the experiments which we make
+to verify it presuppose its truth.... When men began to use the balance
+in chemical analysis, they did not prove by trial, but took for granted,
+as self-evident, that the weight of the whole must be found in the
+aggregate weight of the elements."<a name="FNanchor_37_72" id="FNanchor_37_72"></a><a href="#Footnote_37_72" class="fnanchor">[37]</a> True, it is assumed; but, I
+apprehend, no otherwise than as all experimental inquiry assumes
+provisionally some theory or hypothesis, which is to be finally held
+true or not, according as the experiments decide. The hypothesis chosen
+for this purpose will naturally be one which groups together some
+considerable number of facts already known. The proposition that the
+material of the world, as estimated by weight, is neither increased nor
+diminished by any of the processes of nature or art, had many
+appearances in its favour to begin with. It expressed truly a great
+number of familiar facts. There were other facts which it had the
+appearance of conflicting with, and which made its truth, as an
+universal law of nature, at first doubtful. Because it was doubtful,
+experiments were devised to verify it. Men assumed its truth
+hypothetically, and proceeded to try whether, on more careful
+examination, the phenomena which apparently pointed to a different
+conclusion, would not be found to be consistent with it. This turned out
+to be the case; and from that time the doctrine took its place as an
+universal truth, but as one proved to be such by experience. That the
+theory itself preceded the proof of its truth&mdash;that it had to be
+conceived before it could be proved, and in order that it might be
+proved&mdash;does not imply that it was self-evident, and did not need proof.
+Otherwise all the true theories in the sciences are necessary and
+self-evident; for no one knows better than Dr. Whewell that they all
+began by being assumed, for the purpose of connecting them by deductions
+with those facts of experience on which, as evidence, they now
+confessedly rest.<a name="FNanchor_38_73" id="FNanchor_38_73"></a><a href="#Footnote_38_73" class="fnanchor">[38]</a></p>
+
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_VI" id="BOOK_II_CHAPTER_VI"></a>CHAPTER VI.<br />
+
+THE SAME SUBJECT CONTINUED.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VI_1">� 1.</a> In the examination which formed the subject of the last chapter,
+into the nature of the evidence of those deductive sciences which are
+commonly represented to be systems of necessary truth, we have been led
+to the following conclusions. The results of those sciences are indeed
+necessary, in the sense of necessarily following from certain first
+principles, commonly called axioms and definitions; that is, of being
+certainly true if those axioms and definitions are so; for the word
+necessity, even in this acceptation of it, means no more than certainty.
+But their claim to the character of necessity in any sense beyond this,
+as implying an evidence independent of and superior to observation and
+experience, must depend on the previous establishment of such a claim in
+favour of the definitions and axioms themselves. With regard to axioms,
+we found that, considered as experimental truths, they rest on
+superabundant and obvious evidence. We inquired, whether, since this is
+the case, it be imperative to suppose any other evidence of those truths
+than experimental evidence, any other origin for our belief of them than
+an experimental origin. We decided, that the burden of proof lies with
+those who maintain the affirmative, and we examined, at considerable
+length, such arguments as they have produced. The examination having led
+to the rejection of those arguments, we have thought ourselves warranted
+in concluding that axioms are but a class, the most universal class, of
+inductions from experience; the simplest and easiest cases of
+generalization from the facts furnished to us by our senses or by our
+internal consciousness.</p>
+
+<p>While the axioms of demonstrative sciences thus appeared <span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span>to be
+experimental truths, the definitions, as they are incorrectly called, in
+those sciences, were found by us to be generalizations from experience
+which are not even, accurately speaking, truths; being propositions in
+which, while we assert of some kind of object, some property or
+properties which observation shows to belong to it, we at the same time
+deny that it possesses any other properties, though in truth other
+properties do in every individual instance accompany, and in almost all
+instances modify, the property thus exclusively predicated. The denial,
+therefore, is a mere fiction, or supposition, made for the purpose of
+excluding the consideration of those modifying circumstances, when their
+influence is of too trifling amount to be worth considering, or
+adjourning it, when important, to a more convenient moment.</p>
+
+<p>From these considerations it would appear that Deductive or
+Demonstrative Sciences are all, without exception, Inductive Sciences;
+that their evidence is that of experience; but that they are also, in
+virtue of the peculiar character of one indispensable portion of the
+general formul� according to which their inductions are made,
+Hypothetical Sciences. Their conclusions are only true on certain
+suppositions, which are, or ought to be, approximations to the truth,
+but are seldom, if ever, exactly true; and to this hypothetical
+character is to be ascribed the peculiar certainty, which is supposed to
+be inherent in demonstration.</p>
+
+<p>What we have now asserted, however, cannot be received as universally
+true of Deductive or Demonstrative Sciences, until verified by being
+applied to the most remarkable of all those sciences, that of Numbers;
+the theory of the Calculus; Arithmetic and Algebra. It is harder to
+believe of the doctrines of this science than of any other, either that
+they are not truths <i>� priori</i>, but experimental truths, or that their
+peculiar certainty is owing to their being not absolute but only
+conditional truths. This, therefore, is a case which merits examination
+apart; and the more so, because on this subject we have a double set of
+doctrines to contend with; that of the <i>� priori</i> philosophers on one
+side; and on the other, a theory the most opposite to theirs, which was
+at one time very generally <span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span>received, and is still far from being
+altogether exploded, among metaphysicians.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VI_2">� 2.</a> This theory attempts to solve the difficulty apparently inherent in
+the case, by representing the propositions of the science of numbers as
+merely verbal, and its processes as simple transformations of language,
+substitutions of one expression for another. The proposition, Two and
+one are equal to three, according to these writers, is not a truth, is
+not the assertion of a really existing fact, but a definition of the
+word three; a statement that mankind have agreed to use the name three
+as a sign exactly equivalent to two and one; to call by the former name
+whatever is called by the other more clumsy phrase. According to this
+doctrine, the longest process in algebra is but a succession of changes
+in terminology, by which equivalent expressions are substituted one for
+another; a series of translations of the same fact, from one into
+another language; though how, after such a series of translations, the
+fact itself comes out changed (as when we demonstrate a new geometrical
+theorem by algebra,) they have not explained; and it is a difficulty
+which is fatal to their theory.</p>
+
+<p>It must be acknowledged that there are peculiarities in the processes of
+arithmetic and algebra which render the theory in question very
+plausible, and have not unnaturally made those sciences the stronghold
+of Nominalism. The doctrine that we can discover facts, detect the
+hidden processes of nature, by an artful manipulation of language, is so
+contrary to common sense, that a person must have made some advances in
+philosophy to believe it: men fly to so paradoxical a belief to avoid,
+as they think, some even greater difficulty, which the vulgar do not
+see. What has led many to believe that reasoning is a mere verbal
+process, is, that no other theory seemed reconcileable with the nature
+of the Science of Numbers. For we do not carry any ideas along with us
+when we use the symbols of arithmetic or of algebra. In a geometrical
+demonstration we have a mental diagram, if not one on paper; AB, AC, are
+present to our imagination as lines, intersecting <span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span>other lines, forming
+an angle with one another, and the like; but not so <i>a</i> and <i>b</i>. These
+may represent lines or any other magnitudes, but those magnitudes are
+never thought of; nothing is realized in our imagination but <i>a</i> and
+<i>b</i>. The ideas which, on the particular occasion, they happen to
+represent, are banished from the mind during every intermediate part of
+the process, between the beginning, when the premises are translated
+from things into signs, and the end, when the conclusion is translated
+back from signs into things. Nothing, then, being in the reasoner's mind
+but the symbols, what can seem more inadmissible than to contend that
+the reasoning process has to do with anything more? We seem to have come
+to one of Bacon's Prerogative Instances; an <i>experimentum crucis</i> on the
+nature of reasoning itself.</p>
+
+<p>Nevertheless, it will appear on consideration, that this apparently so
+decisive instance is no instance at all; that there is in every step of
+an arithmetical or algebraical calculation a real induction, a real
+inference of facts from facts; and that what disguises the induction is
+simply its comprehensive nature, and the consequent extreme generality
+of the language. All numbers must be numbers of something: there are no
+such things as numbers in the abstract. <i>Ten</i> must mean ten bodies, or
+ten sounds, or ten beatings of the pulse. But though numbers must be
+numbers of something, they may be numbers of anything. Propositions,
+therefore, concerning numbers, have the remarkable peculiarity that they
+are propositions concerning all things whatever; all objects, all
+existences of every kind, known to our experience. All things possess
+quantity; consist of parts which can be numbered; and in that character
+possess all the properties which are called properties of numbers. That
+half of four is two, must be true whatever the word four represents,
+whether four hours, four miles, or four pounds weight. We need only
+conceive a thing divided into four equal parts, (and all things may be
+conceived as so divided,) to be able to predicate of it every property
+of the number four, that is, every arithmetical proposition in which the
+number four stands on one side of the equation. Algebra extends the
+generalization still farther: every number represents that particular
+<span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span>number of all things without distinction, but every algebraical symbol
+does more, it represents all numbers without distinction. As soon as we
+conceive a thing divided into equal parts, without knowing into what
+number of parts, we may call it <i>a</i> or <i>x</i>, and apply to it, without
+danger of error, every algebraical formula in the books. The
+proposition, 2(<i>a</i> + <i>b</i>) = 2<i>a</i> + 2<i>b</i>, is a truth co-extensive with all
+nature. Since then algebraical truths are true of all things whatever,
+and not, like those of geometry, true of lines only or angles only, it
+is no wonder that the symbols should not excite in our minds ideas of
+any things in particular. When we demonstrate the forty-seventh
+proposition of Euclid, it is not necessary that the words should raise
+in us an image of all right-angled triangles, but only of some one
+right-angled triangle: so in algebra we need not, under the symbol <i>a</i>,
+picture to ourselves all things whatever, but only some one thing; why
+not, then, the letter itself? The mere written characters, <i>a</i>, <i>b</i>,
+<i>x</i>, <i>y</i>, <i>z</i>, serve as well for representatives of Things in general,
+as any more complex and apparently more concrete conception. That we are
+conscious of them however in their character of things, and not of mere
+signs, is evident from the fact that our whole process of reasoning is
+carried on by predicating of them the properties of things. In resolving
+an algebraic equation, by what rules do we proceed? By applying at each
+step to <i>a</i>, <i>b</i>, and <i>x</i>, the proposition that equals added to equals
+make equals; that equals taken from equals leave equals; and other
+propositions founded on these two. These are not properties of language,
+or of signs as such, but of magnitudes, which is as much as to say, of
+all things. The inferences, therefore, which are successively drawn, are
+inferences concerning things, not symbols; though as any Things whatever
+will serve the turn, there is no necessity for keeping the idea of the
+Thing at all distinct, and consequently the process of thought may, in
+this case, be allowed without danger to do what all processes of
+thought, when they have been performed often, will do if permitted,
+namely, to become entirely mechanical. Hence the general language of
+algebra comes to be used familiarly without <span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span>exciting ideas, as all
+other general language is prone to do from mere habit, though in no
+other case than this can it be done with complete safety. But when we
+look back to see from whence the probative force of the process is
+derived, we find that at every single step, unless we suppose ourselves
+to be thinking and talking of the things, and not the mere symbols, the
+evidence fails.</p>
+
+<p>There is another circumstance, which, still more than that which we have
+now mentioned, gives plausibility to the notion that the propositions of
+arithmetic and algebra are merely verbal. That is, that when considered
+as propositions respecting Things, they all have the appearance of being
+identical propositions. The assertion, Two and one are equal to three,
+considered as an assertion respecting objects, as for instance "Two
+pebbles and one pebble are equal to three pebbles," does not affirm
+equality between two collections of pebbles, but absolute identity. It
+affirms that if we put one pebble to two pebbles, those very pebbles are
+three. The objects, therefore, being the very same, and the mere
+assertion that "objects are themselves" being insignificant, it seems
+but natural to consider the proposition, Two and one are equal to three,
+as asserting mere identity of signification between the two names.</p>
+
+<p>This, however, though it looks so plausible, will not bear examination.
+The expression "two pebbles and one pebble," and the expression, "three
+pebbles," stand indeed for the same aggregation of objects, but they by
+no means stand for the same physical fact. They are names of the same
+objects, but of those objects in two different states: though they
+<i>de</i>note the same things, their <i>con</i>notation is different. Three
+pebbles in two separate parcels, and three pebbles in one parcel, do not
+make the same impression on our senses; and the assertion that the very
+same pebbles may by an alteration of place and arrangement be made to
+produce either the one set of sensations or the other, though a very
+familiar proposition, is not an identical one. It is a truth known to us
+by early and constant experience: an inductive truth; and such truths
+are the foundation of the science of Number. The <span class="pagenum"><a name="Page_288" id="Page_288">[Pg 288]</a></span>fundamental truths of
+that science all rest on the evidence of sense; they are proved by
+showing to our eyes and our fingers that any given number of objects,
+ten balls for example, may by separation and re-arrangement exhibit to
+our senses all the different sets of numbers the sum of which is equal
+to ten. All the improved methods of teaching arithmetic to children
+proceed on a knowledge of this fact. All who wish to carry the child's
+<i>mind</i> along with them in learning arithmetic; all who wish to teach
+numbers, and not mere ciphers&mdash;now teach it through the evidence of the
+senses, in the manner we have described.</p>
+
+<p>We may, if we please, call the proposition, "Three is two and one," a
+definition of the number three, and assert that arithmetic, as it has
+been asserted that geometry, is a science founded on definitions. But
+they are definitions in the geometrical sense, not the logical;
+asserting not the meaning of a term only, but along with it an observed
+matter of fact. The proposition, "A circle is a figure bounded by a line
+which has all its points equally distant from a point within it," is
+called the definition of a circle; but the proposition from which so
+many consequences follow, and which is really a first principle in
+geometry, is, that figures answering to this description exist. And thus
+we may call "Three is two and one" a definition of three; but the
+calculations which depend on that proposition do not follow from the
+definition itself, but from an arithmetical theorem presupposed in it,
+namely, that collections of objects exist, which while they impress the
+senses thus, <sup>o</sup><sub>o</sub><sup>o</sup>, may be separated into
+two parts, thus, <span style="font-size:smaller;">o&nbsp;o&nbsp;&nbsp;&nbsp;&nbsp;o</span>. This proposition being granted, we term all such parcels Threes, after
+which the enunciation of the above mentioned physical fact will serve
+also for a definition of the word Three.</p>
+
+<p>The Science of Number is thus no exception to the conclusion we
+previously arrived at, that the processes even of deductive sciences are
+altogether inductive, and that their first principles are
+generalizations from experience. It remains to be examined whether this
+science resembles geometry in the further circumstance, that some of its
+inductions are not <span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span>exactly true; and that the peculiar certainty
+ascribed to it, on account of which its propositions are called
+Necessary Truths, is fictitious and hypothetical, being true in no other
+sense than that those propositions legitimately follow from the
+hypothesis of the truth of premises which are avowedly mere
+approximations to truth.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VI_3">� 3.</a> The inductions of arithmetic are of two sorts: first, those which
+we have just expounded, such as One and one are two, Two and one are
+three, &amp;c., which may be called the definitions of the various numbers,
+in the improper or geometrical sense of the word Definition; and
+secondly, the two following axioms: The sums of equals are equal, The
+differences of equals are equal. These two are sufficient; for the
+corresponding propositions respecting unequals may be proved from these,
+by a <i>reductio ad absurdum</i>.</p>
+
+<p>These axioms, and likewise the so-called definitions, are, as has
+already been said, results of induction; true of all objects whatever,
+and, as it may seem, exactly true, without the hypothetical assumption
+of unqualified truth where an approximation to it is all that exists.
+The conclusions, therefore, it will naturally be inferred, are exactly
+true, and the science of number is an exception to other demonstrative
+sciences in this, that the categorical certainty which is predicable of
+its demonstrations is independent of all hypothesis.</p>
+
+<p>On more accurate investigation, however, it will be found that, even in
+this case, there is one hypothetical element in the ratiocination. In
+all propositions concerning numbers, a condition is implied, without
+which none of them would be true; and that condition is an assumption
+which maybe false. The condition, is that 1 = 1; that all the numbers
+are numbers of the same or of equal units. Let this be doubtful, and not
+one of the propositions of arithmetic will hold true. How can we know
+that one pound and one pound make two pounds, if one of the pounds may
+be troy, and the other avoirdupois? They may not make two pounds of
+either, or of any weight. How can we know that a forty-horse power is
+always equal to itself, unless we assume that all horses are of equal
+strength? It is <span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span>certain that 1 is always equal in <i>number</i> to 1; and
+where the mere number of objects, or of the parts of an object, without
+supposing them to be equivalent in any other respect, is all that is
+material, the conclusions of arithmetic, so far as they go to that
+alone, are true without mixture of hypothesis. There are a few such
+cases; as, for instance, an inquiry into the amount of the population of
+any country. It is indifferent to that inquiry whether they are grown
+people or children, strong or weak, tall or short; the only thing we
+want to ascertain is their number. But whenever, from equality or
+inequality of number, equality or inequality in any other respect is to
+be inferred, arithmetic carried into such inquiries becomes as
+hypothetical a science as geometry. All units must be assumed to be
+equal in that other respect; and this is never accurately true, for one
+actual pound weight is not exactly equal to another, nor one measured
+mile's length to another; a nicer balance, or more accurate measuring
+instruments, would always detect some difference.</p>
+
+<p>What is commonly called mathematical certainty, therefore, which
+comprises the twofold conception of unconditional truth and perfect
+accuracy, is not an attribute of all mathematical truths, but of those
+only which relate to pure Number, as distinguished from Quantity in the
+more enlarged sense; and only so long as we abstain from supposing that
+the numbers are a precise index to actual quantities. The certainty
+usually ascribed to the conclusions of geometry, and even to those of
+mechanics, is nothing whatever but certainty of inference. We can have
+full assurance of particular results under particular suppositions, but
+we cannot have the same assurance that these suppositions are accurately
+true, nor that they include all the data which may exercise an influence
+over the result in any given instance.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VI_4">� 4.</a> It appears, therefore, that the method of all Deductive Sciences is
+hypothetical. They proceed by tracing the consequences of certain
+assumptions; leaving for separate consideration whether the assumptions
+are true or not, and if not <span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span>exactly true, whether they are a
+sufficiently near approximation to the truth. The reason is obvious.
+Since it is only in questions of pure number that the assumptions are
+exactly true, and even there, only so long as no conclusions except
+purely numerical ones are to be founded on them; it must, in all other
+cases of deductive investigation, form a part of the inquiry, to
+determine how much the assumptions want of being exactly true in the
+case in hand. This is generally a matter of observation, to be repeated
+in every fresh case; or if it has to be settled by argument instead of
+observation, may require in every different case different evidence, and
+present every degree of difficulty from the lowest to the highest. But
+the other part of the process&mdash;namely, to determine what else may be
+concluded if we find, and in proportion as we find, the assumptions to
+be true&mdash;may be performed once for all, and the results held ready to be
+employed as the occasions turn up for use. We thus do all beforehand
+that can be so done, and leave the least possible work to be performed
+when cases arise and press for a decision. This inquiry into the
+inferences which can be drawn from assumptions, is what properly
+constitutes Demonstrative Science.</p>
+
+<p>It is of course quite as practicable to arrive at new conclusions from
+facts assumed, as from facts observed; from fictitious, as from real,
+inductions. Deduction, as we have seen, consists of a series of
+inferences in this form&mdash;<i>a</i> is a mark of <i>b</i>, <i>b</i> of <i>c</i>, <i>c</i> of <i>d</i>,
+therefore <i>a</i> is a mark of <i>d</i>, which last may be a truth inaccessible
+to direct observation. In like manner it is allowable to say, <i>suppose</i>
+that <i>a</i> were a mark of <i>b</i>, <i>b</i> of <i>c</i>, and <i>c</i> of <i>d</i>, <i>a</i> would be a
+mark of <i>d</i>, which last conclusion was not thought of by those who laid
+down the premises. A system of propositions as complicated as geometry
+might be deduced from assumptions which are false; as was done by
+Ptolemy, Descartes, and others, in their attempts to explain
+synthetically the phenomena of the solar system on the supposition that
+the apparent motions of the heavenly bodies were the real motions, or
+were produced in some way more or less different from the true one.
+Sometimes the same thing is knowingly <span class="pagenum"><a name="Page_292" id="Page_292">[Pg 292]</a></span>done, for the purpose of showing
+the falsity of the assumption; which is called a <i>reductio ad absurdum</i>.
+In such cases, the reasoning is as follows: <i>a</i> is a mark of <i>b</i>, and
+<i>b</i> of <i>c</i>; now if <i>c</i> were also a mark of <i>d</i>, <i>a</i> would be a mark of
+<i>d</i>; but <i>d</i> is known to be a mark of the absence of <i>a</i>; consequently
+<i>a</i> would be a mark of its own absence, which is a contradiction;
+therefore <i>c</i> is not a mark of <i>d</i>.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VI_5">� 5.</a> It has even been held by some writers, that all ratiocination rests
+in the last resort on a <i>reductio ad absurdum</i>; since the way to enforce
+assent to it, in case of obscurity, would be to show that if the
+conclusion be denied we must deny some one at least of the premises,
+which, as they are all supposed true, would be a contradiction. And in
+accordance with this, many have thought that the peculiar nature of the
+evidence of ratiocination consisted in the impossibility of admitting
+the premises and rejecting the conclusion without a contradiction in
+terms. This theory, however, is inadmissible as an explanation of the
+grounds on which ratiocination itself rests. If any one denies the
+conclusion notwithstanding his admission of the premises, he is not
+involved in any direct and express contradiction until he is compelled
+to deny some premise; and he can only be forced to do this by a
+<i>reductio ad absurdum</i>, that is, by another ratiocination: now, if he
+denies the validity of the reasoning process itself, he can no more be
+forced to assent to the second syllogism than to the first. In truth,
+therefore, no one is ever forced to a contradiction in terms: he can
+only be forced to a contradiction (or rather an infringement) of the
+fundamental maxim of ratiocination, namely, that whatever has a mark,
+has what it is a mark of; or, (in the case of universal propositions,)
+that whatever is a mark of anything, is a mark of whatever else that
+thing is a mark of. For in the case of every correct argument, as soon
+as thrown into the syllogistic form, it is evident without the aid of
+any other syllogism, that he who, admitting the premises, fails to draw
+the conclusion, does not conform to the above axiom.</p>
+
+<p><span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span></p><p>We have now proceeded as far in the theory of Deduction as we can
+advance in the present stage of our inquiry. Any further insight into
+the subject requires that the foundation shall have been laid of the
+philosophic theory of Induction itself; in which theory that of
+deduction, as a mode of induction, which we have now shown it to be,
+will assume spontaneously the place which belongs to it, and will
+receive its share of whatever light may be thrown upon the great
+intellectual operation of which it forms so important a part.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span></p>
+<h3><a name="BOOK_II_CHAPTER_VII" id="BOOK_II_CHAPTER_VII"></a>CHAPTER VII.<br />
+
+EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.</h3>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VII_1">� 1.</a> Polemical discussion is foreign to the plan of this work. But an
+opinion which stands in need of much illustration, can often receive it
+most effectually, and least tediously, in the form of a defence against
+objections. And on subjects concerning which speculative minds are still
+divided, a writer does but half his duty by stating his own doctrine, if
+he does not also examine, and to the best of his ability judge, those of
+other thinkers.</p>
+
+<p>In the dissertation which Mr. Herbert Spencer has prefixed to his, in
+many respects, highly philosophical treatise on the Mind,<a name="FNanchor_39_74" id="FNanchor_39_74"></a><a href="#Footnote_39_74" class="fnanchor">[39]</a> he
+criticises some of the doctrines of the two preceding chapters, and
+propounds a theory of his own on the subject of first principles. Mr.
+Spencer agrees with me in considering axioms to be "simply our earliest
+inductions from experience." But he differs from me "widely as to the
+worth of the test of inconceivableness." He thinks that it is the
+ultimate test of all beliefs. He arrives at this conclusion by two
+steps. First, we never can have any stronger ground for believing
+anything, than that the belief of it "invariably exists." Whenever any
+fact or proposition is invariably believed; that is, if I understand Mr.
+Spencer rightly, believed by all persons, and by oneself at all times;
+it is entitled to be received as one of the primitive truths, or
+original premises of our knowledge. Secondly, the criterion by which we
+decide whether anything is invariably believed to be true, is our
+inability to conceive it as false. "The inconceivability of its negation
+is the test by which we ascertain whether a given belief invariably
+exists <span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span>or not." "For our primary beliefs, the fact of invariable
+existence, tested by an abortive effort to cause their non-existence, is
+the only reason assignable." He thinks this the sole ground of our
+belief in our own sensations. If I believe that I feel cold, I only
+receive this as true because I cannot conceive that I am not feeling
+cold. "While the proposition remains true, the negation of it remains
+inconceivable." There are numerous other beliefs which Mr. Spencer
+considers to rest on the same basis; being chiefly those, or a part of
+those, which the metaphysicians of the Reid and Stewart school consider
+as truths of immediate intuition. That there exists a material world;
+that this is the very world which we directly and immediately perceive,
+and not merely the hidden cause of our perceptions; that Space, Time,
+Force, Extension, Figure, are not modes of our consciousness, but
+objective realities; are regarded by Mr. Spencer as truths known by the
+inconceivableness of their negatives. We cannot, he says, by any effort,
+conceive these objects of thought as mere states of our mind; as not
+having an existence external to us. Their real existence is, therefore,
+as certain as our sensations themselves. The truths which are the
+subject of direct knowledge, being, according to this doctrine, known to
+be truths only by the inconceivability of their negation; and the truths
+which are not the object of direct knowledge, being known as inferences
+from those which are; and those inferences being believed to follow from
+the premises, only because we cannot conceive them not to follow;
+inconceivability is thus the ultimate ground of all assured beliefs.</p>
+
+<p>Thus far, there is no very wide difference between Mr. Spencer's
+doctrine and the ordinary one of philosophers of the intuitive school,
+from Descartes to Dr. Whewell; but at this point Mr. Spencer diverges
+from them. For he does not, like them, set up the test of
+inconceivability as infallible. On the contrary, he holds that it may be
+fallacious, not from any fault in the test itself, but because "men have
+mistaken for inconceivable things, some things which were not
+inconceivable." And he himself, in this very book, denies not a few
+propositions usually regarded as among the most marked examples <span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span>of
+truths whose negations are inconceivable. But occasional failure, he
+says, is incident to all tests. If such failure vitiates "the test of
+inconceivableness," it "must similarly vitiate all tests whatever. We
+consider an inference logically drawn from established premises to be
+true. Yet in millions of cases men have been wrong in the inferences
+they have thought thus drawn. Do we therefore argue that it is absurd to
+consider an inference true on no other ground than that it is logically
+drawn from established premises? No: we say that though men may have
+taken for logical inferences, inferences that were not logical, there
+nevertheless <i>are</i> logical inferences, and that we are justified in
+assuming the truth of what seem to us such, until better instructed.
+Similarly, though men may have thought some things inconceivable which
+were not so, there may still be inconceivable things; and the inability
+to conceive the negation of a thing, may still be our best warrant for
+believing it.... Though occasionally it may prove an imperfect test,
+yet, as our most certain beliefs are capable of no better, to doubt any
+one belief because we have no higher guarantee for it, is really to
+doubt all beliefs." Mr. Spencer's doctrine, therefore, does not erect
+the curable, but only the incurable limitations of the human conceptive
+faculty, into laws of the outward universe.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VII_2">� 2.</a> The doctrine, that "a belief which is proved by the
+inconceivableness of its negation to invariably exist, is true," Mr.
+Spencer enforces by two arguments, one of which may be distinguished as
+positive, and the other as negative.</p>
+
+<p>The positive argument is, that every such belief represents the
+aggregate of all past experience. "Conceding the entire truth of" the
+"position, that during any phase of human progress, the ability or
+inability to form a specific conception wholly depends on the
+experiences men have had; and that, by a widening of their experiences,
+they may, by and by, be enabled to conceive things before inconceivable
+to them; it may still be argued that as, at any time, the best warrant
+men can have for a belief is the perfect agreement of all pre-existing
+experience in support of it, it follows that, at any <span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span>time, the
+inconceivableness of its negation is the deepest test any belief admits
+of.... Objective facts are ever impressing themselves upon us; our
+experience is a register of these objective facts; and the
+inconceivableness of a thing implies that it is wholly at variance with
+the register. Even were this all, it is not clear how, if every truth is
+primarily inductive, any better test of truth could exist. But it must
+be remembered that whilst many of these facts, impressing themselves
+upon us, are occasional; whilst others again are very general; some are
+universal and unchanging. These universal and unchanging facts are, by
+the hypothesis, certain to establish beliefs of which the negations are
+inconceivable; whilst the others are not certain to do this; and if they
+do, subsequent facts will reverse their action. Hence if, after an
+immense accumulation of experiences, there remain beliefs of which the
+negations are still inconceivable, most, if not all of them, must
+correspond to universal objective facts. If there be ... certain
+absolute uniformities in nature; if these uniformities produce, as they
+must, absolute uniformities in our experience; and if ... these absolute
+uniformities in our experience disable us from conceiving the negations
+of them; then answering to each absolute uniformity in nature which we
+can cognize, there must exist in us a belief of which the negation is
+inconceivable, and which is absolutely true. In this wide range of cases
+subjective inconceivableness must correspond to objective impossibility.
+Further experience will produce correspondence where it may not yet
+exist; and we may expect the correspondence to become ultimately
+complete. In nearly all cases this test of inconceivableness must be
+valid now;" (I wish I could think we were so nearly arrived at
+omniscience) "and where it is not, it still expresses the net result of
+our experience up to the present time; which is the most that any test
+can do."</p>
+
+<p>To this I answer: Even if it were true that inconceivableness represents
+"the net result" of all past experience, why should we stop at the
+representative when we can get at the thing represented? If our
+incapacity to conceive the negation of a given supposition is proof of
+its truth, because proving that our experience <span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span>has hitherto been
+uniform in its favour, the real evidence for the supposition is not the
+inconceivableness, but the uniformity of experience. Now this, which is
+the substantial and only proof, is directly accessible. We are not
+obliged to presume it from an incidental consequence. If all past
+experience is in favour of a belief, let this be stated, and the belief
+openly rested on that ground: after which the question arises, what that
+fact may be worth as evidence of its truth? For uniformity of experience
+is evidence in very different degrees: in some cases it is strong
+evidence, in others weak, in others it scarcely amounts to evidence at
+all. That all metals sink in water, was an uniform experience, from the
+origin of the human race to the discovery of potassium in the present
+century by Sir Humphry Davy. That all swans are white, was an uniform
+experience down to the discovery of Australia. In the few cases in which
+uniformity of experience does amount to the strongest possible proof, as
+with such propositions as these, Two straight lines cannot inclose a
+space, Every event has a cause, it is not because their negations are
+inconceivable, which is not always the fact; but because the experience,
+which has been thus uniform, pervades all nature. It will be shown in
+the following Book that none of the conclusions either of induction or
+of deduction can be considered certain, except as far as their truth is
+shown to be inseparably bound up with truths of this class.</p>
+
+<p>I maintain then, first, that uniformity of past experience is very far
+from being universally a criterion of truth. But secondly,
+inconceivableness is still farther from being a test even of that test.
+Uniformity of contrary experience is only one of many causes of
+inconceivability. Tradition handed down from a period of more limited
+knowledge, is one of the commonest. The mere familiarity of one mode of
+production of a phenomenon, often suffices to make every other mode
+appear inconceivable. Whatever connects two ideas by a strong
+association may, and continually does, render their separation in
+thought impossible; as Mr. Spencer, in other parts of his speculations,
+frequently recognises. It was not for want of experience that the
+Cartesians were unable to conceive <span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span>that one body could produce motion
+in another without contact. They had as much experience of other modes
+of producing motion, as they had of that mode. The planets had revolved,
+and heavy bodies had fallen, every hour of their lives. But they fancied
+these phenomena to be produced by a hidden machinery which they did not
+see, because without it they were unable to conceive what they did see.
+The inconceivableness, instead of representing their experience,
+dominated and overrode their experience. It is needless to dwell farther
+on what I have termed the positive argument of Mr. Spencer in support of
+his criterion of truth. I pass to his negative argument, on which he
+lays more stress.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VII_3">� 3.</a> The negative argument is, that, whether inconceivability be good
+evidence or bad, no stronger evidence is to be obtained. That what is
+inconceivable cannot be true, is postulated in every act of thought. It
+is the foundation of all our original premises. Still more it is assumed
+in all conclusions from those premises. The invariability of belief,
+tested by the inconceivableness of its negation, "is our sole warrant
+for every demonstration. Logic is simply a systematization of the
+process by which we indirectly obtain this warrant for beliefs that do
+not directly possess it. To gain the strongest conviction possible
+respecting any complex fact, we either analytically descend from it by
+successive steps, each of which we unconsciously test by the
+inconceivableness of its negation, until we reach some axiom or truth
+which we have similarly tested; or we synthetically ascend from such
+axiom or truth by such steps. In either case we connect some isolated
+belief, with a belief which invariably exists, by a series of
+intermediate beliefs which invariably exist." The following passage sums
+up the whole theory: "When we perceive that the negation of the belief
+is inconceivable, we have all possible warrant for asserting the
+invariability of its existence: and in asserting this, we express alike
+our logical justification of it, and the inexorable necessity we are
+under of holding it.... We have seen that this is the assumption on
+which every conclusion whatever ultimately rests. We have no other
+guarantee <span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span>for the reality of consciousness, of sensations, of personal
+existence; we have no other guarantee for any axiom; we have no other
+guarantee for any step in a demonstration. Hence, as being taken for
+granted in every act of the understanding, it must be regarded as the
+Universal Postulate." But as this postulate which we are under an
+"inexorable necessity" of holding true, is sometimes false; as "beliefs
+that once were shown by the inconceivableness of their negations to
+invariably exist, have since been found untrue," and as "beliefs that
+now possess this character may some day share the same fate;" the canon
+of belief laid down by Mr. Spencer is, that "the most certain
+conclusion" is that "which involves the postulate the fewest times."
+Reasoning, therefore, never ought to prevail against one of the
+immediate beliefs (the belief in Matter, in the outward reality of
+Extension, Space, and the like), because each of these involves the
+postulate only once; while an argument, besides involving it in the
+premises, involves it again in every step of the ratiocination, no one
+of the successive acts of inference being recognised as valid except
+because we cannot conceive the conclusion not to follow from the
+premises.</p>
+
+<p>It will be convenient to take the last part of this argument first. In
+every reasoning, according to Mr. Spencer, the assumption of the
+postulate is renewed at every step. At each inference we judge that the
+conclusion follows from the premises, our sole warrant for that judgment
+being that we cannot conceive it not to follow. Consequently if the
+postulate is fallible, the conclusions of reasoning are more vitiated by
+that uncertainty than direct intuitions; and the disproportion is
+greater, the more numerous the steps of the argument.</p>
+
+<p>To test this doctrine, let us first suppose an argument consisting only
+of a single step, which would be represented by one syllogism. This
+argument does rest on an assumption, and we have seen in the preceding
+chapters what the assumption is. It is, that whatever has a mark, has
+what it is a mark of. The evidence of this axiom I shall not consider at
+<span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span>present;<a name="FNanchor_40_75" id="FNanchor_40_75"></a><a href="#Footnote_40_75" class="fnanchor">[40]</a> let us suppose it (with Mr. Spencer) to be the
+inconceivableness of its reverse.</p>
+
+<p>Let us now add a second step to the argument: we require, what? Another
+assumption? No: the same assumption a second time; and so on to a third,
+and a fourth. I confess I do not see how, on Mr. Spencer's own
+principles, the repetition of the assumption at all weakens the force of
+the argument. If it were necessary the second time to assume some other
+axiom, the argument would no doubt be weakened, since it would be
+necessary to its validity that both axioms should be true, and it might
+happen that one was true and not the other: making two chances of error
+instead of one. But since it is the <i>same</i> axiom, if it is true once it
+is true every time; and if the argument, being of a hundred links,
+assumed the axiom a hundred times, these hundred assumptions would make
+but one chance of error among them all. It is satisfactory that we are
+not obliged to suppose the deductions of pure mathematics to be among
+the most uncertain of argumentative processes, which on Mr. Spencer's
+theory they could hardly fail to be, since they are the longest. But the
+number of steps in an argument does not subtract from its reliableness,
+if no new <i>premises</i>, of an uncertain character, are taken up by the
+way.</p>
+
+<p>To speak next of the premises. Our assurance of their truth, whether
+they be generalities or individual facts, is grounded, in Mr. Spencer's
+opinion, on the inconceivableness of their being false. It is necessary
+to advert to a double meaning of the word inconceivable, which Mr.
+Spencer is aware of, and would sincerely disclaim founding an argument
+upon, but from which his case derives no little advantage
+notwithstanding. By inconceivableness is sometimes meant, inability to
+form or get rid of an <i>idea</i>; sometimes, inability to form or get rid of
+a <i>belief</i>. The former meaning is the most conformable to the analogy of
+language; for a conception <span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span>always means an idea, and never a belief.
+The wrong meaning of "inconceivable" is, however, fully as frequent in
+philosophical discussion as the right meaning, and the intuitive school
+of metaphysicians could not well do without either. To illustrate the
+difference, we will take two contrasted examples. The early physical
+speculators considered antipodes incredible, because inconceivable. But
+antipodes were not inconceivable in the primitive sense of the word. An
+idea of them could be formed without difficulty: they could be
+completely pictured to the mental eye. What was difficult, and as it
+then seemed, impossible, was to apprehend them as believable. The idea
+could be put together, of men sticking on by their feet to the under
+side of the earth; but the belief <i>would</i> follow, that they must fall
+off. Antipodes were not unimaginable, but they were unbelievable.</p>
+
+<p>On the other hand, when I endeavour to conceive an end to extension, the
+two ideas refuse to come together. When I attempt to form a conception
+of the last point of space, I cannot help figuring to myself a vast
+space beyond that last point. The combination is, under the conditions
+of our experience, unimaginable. This double meaning of inconceivable it
+is very important to bear in mind, for the argument from
+inconceivableness almost always turns on the alternate substitution of
+each of those meanings for the other.</p>
+
+<p>In which of these two senses does Mr. Spencer employ the term, when he
+makes it a test of the truth of a proposition that its negation is
+inconceivable? Until Mr. Spencer expressly stated the contrary, I
+inferred from the course of his argument, that he meant unbelievable. He
+has, however, in a paper published in the fifth number of the
+<i>Fortnightly Review</i>, disclaimed this meaning, and declared that by an
+inconceivable proposition he means, now and always, "one of which the
+terms cannot, by any effort, be brought before consciousness in that
+relation which the proposition asserts between them&mdash;a proposition of
+which the subject and predicate offer an insurmountable resistance to
+union in thought." We now, therefore, know positively that Mr. Spencer
+always endeavours to use the word inconceivable in this, its proper,
+sense: but it may yet be questioned whether his endeavour is <span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span>always
+successful; whether the other, and popular use of the word does not
+sometimes creep in with its associations, and prevent him from
+maintaining a clear separation between the two. When, for example, he
+says, that when I feel cold, I cannot conceive that I am not feeling
+cold, this expression cannot be translated into, "I cannot conceive
+myself not feeling cold," for it is evident that I can: the word
+conceive, therefore, is here used to express the recognition of a matter
+of fact&mdash;the perception of truth or falsehood; which I apprehend to be
+exactly the meaning of an act of belief, as distinguished from simple
+conception. Again, Mr. Spencer calls the attempt to conceive something
+which is inconceivable, "an abortive effort to cause the non-existence"
+not of a conception or mental representation, but of a belief. There is
+need, therefore, to revise a considerable part of Mr. Spencer's
+language, if it is to be kept always consistent with his definition of
+inconceivability. But in truth the point is of little importance; since
+inconceivability, in Mr. Spencer's theory, is only a test of truth,
+inasmuch as it is a test of believability. The inconceivableness of a
+supposition is the extreme case of its unbelievability. This is the very
+foundation of Mr. Spencer's doctrine. The invariability of the belief is
+with him the real guarantee. The attempt to conceive the negative, is
+made in order to test the inevitableness of the belief. It should be
+called, an attempt to <i>believe</i> the negative. When Mr. Spencer says that
+while looking at the sun a man cannot conceive that he is looking into
+darkness, he should have said that a man cannot <i>believe</i> that he is
+doing so. For it is surely possible, in broad daylight, to <i>imagine</i>
+oneself looking into darkness.<a name="FNanchor_41_76" id="FNanchor_41_76"></a><a href="#Footnote_41_76" class="fnanchor">[41]</a> As Mr. Spencer himself says, speaking
+of the belief of our own existence: "That he <i>might</i> not exist, he can
+conceive well enough; but that he <i>does</i> not exist, he finds it
+impossible to conceive," <i>i.e.</i> <span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span>to believe. So that the statement
+resolves itself into this: That I exist, and that I have sensations, I
+believe, because I cannot believe otherwise. And in this case every one
+will admit that the necessity is real. Any one's present sensations, or
+other states of subjective consciousness, that one person inevitably
+believes. They are facts known <i>per se</i>: it is impossible to ascend
+beyond them. Their negative is really unbelievable, and therefore there
+is never any question about believing it. Mr. Spencer's theory is not
+needed for these truths.</p>
+
+<p>But according to Mr. Spencer there are other beliefs, relating to other
+things than our own subjective feelings, for which we have the same
+guarantee&mdash;which are, in a similar manner, invariable and necessary.
+With regard to these other beliefs, they cannot be necessary, since they
+do not always exist. There have been, and are, many persons who do not
+believe the reality of an external world, still less the reality of
+extension and figure as the forms of that external world; who do not
+believe that space and time have an existence independent of the
+mind&mdash;nor any other of Mr. Spencer's objective intuitions. The negations
+of these alleged invariable beliefs are not unbelievable, for they are
+believed. It may be maintained, without obvious error, that we cannot
+<i>imagine</i> tangible objects as mere states of our own and other people's
+consciousness; that the perception of them irresistibly suggests to us
+the <i>idea</i> of something external to ourselves: and I am not in a
+condition to say that this is not the fact (though I do not think any
+one is entitled to affirm it of any person besides himself). But many
+thinkers have believed, whether they could conceive it or not, that what
+we represent to ourselves as material objects, are mere modifications of
+consciousness; complex feelings of touch and of muscular action. Mr.
+Spencer may think the inference correct from the unimaginable to the
+unbelievable, because he holds that belief itself is but the persistence
+of an idea, and that what we can succeed in imagining, we cannot at the
+moment help apprehending as believable. But of what consequence is it
+what we apprehend at the moment, if the moment is in contradiction to
+the permanent state of our mind? A person who has been frightened when
+<span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span>an infant by stories of ghosts, though he disbelieves them in after
+years (and perhaps disbelieved them at first), may be unable all his
+life to be in a dark place, in circumstances stimulating to the
+imagination, without mental discomposure. The idea of ghosts, with all
+its attendant terrors, is irresistibly called up in his mind by the
+outward circumstances. Mr. Spencer may say, that while he is under the
+influence of this terror he does not disbelieve in ghosts, but has a
+temporary and uncontrollable belief in them. Be it so; but allowing it
+to be so, which would it be truest to say of this man on the whole&mdash;that
+he believes in ghosts, or that he does not believe in them? Assuredly
+that he does not believe in them. The case is similar with those who
+disbelieve a material world. Though they cannot get rid of the idea;
+though while looking at a solid object they cannot help having the
+conception, and therefore, according to Mr. Spencer's metaphysics, the
+momentary belief, of its externality; even at that moment they would
+sincerely deny holding that belief: and it would be incorrect to call
+them other than disbelievers of the doctrine. The belief therefore is
+not invariable; and the test of inconceivableness fails in the only
+cases to which there could ever be any occasion to apply it.</p>
+
+<p>That a thing may be perfectly believable, and yet may not have become
+conceivable, and that we may habitually believe one side of an
+alternative, and conceive only in the other, is familiarly exemplified
+in the state of mind of educated persons respecting sunrise and sunset.
+All educated persons either know by investigation, or believe on the
+authority of science, that it is the earth and not the sun which moves:
+but there are probably few who habitually <i>conceive</i> the phenomenon
+otherwise than as the ascent or descent of the sun. Assuredly no one can
+do so without a prolonged trial; and it is probably not easier now than
+in the first generation after Copernicus. Mr. Spencer does not say, "In
+looking at sunrise it is impossible not to conceive that it is the sun
+which moves, therefore this is what everybody believes, and we have all
+the evidence for it that we can have for any truth." Yet <span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span>this would be
+an exact parallel to his doctrine about the belief in matter.</p>
+
+<p>The existence of matter, and other Noumena, as distinguished from the
+phenomenal world, remains a question of argument, as it was before; and
+the very general, but neither necessary nor universal, belief in them,
+stands as a psychological phenomenon to be explained, either on the
+hypothesis of its truth, or on some other. The belief is not a
+conclusive proof of its own truth, unless there are no such things as
+<i>idola trib�s</i>; but, being a fact, it calls on antagonists to show, from
+what except the real existence of the thing believed, so general and
+apparently spontaneous a belief can have originated. And its opponents
+have never hesitated to accept this challenge.<a name="FNanchor_42_77" id="FNanchor_42_77"></a><a href="#Footnote_42_77" class="fnanchor">[42]</a> The amount of their
+success in meeting it will probably determine the ultimate verdict of
+philosophers on the question.</p>
+
+
+<p class="newsection"><a name="BOOK_II_CHAPTER_VII_4">� 4.</a> Sir William Hamilton holds as I do, that inconceivability is no
+criterion of impossibility. "There is no ground for inferring a certain
+fact to be impossible, merely from our inability to conceive its
+possibility." "Things there are which <i>may</i>, nay <i>must</i>, be true, of
+which the understanding is wholly unable to construe to itself the
+possibility."<a name="FNanchor_43_78" id="FNanchor_43_78"></a><a href="#Footnote_43_78" class="fnanchor">[43]</a> Sir William Hamilton is however a firm believer in the
+<i>� priori</i> character of many axioms, and of the sciences deduced from
+them; and is so far from considering those axioms to rest on the
+evidence of experience, that he declares certain of them to be true even
+of Noumena&mdash;of the Unconditioned&mdash;of which it is one of the principal
+aims of his philosophy to prove that the nature of our faculties debars
+us from having any knowledge. The axioms to which he attributes this
+exceptional emancipation from the limits which confine all our other
+possibilities of knowledge; the chinks through which, as he represents,
+one ray of light finds its way to us from behind the curtain which veils
+from <span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span>us the mysterious world of Things in themselves,&mdash;are the two
+principles, which he terms, after the schoolmen, the Principle of
+Contradiction, and the Principle of Excluded Middle: the first, that two
+contradictory propositions cannot both be true; the second, that they
+cannot both be false. Armed with these logical weapons, we may boldly
+face Things in themselves, and tender to them the double alternative,
+sure that they must absolutely elect one or the other side, though we
+may be for ever precluded from discovering which. To take his favourite
+example, we cannot conceive the infinite divisibility of matter, and we
+cannot conceive a minimum, or end to divisibility: yet one or the other
+must be true.</p>
+
+<p>As I have hitherto said nothing of the two axioms in question, those of
+Contradiction and of Excluded Middle, it is not unseasonable to consider
+them here. The former asserts that an affirmative proposition and the
+corresponding negative proposition cannot both be true; which has
+generally been held to be intuitively evident. Sir William Hamilton and
+the Germans consider it to be the statement in words of a form or law of
+our thinking faculty. Other philosophers, not less deserving of
+consideration, deem it to be an identical proposition; an assertion
+involved in the meaning of terms; a mode of defining Negation, and the
+word Not.</p>
+
+<p>I am able to go one step with these last. An affirmative assertion and
+its negative are not two independent assertions, connected with each
+other only as mutually incompatible. That if the negative be true, the
+affirmative must be false, really is a mere identical proposition; for
+the negative proposition asserts nothing but the falsity of the
+affirmative, and has no other sense or meaning whatever. The Principium
+Contradictionis should therefore put off the ambitious phraseology which
+gives it the air of a fundamental antithesis pervading nature, and
+should be enunciated in the simpler form, that the same proposition
+cannot at the same time be false and true. But I can go no farther with
+the Nominalists; for I cannot look upon this last as a merely verbal
+proposition. I consider it to be, like other axioms, one of our first
+and most familiar generalizations from experience. The original
+foundation <span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span>of it I take to be, that Belief and Disbelief are two
+different mental states, excluding one another. This we know by the
+simplest observation of our own minds. And if we carry our observation
+outwards, we also find that light and darkness, sound and silence,
+motion and quiescence, equality and inequality, preceding and following,
+succession and simultaneousness, any positive phenomenon whatever and
+its negative, are distinct phenomena, pointedly contrasted, and the one
+always absent where the other is present. I consider the maxim in
+question to be a generalization from all these facts.</p>
+
+<p>In like manner as the Principle of Contradiction (that one of two
+contradictories must be false) means that an assertion cannot be <i>both</i>
+true and false, so the Principle of Excluded Middle, or that one of two
+contradictories must be true, means that an assertion must be <i>either</i>
+true or false: either the affirmative is true, or otherwise the negative
+is true, which means that the affirmative is false. I cannot help
+thinking this principle a surprising specimen of a so-called necessity
+of Thought, since it is not even true, unless with a large
+qualification. A proposition must be either true or false, <i>provided</i>
+that the predicate be one which can in any intelligible sense be
+attributed to the subject; (and as this is always assumed to be the case
+in treatises on logic, the axiom is always laid down there as of
+absolute truth). "Abracadabra is a second intention" is neither true nor
+false. Between the true and the false there is a third possibility, the
+Unmeaning: and this alternative is fatal to Sir William Hamilton's
+extension of the maxim to Noumena. That Matter must either have a
+minimum of divisibility or be infinitely divisible, is more than we can
+ever know. For in the first place, Matter, in any other than the
+phenomenal sense of the term, may not exist: and it will scarcely be
+said that a non-entity must be either infinitely or finitely
+divisible.<a name="FNanchor_44_79" id="FNanchor_44_79"></a><a href="#Footnote_44_79" class="fnanchor">[44]</a> In the second place, though matter, considered as the
+occult cause of our sensations, do really exist, <span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span>yet what we call
+divisibility may be an attribute only of our sensations of sight and
+touch, and not of their uncognizable cause. Divisibility may not be
+predicable at all, in any intelligible sense, of Things in themselves,
+nor therefore of Matter in itself; and the assumed necessity of being
+either infinitely or finitely divisible, may be an inapplicable
+alternative.</p>
+
+<p>On this question I am happy to have the full concurrence of Mr. Herbert
+Spencer, from whose paper in the <i>Fortnightly Review</i> I extract the
+following passage. The germ of an idea identical with that of Mr.
+Spencer may be found in the present chapter, about a page back, but in
+Mr. Spencer it is not an undeveloped thought, but a philosophical
+theory.</p>
+
+<p>"When remembering a certain thing as in a certain place, the place and
+the thing are mentally represented together; while to think of the
+non-existence of the thing in that place, implies a consciousness in
+which the place is represented, but not the thing. Similarly, if instead
+of thinking of an object as colourless, we think of its having colour,
+the change consists in the addition to the concept of an element that
+was before absent from it&mdash;the object cannot be thought of first as red
+and then as not red, without one component of the thought being totally
+expelled from the mind by another. The law of the Excluded Middle, then,
+is simply a generalization of the universal experience that some mental
+states are directly destructive of other states. It formulates a certain
+absolutely constant law, that the appearance of any positive mode of
+consciousness cannot occur without excluding a correlative negative
+mode; and that the negative mode cannot occur without excluding the
+correlative positive mode: the antithesis of positive and negative
+being, indeed, merely an expression of this experience. Hence it follows
+that if consciousness is not in one of the two modes it must be in the
+other."<a name="FNanchor_45_80" id="FNanchor_45_80"></a><a href="#Footnote_45_80" class="fnanchor">[45]</a></p>
+
+<p>I must here close this supplementary chapter, and with it the Second
+Book. The theory of Induction, in the most comprehensive sense of the
+term, will form the subject of the Third.</p>
+
+<div class="footnotes"><h3>FOOTNOTES:</h3>
+
+<div class="footnote"><p><a name="Footnote_1_36" id="Footnote_1_36"></a><a href="#FNanchor_1_36"><span class="label">[1]</span></a> As Sir William Hamilton has pointed out, "Some A is not B"
+may also be converted in the following form: "No B is <i>some</i> A." Some
+men are not negroes; therefore, No negroes are <i>some</i> men (<i>e.g.</i>
+Europeans).</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_37" id="Footnote_2_37"></a><a href="#FNanchor_2_37"><span class="label">[2]</span></a>
+</p>
+
+
+<div class="wider0">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All</td><td align="left">A is B</td><td align="left" rowspan="2"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-right:1em;">contraries.</td></tr>
+<tr><td align="left">No</td><td align="left">A is B</td></tr>
+<tr><td align="left">Some</td><td align="left">A is B</td><td align="left" rowspan="2"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-right:1em;">subcontraries.</td></tr>
+<tr><td align="left">Some</td><td align="left">A is not B</td></tr>
+<tr><td align="left">All</td><td align="left">A is B</td><td align="left" rowspan="2"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-right:1em;">contradictories.</td></tr>
+<tr><td align="left">Some</td><td align="left">A is not B</td></tr>
+<tr><td align="left">No</td><td align="left">A is B</td><td align="left" rowspan="2"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-right:1em;">also contradictories.</td></tr>
+<tr><td align="left">Some</td><td align="left">A is B</td></tr>
+</table></div>
+
+
+<div class="wider0">
+<table border="0" cellpadding="1" cellspacing="0" summary="">
+<tr><td align="left">All</td><td align="left">A is B</td><td align="left" rowspan="2" style="padding-right:1em;"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2" style="padding-right:1em;">and</td><td align="left">A is B</td><td align="left" rowspan="2"><span style="font-size:200%;">}</span></td><td align="left" rowspan="2">respectively subalternate.</td></tr>
+<tr><td align="left">Some</td><td align="left">A is B</td><td align="left">Some A is not B</td></tr>
+</table></div>
+</div>
+
+<div class="footnote"><p><a name="Footnote_3_38" id="Footnote_3_38"></a><a href="#FNanchor_3_38"><span class="label">[3]</span></a> His conclusions are, "The first figure is suited to the
+discovery or proof of the properties of a thing; the second to the
+discovery or proof of the distinctions between things; the third to the
+discovery or proof of instances and exceptions; the fourth to the
+discovery, or exclusion, of the different species of a genus." The
+reference of syllogisms in the last three figures to the <i>dictum de omni
+et nullo</i> is, in Lambert's opinion, strained and unnatural: to each of
+the three belongs, according to him, a separate axiom, co-ordinate and
+of equal authority with that <i>dictum</i>, and to which he gives the names
+of <i>dictum de diverso</i> for the second figure, <i>dictum de exemplo</i> for
+the third, and <i>dictum de reciproco</i> for the fourth. See part i. or
+<i>Dianoiologie</i>, chap. iv. � 229 <i>et seqq.</i> Mr. Bailey, (<i>Theory of
+Reasoning</i>, 2nd ed. pp. 70-74) takes a similar view of the subject.</p></div>
+
+<div class="footnote"><p><a name="Footnote_4_39" id="Footnote_4_39"></a><a href="#FNanchor_4_39"><span class="label">[4]</span></a> Since this chapter was written, two treatises have appeared
+(or rather a treatise and a fragment of a treatise), which aim at a
+further improvement in the theory of the forms of ratiocination: Mr. De
+Morgan's "Formal Logic; or, the Calculus of Inference, Necessary and
+Probable;" and the "New Analytic of Logical Forms," attached as an
+Appendix to Sir William Hamilton's <i>Discussions on Philosophy</i>, and at
+greater length, to his posthumous <i>Lectures on Logic</i>.
+</p><p>
+In Mr. De Morgan's volume&mdash;abounding, in its more popular parts, with
+valuable observations felicitously expressed&mdash;the principal feature of
+originality is an attempt to bring within strict technical rules the
+cases in which a conclusion can be drawn from premises of a form usually
+classed as particular. Mr. De Morgan observes, very justly, that from
+the premises Most Bs are Cs, most Bs are As, it may be concluded with
+certainty that some As are Cs, since two portions of the class B, each
+of them comprising more than half, must necessarily in part consist of
+the same individuals. Following out this line of thought, it is equally
+evident that if we knew exactly what proportion the "most" in each of
+the premises bear to the entire class B, we could increase in a
+corresponding degree the definiteness of the conclusion. Thus if 60 per
+cent of B are included in C, and 70 per cent in A, 30 per cent at least
+must be common to both; in other words, the number of As which are Cs,
+and of Cs which are As, must be at least equal to 30 per cent of the
+class B. Proceeding on this conception of "numerically definite
+propositions," and extending it to such forms as these:&mdash;"45 Xs (or
+more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
+them to be found among 70 Ys," and examining what inferences admit of
+being drawn from the various combinations which may be made of premises
+of this description, Mr. De Morgan establishes universal formul� for
+such inferences; creating for that purpose not only a new technical
+language, but a formidable array of symbols analogous to those of
+algebra.
+</p><p>
+Since it is undeniable that inferences, in the cases examined by Mr. De
+Morgan, can legitimately be drawn, and that the ordinary theory takes no
+account of them, I will not say that it was not worth while to show in
+detail how these also could be reduced to formul� as rigorous as those
+of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
+more than once, as a school exercise); but I question if its results are
+worth studying and mastering for any practical purpose. The practical
+use of technical forms of reasoning is to bar out fallacies: but the
+fallacies which require to be guarded against in ratiocination properly
+so called, arise from the incautious use of the common forms of
+language; and the logician must track the fallacy into that territory,
+instead of waiting for it on a territory of his own. While he remains
+among propositions which have acquired the numerical precision of the
+Calculus of Probabilities, the enemy is left in possession of the only
+ground on which he can be formidable. And since the propositions (short
+of universal) on which a thinker has to depend, either for purposes of
+speculation or of practice, do not, except in a few peculiar cases,
+admit of any numerical precision; common reasoning cannot be translated
+into Mr. De Morgan's forms, which therefore cannot serve any purpose as
+a test of it.
+</p><p>
+Sir William Hamilton's theory of the "quantification of the predicate"
+(concerning the originality of which in his case there can be no doubt,
+however Mr. De Morgan may have also, and independently, originated an
+equivalent doctrine) may be briefly described as follows:&mdash;
+</p><p>
+"Logically" (I quote his own words) "we ought to take into account the
+quantity, always understood in thought, but usually, for manifest
+reasons, elided in its expression, not only of the subject, but also of
+the predicate of a judgment." All A is B, is equivalent to all A is
+<i>some</i> B. No A is B, to No A is <i>any</i> B. Some A is B, is tantamount to
+some A is <i>some</i> B. Some A is not B, to Some A is <i>not any</i> B. As in
+these forms of assertion the predicate is exactly coextensive with the
+subject, they all admit of simple conversion; and by this we obtain two
+additional forms&mdash;Some B is <i>all</i> A, and No B is <i>some</i> A. We may also
+make the assertion All A is all B, which will be true if the classes A
+and B are exactly coextensive. The last three forms, though conveying
+real assertions, have no place in the ordinary classification of
+Propositions. All propositions, then, being supposed to be translated
+into this language, and written each in that one of the preceding forms
+which answers to its signification, there emerges a new set of
+syllogistic rules, materially different from the common ones. A general
+view of the points of difference may be given in the words of Sir W.
+Hamilton (<i>Discussions</i>, 2nd ed. p. 651):&mdash;
+</p><p>
+"The revocation of the two terms of a Proposition to their true
+relation; a proposition being always an <i>equation</i> of its subject and
+its predicate.
+</p><p>
+"The consequent reduction of the Conversion of Propositions from three
+species to one&mdash;that of Simple Conversion.
+</p><p>
+"The reduction of all the <i>General Laws</i> of Categorical Syllogisms to a
+single Canon.
+</p><p>
+"The evolution from that one canon of all the Species and varieties of
+Syllogisms.
+</p><p>
+"The abrogation of all the <i>Special Laws</i> of Syllogism.
+</p><p>
+"A demonstration of the exclusive possibility of Three syllogistic
+Figures; and (on new grounds) the scientific and final abolition of the
+Fourth.
+</p><p>
+"A manifestation that Figure is an unessential variation in syllogistic
+form; and the consequent absurdity of Reducing the syllogisms of the
+other figures to the first.
+</p><p>
+"An enouncement of <i>one Organic Principle</i> for each Figure.
+</p><p>
+"A determination of the true number of the Legitimate Moods; with
+</p><p>
+"Their amplification in number (thirty-six);
+</p><p>
+"Their numerical equality under all the figures; and
+</p><p>
+"Their relative equivalence, or virtual identity, throughout every
+schematic difference.
+</p><p>
+"That, in the second and third figures, the extremes holding both the
+same relation to the middle term, there is not, as in the first, an
+opposition and subordination between a term major and a term minor,
+mutually containing and contained, in the counter wholes of Extension
+and Comprehension.
+</p><p>
+"Consequently, in the second and third figures, there is no determinate
+major and minor premise, and there are two indifferent conclusions:
+whereas in the first the premises are determinate, and there is a single
+proximate conclusion."
+</p><p>
+This doctrine, like that of Mr. De Morgan previously noticed, is a real
+addition to the syllogistic theory; and has moreover this advantage over
+Mr. De Morgan's "numerically definite Syllogism," that the forms it
+supplies are really available as a test of the correctness of
+ratiocination; since propositions in the common form may always have
+their predicates quantified, and so be made amenable to Sir W.
+Hamilton's rules. Considered however as a contribution to the <i>Science</i>
+of Logic, that is, to the analysis of the mental processes concerned in
+reasoning, the new doctrine appears to me, I confess, not merely
+superfluous, but erroneous; since the form in which it clothes
+propositions does not, like the ordinary form, express what is in the
+mind of the speaker when he enunciates the proposition. I cannot think
+Sir William Hamilton right in maintaining that the quantity of the
+predicate is "always understood in thought." It is implied, but is not
+present to the mind of the person who asserts the proposition. The
+quantification of the predicate, instead of being a means of bringing
+out more clearly the meaning of the proposition, actually leads the mind
+out of the proposition, into another order of ideas. For when we say,
+All men are mortal, we simply mean to affirm the attribute mortality of
+all men; without thinking at all of the <i>class</i> mortal in the concrete,
+or troubling ourselves about whether it contains any other beings or
+not. It is only for some artificial purpose that we ever look at the
+proposition in the aspect in which the predicate also is thought of as a
+class-name, either including the subject only, or the subject and
+something more. (See above, p. <a href="#Page_104">104</a>.)
+</p><p>
+For a fuller discussion of this subject, see the twenty-second chapter
+of a work already referred to, "An Examination of Sir William Hamilton's
+Philosophy."</p></div>
+
+<div class="footnote"><p><a name="Footnote_5_40" id="Footnote_5_40"></a><a href="#FNanchor_5_40"><span class="label">[5]</span></a> Mr. Herbert Spencer (<i>Principles of Psychology</i>, pp.
+125-7), though his theory of the syllogism coincides with all that is
+essential of mine, thinks it a logical fallacy to present the two axioms
+in the text, as the regulating principles of syllogism. He charges me
+with falling into the error pointed out by Archbishop Whately and
+myself, of confounding exact likeness with literal identity; and
+maintains, that we ought not to say that Socrates possesses <i>the same</i>
+attributes which are connoted by the word Man, but only that he
+possesses attributes <i>exactly like</i> them: according to which
+phraseology, Socrates, and the attribute mortality, are not two things
+coexisting with the same thing, as the axiom asserts, but two things
+coexisting with two different things.
+</p><p>
+The question between Mr. Spencer and me is merely one of language; for
+neither of us (if I understand Mr. Spencer's opinions rightly) believes
+an attribute to be a real thing, possessed of objective existence; we
+believe it to be a particular mode of naming our sensations, or our
+expectations of sensation, when looked at in their relation to an
+external object which excites them. The question raised by Mr. Spencer
+does not, therefore, concern the properties of any really existing
+thing, but the comparative appropriateness, for philosophical purposes,
+of two different modes of using a name. Considered in this point of
+view, the phraseology I have employed, which is that commonly used by
+philosophers, seems to me to be the best. Mr. Spencer is of opinion that
+because Socrates and Alcibiades are not the same man, the attribute
+which constitutes them men should not be called the same attribute; that
+because the humanity of one man and that of another express themselves
+to our senses not by the same individual sensations but by sensations
+exactly alike, humanity ought to be regarded as a different attribute in
+every different man. But on this showing, the humanity even of any one
+man should be considered as different attributes now and half-an-hour
+hence; for the sensations by which it will then manifest itself to my
+organs will not be a continuation of my present sensations, but a
+repetition of them; fresh sensations, not identical with, but only
+exactly like the present. If every general conception, instead of being
+"the One in the Many," were considered to be as many different
+conceptions as there are things to which it is applicable, there would
+be no such thing as general language. A name would have no general
+meaning if <i>man</i> connoted one thing when predicated of John, and
+another, though closely resembling, thing when predicated of William.
+Accordingly a recent pamphlet asserts the impossibility of general
+knowledge on this precise ground.
+</p><p>
+The meaning of any general name is some outward or inward phenomenon,
+consisting, in the last resort, of feelings; and these feelings, if
+their continuity is for an instant broken, are no longer the same
+feelings, in the sense of individual identity. What, then, is the common
+something which gives a meaning to the general name? Mr. Spencer can
+only say, it is the similarity of the feelings; and I rejoin, the
+attribute is precisely that similarity. The names of attributes are in
+their ultimate analysis names for the resemblances of our sensations (or
+other feelings). Every general name, whether abstract or concrete,
+denotes or connotes one or more of those resemblances. It will not,
+probably, be denied, that if a hundred sensations are undistinguishably
+alike, their resemblance ought to be spoken of as one resemblance, and
+not a hundred resemblances which merely <i>resemble</i> one another. The
+things compared are many, but the something common to all of them must
+be conceived as one, just as the name is conceived as one, though
+corresponding to numerically different sensations of sound each time it
+is pronounced. The general term <i>man</i> does not connote the sensations
+derived once from one man, which, once gone, can no more occur again
+than the same flash of lightning. It connotes the general type of the
+sensations derived always from all men, and the power (always thought of
+as one) of producing sensations of that type. And the axiom might be
+thus worded: Two <i>types of sensation</i> each of which coexists with a
+third type, coexist with another; or Two <i>powers</i> each of which coexists
+with a third power coexist with one another.
+</p><p>
+Mr. Spencer has misunderstood me in another particular. He supposes that
+the coexistence spoken of in the axiom, of two things with the same
+third thing, means simultaneousness in time. The coexistence meant is
+that of being jointly attributes of the same subject. The attribute of
+being born without teeth, and the attribute of having thirty-two teeth
+in mature age, are in this sense coexistent, both being attributes of
+man, though <i>ex vi termini</i> never of the same man at the same time.</p></div>
+
+<div class="footnote"><p><a name="Footnote_6_41" id="Footnote_6_41"></a><a href="#FNanchor_6_41"><span class="label">[6]</span></a> Supra, p. <a href="#Page_128">128</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_7_42" id="Footnote_7_42"></a><a href="#FNanchor_7_42"><span class="label">[7]</span></a> <i>Logic</i>, p. 239 (9th ed.).</p></div>
+
+<div class="footnote"><p><a name="Footnote_8_43" id="Footnote_8_43"></a><a href="#FNanchor_8_43"><span class="label">[8]</span></a> It is hardly necessary to say, that I am not contending for
+any such absurdity as that we <i>actually</i> "ought to have known" and
+considered the case of every individual man, past, present, and future,
+before affirming that all men are mortal: although this interpretation
+has been, strangely enough, put upon the preceding observations. There
+is no difference between me and Archbishop Whately, or any other
+defender of the syllogism, on the practical part of the matter; I am
+only pointing out an inconsistency in the logical theory of it, as
+conceived by almost all writers. I do not say that a person who
+affirmed, before the Duke of Wellington was born, that all men are
+mortal, <i>knew</i> that the Duke of Wellington was mortal; but I do say that
+he <i>asserted</i> it; and I ask for an explanation of the apparent logical
+fallacy, of adducing in proof of the Duke of Wellington's mortality, a
+general statement which presupposes it. Finding no sufficient resolution
+of this difficulty in any of the writers on Logic, I have attempted to
+supply one.</p></div>
+
+<div class="footnote"><p><a name="Footnote_9_44" id="Footnote_9_44"></a><a href="#FNanchor_9_44"><span class="label">[9]</span></a> The language of ratiocination would, I think, be brought
+into closer agreement with the real nature of the process, if the
+general propositions employed in reasoning, instead of being in the form
+All men are mortal, or Every man is mortal, were expressed in the form
+Any man is mortal. This mode of expression, exhibiting as the type of
+all reasoning from experience "The men A, B, C, &amp;c. are so and so,
+therefore <i>any</i> man is so and so," would much better manifest the true
+idea&mdash;that inductive reasoning is always, at bottom, inference from
+particulars to particulars, and that the whole function of general
+propositions in reasoning, is to vouch for the legitimacy of such
+inferences.</p></div>
+
+<div class="footnote"><p><a name="Footnote_10_45" id="Footnote_10_45"></a><a href="#FNanchor_10_45"><span class="label">[10]</span></a> Review of Quetelet on Probabilities, <i>Essays</i>, p. 367.</p></div>
+
+<div class="footnote"><p><a name="Footnote_11_46" id="Footnote_11_46"></a><a href="#FNanchor_11_46"><span class="label">[11]</span></a> <i>Philosophy of Discovery</i>, p. 289.</p></div>
+
+<div class="footnote"><p><a name="Footnote_12_47" id="Footnote_12_47"></a><a href="#FNanchor_12_47"><span class="label">[12]</span></a> <i>Theory of Reasoning</i>, ch. iv. to which I may refer for an
+able statement and enforcement of the grounds of the doctrine.</p></div>
+
+<div class="footnote"><p><a name="Footnote_13_48" id="Footnote_13_48"></a><a href="#FNanchor_13_48"><span class="label">[13]</span></a> It is very probable that the doctrine is not new, and that
+it was, as Sir John Herschel thinks, substantially anticipated by
+Berkeley. But I certainly am not aware that it is (as has been affirmed
+by one of my ablest and most candid critics) "among the standing marks
+of what is called the empirical philosophy."</p></div>
+
+<div class="footnote"><p><a name="Footnote_14_49" id="Footnote_14_49"></a><a href="#FNanchor_14_49"><span class="label">[14]</span></a> <i>Logic</i>, book iv. ch. i. sect. 1.</p></div>
+
+<div class="footnote"><p><a name="Footnote_15_50" id="Footnote_15_50"></a><a href="#FNanchor_15_50"><span class="label">[15]</span></a> See the important chapter on Belief, in Professor Bain's
+great treatise, <i>The Emotions and the Will</i>, pp. 581-4.</p></div>
+
+<div class="footnote"><p><a name="Footnote_16_51" id="Footnote_16_51"></a><a href="#FNanchor_16_51"><span class="label">[16]</span></a> A writer in the "British Quarterly Review" (August 1846),
+in a review of this treatise, endeavours to show that there is no
+<i>petitio principii</i> in the syllogism, by denying that the proposition,
+All men are mortal, asserts or assumes that Socrates is mortal. In
+support of this denial, he argues that we may, and in fact do, admit the
+general proposition that all men are mortal, without having particularly
+examined the case of Socrates, and even without knowing whether the
+individual so named is a man or something else. But this of course was
+never denied. That we can and do draw conclusions concerning cases
+specifically unknown to us, is the datum from which all who discuss this
+subject must set out. The question is, in what terms the evidence, or
+ground, on which we draw these conclusions, may best be
+designated&mdash;whether it is most correct to say, that the unknown case is
+proved by known cases, or that it is proved by a general proposition
+including both sets of cases, the unknown and the known? I contend for
+the former mode of expression. I hold it an abuse of language to say,
+that the proof that Socrates is mortal, is that all men are mortal. Turn
+it in what way we will, this seems to me to be asserting that a thing is
+the proof of itself. Whoever pronounces the words, All men are mortal,
+has affirmed that Socrates is mortal, though he may never have heard of
+Socrates; for since Socrates, whether known to be so or not, really is a
+man, he is included in the words, All men, and in every assertion of
+which they are the subject. If the reviewer does not see that there is a
+difficulty here, I can only advise him to reconsider the subject until
+he does: after which he will be a better judge of the success or failure
+of an attempt to remove the difficulty. That he had reflected very
+little on the point when he wrote his remarks, is shown by his oversight
+respecting the <i>dictum de omni et nullo</i>. He acknowledges that this
+maxim as commonly expressed,&mdash;"Whatever is true of a class, is true of
+everything included in the class," is a mere identical proposition,
+since the class <i>is</i> nothing but the things included in it. But he
+thinks this defect would be cured by wording the maxim thus,&mdash;"Whatever
+is true of a class, is true of everything which <i>can be shown</i> to be a
+member of the class:" as if a thing could "be shown" to be a member of
+the class without being one. If a class means the sum of all the things
+included in the class, the things which can "be shown" to be included in
+it are part of the sum, and the <i>dictum</i> is as much an identical
+proposition with respect to them as to the rest. One would almost
+imagine that, in the reviewer's opinion, things are not members of a
+class until they are called up publicly to take their place in it&mdash;that
+so long, in fact, as Socrates is not known to be a man, he <i>is not</i> a
+man, and any assertion which can be made concerning men does not at all
+regard him, nor is affected as to its truth or falsity by anything in
+which he is concerned.
+</p><p>
+The difference between the reviewer's theory and mine may be thus
+stated. Both admit that when we say, All men are mortal, we make an
+assertion reaching beyond the sphere of our knowledge of individual
+cases; and that when a new individual, Socrates, is brought within the
+field of our knowledge by means of the minor premise, we learn that we
+have already made an assertion respecting Socrates without knowing it:
+our own general formula being, to that extent, for the first time
+<i>interpreted</i> to us. But according to the reviewer's theory, the smaller
+assertion is proved by the larger: while I contend, that both assertions
+are proved together, by the same evidence, namely, the grounds of
+experience on which the general assertion was made, and by which it must
+be justified.
+</p><p>
+The reviewer says, that if the major premise included the conclusion,
+"we should be able to affirm the conclusion without the intervention of
+the minor premise; but every one sees that that is impossible." A
+similar argument is urged by Mr. De Morgan (<i>Formal Logic</i>, p. 259):
+"The whole objection tacitly assumes the superfluity of the minor; that
+is, tacitly assumes we know Socrates<a name="FNanchor_46_81" id="FNanchor_46_81"></a><a href="#Footnote_46_81" class="fnanchor">[46]</a> to be a man as soon as we know
+him to be Socrates." The objection would be well grounded if the
+assertion that the major premise includes the conclusion, meant that it
+individually specifies all it includes. As however the only indication
+it gives is a description by marks, we have still to compare any new
+individual with the marks; and to show that this comparison has been
+made, is the office of the minor. But since, by supposition, the new
+individual has the marks, whether we have ascertained him to have them
+or not; if we have affirmed the major premise, we have asserted him to
+be mortal. Now my position is that this assertion cannot be a necessary
+part of the argument. It cannot be a necessary condition of reasoning
+that we should begin by making an assertion, which is afterwards to be
+employed in proving a part of itself. I can conceive only one way out of
+this difficulty, viz. that what really forms the proof is <i>the other</i>
+part of the assertion; the portion of it, the truth of which has been
+ascertained previously: and that the unproved part is bound up in one
+formula with the proved part in mere anticipation, and as a memorandum
+of the nature of the conclusions which we are prepared to prove.
+</p><p>
+With respect to the minor premise in its formal shape, the minor as it
+stands in the syllogism, predicating of Socrates a definite class name,
+I readily admit that it is no more a necessary part of reasoning than
+the major. When there is a major, doing its work by means of a class
+name, minors are needed to interpret it: but reasoning can be carried on
+without either the one or the other. They are not the conditions of
+reasoning, but a precaution against erroneous reasoning. The only minor
+premise necessary to reasoning in the example under consideration, is,
+Socrates is <i>like</i> A, B, C, and the other individuals who are known to
+have died. And this is the only universal type of that step in the
+reasoning process which is represented by the minor. Experience,
+however, of the uncertainty of this loose mode of inference, teaches the
+expediency of determining beforehand what <i>kind</i> of likeness to the
+cases observed, is necessary to bring an unobserved case within the same
+predicate; and the answer to this question is the major. Thus the
+syllogistic major and the syllogistic minor start into existence
+together, and are called forth by the same exigency. When we conclude
+from personal experience without referring to any record&mdash;to any general
+theorems, either written, or traditional, or mentally registered by
+ourselves as conclusions of our own drawing, we do not use, in our
+thoughts, either a major or a minor, such as the syllogism puts into
+words. When, however, we revise this rough inference from particulars to
+particulars, and substitute a careful one, the revision consists in
+selecting two syllogistic premises. But this neither alters nor adds to
+the evidence we had before; it only puts us in a better position for
+judging whether our inference from particulars to particulars is well
+grounded.</p></div>
+
+<div class="footnote"><p><a name="Footnote_17_52" id="Footnote_17_52"></a><a href="#FNanchor_17_52"><span class="label">[17]</span></a> Infra, <a href="#BOOK_III_CHAPTER_II">book iii. ch. ii.</a></p></div>
+
+<div class="footnote"><p><a name="Footnote_18_53" id="Footnote_18_53"></a><a href="#FNanchor_18_53"><span class="label">[18]</span></a> Infra, <a href="#BOOK_III_CHAPTER_IV_3">book iii. ch. iv. � 3</a>, and elsewhere.</p></div>
+
+<div class="footnote"><p><a name="Footnote_19_54" id="Footnote_19_54"></a><a href="#FNanchor_19_54"><span class="label">[19]</span></a> <i>Mechanical Euclid</i>, pp. 149 <i>et seqq.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_20_55" id="Footnote_20_55"></a><a href="#FNanchor_20_55"><span class="label">[20]</span></a> We might, it is true, insert this property into the
+definition of parallel lines, framing the definition so as to require,
+both that when produced indefinitely they shall never meet, and also
+that any straight line which intersects one of them shall, if prolonged,
+meet the other. But by doing this we by no means get rid of the
+assumption; we are still obliged to take for granted the geometrical
+truth, that all straight lines in the same plane, which have the former
+of these properties, have also the latter. For if it were possible that
+they should not, that is, if any straight lines other than those which
+are parallel according to the definition, had the property of never
+meeting although indefinitely produced, the demonstrations of the
+subsequent portions of the theory of parallels could not be maintained.</p></div>
+
+<div class="footnote"><p><a name="Footnote_21_56" id="Footnote_21_56"></a><a href="#FNanchor_21_56"><span class="label">[21]</span></a> Some persons find themselves prevented from believing that
+the axiom, Two straight lines cannot inclose a space, could ever become
+known to us through experience, by a difficulty which may be stated as
+follows. If the straight lines spoken of are those contemplated in the
+definition&mdash;lines absolutely without breadth and absolutely
+straight;&mdash;that such are incapable of inclosing a space is not proved by
+experience, for lines such as these do not present themselves in our
+experience. If, on the other hand, the lines meant are such straight
+lines as we do meet with in experience, lines straight enough for
+practical purposes, but in reality slightly zigzag, and with some,
+however trifling, breadth; as applied to these lines the axiom is not
+true, for two of them may, and sometimes do, inclose a small portion of
+space. In neither case, therefore, does experience prove the axiom.
+</p><p>
+Those who employ this argument to show that geometrical axioms cannot be
+proved by induction, show themselves unfamiliar with a common and
+perfectly valid mode of inductive proof; proof by approximation. Though
+experience furnishes us with no lines so unimpeachably straight that two
+of them are incapable of inclosing the smallest space, it presents us
+with gradations of lines possessing less and less either of breadth or
+of flexure, of which series the straight line of the definition is the
+ideal limit. And observation shows that just as much, and as nearly, as
+the straight lines of experience approximate to having no breadth or
+flexure, so much and so nearly does the space-inclosing power of any two
+of them approach to zero. The inference that if they had no breadth or
+flexure at all, they would inclose no space at all, is a correct
+inductive inference from these facts, conformable to one of the four
+Inductive Methods hereinafter characterized, the Method of Concomitant
+Variations; of which the mathematical Doctrine of Limits presents the
+extreme case.</p></div>
+
+<div class="footnote"><p><a name="Footnote_22_57" id="Footnote_22_57"></a><a href="#FNanchor_22_57"><span class="label">[22]</span></a> Whewell's <i>History of Scientific Ideas</i>, i. 140.</p></div>
+
+<div class="footnote"><p><a name="Footnote_23_58" id="Footnote_23_58"></a><a href="#FNanchor_23_58"><span class="label">[23]</span></a> Dr. Whewell (<i>Philosophy of Discovery</i>, p. 289) thinks it
+unreasonable to contend that we know by experience, that our idea of a
+line exactly resembles a real line. "It does not appear," he says, "how
+we can compare our ideas with the realities, since we know the realities
+only by our ideas." We know the realities (I conceive) by our senses.
+Dr. Whewell surely does not hold the "doctrine of perception by means of
+ideas," which Reid gave himself so much trouble to refute.
+</p><p>
+If Dr. Whewell doubts whether we compare our ideas with the
+corresponding sensations, and assume that they resemble, let me ask on
+what evidence do we judge that a portrait of a person not present is
+like the original. Surely because it is like our idea, or mental image
+of the person, and because our idea is like the man himself.
+</p><p>
+Dr. Whewell also says, that it does not appear why this resemblance of
+ideas to the sensations of which they are copies, should be spoken of as
+if it were a peculiarity of one class of ideas, those of space. My reply
+is, that I do not so speak of it. The peculiarity I contend for is only
+one of degree. All our ideas of sensation of course resemble the
+corresponding sensations, but they do so with very different degrees of
+exactness and of reliability. No one, I presume, can recal in
+imagination a colour or an odour with the same distinctness and accuracy
+with which almost every one can mentally reproduce an image of a
+straight line or a triangle. To the extent, however, of their
+capabilities of accuracy, our recollections of colours or of odours may
+serve as subjects of experimentation, as well as those of lines and
+spaces, and may yield conclusions which will be true of their external
+prototypes. A person in whom, either from natural gift or from
+cultivation, the impressions of colour were peculiarly vivid and
+distinct, if asked which of two blue flowers was of the darkest tinge,
+though he might never have compared the two, or even looked at them
+together, might be able to give a confident answer on the faith of his
+distinct recollection of the colours; that is, he might examine his
+mental pictures, and find there a property of the outward objects. But
+in hardly any case except that of simple geometrical forms, could this
+be done by mankind generally, with a degree of assurance equal to that
+which is given by a contemplation of the objects themselves. Persons
+differ most widely in the precision of their recollection, even of
+forms: one person, when he has looked any one in the face for half a
+minute, can draw an accurate likeness of him from memory; another may
+have seen him every day for six months, and hardly know whether his nose
+is long or short. But everybody has a perfectly distinct mental image of
+a straight line, a circle, or a rectangle. And every one concludes
+confidently from these mental images to the corresponding outward
+things. The truth is, that we may, and continually do, study nature in
+our recollections, when the objects themselves are absent; and in the
+case of geometrical forms we can perfectly, but in most other cases only
+imperfectly, trust our recollections.</p></div>
+
+<div class="footnote"><p><a name="Footnote_24_59" id="Footnote_24_59"></a><a href="#FNanchor_24_59"><span class="label">[24]</span></a> <i>History of Scientific Ideas</i>, i. 65-67.</p></div>
+
+<div class="footnote"><p><a name="Footnote_25_60" id="Footnote_25_60"></a><a href="#FNanchor_25_60"><span class="label">[25]</span></a> Ibid. 60.</p></div>
+
+<div class="footnote"><p><a name="Footnote_26_61" id="Footnote_26_61"></a><a href="#FNanchor_26_61"><span class="label">[26]</span></a> <i>History of Scientific Ideas</i>, i. 58, 59.</p></div>
+
+<div class="footnote"><p><a name="Footnote_27_62" id="Footnote_27_62"></a><a href="#FNanchor_27_62"><span class="label">[27]</span></a> "If all mankind had spoken one language, we cannot doubt
+that there would have been a powerful, perhaps a universal, school of
+philosophers, who would have believed in the inherent connexion between
+names and things, who would have taken the sound <i>man</i> to be the mode of
+agitating the air which is essentially communicative of the ideas of
+reason, cookery, bipedality, &amp;c."&mdash;De Morgan, <i>Formal Logic</i>, p. 246.</p></div>
+
+<div class="footnote"><p><a name="Footnote_28_63" id="Footnote_28_63"></a><a href="#FNanchor_28_63"><span class="label">[28]</span></a> It would be difficult to name a man more remarkable at
+once for the greatness and the wide range of his mental accomplishments,
+than Leibnitz. Yet this eminent man gave as a reason for rejecting
+Newton's scheme of the solar system, that God <i>could not</i> make a body
+revolve round a distant centre, unless either by some impelling
+mechanism, or by miracle:&mdash;"Tout ce qui n'est pas explicable" says he in
+a letter to the Abb� Conti, "par la nature des cr�atures, est
+miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de
+nature; donc la chose est naturelle. Il faut que la loi soit ex�cutable
+par les natures des cr�atures. Si Dieu donnait cette loi, par exemple, �
+un corps libre, de tourner � l'entour d'un certain centre, <i>il faudrait
+ou qu'il y joign�t d'autres corps qui par leur impulsion l'obligeassent
+de rester toujours dans son orbite circulaire, ou qu'il m�t un ange �
+ses trousses, ou enfin il faudrait qu'il y concour�t
+extraordinairement</i>; car naturellement il s'�cartera par la
+tangente."&mdash;<i>Works of Leibnitz</i>, ed. Dutens, iii. 446.</p></div>
+
+<div class="footnote"><p><a name="Footnote_29_64" id="Footnote_29_64"></a><a href="#FNanchor_29_64"><span class="label">[29]</span></a> <i>Novum Organum Renovatum</i>, pp. 32, 33.</p></div>
+
+<div class="footnote"><p><a name="Footnote_30_65" id="Footnote_30_65"></a><a href="#FNanchor_30_65"><span class="label">[30]</span></a> <i>History of Scientific Ideas</i>, i. 264.</p></div>
+
+<div class="footnote"><p><a name="Footnote_31_66" id="Footnote_31_66"></a><a href="#FNanchor_31_66"><span class="label">[31]</span></a> <i>Hist. Sc. Id.</i>, i. 263.</p></div>
+
+<div class="footnote"><p><a name="Footnote_32_67" id="Footnote_32_67"></a><a href="#FNanchor_32_67"><span class="label">[32]</span></a> Ibid. 240.</p></div>
+
+<div class="footnote"><p><a name="Footnote_33_68" id="Footnote_33_68"></a><a href="#FNanchor_33_68"><span class="label">[33]</span></a> <i>Hist. Sc. Id.</i>, ii. 25, 26.</p></div>
+
+<div class="footnote"><p><a name="Footnote_34_69" id="Footnote_34_69"></a><a href="#FNanchor_34_69"><span class="label">[34]</span></a> <i>Phil. of Disc.</i>, p. 339.</p></div>
+
+<div class="footnote"><p><a name="Footnote_35_70" id="Footnote_35_70"></a><a href="#FNanchor_35_70"><span class="label">[35]</span></a> <i>Phil. of Disc.</i>, p. 338.</p></div>
+
+<div class="footnote"><p><a name="Footnote_36_71" id="Footnote_36_71"></a><a href="#FNanchor_36_71"><span class="label">[36]</span></a> Ib. p. 463.</p></div>
+
+<div class="footnote"><p><a name="Footnote_37_72" id="Footnote_37_72"></a><a href="#FNanchor_37_72"><span class="label">[37]</span></a> <i>Phil. of Disc.</i>, pp. 472, 473.</p></div>
+
+<div class="footnote"><p><a name="Footnote_38_73" id="Footnote_38_73"></a><a href="#FNanchor_38_73"><span class="label">[38]</span></a> The <i>Quarterly Review</i> for June 1841, contained an article
+of great ability on Dr. Whewell's two great works (since acknowledged
+and reprinted in Sir John Herschel's Essays) which maintains, on the
+subject of axioms, the doctrine advanced in the text, that they are
+generalizations from experience, and supports that opinion by a line of
+argument strikingly coinciding with mine. When I state that the whole of
+the present chapter (except the last four pages, added in the fifth
+edition) was written before I had seen the article, (the greater part,
+indeed, before it was published,) it is not my object to occupy the
+reader's attention with a matter so unimportant as the degree of
+originality which may or may not belong to any portion of my own
+speculations, but to obtain for an opinion which is opposed to reigning
+doctrines, the recommendation derived from a striking concurrence of
+sentiment between two inquirers entirely independent of one another. I
+embrace the opportunity of citing from a writer of the extensive
+acquirements in physical and metaphysical knowledge and the capacity of
+systematic thought which the article evinces, passages so remarkably in
+unison with my own views as the following:&mdash;
+</p><p>
+"The truths of geometry are summed up and embodied in its definitions
+and axioms.... Let us turn to the axioms, and what do we find? A string
+of propositions concerning magnitude in the abstract, which are equally
+true of space, time, force, number, and every other magnitude
+susceptible of aggregation and subdivision. Such propositions, where
+they are not mere definitions, as some of them are, carry their
+inductive origin on the face of their enunciation.... Those which
+declare that two straight lines cannot inclose a space, and that two
+straight lines which cut one another cannot both be parallel to a third,
+are in reality the only ones which express characteristic properties of
+space, and these it will be worth while to consider more nearly. Now the
+only clear notion we can form of straightness is uniformity of
+direction, for space in its ultimate analysis is nothing but an
+assemblage of distances and directions. And (not to dwell on the notion
+of continued contemplation, <i>i.e.</i>, mental experience, as included in
+the very idea of uniformity; nor on that of transfer of the
+contemplating being from point to point, and of experience, during such
+transfer, of the homogeneity of the interval passed over) we cannot even
+propose the proposition in an intelligible form to any one whose
+experience ever since he was born has not assured him of the fact. The
+unity of direction, or that we cannot march from a given point by more
+than one path direct to the same object, is matter of practical
+experience long before it can by possibility become matter of abstract
+thought. <i>We cannot attempt mentally to exemplify the conditions of the
+assertion in an imaginary case opposed to it, without violating our
+habitual recollection of this experience, and defacing our mental
+picture of space as grounded on it.</i> What but experience, we may ask,
+can possibly assure us of the homogeneity of the parts of distance,
+time, force, and measurable aggregates in general, on which the truth of
+the other axioms depends? As regards the latter axiom, after what has
+been said it must be clear that the very same course of remarks equally
+applies to its case, and that its truth is quite as much forced on the
+mind as that of the former by daily and hourly experience, ...
+<i>including always, be it observed, in our notion of experience, that
+which is gained by contemplation of the inward picture which the mind
+forms to itself in any proposed case, or which it arbitrarily selects as
+an example&mdash;such picture, in virtue of the extreme simplicity of these
+primary relations, being called up by the imagination with as much
+vividness and clearness as could be done by any external impression,
+which is the only meaning we can attach to the word intuition, as
+applied to such relations</i>."
+</p><p>
+And again, of the axioms of mechanics:&mdash;"As we admit no such
+propositions, other than as truths inductively collected from
+observation, even in geometry itself, it can hardly be expected that, in
+a science of obviously contingent relations, we should acquiesce in a
+contrary view. Let us take one of these axioms and examine its evidence:
+for instance, that equal forces perpendicularly applied at the opposite
+ends of equal arms of a straight lever will balance each other. What but
+experience, we may ask, in the first place, can possibly inform us that
+a force so applied will have any tendency to turn the lever on its
+centre at all? or that force can be so transmitted along a rigid line
+perpendicular to its direction, as to act elsewhere in space than along
+its own line of action? Surely this is so far from being self-evident
+that it has even a paradoxical appearance, which is only to be removed
+by giving our lever thickness, material composition, and molecular
+powers. Again, we conclude, that the two forces, being equal and applied
+under precisely similar circumstances, must, if they exert any effort at
+all to turn the lever, exert equal and opposite efforts: but what <i>�
+priori</i> reasoning can possibly assure us that they <i>do</i> act under
+precisely similar circumstances? that points which differ in place <i>are</i>
+similarly circumstanced as regards the exertion of force? that universal
+space may not have relations to universal force&mdash;or, at all events, that
+the organization of the material universe may not be such as to place
+that portion of space occupied by it in such relations to the forces
+exerted in it, as may invalidate the absolute similarity of
+circumstances assumed? Or we may argue, what have we to do with the
+notion of angular movement in the lever at all? The case is one of rest,
+and of quiescent destruction of force by force. Now how is this
+destruction effected? Assuredly by the counter-pressure which supports
+the fulcrum. But would not this destruction equally arise, and by the
+same amount of counter-acting force, if each force simply pressed its
+own half of the lever against the fulcrum? And what can assure us that
+it is not so, except removal of one or other force, and consequent
+tilting of the lever? The other fundamental axiom of statics, that the
+pressure on the point of support is the sum of the weights ... is merely
+a scientific transformation and more refined mode of stating a coarse
+and obvious result of universal experience, viz. that the weight of a
+rigid body is the same, handle it or suspend it in what position or by
+what point we will, and that whatever sustains it sustains its total
+weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever
+made a trial for the purpose of showing that the pressure on the support
+is equal to the sum of the weights.' ... But it is precisely because in
+every action of his life from earliest infancy he has been continually
+making the trial, and seeing it made by every other living being about
+him, that he never dreams of staking its result on one additional
+attempt made with scientific accuracy. This would be as if a man should
+resolve to decide by experiment whether his eyes were useful for the
+purpose of seeing, by hermetically sealing himself up for half an hour
+in a metal case."
+</p><p>
+On the "paradox of universal propositions obtained by experience," the
+same writer says: "If there be necessary and universal truths
+expressible in propositions of axiomatic simplicity and obviousness, and
+having for their subject-matter the elements of all our experience and
+all our knowledge, surely these are the truths which, if experience
+suggest to us any truths at all, it ought to suggest most readily,
+clearly, and unceasingly. If it were a truth, universal and necessary,
+that a net is spread over the whole surface of every planetary globe, we
+should not travel far on our own without getting entangled in its
+meshes, and making the necessity of some means of extrication an axiom
+of locomotion.... There is, therefore, nothing paradoxical, but the
+reverse, in our being led by observation to a recognition of such
+truths, as <i>general</i> propositions, coextensive at least with all human
+experience. That they pervade all the objects of experience, must ensure
+their continual suggestion <i>by</i> experience; that they are true, must
+ensure that consistency of suggestion, that iteration of uncontradicted
+assertion, which commands implicit assent, and removes all occasion of
+exception; that they are simple, and admit of no misunderstanding, must
+secure their admission by every mind."
+</p><p>
+"A truth, necessary and universal, relative to any object of our
+knowledge, must verify itself in every instance where that object is
+before our contemplation, and if at the same time it be simple and
+intelligible, its verification must be obvious. <i>The sentiment of such a
+truth cannot, therefore, but be present to our minds whenever that
+object is contemplated, and must therefore make a part of the mental
+picture or idea of that object which we may on any occasion summon
+before our imagination.... All propositions, therefore, become not only
+untrue but inconceivable</i>, if ... axioms be violated in their
+enunciation."
+</p><p>
+Another eminent mathematician had previously sanctioned by his authority
+the doctrine of the origin of geometrical axioms in experience.
+"Geometry is thus founded likewise on observation; but of a kind so
+familiar and obvious, that the primary notions which it furnishes might
+seem intuitive."&mdash;<i>Sir John Leslie</i>, quoted by Sir William Hamilton,
+<i>Discourses</i>, &amp;c. p. 272.</p></div>
+
+<div class="footnote"><p><a name="Footnote_39_74" id="Footnote_39_74"></a><a href="#FNanchor_39_74"><span class="label">[39]</span></a> <i>Principles of Psychology.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_40_75" id="Footnote_40_75"></a><a href="#FNanchor_40_75"><span class="label">[40]</span></a> Mr. Spencer is mistaken in supposing me to claim any
+peculiar "necessity" for this axiom as compared with others. I have
+corrected the expressions which led him into that misapprehension of my
+meaning.</p></div>
+
+<div class="footnote"><p><a name="Footnote_41_76" id="Footnote_41_76"></a><a href="#FNanchor_41_76"><span class="label">[41]</span></a> Mr. Spencer makes a distinction between conceiving myself
+looking into darkness, and conceiving <i>that I am</i> then and there looking
+into darkness. To me it seems that this change of the expression to the
+form <i>I am</i>, just marks the transition from conception to belief, and
+that the phrase "to conceive that <i>I am</i>," or "that anything <i>is</i>," is
+not consistent with using the word conceive in its rigorous sense.</p></div>
+
+<div class="footnote"><p><a name="Footnote_42_77" id="Footnote_42_77"></a><a href="#FNanchor_42_77"><span class="label">[42]</span></a> I have myself accepted the contest, and fought it out on
+this battleground, in the eleventh chapter of <i>An Examination of Sir
+William Hamilton's Philosophy</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_43_78" id="Footnote_43_78"></a><a href="#FNanchor_43_78"><span class="label">[43]</span></a> <i>Discussions</i>, &amp;c., 2nd ed. p. 624.</p></div>
+
+<div class="footnote"><p><a name="Footnote_44_79" id="Footnote_44_79"></a><a href="#FNanchor_44_79"><span class="label">[44]</span></a> If it be said that the <i>existence</i> of matter is among the
+things proved by the principle of Excluded Middle, that principle must
+prove also the existence of dragons and hippogriffs, because they must
+be either scaly or not scaly, creeping or not creeping, and so forth.</p></div>
+
+<div class="footnote"><p><a name="Footnote_45_80" id="Footnote_45_80"></a><a href="#FNanchor_45_80"><span class="label">[45]</span></a> For further considerations respecting the axioms of
+Contradiction and Excluded Middle, see the twenty-first chapter of <i>An
+Examination of Sir William Hamilton's Philosophy</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_46_81" id="Footnote_46_81"></a><a href="#FNanchor_46_81"><span class="label">[46]</span></a> Mr. De Morgan says "Plato," but to prevent confusion I
+have kept to my own <i>exemplum</i>.</p></div>
+</div>
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span></p>
+<h2><a name="BOOK_III" id="BOOK_III"></a>BOOK III.<br />
+
+OF INDUCTION.</h2>
+
+
+<p><span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span></p>
+<blockquote><p>"According to the doctrine now stated, the highest, or rather the only
+proper object of physics, is to ascertain those established conjunctions
+of successive events, which constitute the order of the universe; to
+record the phenomena which it exhibits to our observations, or which it
+discloses to our experiments; and to refer these phenomena to their
+general laws."&mdash;<span class="smcap">D. Stewart</span>, <i>Elements of the Philosophy of the Human
+Mind</i>, vol. ii. chap. iv. sect. 1.</p></blockquote>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_I" id="BOOK_III_CHAPTER_I"></a>CHAPTER I.<br />
+
+PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_I_1">� 1.</a> The portion of the present inquiry upon which we are now about to
+enter, may be considered as the principal, both from its surpassing in
+intricacy all the other branches, and because it relates to a process
+which has been shown in the preceding Book to be that in which the
+investigation of nature essentially consists. We have found that all
+Inference, consequently all Proof, and all discovery of truths not
+self-evident, consists of inductions, and the interpretation of
+inductions: that all our knowledge, not intuitive, comes to us
+exclusively from that source. What Induction is, therefore, and what
+conditions render it legitimate, cannot but be deemed the main question
+of the science of logic&mdash;the question which includes all others. It is,
+however, one which professed writers on logic have almost entirely
+passed over. The generalities of the subject have not been altogether
+neglected by metaphysicians; but, for want of sufficient acquaintance
+with the processes by which science has actually succeeded in
+establishing general truths, their analysis of the inductive operation,
+even when unexceptionable as to correctness, has not been specific
+enough to be made the foundation of practical rules, which might be for
+induction itself what the rules of the syllogism are for the
+interpretation of induction: while those by whom physical science has
+been carried to its present state of improvement&mdash;and who, to arrive at
+a complete theory of the process, needed only to generalize, and adapt
+to all varieties of problems, the methods which they themselves employed
+in their habitual pursuits&mdash;never until very lately made any serious
+attempt to philosophize on the subject, nor regarded the mode in which
+<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span>they arrived at their conclusions as deserving of study, independently
+of the conclusions themselves.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_I_2">� 2.</a> For the purposes of the present inquiry, Induction may be defined,
+the operation of discovering and proving general propositions. It is
+true that (as already shown) the process of indirectly ascertaining
+individual facts, is as truly inductive as that by which we establish
+general truths. But it is not a different kind of induction; it is a
+form of the very same process: since, on the one hand, generals are but
+collections of particulars, definite in kind but indefinite in number;
+and on the other hand, whenever the evidence which we derive from
+observation of known cases justifies us in drawing an inference
+respecting even one unknown case, we should on the same evidence be
+justified in drawing a similar inference with respect to a whole class
+of cases. The inference either does not hold at all, or it holds in all
+cases of a certain description; in all cases which, in certain definable
+respects, resemble those we have observed.</p>
+
+<p>If these remarks are just; if the principles and rules of inference are
+the same whether we infer general propositions or individual facts; it
+follows that a complete logic of the sciences would be also a complete
+logic of practical business and common life. Since there is no case of
+legitimate inference from experience, in which the conclusion may not
+legitimately be a general proposition; an analysis of the process by
+which general truths are arrived at, is virtually an analysis of all
+induction whatever. Whether we are inquiring into a scientific principle
+or into an individual fact, and whether we proceed by experiment or by
+ratiocination, every step in the train of inferences is essentially
+inductive, and the legitimacy of the induction depends in both cases on
+the same conditions.</p>
+
+<p>True it is that in the case of the practical inquirer, who is
+endeavouring to ascertain facts not for the purposes of science but for
+those of business, such for instance as the advocate or the judge, the
+chief difficulty is one in which the principles of induction will afford
+him no assistance. It lies not in making his inductions, but in the
+selection of them; in choosing from <span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span>among all general propositions
+ascertained to be true, those which furnish marks by which he may trace
+whether the given subject possesses or not the predicate in question. In
+arguing a doubtful question of fact before a jury, the general
+propositions or principles to which the advocate appeals are mostly, in
+themselves, sufficiently trite, and assented to as soon as stated: his
+skill lies in bringing his case under those propositions or principles;
+in calling to mind such of the known or received maxims of probability
+as admit of application to the case in hand, and selecting from among
+them those best adapted to his object. Success is here dependent on
+natural or acquired sagacity, aided by knowledge of the particular
+subject, and of subjects allied with it. Invention, though it can be
+cultivated, cannot be reduced to rule; there is no science which will
+enable a man to bethink himself of that which will suit his purpose.</p>
+
+<p>But when he <i>has</i> thought of something, science can tell him whether
+that which he has thought of will suit his purpose or not. The inquirer
+or arguer must be guided by his own knowledge and sagacity in the choice
+of the inductions out of which he will construct his argument. But the
+validity of the argument when constructed, depends on principles and
+must be tried by tests which are the same for all descriptions of
+inquiries, whether the result be to give A an estate, or to enrich
+science with a new general truth. In the one case and in the other, the
+senses, or testimony, must decide on the individual facts; the rules of
+the syllogism will determine whether, those facts being supposed
+correct, the case really falls within the formul� of the different
+inductions under which it has been successively brought; and finally,
+the legitimacy of the inductions themselves must be decided by other
+rules, and these it is now our purpose to investigate. If this third
+part of the operation be, in many of the questions of practical life,
+not the most, but the least arduous portion of it, we have seen that
+this is also the case in some great departments of the field of science;
+in all those which are principally deductive, and most of all in
+mathematics; where the inductions themselves are few in number, and so
+obvious and elementary that they seem to stand in no need of the
+evidence of experience, while to combine them so as to <span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span>prove a given
+theorem or solve a problem, may call for the utmost powers of invention
+and contrivance with which our species is gifted.</p>
+
+<p>If the identity of the logical processes which prove particular facts
+and those which establish general scientific truths, required any
+additional confirmation, it would be sufficient to consider that in many
+branches of science, single facts have to be proved, as well as
+principles; facts as completely individual as any that are debated in a
+court of justice; but which are proved in the same manner as the other
+truths of the science, and without disturbing in any degree the
+homogeneity of its method. A remarkable example of this is afforded by
+astronomy. The individual facts on which that science grounds its most
+important deductions, such facts as the magnitudes of the bodies of the
+solar system, their distances from one another, the figure of the earth,
+and its rotation, are scarcely any of them accessible to our means of
+direct observation: they are proved indirectly, by the aid of inductions
+founded on other facts which we can more easily reach. For example, the
+distance of the moon from the earth was determined by a very circuitous
+process. The share which direct observation had in the work consisted in
+ascertaining, at one and the same instant, the zenith distances of the
+moon, as seen from two points very remote from one another on the
+earth's surface. The ascertainment of these angular distances
+ascertained their supplements; and since the angle at the earth's centre
+subtended by the distance between the two places of observation was
+deducible by spherical trigonometry from the latitude and longitude of
+those places, the angle at the moon subtended by the same line became
+the fourth angle of a quadrilateral of which the other three angles were
+known. The four angles being thus ascertained, and two sides of the
+quadrilateral being radii of the earth; the two remaining sides and the
+diagonal, or in other words, the moon's distance from the two places of
+observation and from the centre of the earth, could be ascertained, at
+least in terms of the earth's radius, from elementary theorems of
+geometry. At each step in this demonstration we take in a <span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span>new
+induction, represented, in the aggregate of its results, by a general
+proposition.</p>
+
+<p>Not only is the process by which an individual astronomical fact was
+thus ascertained, exactly similar to those by which the same science
+establishes its general truths, but also (as we have shown to be the
+case in all legitimate reasoning) a general proposition might have been
+concluded instead of a single fact. In strictness, indeed, the result of
+the reasoning <i>is</i> a general proposition; a theorem respecting the
+distance, not of the moon in particular, but of any inaccessible object:
+showing in what relation that distance stands to certain other
+quantities. And although the moon is almost the only heavenly body the
+distance of which from the earth can really be thus ascertained, this is
+merely owing to the accidental circumstances of the other heavenly
+bodies, which render them incapable of affording such data as the
+application of the theorem requires; for the theorem itself is as true
+of them as it is of the moon.<a name="FNanchor_1_82" id="FNanchor_1_82"></a><a href="#Footnote_1_82" class="fnanchor">[1]</a></p>
+
+<p><span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span></p><p>We shall fall into no error, then, if in treating of Induction, we
+limit our attention to the establishment of general propositions. The
+principles and rules of Induction as directed to this end, are the
+principles and rules of all Induction; and the logic of Science is the
+universal Logic, applicable to all inquiries in which man can engage.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_II" id="BOOK_III_CHAPTER_II"></a>CHAPTER II.<br />
+
+OF INDUCTIONS IMPROPERLY SO CALLED.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_II_1">� 1.</a> Induction, then, is that operation of the mind, by which we infer
+that what we know to be true in a particular case or cases, will be true
+in all cases which resemble the former in certain assignable respects.
+In other words, Induction is the process by which we conclude that what
+is true of certain individuals of a class is true of the whole class, or
+that what is true at certain times will be true in similar circumstances
+at all times.</p>
+
+<p>This definition excludes from the meaning of the term Induction, various
+logical operations, to which it is not unusual to apply that name.</p>
+
+<p>Induction, as above defined, is a process of inference; it proceeds from
+the known to the unknown; and any operation involving no inference, any
+process in which what seems the conclusion is no wider than the premises
+from which it is drawn, does not fall within the meaning of the term.
+Yet in the common books of Logic we find this laid down as the most
+perfect, indeed the only quite perfect, form of induction. In those
+books, every process which sets out from a less general and terminates
+in a more general expression,&mdash;which admits of being stated in the form,
+"This and that A are B, therefore every A is B,"&mdash;is called an
+induction, whether anything be really concluded or not: and the
+induction is asserted not to be perfect, unless every single individual
+of the class A is included in the antecedent, or premise: that is,
+unless what we affirm of the class has already been ascertained to be
+true of every individual in it, so that the nominal conclusion is not
+really a conclusion, but a mere reassertion of the premises. If we were
+to say, All the planets shine by the sun's light, from observation of
+each <span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span>separate planet, or All the Apostles were Jews, because this is
+true of Peter, Paul, John, and every other apostle,&mdash;these, and such as
+these, would, in the phraseology in question, be called perfect, and the
+only perfect, Inductions. This, however, is a totally different kind of
+induction from ours; it is not an inference from facts known to facts
+unknown, but a mere short-hand registration of facts known. The two
+simulated arguments which we have quoted, are not generalizations; the
+propositions purporting to be conclusions from them, are not really
+general propositions. A general proposition is one in which the
+predicate is affirmed or denied of an unlimited number of individuals;
+namely, all, whether few or many, existing or capable of existing, which
+possess the properties connoted by the subject of the proposition. "All
+men are mortal" does not mean all now living, but all men past, present,
+and to come. When the signification of the term is limited so as to
+render it a name not for any and every individual falling under a
+certain general description, but only for each of a number of
+individuals designated as such, and as it were counted off individually,
+the proposition, though it may be general in its language, is no general
+proposition, but merely that number of singular propositions, written in
+an abridged character. The operation may be very useful, as most forms
+of abridged notation are; but it is no part of the investigation of
+truth, though often bearing an important part in the preparation of the
+materials for that investigation.</p>
+
+<p>As we may sum up a definite number of singular propositions in one
+proposition, which will be apparently, but not really, general, so we
+may sum up a definite number of general propositions in one proposition,
+which will be apparently, but not really, more general. If by a separate
+induction applied to every distinct species of animals, it has been
+established that each possesses a nervous system, and we affirm
+thereupon that all animals have a nervous system; this looks like a
+generalization, though as the conclusion merely affirms of all what has
+already been affirmed of each, it seems to tell us nothing but what we
+knew before. A distinction however <span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span>must be made. If in concluding that
+all animals have a nervous system, we mean the same thing and no more as
+if we had said "all known animals," the proposition is not general, and
+the process by which it is arrived at is not induction. But if our
+meaning is that the observations made of the various species of animals
+have discovered to us a law of animal nature, and that we are in a
+condition to say that a nervous system will be found even in animals yet
+undiscovered, this indeed is an induction; but in this case the general
+proposition contains more than the sum of the special propositions from
+which it is inferred. The distinction is still more forcibly brought out
+when we consider, that if this real generalization be legitimate at all,
+its legitimacy probably does not require that we should have examined
+without exception every known species. It is the number and nature of
+the instances, and not their being the whole of those which happen to be
+known, that makes them sufficient evidence to prove a general law: while
+the more limited assertion, which stops at all known animals, cannot be
+made unless we have rigorously verified it in every species. In like
+manner (to return to a former example) we might have inferred, not that
+all <i>the</i> planets, but that all <i>planets</i>, shine by reflected light: the
+former is no induction; the latter is an induction, and a bad one, being
+disproved by the case of double stars&mdash;self-luminous bodies which are
+properly planets, since they revolve round a centre.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_II_2">� 2.</a> There are several processes used in mathematics which require to be
+distinguished from Induction, being not unfrequently called by that
+name, and being so far similar to Induction properly so called, that the
+propositions they lead to are really general propositions. For example,
+when we have proved with respect to the circle, that a straight line
+cannot meet it in more than two points, and when the same thing has been
+successively proved of the ellipse, the parabola, and the hyperbola, it
+may be laid down as an universal property of the sections of the cone.
+The distinction drawn in the two previous examples can have no place
+here, there being <span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span>no difference between all <i>known</i> sections of the
+cone and <i>all</i> sections, since a cone demonstrably cannot be intersected
+by a plane except in one of these four lines. It would be difficult,
+therefore, to refuse to the proposition arrived at, the name of a
+generalization, since there is no room for any generalization beyond it.
+But there is no induction, because there is no inference: the conclusion
+is a mere summing up of what was asserted in the various propositions
+from which it is drawn. A case somewhat, though not altogether, similar,
+is the proof of a geometrical theorem by means of a diagram. Whether the
+diagram be on paper or only in the imagination, the demonstration (as
+formerly observed<a name="FNanchor_2_83" id="FNanchor_2_83"></a><a href="#Footnote_2_83" class="fnanchor">[2]</a>) does not prove directly the general theorem; it
+proves only that the conclusion, which the theorem asserts generally, is
+true of the particular triangle or circle exhibited in the diagram; but
+since we perceive that in the same way in which we have proved it of
+that circle, it might also be proved of any other circle, we gather up
+into one general expression all the singular propositions susceptible of
+being thus proved, and embody them in an universal proposition. Having
+shown that the three angles of the triangle ABC are together equal to
+two right angles, we conclude that this is true of every other triangle,
+not because it is true of ABC, but for the same reason which proved it
+to be true of ABC. If this were to be called Induction, an appropriate
+name for it would be, induction by parity of reasoning. But the term
+cannot properly belong to it; the characteristic quality of Induction is
+wanting, since the truth obtained, though really general, is not
+believed on the evidence of particular instances. We do not conclude
+that all triangles have the property because some triangles have, but
+from the ulterior demonstrative evidence which was the ground of our
+conviction in the particular instances.</p>
+
+<p>There are nevertheless, in mathematics, some examples of so-called
+Induction, in which the conclusion does bear the appearance of a
+generalization grounded on some of the particular cases included in it.
+A mathematician, when he has <span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span>calculated a sufficient number of the
+terms of an algebraical or arithmetical series to have ascertained what
+is called the <i>law</i> of the series, does not hesitate to fill up any
+number of the succeeding terms without repeating the calculations. But I
+apprehend he only does so when it is apparent from <i>� priori</i>
+considerations (which might be exhibited in the form of demonstration)
+that the mode of formation of the subsequent terms, each from that which
+preceded it, must be similar to the formation of the terms which have
+been already calculated. And when the attempt has been hazarded without
+the sanction of such general considerations, there are instances on
+record in which it has led to false results.</p>
+
+<p>It is said that Newton discovered the binomial theorem by induction; by
+raising a binomial successively to a certain number of powers, and
+comparing those powers with one another until he detected the relation
+in which the algebraic formula of each power stands to the exponent of
+that power, and to the two terms of the binomial. The fact is not
+improbable: but a mathematician like Newton, who seemed to arrive <i>per
+saltum</i> at principles and conclusions that ordinary mathematicians only
+reached by a succession of steps, certainly could not have performed the
+comparison in question without being led by it to the <i>� priori</i> ground
+of the law; since any one who understands sufficiently the nature of
+multiplication to venture upon multiplying several lines of symbols at
+one operation, cannot but perceive that in raising a binomial to a
+power, the coefficients must depend on the laws of permutation and
+combination: and as soon as this is recognised, the theorem is
+demonstrated. Indeed, when once it was seen that the law prevailed in a
+few of the lower powers, its identity with the law of permutation would
+at once suggest the considerations which prove it to obtain universally.
+Even, therefore, such cases as these, are but examples of what I have
+called Induction by parity of reasoning, that is, not really Induction,
+because not involving inference of a general proposition from particular
+instances.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_II_3">� 3.</a> There remains a third improper use of the term <span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span>Induction, which it
+is of real importance to clear up, because the theory of Induction has
+been, in no ordinary degree, confused by it, and because the confusion
+is exemplified in the most recent and elaborate treatise on the
+inductive philosophy which exists in our language. The error in question
+is that of confounding a mere description, by general terms, of a set of
+observed phenomena, with an induction from them.</p>
+
+<p>Suppose that a phenomenon consists of parts, and that these parts are
+only capable of being observed separately, and as it were piecemeal.
+When the observations have been made, there is a convenience (amounting
+for many purposes to a necessity) in obtaining a representation of the
+phenomenon as a whole, by combining, or as we may say, piecing these
+detached fragments together. A navigator sailing in the midst of the
+ocean discovers land: he cannot at first, or by any one observation,
+determine whether it is a continent or an island; but he coasts along
+it, and after a few days finds himself to have sailed completely round
+it: he then pronounces it an island. Now there was no particular time or
+place of observation at which he could perceive that this land was
+entirely surrounded by water: he ascertained the fact by a succession of
+partial observations, and then selected a general expression which
+summed up in two or three words the whole of what he so observed. But is
+there anything of the nature of an induction in this process? Did he
+infer anything that had not been observed, from something else which
+had? Certainly not. He had observed the whole of what the proposition
+asserts. That the land in question is an island, is not an inference
+from the partial facts which the navigator saw in the course of his
+circumnavigation; it is the facts themselves; it is a summary of those
+facts; the description of a complex fact, to which those simpler ones
+are as the parts of a whole.</p>
+
+<p>Now there is, I conceive, no difference in kind between this simple
+operation, and that by which Kepler ascertained the nature of the
+planetary orbits: and Kepler's operation, all at least that was
+characteristic in it, was not more an inductive act than that of our
+supposed navigator.</p>
+
+<p><span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span></p><p>The object of Kepler was to determine the real path described by each
+of the planets, or let us say by the planet Mars (since it was of that
+body that he first established the two of his three laws which did not
+require a comparison of planets). To do this there was no other mode
+than that of direct observation: and all which observation could do was
+to ascertain a great number of the successive places of the planet; or
+rather, of its apparent places. That the planet occupied successively
+all these positions, or at all events, positions which produced the same
+impressions on the eye, and that it passed from one of these to another
+insensibly, and without any apparent breach of continuity; thus much the
+senses, with the aid of the proper instruments, could ascertain. What
+Kepler did more than this, was to find what sort of a curve these
+different points would make, supposing them to be all joined together.
+He expressed the whole series of the observed places of Mars by what Dr.
+Whewell calls the general conception of an ellipse. This operation was
+far from being as easy as that of the navigator who expressed the series
+of his observations on successive points of the coast by the general
+conception of an island. But it is the very same sort of operation; and
+if the one is not an induction but a description, this must also be true
+of the other.</p>
+
+<p>The only real induction concerned in the case, consisted in inferring
+that because the observed places of Mars were correctly represented by
+points in an imaginary ellipse, therefore Mars would continue to revolve
+in that same ellipse; and in concluding (before the gap had been filled
+up by further observations) that the positions of the planet during the
+time which intervened between two observations, must have coincided with
+the intermediate points of the curve. For these were facts which had not
+been directly observed. They were inferences from the observations;
+facts inferred, as distinguished from facts seen. But these inferences
+were so far from being a part of Kepler's philosophical operation, that
+they had been drawn long before he was born. Astronomers had long known
+that the planets periodically returned to the same places. When this had
+been ascertained, there was no <span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span>induction left for Kepler to make, nor
+did he make any further induction. He merely applied his new conception
+to the facts inferred, as he did to the facts observed. Knowing already
+that the planets continued to move in the same paths; when he found that
+an ellipse correctly represented the past path, he knew that it would
+represent the future path. In finding a compendious expression for the
+one set of facts, he found one for the other: but he found the
+expression only, not the inference; nor did he (which is the true test
+of a general truth) add anything to the power of prediction already
+possessed.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_II_4">� 4.</a> The descriptive operation which enables a number of details to be
+summed up in a single proposition, Dr. Whewell, by an aptly chosen
+expression, has termed the Colligation of Facts. In most of his
+observations concerning that mental process I fully agree, and would
+gladly transfer all that portion of his book into my own pages. I only
+think him mistaken in setting up this kind of operation, which according
+to the old and received meaning of the term, is not induction at all, as
+the type of induction generally; and laying down, throughout his work,
+as principles of induction, the principles of mere colligation.</p>
+
+<p>Dr. Whewell maintains that the general proposition which binds together
+the particular facts, and makes them, as it were, one fact, is not the
+mere sum of those facts, but something more, since there is introduced a
+conception of the mind, which did not exist in the facts themselves.
+"The particular facts," says he,<a name="FNanchor_3_84" id="FNanchor_3_84"></a><a href="#Footnote_3_84" class="fnanchor">[3]</a> "are not merely brought together,
+but there is a new element added to the combination by the very act of
+thought by which they are combined.... When the Greeks, after long
+observing the motions of the planets, saw that these motions might be
+rightly considered as produced by the motion of one wheel revolving in
+the inside of another wheel, these wheels were creations of their minds,
+added to the facts which they perceived by sense. And even <span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span>if the
+wheels were no longer supposed to be material, but were reduced to mere
+geometrical spheres or circles, they were not the less products of the
+mind alone,&mdash;something additional to the facts observed. The same is the
+case in all other discoveries. The facts are known, but they are
+insulated and unconnected, till the discoverer supplies from his own
+store a principle of connexion. The pearls are there, but they will not
+hang together till some one provides the string."</p>
+
+<p>Let me first remark that Dr. Whewell, in this passage, blends together,
+indiscriminately, examples of both the processes which I am endeavouring
+to distinguish from one another. When the Greeks abandoned the
+supposition that the planetary motions were produced by the revolution
+of material wheels, and fell back upon the idea of "mere geometrical
+spheres or circles," there was more in this change of opinion than the
+mere substitution of an ideal curve for a physical one. There was the
+abandonment of a theory, and the replacement of it by a mere
+description. No one would think of calling the doctrine of material
+wheels a mere description. That doctrine was an attempt to point out the
+force by which the planets were acted upon, and compelled to move in
+their orbits. But when, by a great step in philosophy, the materiality
+of the wheels was discarded, and the geometrical forms alone retained,
+the attempt to account for the motions was given up, and what was left
+of the theory was a mere description of the orbits. The assertion that
+the planets were carried round by wheels revolving in the inside of
+other wheels, gave place to the proposition, that they moved in the same
+lines which would be traced by bodies so carried: which was a mere mode
+of representing the sum of the observed facts; as Kepler's was another
+and a better mode of representing the same observations.</p>
+
+<p>It is true that for these simply descriptive operations, as well as for
+the erroneous inductive one, a conception of the mind was required. The
+conception of an ellipse must have presented itself to Kepler's mind,
+before he could identify the planetary orbits with it. According to Dr.
+Whewell, the conception <span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span>was something added to the facts. He expresses
+himself as if Kepler had put something into the facts by his mode of
+conceiving them. But Kepler did no such thing. The ellipse was in the
+facts before Kepler recognised it; just as the island was an island
+before it had been sailed round. Kepler did not <i>put</i> what he had
+conceived into the facts, but <i>saw</i> it in them. A conception implies,
+and corresponds to, something conceived: and though the conception
+itself is not in the facts, but in our mind, yet if it is to convey any
+knowledge relating to them, it must be a conception <i>of</i> something which
+really is in the facts, some property which they actually possess, and
+which they would manifest to our senses, if our senses were able to take
+cognizance of it. If, for instance, the planet left behind it in space a
+visible track, and if the observer were in a fixed position at such a
+distance from the plane of the orbit as would enable him to see the
+whole of it at once, he would see it to be an ellipse; and if gifted
+with appropriate instruments and powers of locomotion, he could prove it
+to be such by measuring its different dimensions. Nay, further: if the
+track were visible, and he were so placed that he could see all parts of
+it in succession, but not all of them at once, he might be able, by
+piecing together his successive observations, to discover both that it
+was an ellipse and that the planet moved in it. The case would then
+exactly resemble that of the navigator who discovers the land to be an
+island by sailing round it. If the path was visible, no one I think
+would dispute that to identify it with an ellipse is to describe it: and
+I cannot see why any difference should be made by its not being directly
+an object of sense, when every point in it is as exactly ascertained as
+if it were so.</p>
+
+<p>Subject to the indispensable condition which has just been stated, I
+cannot conceive that the part which conceptions have in the operation of
+studying facts, has ever been overlooked or undervalued. No one ever
+disputed that in order to reason about anything we must have a
+conception of it; or that when we include a multitude of things under a
+general expression, there is implied in the expression a conception of
+something common to those things. But it <span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span>by no means follows that the
+conception is necessarily pre-existent, or constructed by the mind out
+of its own materials. If the facts are rightly classed under the
+conception, it is because there is in the facts themselves something of
+which the conception is itself a copy; and which if we cannot directly
+perceive, it is because of the limited power of our organs, and not
+because the thing itself is not there. The conception itself is often
+obtained by abstraction from the very facts which, in Dr. Whewell's
+language, it is afterwards called in to connect. This he himself admits,
+when he observes, (which he does on several occasions,) how great a
+service would be rendered to the science of physiology by the
+philosopher "who should establish a precise, tenable, and consistent
+conception of life."<a name="FNanchor_4_85" id="FNanchor_4_85"></a><a href="#Footnote_4_85" class="fnanchor">[4]</a> Such a conception can only be abstracted from
+the phenomena of life itself; from the very facts which it is put in
+requisition to connect. In other cases, no doubt, instead of collecting
+the conception from the very phenomena which we are attempting to
+colligate, we select it from among those which have been previously
+collected by abstraction from other facts. In the instance of Kepler's
+laws, the latter was the case. The facts being out of the reach of being
+observed, in any such manner as would have enabled the senses to
+identify directly the path of the planet, the conception requisite for
+framing a general description of that path could not be collected by
+abstraction from the observations themselves; the mind had to supply
+hypothetically, from among the conceptions it had obtained from other
+portions of its experience, some one which would correctly represent the
+series of the observed facts. It had to frame a supposition respecting
+the general course of the phenomenon, and ask itself, If this be the
+general description, what will the details be? and then compare these
+with the details actually observed. If they agreed, the hypothesis would
+serve for a description of the phenomenon: if not, it was necessarily
+abandoned, and another tried. It is such a case as this which gives rise
+to the doctrine that <span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span>the mind, in framing the descriptions, adds
+something of its own which it does not find in the facts.</p>
+
+<p>Yet it is a fact surely, that the planet does describe an ellipse; and a
+fact which we could see, if we had adequate visual organs and a suitable
+position. Not having these advantages, but possessing the conception of
+an ellipse, or (to express the meaning in less technical language)
+knowing what an ellipse was, Kepler tried whether the observed places of
+the planet were consistent with such a path. He found they were so; and
+he, consequently, asserted as a fact that the planet moved in an
+ellipse. But this fact, which Kepler did not add to, but found in, the
+motions of the planet, namely, that it occupied in succession the
+various points in the circumference of a given ellipse, was the very
+fact, the separate parts of which had been separately observed; it was
+the sum of the different observations.</p>
+
+<p>Having stated this fundamental difference between my opinion and that of
+Dr. Whewell, I must add, that his account of the manner in which a
+conception is selected, suitable to express the facts, appears to me
+perfectly just. The experience of all thinkers will, I believe, testify
+that the process is tentative; that it consists of a succession of
+guesses; many being rejected, until one at last occurs fit to be chosen.
+We know from Kepler himself that before hitting upon the "conception" of
+an ellipse, he tried nineteen other imaginary paths, which, finding them
+inconsistent with the observations, he was obliged to reject. But as Dr.
+Whewell truly says, the successful hypothesis, though a guess, ought
+generally to be called, not a lucky, but a skilful guess. The guesses
+which serve to give mental unity and wholeness to a chaos of scattered
+particulars, are accidents which rarely occur to any minds but those
+abounding in knowledge and disciplined in intellectual combinations.</p>
+
+<p>How far this tentative method, so indispensable as a means to the
+colligation of facts for purposes of description, admits of application
+to Induction itself, and what functions belong to it in that department,
+will be considered in the chapter of the present Book which relates to
+Hypotheses. On the present <span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span>occasion we have chiefly to distinguish this
+process of Colligation from Induction properly so called; and that the
+distinction may be made clearer, it is well to advert to a curious and
+interesting remark, which is as strikingly true of the former operation,
+as it appears to me unequivocally false of the latter.</p>
+
+<p>In different stages of the progress of knowledge, philosophers have
+employed, for the colligation of the same order of facts, different
+conceptions. The early rude observations of the heavenly bodies, in
+which minute precision was neither attained nor sought, presented
+nothing inconsistent with the representation of the path of a planet as
+an exact circle, having the earth for its centre. As observations
+increased in accuracy, and facts were disclosed which were not
+reconcileable with this simple supposition; for the colligation of those
+additional facts, the supposition was varied; and varied again and again
+as facts became more numerous and precise. The earth was removed from
+the centre to some other point within the circle; the planet was
+supposed to revolve in a smaller circle called an epicycle, round an
+imaginary point which revolved in a circle round the earth: in
+proportion as observation elicited fresh facts contradictory to these
+representations, other epicycles and other excentrics were added,
+producing additional complication; until at last Kepler swept all these
+circles away, and substituted the conception of an exact ellipse. Even
+this is found not to represent with complete correctness the accurate
+observations of the present day, which disclose many slight deviations
+from an orbit exactly elliptical. Now Dr. Whewell has remarked that
+these successive general expressions, though apparently so conflicting,
+were all correct: they all answered the purpose of colligation; they all
+enabled the mind to represent to itself with facility, and by a
+simultaneous glance, the whole body of facts at the time ascertained:
+each in its turn served as a correct description of the phenomena, so
+far as the senses had up to that time taken cognizance of them. If a
+necessity afterwards arose for discarding one of these general
+descriptions of the planet's orbit, and framing a different imaginary
+line, by which to express the series of observed positions, <span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span>it was
+because a number of new facts had now been added, which it was necessary
+to combine with the old facts into one general description. But this did
+not affect the correctness of the former expression, considered as a
+general statement of the only facts which it was intended to represent.
+And so true is this, that, as is well remarked by M. Comte, these
+ancient generalizations, even the rudest and most imperfect of them,
+that of uniform movement in a circle, are so far from being entirely
+false, that they are even now habitually employed by astronomers when
+only a rough approximation to correctness is required. "L'astronomie
+moderne, en d�truisant sans retour les hypoth�ses primitives, envisag�es
+comme lois r�elles du monde, a soigneusement maintenu leur valeur
+positive et permanente, la propri�t� de repr�senter commod�ment les
+ph�nom�nes quand il s'agit d'une premi�re �bauche. Nos ressources � cet
+�gard sont m�me bien plus �tendues, pr�cis�ment � cause que nous ne nous
+faisons aucune illusion sur la r�alit� des hypoth�ses; ce qui nous
+permet d'employer sans scrupule, en chaque cas, celle que nous jugeons
+la plus avantageuse."<a name="FNanchor_5_86" id="FNanchor_5_86"></a><a href="#Footnote_5_86" class="fnanchor">[5]</a></p>
+
+<p>Dr. Whewell's remark, therefore, is philosophically correct. Successive
+expressions for the colligation of observed facts, or in other words,
+successive descriptions of a phenomenon as a whole, which has been
+observed only in parts, may, though conflicting, be all correct as far
+as they go. But it would surely be absurd to assert this of conflicting
+inductions.</p>
+
+<p>The scientific study of facts may be undertaken for three different
+purposes: the simple description of the facts; their explanation; or
+their prediction: meaning by prediction, the determination of the
+conditions under which similar facts may be expected again to occur. To
+the first of these three operations the name of Induction does not
+properly belong: to the other two it does. Now, Dr. Whewell's
+observation is true of the first alone. Considered as a mere
+description, the circular theory of the heavenly motions represents
+perfectly well their general features: and by adding epicycles without
+<span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span>limit, those motions, even as now known to us, might be expressed with
+any degree of accuracy that might be required. The elliptical theory, as
+a mere description, would have a great advantage in point of simplicity,
+and in the consequent facility of conceiving it and reasoning about it;
+but it would not really be more true than the other. Different
+descriptions, therefore, may be all true: but not, surely, different
+explanations. The doctrine that the heavenly bodies moved by a virtue
+inherent in their celestial nature; the doctrine that they were moved by
+impact, (which led to the hypothesis of vortices as the only impelling
+force capable of whirling bodies in circles,) and the Newtonian
+doctrine, that they are moved by the composition of a centripetal with
+an original projectile force; all these are explanations, collected by
+real induction from supposed parallel cases; and they were all
+successively received by philosophers, as scientific truths on the
+subject of the heavenly bodies. Can it be said of these, as was said of
+the different descriptions, that they are all true as far as they go? Is
+it not clear that only one can be true in any degree, and the other two
+must be altogether false? So much for explanations: let us now compare
+different predictions: the first, that eclipses will occur when one
+planet or satellite is so situated as to cast its shadow upon another;
+the second, that they will occur when some great calamity is impending
+over mankind. Do these two doctrines only differ in the degree of their
+truth, as expressing real facts with unequal degrees of accuracy?
+Assuredly the one is true, and the other absolutely false.<a name="FNanchor_6_87" id="FNanchor_6_87"></a><a href="#Footnote_6_87" class="fnanchor">[6]</a></p>
+
+<p><span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span></p><p>In every way, therefore, it is evident that to explain induction as the
+colligation of facts by means of appropriate conceptions, that is,
+conceptions which will really express <span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span>them, is to confound mere
+description of the observed facts with inference from those facts, and
+ascribe to the latter what is a characteristic property of the former.</p>
+
+<p><span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span></p><p>There is, however, between Colligation and Induction, a real
+correlation, which it is important to conceive correctly. Colligation is
+not always induction; but induction is always colligation. The assertion
+that the planets move in ellipses, was but a mode of representing
+observed facts; it was but a colligation; while the assertion that they
+are drawn, or tend, towards the sun, was the statement of a new fact,
+inferred by induction. But the induction, once made, accomplishes the
+purposes of colligation likewise. It brings the same facts, which Kepler
+had connected by his conception of an ellipse, under the additional
+conception of bodies acted upon by a central force, and serves therefore
+as a new bond of connexion for those facts; a new principle for their
+classification.</p>
+
+<p>Further, the descriptions which are improperly confounded with
+induction, are nevertheless a necessary preparation for induction; no
+less necessary than correct observation of the facts themselves. Without
+the previous colligation of detached observations by means of one
+general conception, we could never have obtained any basis for an
+induction, except in the case of phenomena of very limited compass. We
+should not be able to affirm any predicates at all, of a subject
+incapable of being observed otherwise than piecemeal: much less could we
+extend those predicates by induction to other similar subjects.
+Induction, therefore, always presupposes, not only that the necessary
+observations are made with the necessary accuracy, but also that the
+results of these observations are, so far as practicable, connected
+together by general descriptions, enabling the mind to represent to
+itself as wholes whatever phenomena are capable of being so represented.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_II_5">� 5.</a> Dr. Whewell has replied at some length to the preceding
+observations, re-stating his opinions, but without (as far as I can
+perceive) adding anything material to his former arguments. Since,
+however, mine have not had the good fortune to make any impression upon
+him, I will subjoin a few remarks, tending to show more clearly in what
+our difference <span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span>of opinion consists, as well as, in some measure, to
+account for it.</p>
+
+<p>Nearly all the definitions of induction, by writers of authority, make
+it consist in drawing inferences from known cases to unknown; affirming
+of a class, a predicate which has been found true of some cases
+belonging to the class; concluding, because some things have a certain
+property, that other things which resemble them have the same
+property&mdash;or because a thing has manifested a property at a certain
+time, that it has and will have that property at other times.</p>
+
+<p>It will scarcely be contended that Kepler's operation was an Induction
+in this sense of the term. The statement, that Mars moves in an
+elliptical orbit, was no generalization from individual cases to a class
+of cases. Neither was it an extension to all time, of what had been
+found true at some particular time. The whole amount of generalization
+which the case admitted of, was already completed, or might have been
+so. Long before the elliptic theory was thought of, it had been
+ascertained that the planets returned periodically to the same apparent
+places; the series of these places was, or might have been, completely
+determined, and the apparent course of each planet marked out on the
+celestial globe in an uninterrupted line. Kepler did not extend an
+observed truth to other cases than those in which it had been observed:
+he did not widen the <i>subject</i> of the proposition which expressed the
+observed facts. The alteration he made was in the predicate. Instead of
+saying, the successive places of Mars are so and so, he summed them up
+in the statement, that the successive places of Mars are points in an
+ellipse. It is true, this statement, as Dr. Whewell says, was not the
+sum of the observations <i>merely</i>; it was the sum of the observations
+<i>seen under a new point of view</i>.<a name="FNanchor_7_88" id="FNanchor_7_88"></a><a href="#Footnote_7_88" class="fnanchor">[7]</a> But it was not the sum of <i>more</i>
+than the observations, as a real induction is. It took in no cases but
+those which had been actually observed, or which could have been
+inferred from the observations before the new point of view presented
+itself. There was not that transition from <span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span>known cases to unknown,
+which constitutes Induction in the original and acknowledged meaning of
+the term.</p>
+
+<p>Old definitions, it is true, cannot prevail against new knowledge: and
+if the Keplerian operation, as a logical process, be really identical
+with what takes place in acknowledged induction, the definition of
+induction ought to be so widened as to take it in; since scientific
+language ought to adapt itself to the true relations which subsist
+between the things it is employed to designate. Here then it is that I
+am at issue with Dr. Whewell. He does think the operations identical. He
+allows of no logical process in any case of induction, other than what
+there was in Kepler's case, namely, guessing until a guess is found
+which tallies with the facts; and accordingly, as we shall see
+hereafter, he rejects all canons of induction, because it is not by
+means of them that we guess. Dr. Whewell's theory of the logic of
+science would be very perfect if it did not pass over altogether the
+question of Proof. But in my apprehension there is such a thing as
+proof, and inductions differ altogether from descriptions in their
+relation to that element. Induction is proof; it is inferring something
+unobserved from something observed: it requires, therefore, an
+appropriate test of proof; and to provide that test, is the special
+purpose of inductive logic. When, on the contrary, we merely collate
+known observations, and, in Dr. Whewell's phraseology, connect them by
+means of a new conception; if the conception does serve to connect the
+observations, we have all we want. As the proposition in which it is
+embodied pretends to no other truth than what it may share with many
+other modes of representing the same facts, to be consistent with the
+facts is all it requires: it neither needs nor admits of proof; though
+it may serve to prove other things, inasmuch as, by placing the facts in
+mental connexion with other facts, not previously seen to resemble them,
+it assimilates the case to another class of phenomena, concerning which
+real Inductions have already been made. Thus Kepler's so-called law
+brought the orbit of Mars into the class ellipse, and by doing so,
+proved all the properties of an ellipse <span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span>to be true of the orbit: but in
+this proof Kepler's law supplied the minor premise, and not (as is the
+case with real Inductions) the major.</p>
+
+<p>Dr. Whewell calls nothing Induction where there is not a new mental
+conception introduced, and everything induction where there is. But this
+is to confound two very different things, Invention and Proof. The
+introduction of a new conception belongs to Invention: and invention may
+be required in any operation, but is the essence of none. A new
+conception may be introduced for descriptive purposes, and so it may for
+inductive purposes. But it is so far from constituting induction, that
+induction does not necessarily stand in need of it. Most inductions
+require no conception but what was present in every one of the
+particular instances on which the induction is grounded. That all men
+are mortal is surely an inductive conclusion; yet no new conception is
+introduced by it. Whoever knows that any man has died, has all the
+conceptions involved in the inductive generalization. But Dr. Whewell
+considers the process of invention which consists in framing a new
+conception consistent with the facts, to be not merely a necessary part
+of all induction, but the whole of it.</p>
+
+<p>The mental operation which extracts from a number of detached
+observations certain general characters in which the observed phenomena
+resemble one another, or resemble other known facts, is what Bacon,
+Locke, and most subsequent metaphysicians, have understood by the word
+Abstraction. A general expression obtained by abstraction, connecting
+known facts by means of common characters, but without concluding from
+them to unknown, may, I think, with strict logical correctness, be
+termed a Description; nor do I know in what other way things can ever be
+described. My position, however, does not depend on the employment of
+that particular word; I am quite content to use Dr. Whewell's term
+Colligation, or the more general phrases, "mode of representing, or of
+expressing, phenomena:" provided it be clearly seen that the process is
+not Induction, but something radically different.</p>
+
+<p><span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span></p><p>What more may usefully be said on the subject of Colligation, or of the
+correlative expression invented by Dr. Whewell, the Explication of
+Conceptions, and generally on the subject of ideas and mental
+representations as connected with the study of facts, will find a more
+appropriate place in the Fourth Book, on the Operations Subsidiary to
+Induction: to which I must refer the reader for the removal of any
+difficulty which the present discussion may have left.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_III" id="BOOK_III_CHAPTER_III"></a>CHAPTER III.<br />
+
+OF THE GROUND OF INDUCTION.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_III_1">� 1.</a> Induction properly so called, as distinguished from those mental
+operations, sometimes though improperly designated by the name, which I
+have attempted in the preceding chapter to characterize, may, then, be
+summarily defined as Generalization from Experience. It consists in
+inferring from some individual instances in which a phenomenon is
+observed to occur, that it occurs in all instances of a certain class;
+namely, in all which <i>resemble</i> the former, in what are regarded as the
+material circumstances.</p>
+
+<p>In what way the material circumstances are to be distinguished from
+those which are immaterial, or why some of the circumstances are
+material and others not so, we are not yet ready to point out. We must
+first observe, that there is a principle implied in the very statement
+of what Induction is; an assumption with regard to the course of nature
+and the order of the universe; namely, that there are such things in
+nature as parallel cases; that what happens once, will, under a
+sufficient degree of similarity of circumstances, happen again, and not
+only again, but as often as the same circumstances recur. This, I say,
+is an assumption, involved in every case of induction. And, if we
+consult the actual course of nature, we find that the assumption is
+warranted. The universe, so far as known to us, is so constituted, that
+whatever is true in any one case, is true in all cases of a certain
+description; the only difficulty is, to find what description.</p>
+
+<p>This universal fact, which is our warrant for all inferences from
+experience, has been described by different philosophers in different
+forms of language: that the course of nature is uniform; that the
+universe is governed by general laws; and <span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span>the like. One of the most
+usual of these modes of expression, but also one of the most inadequate,
+is that which has been brought into familiar use by the metaphysicians
+of the school of Reid and Stewart. The disposition of the human mind to
+generalize from experience,&mdash;a propensity considered by these
+philosophers as an instinct of our nature,&mdash;they usually describe under
+some such name as "our intuitive conviction that the future will
+resemble the past." Now it has been well pointed out by Mr. Bailey,<a name="FNanchor_8_89" id="FNanchor_8_89"></a><a href="#Footnote_8_89" class="fnanchor">[8]</a>
+that (whether the tendency be or not an original and ultimate element of
+our nature), Time, in its modifications of past, present, and future,
+has no concern either with the belief itself, or with the grounds of it.
+We believe that fire will burn to-morrow, because it burned to-day and
+yesterday; but we believe, on precisely the same grounds, that it burned
+before we were born, and that it burns this very day in Cochin-China. It
+is not from the past to the future, as past and future, that we infer,
+but from the known to the unknown; from facts observed to facts
+unobserved; from what we have perceived, or been directly conscious of,
+to what has not come within our experience. In this last predicament is
+the whole region of the future; but also the vastly greater portion of
+the present and of the past.</p>
+
+<p>Whatever be the most proper mode of expressing it, the proposition that
+the course of nature is uniform, is the fundamental principle, or
+general axiom, of Induction. It would yet be a great error to offer this
+large generalization as any explanation of the inductive process. On the
+contrary, I hold it to be itself an instance of induction, and induction
+by no means of the most obvious kind. Far from being the first induction
+we make, it is one of the last, or at all events one of those which are
+latest in attaining strict philosophical accuracy. As a general maxim,
+indeed, it has scarcely entered into the minds of any but philosophers;
+nor even by them, as we shall have many opportunities of remarking, have
+its extent and limits been always very justly conceived. The truth is,
+that this great generalization is itself founded on prior
+generalizations. <span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span>The obscurer laws of nature were discovered by means
+of it, but the more obvious ones must have been understood and assented
+to as general truths before it was ever heard of. We should never have
+thought of affirming that all phenomena take place according to general
+laws, if we had not first arrived, in the case of a great multitude of
+phenomena, at some knowledge of the laws themselves; which could be done
+no otherwise than by induction. In what sense, then, can a principle,
+which is so far from being our earliest induction, be regarded as our
+warrant for all the others? In the only sense, in which (as we have
+already seen) the general propositions which we place at the head of our
+reasonings when we throw them into syllogisms, ever really contribute to
+their validity. As Archbishop Whately remarks, every induction is a
+syllogism with the major premise suppressed; or (as I prefer expressing
+it) every induction may be thrown into the form of a syllogism, by
+supplying a major premise. If this be actually done, the principle which
+we are now considering, that of the uniformity of the course of nature,
+will appear as the ultimate major premise of all inductions, and will,
+therefore, stand to all inductions in the relation in which, as has been
+shown at so much length, the major proposition of a syllogism always
+stands to the conclusion; not contributing at all to prove it, but being
+a necessary condition of its being proved; since no conclusion is
+proved, for which there cannot be found a true major premise.<a name="FNanchor_9_90" id="FNanchor_9_90"></a><a href="#Footnote_9_90" class="fnanchor">[9]</a></p>
+
+<p><span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span></p><p>The statement, that the uniformity of the course of nature is the
+ultimate major premise in all cases of induction, may be thought to
+require some explanation. The immediate major premise in every inductive
+argument, it certainly is not. Of that, Archbishop Whately's must be
+held to be the correct account. The induction, "John, Peter, &amp;c. are
+mortal, therefore all mankind are mortal," may, as he justly says, be
+thrown into a syllogism by prefixing as a major premise (what is at any
+rate a necessary condition of the validity of the argument) namely, that
+what is true of John, Peter, &amp;c. is true of all mankind. But how came we
+by this major premise? It is not self-evident; nay, in all cases of
+unwarranted generalization, it is not true. How, then, is it arrived at?
+Necessarily either by induction or ratiocination; and if by induction,
+the process, like all other inductive arguments, may be thrown into the
+form of a syllogism. This previous syllogism it is, therefore, necessary
+to construct. There is, in the long run, only one possible construction.
+The real proof that what is true of John, Peter, &amp;c. is true of all
+mankind, can only be, that a different supposition would be inconsistent
+with the uniformity which we know to exist in the course of nature.
+<span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span>Whether there would be this inconsistency or not, may be a matter of
+long and delicate inquiry; but unless there would, we have no sufficient
+ground for the major of the inductive syllogism. It hence appears, that
+if we throw the whole course of any inductive argument into a series of
+syllogisms, we shall arrive by more or fewer steps at an ultimate
+syllogism, which will have for its major premise the principle, or
+axiom, of the uniformity of the course of nature.<a name="FNanchor_10_91" id="FNanchor_10_91"></a><a href="#Footnote_10_91" class="fnanchor">[10]</a></p>
+
+<p>It was not to be expected that in the case of this axiom, any more than
+of other axioms, there should be unanimity among thinkers with respect
+to the grounds on which it is to be received as true. I have already
+stated that I regard it as itself a generalization from experience.
+Others hold it to be a principle which, antecedently to any verification
+by experience, we are compelled by the constitution of our thinking
+faculty to assume as true. Having so recently, and at so much length,
+combated a similar doctrine as applied to the axioms of mathematics, by
+arguments which are in a great measure applicable to the present case, I
+shall defer the more particular discussion of this controverted point in
+regard to the fundamental axiom of induction, until a more advanced
+period of our inquiry.<a name="FNanchor_11_92" id="FNanchor_11_92"></a><a href="#Footnote_11_92" class="fnanchor">[11]</a> <span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span>At present it is of more importance to
+understand thoroughly the import of the axiom itself. For the
+proposition, that the course of nature is uniform, possesses rather the
+brevity suitable to popular, than the precision requisite in
+philosophical language: its terms require to be explained, and a
+stricter than their ordinary signification given to them, before the
+truth of the assertion can be admitted.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_III_2">� 2.</a> Every person's consciousness assures him that he does not always
+expect uniformity in the course of events; he does not always believe
+that the unknown will be similar to the known, that the future will
+resemble the past. Nobody believes that the succession of rain and fine
+weather will be the same in every future year as in the present. Nobody
+expects to have the same dreams repeated every night. On the contrary,
+everybody mentions it as something extraordinary, if the course of
+nature is constant, and resembles itself, in these particulars. To look
+for constancy where constancy is not to be expected, as for instance
+that a day which has once brought good fortune will always be a
+fortunate day, is justly accounted superstition.</p>
+
+<p>The course of nature, in truth, is not only uniform, it is also
+infinitely various. Some phenomena are always seen to recur in the very
+same combinations in which we met with them at first; others seem
+altogether capricious; while some, which we had been accustomed to
+regard as bound down exclusively to a particular set of combinations, we
+unexpectedly find detached from some of the elements with which we had
+hitherto found them conjoined, and united to others of quite a contrary
+description. To an inhabitant of Central Africa, fifty years ago, no
+fact probably appeared to rest on more uniform experience than this,
+that all human beings are black. To Europeans, not many years ago, the
+proposition, All swans are white, appeared an equally unequivocal
+instance of uniformity in the course of nature. Further experience has
+proved to both that they were mistaken; but they had to wait fifty
+centuries for this experience. During that long time, <span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span>mankind believed
+in an uniformity of the course of nature where no such uniformity really
+existed.</p>
+
+<p>According to the notion which the ancients entertained of induction, the
+foregoing were cases of as legitimate inference as any inductions
+whatever. In these two instances, in which, the conclusion being false,
+the ground of inference must have been insufficient, there was,
+nevertheless, as much ground for it as this conception of induction
+admitted of. The induction of the ancients has been well described by
+Bacon, under the name of "Inductio per enumerationem simplicem, ubi non
+reperitur instantia contradictoria." It consists in ascribing the
+character of general truths to all propositions which are true in every
+instance that we happen to know of. This is the kind of induction which
+is natural to the mind when unaccustomed to scientific methods. The
+tendency, which some call an instinct, and which others account for by
+association, to infer the future from the past, the known from the
+unknown, is simply a habit of expecting that what has been found true
+once or several times, and never yet found false, will be found true
+again. Whether the instances are few or many, conclusive or
+inconclusive, does not much affect the matter: these are considerations
+which occur only on reflection; the unprompted tendency of the mind is
+to generalize its experience, provided this points all in one direction;
+provided no other experience of a conflicting character comes unsought.
+The notion of seeking it, of experimenting for it, of <i>interrogating</i>
+nature (to use Bacon's expression) is of much later growth. The
+observation of nature, by uncultivated intellects, is purely passive:
+they accept the facts which present themselves, without taking the
+trouble of searching for more: it is a superior mind only which asks
+itself what facts are needed to enable it to come to a safe conclusion,
+and then looks out for these.</p>
+
+<p>But though we have always a propensity to generalize from unvarying
+experience, we are not always warranted in doing so. Before we can be at
+liberty to conclude that something is universally true because we have
+never known an <span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span>instance to the contrary, we must have reason to believe
+that if there were in nature any instances to the contrary, we should
+have known of them. This assurance, in the great majority of cases, we
+cannot have, or can have only in a very moderate degree. The possibility
+of having it, is the foundation on which we shall see hereafter that
+induction by simple enumeration may in some remarkable cases amount
+practically to proof.<a name="FNanchor_12_93" id="FNanchor_12_93"></a><a href="#Footnote_12_93" class="fnanchor">[12]</a> No such assurance, however, can be had, on any
+of the ordinary subjects of scientific inquiry. Popular notions are
+usually founded on induction by simple enumeration; in science it
+carries us but a little way. We are forced to begin with it; we must
+often rely on it provisionally, in the absence of means of more
+searching investigation. But, for the accurate study of nature, we
+require a surer and a more potent instrument.</p>
+
+<p>It was, above all, by pointing out the insufficiency of this rude and
+loose conception of Induction, that Bacon merited the title so generally
+awarded to him, of Founder of the Inductive Philosophy. The value of his
+own contributions to a more philosophical theory of the subject has
+certainly been exaggerated. Although (along with some fundamental
+errors) his writings contain, more or less fully developed, several of
+the most important principles of the Inductive Method, physical
+investigation has now far outgrown the Baconian conception of Induction.
+Moral and political inquiry, indeed, are as yet far behind that
+conception. The current and approved modes of reasoning on these
+subjects are still of the same vicious description against which Bacon
+protested; the method almost exclusively employed by those professing to
+treat such matters inductively, is the very <i>inductio per enumerationem
+simplicem</i> which he condemns; and the experience which we hear so
+confidently appealed to by all sects, parties, and interests, is still,
+in his own emphatic words, <i>mera palpatio</i>.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_III_3">� 3.</a> In order to a better understanding of the problem <span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span>which the
+logician must solve if he would establish a scientific theory of
+Induction, let us compare a few cases of incorrect inductions with
+others which are acknowledged to be legitimate. Some, we know, which
+were believed for centuries to be correct, were nevertheless incorrect.
+That all swans are white, cannot have been a good induction, since the
+conclusion has turned out erroneous. The experience, however, on which
+the conclusion rested, was genuine. From the earliest records, the
+testimony of the inhabitants of the known world was unanimous on the
+point. The uniform experience, therefore, of the inhabitants of the
+known world, agreeing in a common result, without one known instance of
+deviation from that result, is not always sufficient to establish a
+general conclusion.</p>
+
+<p>But let us now turn to an instance apparently not very dissimilar to
+this. Mankind were wrong, it seems, in concluding that all swans were
+white: are we also wrong, when we conclude that all men's heads grow
+above their shoulders, and never below, in spite of the conflicting
+testimony of the naturalist Pliny? As there were black swans, though
+civilized people had existed for three thousand years on the earth
+without meeting with them, may there not also be "men whose heads do
+grow beneath their shoulders," notwithstanding a rather less perfect
+unanimity of negative testimony from observers? Most persons would
+answer No; it was more credible that a bird should vary in its colour,
+than that men should vary in the relative position of their principal
+organs. And there is no doubt that in so saying they would be right: but
+to say why they are right, would be impossible, without entering more
+deeply than is usually done, into the true theory of Induction.</p>
+
+<p>Again, there are cases in which we reckon with the most unfailing
+confidence upon uniformity, and other cases in which we do not count
+upon it at all. In some we feel complete assurance that the future will
+resemble the past, the unknown be precisely similar to the known. In
+others, however invariable may be the result obtained from the instances
+which have been observed, we draw from them no more than <span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span>a very feeble
+presumption that the like result will hold in all other cases. That a
+straight line is the shortest distance between two points, we do not
+doubt to be true even in the region of the fixed stars. When a chemist
+announces the existence and properties of a newly-discovered substance,
+if we confide in his accuracy, we feel assured that the conclusions he
+has arrived at will hold universally, though the induction be founded
+but on a single instance. We do not withhold our assent, waiting for a
+repetition of the experiment; or if we do, it is from a doubt whether
+the one experiment was properly made, not whether if properly made it
+would be conclusive. Here, then, is a general law of nature, inferred
+without hesitation from a single instance; an universal proposition from
+a singular one. Now mark another case, and contrast it with this. Not
+all the instances which have been observed since the beginning of the
+world, in support of the general proposition that all crows are black,
+would be deemed a sufficient presumption of the truth of the
+proposition, to outweigh the testimony of one unexceptionable witness
+who should affirm that in some region of the earth not fully explored,
+he had caught and examined a crow, and had found it to be grey.</p>
+
+<p>Why is a single instance, in some cases, sufficient for a complete
+induction, while in others, myriads of concurring instances, without a
+single exception known or presumed, go such a very little way towards
+establishing an universal proposition? Whoever can answer this question
+knows more of the philosophy of logic than the wisest of the ancients,
+and has solved the problem of induction.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_IV" id="BOOK_III_CHAPTER_IV"></a>CHAPTER IV.<br />
+
+OF LAWS OF NATURE.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IV_1">� 1.</a> In the contemplation of that uniformity in the course of nature,
+which is assumed in every inference from experience, one of the first
+observations that present themselves is, that the uniformity in question
+is not properly uniformity, but uniformities. The general regularity
+results from the coexistence of partial regularities. The course of
+nature in general is constant, because the course of each of the various
+phenomena that compose it is so. A certain fact invariably occurs
+whenever certain circumstances are present, and does not occur when they
+are absent; the like is true of another fact; and so on. From these
+separate threads of connexion between parts of the great whole which we
+term nature, a general tissue of connexion unavoidably weaves itself, by
+which the whole is held together. If A is always accompanied by D, B by
+E, and C by F, it follows that A B is accompanied by D E, A C by D F, B
+C by E F, and finally A B C by D E F; and thus the general character of
+regularity is produced, which, along with and in the midst of infinite
+diversity, pervades all nature.</p>
+
+<p>The first point, therefore, to be noted in regard to what is called the
+uniformity of the course of nature, is, that it is itself a complex
+fact, compounded of all the separate uniformities which exist in respect
+to single phenomena. These various uniformities, when ascertained by
+what is regarded as a sufficient induction, we call in common parlance,
+Laws of Nature. Scientifically speaking, that title is employed in a
+more restricted sense, to designate the uniformities when reduced to
+their most simple expression. Thus in the illustration already employed,
+there were seven uniformities; all of which, if considered sufficiently
+certain, would in the more lax application <span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span>of the term, be called laws
+of nature. But of the seven, three alone are properly distinct and
+independent: these being presupposed, the others follow of course. The
+three first, therefore, according to the stricter acceptation, are
+called laws of nature; the remainder not; because they are in truth mere
+<i>cases</i> of the three first; virtually included in them; said, therefore,
+to <i>result</i> from them: whoever affirms those three has already affirmed
+all the rest.</p>
+
+<p>To substitute real examples for symbolical ones, the following are three
+uniformities, or call them laws of nature: the law that air has weight,
+the law that pressure on a fluid is propagated equally in all
+directions, and the law that pressure in one direction, not opposed by
+equal pressure in the contrary direction, produces motion, which does
+not cease until equilibrium is restored. From these three uniformities
+we should be able to predict another uniformity, namely, the rise of the
+mercury in the Torricellian tube. This, in the stricter use of the
+phrase, is not a law of nature. It is the result of laws of nature. It
+is a <i>case</i> of each and every one of the three laws: and is the only
+occurrence by which they could all be fulfilled. If the mercury were not
+sustained in the barometer, and sustained at such a height that the
+column of mercury were equal in weight to a column of the atmosphere of
+the same diameter; here would be a case, either of the air not pressing
+upon the surface of the mercury with the force which is called its
+weight, or of the downward pressure on the mercury not being propagated
+equally in an upward direction, or of a body pressed in one direction
+and not in the direction opposite, either not moving in the direction in
+which it is pressed, or stopping before it had attained equilibrium. If
+we knew, therefore, the three simple laws, but had never tried the
+Torricellian experiment, we might <i>deduce</i> its result from those laws.
+The known weight of the air, combined with the position of the
+apparatus, would bring the mercury within the first of the three
+inductions; the first induction would bring it within the second, and
+the second within the third, in the manner which we characterized in
+treating of Ratiocination. We should thus come to know the more complex
+uniformity, independently <span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span>of specific experience, through our knowledge
+of the simpler ones from which it results; though, for reasons which
+will appear hereafter, <i>verification</i> by specific experience would still
+be desirable, and might possibly be indispensable.</p>
+
+<p>Complex uniformities which, like this, are mere cases of simpler ones,
+and have, therefore, been virtually affirmed in affirming those, may
+with propriety be called <i>laws</i>, but can scarcely, in the strictness of
+scientific speech, be termed Laws of Nature. It is the custom in
+science, wherever regularity of any kind can be traced, to call the
+general proposition which expresses the nature of that regularity, a
+law; as when, in mathematics, we speak of the law of decrease of the
+successive terms of a converging series. But the expression <i>law of
+nature</i> has generally been employed with a sort of tacit reference to
+the original sense of the word law, namely, the expression of the will
+of a superior. When, therefore, it appeared that any of the uniformities
+which were observed in nature, would result spontaneously from certain
+other uniformities, no separate act of creative will being supposed
+necessary for the production of the derivative uniformities, these have
+not usually been spoken of as laws of nature. According to one mode of
+expression, the question, What are the laws of nature? may be stated
+thus:&mdash;What are the fewest and simplest assumptions, which being
+granted, the whole existing order of nature would result? Another mode
+of stating it would be thus: What are the fewest general propositions
+from which all the uniformities which exist in the universe might be
+deductively inferred?</p>
+
+<p>Every great advance which marks an epoch in the progress of science, has
+consisted in a step made towards the solution of this problem. Even a
+simple colligation of inductions already made, without any fresh
+extension of the inductive inference, is already an advance in that
+direction. When Kepler expressed the regularity which exists in the
+observed motions of the heavenly bodies, by the three general
+propositions called his laws, he, in so doing, pointed out three simple
+suppositions which, instead of a much greater number, would suffice to
+construct the whole scheme of the heavenly motions, <span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span>so far as it was
+known up to that time. A similar and still greater step was made when
+these laws, which at first did not seem to be included in any more
+general truths, were discovered to be cases of the three laws of motion,
+as obtaining among bodies which mutually tend towards one another with a
+certain force, and have had a certain instantaneous impulse originally
+impressed upon them. After this great discovery, Kepler's three
+propositions, though still called laws, would hardly, by any person
+accustomed to use language with precision, be termed laws of nature:
+that phrase would be reserved for the simpler and more general laws into
+which Newton is said to have resolved them.</p>
+
+<p>According to this language, every well-grounded inductive generalization
+is either a law of nature, or a result of laws of nature, capable, if
+those laws are known, of being predicted from them. And the problem of
+Inductive Logic may be summed up in two questions: how to ascertain the
+laws of nature; and how, after having ascertained them, to follow them
+into their results. On the other hand, we must not suffer ourselves to
+imagine that this mode of statement amounts to a real analysis, or to
+anything but a mere verbal transformation of the problem; for the
+expression, Laws of Nature, <i>means</i> nothing but the uniformities which
+exist among natural phenomena (or, in other words, the results of
+induction), when reduced to their simplest expression. It is, however,
+something to have advanced so far, as to see that the study of nature is
+the study of laws, not <i>a</i> law; of uniformities, in the plural number:
+that the different natural phenomena have their separate rules or modes
+of taking place, which, though much intermixed and entangled with one
+another, may, to a certain extent, be studied apart: that (to resume our
+former metaphor) the regularity which exists in nature is a web composed
+of distinct threads, and only to be understood by tracing each of the
+threads separately; for which purpose it is often necessary to unravel
+some portion of the web, and exhibit the fibres apart. The rules of
+experimental inquiry are the contrivances for unravelling the web.</p>
+
+
+<p><span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_IV_2">� 2.</a> In thus attempting to ascertain the general order of nature by
+ascertaining the particular order of the occurrence of each one of the
+phenomena of nature, the most scientific proceeding can be no more than
+an improved form of that which was primitively pursued by the human
+understanding, while undirected by science. When mankind first formed
+the idea of studying phenomena according to a stricter and surer method
+than that which they had in the first instance spontaneously adopted,
+they did not, conformably to the well-meant but impracticable precept of
+Descartes, set out from the supposition that nothing had been already
+ascertained. Many of the uniformities existing among phenomena are so
+constant, and so open to observation, as to force themselves upon
+involuntary recognition. Some facts are so perpetually and familiarly
+accompanied by certain others, that mankind learnt, as children learn,
+to expect the one where they found the other, long before they knew how
+to put their expectation into words by asserting, in a proposition, the
+existence of a connexion between those phenomena. No science was needed
+to teach that food nourishes, that water drowns, or quenches thirst,
+that the sun gives light and heat, that bodies fall to the ground. The
+first scientific inquirers assumed these and the like as known truths,
+and set out from them to discover others which were unknown: nor were
+they wrong in so doing, subject, however, as they afterwards began to
+see, to an ulterior revision of these spontaneous generalizations
+themselves, when the progress of knowledge pointed out limits to them,
+or showed their truth to be contingent on some circumstance not
+originally attended to. It will appear, I think, from the subsequent
+part of our inquiry, that there is no logical fallacy in this mode of
+proceeding; but we may see already that any other mode is rigorously
+impracticable: since it is impossible to frame any scientific method of
+induction, or test of the correctness of inductions, unless on the
+hypothesis that some inductions deserving of reliance have been already
+made.</p>
+
+<p>Let us revert, for instance, to one of our former illustrations, <span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span>and
+consider why it is that, with exactly the same amount of evidence, both
+negative and positive, we did not reject the assertion that there are
+black swans, while we should refuse credence to any testimony which
+asserted that there were men wearing their heads underneath their
+shoulders. The first assertion was more credible than the latter. But
+why more credible? So long as neither phenomenon had been actually
+witnessed, what reason was there for finding the one harder to be
+believed than the other? Apparently because there is less constancy in
+the colours of animals, than in the general structure of their anatomy.
+But how do we know this? Doubtless, from experience. It appears, then,
+that we need experience to inform us, in what degree, and in what cases,
+or sort of cases, experience is to be relied on. Experience must be
+consulted in order to learn from it under what circumstances arguments
+from it will be valid. We have no ulterior test to which we subject
+experience in general; but we make experience its own test. Experience
+testifies, that among the uniformities which it exhibits or seems to
+exhibit, some are more to be relied on than others; and uniformity,
+therefore, may be presumed, from any given number of instances, with a
+greater degree of assurance, in proportion as the case belongs to a
+class in which the uniformities have hitherto been found more uniform.</p>
+
+<p>This mode of correcting one generalization by means of another, a
+narrower generalization by a wider, which common sense suggests and
+adopts in practice, is the real type of scientific Induction. All that
+art can do is but to give accuracy and precision to this process, and
+adapt it to all varieties of cases, without any essential alteration in
+its principle.</p>
+
+<p>There are of course no means of applying such a test as that above
+described, unless we already possess a general knowledge of the
+prevalent character of the uniformities existing throughout nature. The
+indispensable foundation, therefore, of a scientific formula of
+induction, must be a survey of the inductions to which mankind have been
+conducted in unscientific practice; with the special purpose of
+<span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span>ascertaining what kinds of uniformities have been found perfectly
+invariable, pervading all nature, and what are those which have been
+found to vary with difference of time, place, or other changeable
+circumstances.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IV_3">� 3.</a> The necessity of such a survey is confirmed by the consideration,
+that the stronger inductions are the touchstone to which we always
+endeavour to bring the weaker. If we find any means of deducing one of
+the less strong inductions from stronger ones, it acquires, at once, all
+the strength of those from which it is deduced; and even adds to that
+strength; since the independent experience on which the weaker induction
+previously rested, becomes additional evidence of the truth of the
+better established law in which it is now found to be included. We may
+have inferred, from historical evidence, that the uncontrolled power of
+a monarch, of an aristocracy, or of the majority, will often be abused:
+but we are entitled to rely on this generalization with much greater
+assurance when it is shown to be a corollary from still better
+established facts; the very low degree of elevation of character ever
+yet attained by the average of mankind, and the little efficacy, for the
+most part, of the modes of education hitherto practised, in maintaining
+the predominance of reason and conscience over the selfish propensities.
+It is at the same time obvious that even these more general facts derive
+an accession of evidence from the testimony which history bears to the
+effects of despotism. The strong induction becomes still stronger when a
+weaker one has been bound up with it.</p>
+
+<p>On the other hand, if an induction conflicts with stronger inductions,
+or with conclusions capable of being correctly deduced from them, then,
+unless on reconsideration it should appear that some of the stronger
+inductions have been expressed with greater universality than their
+evidence warrants, the weaker one must give way. The opinion so long
+prevalent that a comet, or any other unusual appearance in the heavenly
+regions, was the precursor of calamities to mankind, or to those at
+least who witnessed it; the belief in the veracity of the oracles of
+Delphi or Dodona; the reliance <span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span>on astrology, or on the
+weather-prophecies in almanacs, were doubtless inductions supposed to be
+grounded on experience:<a name="FNanchor_13_94" id="FNanchor_13_94"></a><a href="#Footnote_13_94" class="fnanchor">[13]</a> and faith in such delusions seems quite
+capable of holding out against a great multitude of failures, provided
+it be nourished by a reasonable number of casual coincidences between
+the prediction and the event. What has really put an end to these
+insufficient inductions, is their inconsistency with the stronger
+inductions subsequently obtained by scientific inquiry, respecting the
+causes on which terrestrial events really depend; and where those
+scientific truths have not yet penetrated, the same or similar delusions
+still prevail.</p>
+
+<p>It may be affirmed as a general principle, that all inductions, whether
+strong or weak, which can be connected by ratiocination, are
+confirmatory of one another; while any which lead deductively to
+consequences that are incompatible, <span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span>become mutually each other's test,
+showing that one or other must be given up, or at least more guardedly
+expressed. In the case of inductions which confirm each other, the one
+which becomes a conclusion from ratiocination rises to at least the
+level of certainty of the weakest of those from which it is deduced;
+while in general all are more or less increased in certainty. Thus the
+Torricellian experiment, though a mere case of three more general laws,
+not only strengthened greatly the evidence on which those laws rested,
+but converted one of them (the weight of the atmosphere) from a doubtful
+generalization into a completely established doctrine.</p>
+
+<p>If, then, a survey of the uniformities which have been ascertained to
+exist in nature, should point out some which, as far as any human
+purpose requires certainty, may be considered quite certain and quite
+universal; then by means of these uniformities we may be able to raise
+multitudes of other inductions to the same point in the scale. For if we
+can show, with respect to any inductive inference, that either it must
+be true, or one of these certain and universal inductions must admit of
+an exception; the former generalization will attain the same certainty,
+and indefeasibleness within the bounds assigned to it, which are the
+attributes of the latter. It will be proved to be a law; and if not a
+result of other and simpler laws, it will be a law of nature.</p>
+
+<p>There are such certain and universal inductions; and it is because there
+are such, that a Logic of Induction is possible.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_V" id="BOOK_III_CHAPTER_V"></a>CHAPTER V.<br />
+
+OF THE LAW OF UNIVERSAL CAUSATION.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_1">� 1.</a> The phenomena of nature exist in two distinct relations to one
+another; that of simultaneity, and that of succession. Every phenomenon
+is related, in an uniform manner, to some phenomena that coexist with
+it, and to some that have preceded and will follow it.</p>
+
+<p>Of the uniformities which exist among synchronous phenomena, the most
+important, on every account, are the laws of number; and next to them
+those of space, or, in other words, of extension and figure. The laws of
+number are common to synchronous and successive phenomena. That two and
+two make four, is equally true whether the second two follow the first
+two or accompany them. It is as true of days and years as of feet and
+inches. The laws of extension and figure (in other words, the theorems
+of geometry, from its lowest to its highest branches) are, on the
+contrary, laws of simultaneous phenomena only. The various parts of
+space, and of the objects which are said to fill space, coexist; and the
+unvarying laws which are the subject of the science of geometry, are an
+expression of the mode of their coexistence.</p>
+
+<p>This is a class of laws, or in other words, of uniformities, for the
+comprehension and proof of which it is not necessary to suppose any
+lapse of time, any variety of facts or events succeeding one another. If
+all the objects in the universe were unchangeably fixed, and had
+remained in that condition from eternity, the propositions of geometry
+would still be true of those objects. All things which possess
+extension, or, in other words, which fill space, are subject to
+geometrical laws. Possessing extension, they possess figure; possessing
+figure, they must possess some figure in particular, and have all the
+properties which geometry assigns to that figure. If one body be <span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span>a
+sphere and another a cylinder, of equal height and diameter, the one
+will be exactly two-thirds of the other, let the nature and quality of
+the material be what it will. Again, each body, and each point of a
+body, must occupy some place or position among other bodies; and the
+position of two bodies relatively to each other, of whatever nature the
+bodies be, may be unerringly inferred from the position of each of them
+relatively to any third body.</p>
+
+<p>In the laws of number, then, and in those of space, we recognise in the
+most unqualified manner, the rigorous universality of which we are in
+quest. Those laws have been in all ages the type of certainty, the
+standard of comparison for all inferior degrees of evidence. Their
+invariability is so perfect, that it renders us unable even to conceive
+any exception to them; and philosophers have been led, though (as I have
+endeavoured to show) erroneously, to consider their evidence as lying
+not in experience, but in the original constitution of the intellect. If
+therefore, from the laws of space and number, we were able to deduce
+uniformities of any other description, this would be conclusive evidence
+to us that those other uniformities possessed the same rigorous
+certainty. But this we cannot do. From laws of space and number alone,
+nothing can be deduced but laws of space and number.</p>
+
+<p>Of all truths relating to phenomena, the most valuable to us are those
+which relate to the order of their succession. On a knowledge of these
+is founded every reasonable anticipation of future facts, and whatever
+power we possess of influencing those facts to our advantage. Even the
+laws of geometry are chiefly of practical importance to us as being a
+portion of the premises from which the order of the succession of
+phenomena may be inferred. Inasmuch as the motion of bodies, the action
+of forces, and the propagation of influences of all sorts, take place in
+certain lines and over definite spaces, the properties of those lines
+and spaces are an important part of the laws to which those phenomena
+are themselves subject. Again, motions, forces or other influences, and
+times, are numerable quantities; and the properties of number are
+applicable to them as to all other things. But though the laws of number
+<span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span>and space are important elements in the ascertainment of uniformities
+of succession, they can do nothing towards it when taken by themselves.
+They can only be made instrumental to that purpose when we combine with
+them additional premises, expressive of uniformities of succession
+already known. By taking, for instance, as premises these propositions,
+that bodies acted upon by an instantaneous force move with uniform
+velocity in straight lines; that bodies acted upon by a continuous force
+move with accelerated velocity in straight lines; and that bodies acted
+upon by two forces in different directions move in the diagonal of a
+parallelogram, whose sides represent the direction and quantity of those
+forces; we may by combining these truths with propositions relating to
+the properties of straight lines and of parallelograms, (as that a
+triangle is half a parallelogram of the same base and altitude,) deduce
+another important uniformity of succession, viz., that a body moving
+round a centre of force describes areas proportional to the times. But
+unless there had been laws of succession in our premises, there could
+have been no truths of succession in our conclusions. A similar remark
+might be extended to every other class of phenomena really peculiar;
+and, had it been attended to, would have prevented many chimerical
+attempts at demonstrations of the indemonstrable, and explanations which
+do not explain.</p>
+
+<p>It is not, therefore, enough for us that the laws of space, which are
+only laws of simultaneous phenomena, and the laws of number, which
+though true of successive phenomena do not relate to their succession,
+possess the rigorous certainty and universality of which we are in
+search. We must endeavour to find some law of succession which has those
+same attributes, and is therefore fit to be made the foundation of
+processes for discovering, and of a test for verifying, all other
+uniformities of succession. This fundamental law must resemble the
+truths of geometry in their most remarkable peculiarity, that of never
+being, in any instance whatever, defeated or suspended by any change of
+circumstances.</p>
+
+<p>Now among all those uniformities in the succession of phenomena, which
+common observation is sufficient to bring <span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span>to light, there are very few
+which have any, even apparent, pretension to this rigorous
+indefeasibility: and of those few, one only has been found capable of
+completely sustaining it. In that one, however, we recognise a law which
+is universal also in another sense; it is coextensive with the entire
+field of successive phenomena, all instances whatever of succession
+being examples of it. This law is the Law of Causation. The truth that
+every fact which has a beginning has a cause, is coextensive with human
+experience.</p>
+
+<p>This generalization may appear to some minds not to amount to much,
+since after all it asserts only this: "it is a law; that every event
+depends on some law:" "it is a law, that there is a law for everything."
+We must not, however, conclude that the generality of the principle is
+merely verbal; it will be found on inspection to be no vague or
+unmeaning assertion, but a most important and really fundamental truth.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_2">� 2.</a> The notion of Cause being the root of the whole theory of
+Induction, it is indispensable that this idea should, at the very outset
+of our inquiry, be, with the utmost practicable degree of precision,
+fixed and determined. If, indeed, it were necessary for the purpose of
+inductive logic that the strife should be quelled, which has so long
+raged among the different schools of metaphysicians, respecting the
+origin and analysis of our idea of causation; the promulgation, or at
+least the general reception, of a true theory of induction, might be
+considered desperate for a long time to come. But the science of the
+Investigation of Truth by means of Evidence, is happily independent of
+many of the controversies which perplex the science of the ultimate
+constitution of the human mind, and is under no necessity of pushing the
+analysis of mental phenomena to that extreme limit which alone ought to
+satisfy a metaphysician.</p>
+
+<p>I premise, then, that when in the course of this inquiry I speak of the
+cause of any phenomenon, I do not mean a cause which is not itself a
+phenomenon; I make no research into the ultimate or ontological cause of
+anything. To adopt a distinction familiar in the writings of the Scotch
+metaphysicians, <span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span>and especially of Reid, the causes with which I concern
+myself are not <i>efficient</i>, but <i>physical</i> causes. They are causes in
+that sense alone, in which one physical fact is said to be the cause of
+another. Of the efficient causes of phenomena, or whether any such
+causes exist at all, I am not called upon to give an opinion. The notion
+of causation is deemed, by the schools of metaphysics most in vogue at
+the present moment, to imply a mysterious and most powerful tie, such as
+cannot, or at least does not, exist between any physical fact and that
+other physical fact on which it is invariably consequent, and which is
+popularly termed its cause: and thence is deduced the supposed necessity
+of ascending higher, into the essences and inherent constitution of
+things, to find the true cause, the cause which is not only followed by,
+but actually produces, the effect. No such necessity exists for the
+purposes of the present inquiry, nor will any such doctrine be found in
+the following pages. The only notion of a cause, which the theory of
+induction requires, is such a notion as can be gained from experience.
+The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it; independently of all
+consideration respecting the ultimate mode of production of phenomena,
+and of every other question regarding the nature of "Things in
+themselves."</p>
+
+<p>Between the phenomena, then, which exist at any instant, and the
+phenomena which exist at the succeeding instant, there is an invariable
+order of succession; and, as we said in speaking of the general
+uniformity of the course of nature, this web is composed of separate
+fibres; this collective order is made up of particular sequences,
+obtaining invariably among the separate parts. To certain facts, certain
+facts always do, and, as we believe, will continue to, succeed. The
+invariable antecedent is termed the cause; the invariable consequent,
+the effect. And the universality of the law of causation consists in
+this, that every consequent is connected in this manner with some
+particular antecedent, or set of antecedents. <span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span>Let the fact be what it
+may, if it has begun to exist, it was preceded by some fact or facts,
+with which it is invariably connected. For every event there exists some
+combination of objects or events, some given concurrence of
+circumstances, positive and negative, the occurrence of which is always
+followed by that phenomenon. We may not have found out what this
+concurrence of circumstances may be; but we never doubt that there is
+such a one, and that it never occurs without having the phenomenon in
+question as its effect or consequence. On the universality of this truth
+depends the possibility of reducing the inductive process to rules. The
+undoubted assurance we have that there is a law to be found if we only
+knew how to find it, will be seen presently to be the source from which
+the canons of the Inductive Logic derive their validity.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_3">� 3.</a> It is seldom, if ever, between a consequent and a single
+antecedent, that this invariable sequence subsists. It is usually
+between a consequent and the sum of several antecedents; the concurrence
+of all of them being requisite to produce, that is, to be certain of
+being followed by, the consequent. In such cases it is very common to
+single out one only of the antecedents under the denomination of Cause,
+calling the others merely Conditions. Thus, if a person eats of a
+particular dish, and dies in consequence, that is, would not have died
+if he had not eaten of it, people would be apt to say that eating of
+that dish was the cause of his death. There needs not, however, be any
+invariable connexion between eating of the dish and death; but there
+certainly is, among the circumstances which took place, some combination
+or other on which death is invariably consequent: as, for instance, the
+act of eating of the dish, combined with a particular bodily
+constitution, a particular state of present health, and perhaps even a
+certain state of the atmosphere; the whole of which circumstances
+perhaps constituted in this particular case the <i>conditions</i> of the
+phenomenon, or, in other words, the set of antecedents which determined
+it, and but for which it would not have happened. The real Cause, is the
+whole of these <span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span>antecedents; and we have, philosophically speaking, no
+right to give the name of cause to one of them, exclusively of the
+others. What, in the case we have supposed, disguises the incorrectness
+of the expression, is this: that the various conditions, except the
+single one of eating the food, were not <i>events</i> (that is, instantaneous
+changes, or successions of instantaneous changes) but <i>states</i>,
+possessing more or less of permanency; and might therefore have preceded
+the effect by an indefinite length of duration, for want of the event
+which was requisite to complete the required concurrence of conditions:
+while as soon as that event, eating the food, occurs, no other cause is
+waited for, but the effect begins immediately to take place: and hence
+the appearance is presented of a more immediate and close connexion
+between the effect and that one antecedent, than between the effect and
+the remaining conditions. But though we may think proper to give the
+name of cause to that one condition, the fulfilment of which completes
+the tale, and brings about the effect without further delay; this
+condition has really no closer relation to the effect than any of the
+other conditions has. The production of the consequent required that
+they should all <i>exist</i> immediately previous, though not that they
+should all <i>begin</i> to exist immediately previous. The statement of the
+cause is incomplete, unless in some shape or other we introduce all the
+conditions. A man takes mercury, goes out of doors, and catches cold. We
+say, perhaps, that the cause of his taking cold was exposure to the air.
+It is clear, however, that his having taken mercury may have been a
+necessary condition of catching cold; and though it might consist with
+usage to say that the cause of his attack was exposure to the air, to be
+accurate we ought to say that the cause was exposure to the air while
+under the effect of mercury.</p>
+
+<p>If we do not, when aiming at accuracy, enumerate all the conditions, it
+is only because some of them will in most cases be understood without
+being expressed, or because for the purpose in view they may without
+detriment be overlooked. For example, when we say, the cause of a man's
+death was <span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span>that his foot slipped in climbing a ladder, we omit as a
+thing unnecessary to be stated the circumstance of his weight, though
+quite as indispensable a condition of the effect which took place. When
+we say that the assent of the crown to a bill makes it law, we mean that
+the assent, being never given until all the other conditions are
+fulfilled, makes up the sum of the conditions, though no one now regards
+it as the principal one. When the decision of a legislative assembly has
+been determined by the casting vote of the chairman, we sometimes say
+that this one person was the cause of all the effects which resulted
+from the enactment. Yet we do not really suppose that his single vote
+contributed more to the result than that of any other person who voted
+in the affirmative; but, for the purpose we have in view, which is to
+insist on his individual responsibility, the part which any other person
+had in the transaction is not material.</p>
+
+<p>In all these instances the fact which was dignified with the name of
+cause, was the one condition which came last into existence. But it must
+not be supposed that in the employment of the term this or any other
+rule is always adhered to. Nothing can better show the absence of any
+scientific ground for the distinction between the cause of a phenomenon
+and its conditions, than the capricious manner in which we select from
+among the conditions that which we choose to denominate the cause.
+However numerous the conditions may be, there is hardly any of them
+which may not, according to the purpose of our immediate discourse,
+obtain that nominal pre-eminence. This will be seen by analysing the
+conditions of some one familiar phenomenon. For example, a stone thrown
+into water falls to the bottom. What are the conditions of this event?
+In the first place there must be a stone, and water, and the stone must
+be thrown into the water; but these suppositions forming part of the
+enunciation of the phenomenon itself, to include them also among the
+conditions would be a vicious tautology; and this class of conditions,
+therefore, have never received the name of cause from any but the
+Aristotelians, by whom they were called the <i>material</i> cause, <span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span><i>causa
+materialis</i>. The next condition is, there must be an earth: and
+accordingly it is often said, that the fall of a stone is caused by the
+earth; or by a power or property of the earth, or a force exerted by the
+earth, all of which are merely roundabout ways of saying that it is
+caused by the earth; or, lastly, the earth's attraction; which also is
+only a technical mode of saying that the earth causes the motion, with
+the additional particularity that the motion is towards the earth, which
+is not a character of the cause, but of the effect. Let us now pass to
+another condition. It is not enough that the earth should exist; the
+body must be within that distance from it, in which the earth's
+attraction preponderates over that of any other body. Accordingly we may
+say, and the expression would be confessedly correct, that the cause of
+the stone's falling is its being <i>within the sphere</i> of the earth's
+attraction. We proceed to a further condition. The stone is immersed in
+water: it is therefore a condition of its reaching the ground, that its
+specific gravity exceed that of the surrounding fluid, or in other words
+that it surpass in weight an equal volume of water. Accordingly any one
+would be acknowledged to speak correctly who said, that the cause of the
+stone's going to the bottom is its exceeding in specific gravity the
+fluid in which it is immersed.</p>
+
+<p>Thus we see that each and every condition of the phenomenon may be taken
+in its turn, and, with equal propriety in common parlance, but with
+equal impropriety in scientific discourse, may be spoken of as if it
+were the entire cause. And in practice, that particular condition is
+usually styled the cause, whose share in the matter is superficially the
+most conspicuous, or whose requisiteness to the production of the effect
+we happen to be insisting on at the moment. So great is the force of
+this last consideration, that it sometimes induces us to give the name
+of cause even to one of the negative conditions. We say, for example,
+The army was surprised because the sentinel was off his post. But since
+the sentinel's absence was not what created the enemy, or put the
+soldiers asleep, how did it cause them to be surprised? All that is
+really meant is, that the event would not have happened if he had <span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span>been
+at his duty. His being off his post was no producing cause, but the mere
+absence of a preventing cause: it was simply equivalent to his
+non-existence. From nothing, from a mere negation, no consequences can
+proceed. All effects are connected, by the law of causation, with some
+set of <i>positive</i> conditions; negative ones, it is true, being almost
+always required in addition. In other words, every fact or phenomenon
+which has a beginning, invariably arises when some certain combination
+of positive facts exists, provided certain other positive facts do not
+exist.</p>
+
+<p>There is, no doubt, a tendency (which our first example, that of death
+from taking a particular food, sufficiently illustrates) to associate
+the idea of causation with the proximate antecedent <i>event</i>, rather than
+with any of the antecedent <i>states</i>, or permanent facts, which may
+happen also to be conditions of the phenomenon; the reason being that
+the event not only exists, but begins to exist immediately previous;
+while the other conditions may have pre-existed for an indefinite time.
+And this tendency shows itself very visibly in the different logical
+fictions which are resorted to, even by men of science, to avoid the
+necessity of giving the name of cause to anything which had existed for
+an indeterminate length of time before the effect. Thus, rather than say
+that the earth causes the fall of bodies, they ascribe it to a <i>force</i>
+exerted by the earth, or an <i>attraction</i> by the earth, abstractions
+which they can represent to themselves as exhausted by each effort, and
+therefore constituting at each successive instant a fresh fact,
+simultaneous with, or only immediately preceding, the effect. Inasmuch
+as the coming of the circumstance which completes the assemblage of
+conditions, is a change or event, it thence happens that an event is
+always the antecedent in closest apparent proximity to the consequent:
+and this may account for the illusion which disposes us to look upon the
+proximate event as standing more peculiarly in the position of a cause
+than any of the antecedent states. But even this peculiarity, of being
+in closer proximity to the effect than any other of its conditions, is,
+as we have already seen, far from being necessary to the common notion
+of a cause; with which notion, on the contrary, any one of the
+<span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span>conditions, either positive or negative, is found, on occasion,
+completely to accord.<a name="FNanchor_14_95" id="FNanchor_14_95"></a><a href="#Footnote_14_95" class="fnanchor">[14]</a></p>
+
+<p>The cause, then, philosophically speaking, is the sum total of the
+conditions, positive and negative taken together; the whole of the
+contingencies of every description, which being realized, the consequent
+invariably follows. The negative <span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span>conditions, however, of any
+phenomenon, a special enumeration of which would generally be very
+prolix, may be all summed up under one head, namely, the absence of
+preventing or counteracting causes. The convenience of this mode of
+expression is mainly grounded on the fact, that the effects of any cause
+in counteracting another cause may in most cases be, with strict
+scientific exactness, regarded as a mere extension of its own proper and
+separate effects. If gravity retards the upward motion of a projectile,
+and deflects it into a parabolic trajectory, it produces, in so doing,
+the very same kind of effect, and even <span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span>(as mathematicians know) the
+same quantity of effect, as it does in its ordinary operation of causing
+the fall of bodies when simply deprived of their support. If an alkaline
+solution mixed with an acid destroys its sourness, and prevents it from
+reddening vegetable blues, it is because the specific effect of the
+alkali is to combine with the acid, and form a compound with totally
+different qualities. This property, which causes of all descriptions
+possess, of preventing the effects of other causes by virtue (for the
+most part) of the same laws according to which they produce their
+own,<a name="FNanchor_15_96" id="FNanchor_15_96"></a><a href="#Footnote_15_96" class="fnanchor">[15]</a> enables us, by establishing <span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span>the general axiom that all causes
+are liable to be counteracted in their effects by one another, to
+dispense with the consideration of negative conditions entirely, and
+limit the notion of cause to the assemblage of the positive conditions
+of the phenomenon: one negative condition invariably understood, and the
+same in all instances (namely, the absence of counteracting causes)
+being sufficient, along with the sum of the positive conditions, to make
+up the whole set of circumstances on which the phenomenon is dependent.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_4">� 4.</a> Among the positive conditions, as we have seen that there are some
+to which, in common parlance, the term cause is more readily and
+frequently awarded, so there are others to which it is, in ordinary
+circumstances, refused. In most cases of causation a distinction is
+commonly drawn between something which acts, and some other thing which
+is acted upon; between an <i>agent</i> and a <i>patient</i>. Both of these, it
+would be universally allowed, are conditions of the phenomenon; but it
+would be thought absurd to call the latter the cause, that title being
+reserved for the former. The distinction, however, vanishes on
+examination, or rather is found to be only verbal; arising from an
+incident of mere expression, namely, that the object said to be acted
+upon, and which is considered as the scene in which the effect takes
+place, is commonly included in the phrase by which the effect is spoken
+of, so that if it were also reckoned as part of the cause, the seeming
+incongruity would arise of its being supposed to cause itself. In the
+instance which we have already had, of falling bodies, the question was
+thus put: What is the cause which makes a stone fall? and if the answer
+had been "the stone itself," the expression would have been in apparent
+contradiction to the meaning of the word cause. The stone, therefore, is
+conceived as the patient, and the earth (or, according to the common and
+most unphilosophical practice, some occult quality of the earth) is
+represented as the agent or cause. But that there is nothing fundamental
+in the distinction may be seen from this, that it is quite possible to
+conceive the stone as causing its own fall, provided the language
+employed be such as to save <span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span>the mere verbal incongruity. We might say
+that the stone moves towards the earth by the properties of the matter
+composing it; and according to this mode of presenting the phenomenon,
+the stone itself might without impropriety be called the agent; though,
+to save the established doctrine of the inactivity of matter, men
+usually prefer here also to ascribe the effect to an occult quality, and
+say that the cause is not the stone itself, but the <i>weight</i> or
+<i>gravitation</i> of the stone.</p>
+
+<p>Those who have contended for a radical distinction between agent and
+patient, have generally conceived the agent as that which causes some
+state of, or some change in the state of, another object which is called
+the patient. But a little reflection will show that the licence we
+assume of speaking of phenomena as <i>states</i> of the various objects which
+take part in them, (an artifice of which so much use has been made by
+some philosophers, Brown in particular, for the apparent explanation of
+phenomena,) is simply a sort of logical fiction, useful sometimes as one
+among several modes of expression, but which should never be supposed to
+be the enunciation of a scientific truth. Even those attributes of an
+object which might seem with greatest propriety to be called states of
+the object itself, its sensible qualities, its colour, hardness, shape,
+and the like, are in reality (as no one has pointed out more clearly
+than Brown himself) phenomena of causation, in which the substance is
+distinctly the agent, or producing cause, the patient being our own
+organs, and those of other sentient beings. What we call states of
+objects, are always sequences into which the objects enter, generally as
+antecedents or causes; and things are never more active than in the
+production of those phenomena in which they are said to be acted upon.
+Thus, in the example of a stone falling to the earth, according to the
+theory of gravitation the stone is as much an agent as the earth, which
+not only attracts, but is itself attracted by, the stone. In the case of
+a sensation produced in our organs, the laws of our organization, and
+even those of our minds, are as directly operative in determining the
+effect produced, as the <span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span>laws of the outward object. Though we call
+prussic acid the agent of a person's death, the whole of the vital and
+organic properties of the patient are as actively instrumental as the
+poison, in the chain of effects which so rapidly terminates his sentient
+existence. In the process of education, we may call the teacher the
+agent, and the scholar only the material acted upon; yet in truth all
+the facts which pre-existed in the scholar's mind exert either
+co-operating or counteracting agencies in relation to the teacher's
+efforts. It is not light alone which is the agent in vision, but light
+coupled with the active properties of the eye and brain, and with those
+of the visible object. The distinction between agent and patient is
+merely verbal: patients are always agents; in a great proportion,
+indeed, of all natural phenomena, they are so to such a degree as to
+react forcibly on the causes which acted upon them: and even when this
+is not the case, they contribute, in the same manner as any of the other
+conditions, to the production of the effect of which they are vulgarly
+treated as the mere theatre. All the positive conditions of a phenomenon
+are alike agents, alike active; and in any expression of the cause which
+professes to be complete, none of them can with reason be excluded,
+except such as have already been implied in the words used for
+describing the effect; nor by including even these would there be
+incurred any but a merely verbal impropriety.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_5">� 5.</a> It now remains to advert to a distinction which is of first-rate
+importance both for clearing up the notion of cause, and for obviating a
+very specious objection often made against the view which we have taken
+of the subject.</p>
+
+<p>When we define the cause of anything (in the only sense in which the
+present inquiry has any concern with causes) to be "the antecedent which
+it invariably follows," we do not use this phrase as exactly synonymous
+with "the antecedent which it invariably <i>has</i> followed in our past
+experience." Such a mode of conceiving causation would be liable to the
+objection very plausibly urged by Dr. Reid, namely, that according to
+this doctrine night must be the cause of day, and day the <span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span>cause of
+night; since these phenomena have invariably succeeded one another from
+the beginning of the world. But it is necessary to our using the word
+cause, that we should believe not only that the antecedent always <i>has</i>
+been followed by the consequent, but that, as long as the present
+constitution of things<a name="FNanchor_16_97" id="FNanchor_16_97"></a><a href="#Footnote_16_97" class="fnanchor">[16]</a> endures, it always <i>will</i> be so. And this
+would not be true of day and night. We do not believe that night will be
+followed by day under all imaginable circumstances, but only that it
+will be so <i>provided</i> the sun rises above the horizon. If the sun ceased
+to rise, which, for aught we know, may be perfectly compatible with the
+general laws of matter, night would be, or might be, eternal. On the
+other hand, if the sun is above the horizon, his light not extinct, and
+no opaque body between us and him, we believe firmly that unless a
+change takes place in the properties of matter, this combination of
+antecedents will be followed by the consequent, day; that if the
+combination of antecedents could be indefinitely prolonged, it would be
+always day; and that if the same combination had always existed, it
+would always have been day, quite independently of night as a previous
+condition. Therefore is it that we do not call night the cause, nor even
+a condition, of day. The existence of the sun (or some such luminous
+body), and there being no opaque medium in a straight line<a name="FNanchor_17_98" id="FNanchor_17_98"></a><a href="#Footnote_17_98" class="fnanchor">[17]</a> between
+that body and the part of the earth where we are situated, are the sole
+conditions; and the union of these, without the addition of any
+superfluous circumstance, constitutes the cause. This is what writers
+mean when they say that the notion of cause <span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span>involves the idea of
+necessity. If there be any meaning which confessedly belongs to the term
+necessity, it is <i>unconditionalness</i>. That which is necessary, that
+which <i>must</i> be, means that which will be, whatever supposition we may
+make in regard to all other things. The succession of day and night
+evidently is not necessary in this sense. It is conditional on the
+occurrence of other antecedents. That which will be followed by a given
+consequent when, and only when, some third circumstance also exists, is
+not the cause, even though no case should ever have occurred in which
+the phenomenon took place without it.</p>
+
+<p>Invariable sequence, therefore, is not synonymous with causation, unless
+the sequence, besides being invariable, is unconditional. There are
+sequences, as uniform in past experience as any others whatever, which
+yet we do not regard as cases of causation, but as conjunctions in some
+sort accidental. Such, to an accurate thinker, is that of day and night.
+The one might have existed for any length of time, and the other not
+have followed the sooner for its existence; it follows only if certain
+other antecedents exist; and where those antecedents existed, it would
+follow in any case. No one, probably, ever called night the cause of
+day; mankind must so soon have arrived at the very obvious
+generalization, that the state of general illumination which we call day
+would follow from the presence of a sufficiently luminous body, whether
+darkness had preceded or not.</p>
+
+<p>We may define, therefore, the cause of a phenomenon, to be the
+antecedent, or the concurrence of antecedents, on which it is invariably
+and <i>unconditionally</i> consequent. Or if we adopt the convenient
+modification of the meaning of the word cause, which confines it to the
+assemblage of positive conditions without the negative, then instead of
+"unconditionally," we must say, "subject to no other than negative
+conditions."</p>
+
+<p>To some it may appear, that the sequence between night and day being
+invariable in our experience, we have as much ground in this case as
+experience can give in any case, for recognising the two phenomena as
+cause and effect; and that <span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span>to say that more is necessary&mdash;to require a
+belief that the succession is unconditional, or in other words that it
+would be invariable under all changes of circumstances, is to
+acknowledge in causation an element of belief not derived from
+experience. The answer to this is, that it is experience itself which
+teaches us that one uniformity of sequence is conditional and another
+unconditional. When we judge that the succession of night and day is a
+derivative sequence, depending on something else, we proceed on grounds
+of experience. It is the evidence of experience which convinces us that
+day could equally exist without being followed by night, and that night
+could equally exist without being followed by day. To say that these
+beliefs are "not generated by our mere observation of sequence,"<a name="FNanchor_18_99" id="FNanchor_18_99"></a><a href="#Footnote_18_99" class="fnanchor">[18]</a> is
+to forget that twice in every twenty-four hours, when the sky is clear,
+we have an <i>experimentum crucis</i> that the cause of day is the sun. We
+have an experimental knowledge of the sun which justifies us on
+experimental grounds in concluding, that if the sun were always above
+the horizon there would be day, though there had been no night, and that
+if the sun were always below the horizon there would be night, though
+there had been no day. We thus know from experience that the succession
+of night and day is not unconditional. Let me add, that the antecedent
+which is only conditionally invariable, is not the invariable
+antecedent. Though a fact may, in experience, have always been followed
+by another fact, yet if the remainder of our experience teaches us that
+it might not always be so followed, or if the experience itself is such
+as leaves room for a possibility that the known cases may not correctly
+represent all possible cases, the hitherto invariable antecedent is not
+accounted the cause; but why? Because we are not sure that it <i>is</i> the
+invariable antecedent.</p>
+
+<p>Such cases of sequence as that of day and night not only do not
+contradict the doctrine which resolves causation into invariable
+sequence, but are necessarily implied in that doctrine. It is evident,
+that from a limited number of unconditional <span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span>sequences, there will
+result a much greater number of conditional ones. Certain causes being
+given, that is, certain antecedents which are unconditionally followed
+by certain consequents; the mere coexistence of these causes will give
+rise to an unlimited number of additional uniformities. If two causes
+exist together, the effects of both will exist together; and if many
+causes coexist, these causes (by what we shall term hereafter the
+intermixture of their laws) will give rise to new effects, accompanying
+or succeeding one another in some particular order, which order will be
+invariable while the causes continue to coexist, but no longer. The
+motion of the earth in a given orbit round the sun, is a series of
+changes which follow one another as antecedents and consequents, and
+will continue to do so while the sun's attraction, and the force with
+which the earth tends to advance in a direct line through space,
+continue to coexist in the same quantities as at present. But vary
+either of these causes, and this particular succession of motions would
+cease to take place. The series of the earth's motions, therefore,
+though a case of sequence invariable within the limits of human
+experience, is not a case of causation. It is not unconditional.</p>
+
+<p>This distinction between the relations of succession which so far as we
+know are unconditional, and those relations, whether of succession or of
+coexistence, which, like the earth's motions, or the succession of day
+and night, depend on the existence or on the coexistence of other
+antecedent facts&mdash;corresponds to the great division which Dr. Whewell
+and other writers have made of the field of science, into the
+investigation of what they term the Laws of Phenomena, and the
+investigation of causes; a phraseology, as I conceive, not
+philosophically sustainable, inasmuch as the ascertainment of causes,
+such causes as the human faculties can ascertain, namely, causes which
+are themselves phenomena, is, therefore, merely the ascertainment of
+other and more universal Laws of Phenomena. And let me here observe,
+that Dr. Whewell, and in some degree even Sir John Herschel, seem to
+have misunderstood the meaning of those writers who, like <span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span>M. Comte,
+limit the sphere of scientific investigation to Laws of Phenomena, and
+speak of the inquiry into causes as vain and futile. The causes which M.
+Comte designates as inaccessible, are efficient causes. The
+investigation of physical, as opposed to efficient, causes (including
+the study of all the active forces in Nature, considered as facts of
+observation) is as important a part of M. Comte's conception of science
+as of Dr. Whewell's. His objection to the <i>word</i> cause is a mere matter
+of nomenclature, in which, as a matter of nomenclature, I consider him
+to be entirely wrong. "Those," it is justly remarked by Mr. Bailey,<a name="FNanchor_19_100" id="FNanchor_19_100"></a><a href="#Footnote_19_100" class="fnanchor">[19]</a>
+"who, like M. Comte, object to designate <i>events</i> as causes, are
+objecting without any real ground to a mere but extremely convenient
+generalization, to a very useful common name, the employment of which
+involves, or needs involve, no particular theory." To which it may be
+added, that by rejecting this form of expression, M. Comte leaves
+himself without any term for marking a distinction which, however
+incorrectly expressed, is not only real, but is one of the fundamental
+distinctions in science; indeed it is on this alone, as we shall
+hereafter find, that the possibility rests of framing a rigorous Canon
+of Induction. And as things left without a name are apt to be forgotten,
+a Canon of that description is not one of the many benefits which the
+philosophy of Induction has received from M. Comte's great powers.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_6">� 6.</a> Does a cause always stand with its effect in the relation of
+antecedent and consequent? Do we not often say of two simultaneous facts
+that they are cause and effect&mdash;as when we say that fire is the cause of
+warmth, the sun and moisture the cause of vegetation, and the like?
+Since a cause does not necessarily perish because its effect has been
+produced, the two things do very generally coexist; and there are some
+appearances, and some common expressions, seeming to imply not only that
+causes may, but that they must, be contemporaneous with their effects.
+<i>Cessante caus� cessat et <span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span>effectus</i>, has been a dogma of the schools:
+the necessity for the continued existence of the cause in order to the
+continuance of the effect, seems to have been once a generally received
+doctrine. Kepler's numerous attempts to account for the motions of the
+heavenly bodies on mechanical principles, were rendered abortive by his
+always supposing that the agency which set those bodies in motion must
+continue to operate in order to keep up the motion which it at first
+produced. Yet there were at all times many familiar instances of the
+continuance of effects, long after their causes had ceased. A <i>coup de
+soleil</i> gives a person a brain fever: will the fever go off as soon as
+he is moved out of the sunshine? A sword is run through his body: must
+the sword remain in his body in order that he may continue dead? A
+ploughshare once made, remains a ploughshare, without any continuance of
+heating and hammering, and even after the man who heated and hammered it
+has been gathered to his fathers. On the other hand, the pressure which
+forces up the mercury in an exhausted tube must be continued in order to
+sustain it in the tube. This (it may be replied) is because another
+force is acting without intermission, the force of gravity, which would
+restore it to its level, unless counterpoised by a force equally
+constant. But again; a tight bandage causes pain, which pain will
+sometimes go off as soon as the bandage is removed. The illumination
+which the sun diffuses over the earth ceases when the sun goes down.</p>
+
+<p>There is, therefore, a distinction to be drawn. The conditions which are
+necessary for the first production of a phenomenon, are occasionally
+also necessary for its continuance; though more commonly its continuance
+requires no condition except negative ones. Most things, once produced,
+continue as they are, until something changes or destroys them; but some
+require the permanent presence of the agencies which produced them at
+first. These may, if we please, be considered as instantaneous
+phenomena, requiring to be renewed at each instant by the cause by which
+they were at first generated. Accordingly, the illumination of any given
+point of space has always been looked upon as an instantaneous fact,
+which <span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span>perishes and is perpetually renewed as long as the necessary
+conditions subsist. If we adopt this language we avoid the necessity of
+admitting that the continuance of the cause is ever required to maintain
+the effect. We may say, it is not required to maintain, but to
+reproduce, the effect, or else to counteract some force tending to
+destroy it. And this may be a convenient phraseology. But it is only a
+phraseology. The fact remains, that in some cases (though these are a
+minority) the continuance of the conditions which produced an effect is
+necessary to the continuance of the effect.</p>
+
+<p>As to the ulterior question, whether it is strictly necessary that the
+cause, or assemblage of conditions, should precede, by ever so short an
+instant, the production of the effect, (a question raised and argued
+with much ingenuity by Sir John Herschel in an Essay already
+quoted,<a name="FNanchor_20_101" id="FNanchor_20_101"></a><a href="#Footnote_20_101" class="fnanchor">[20]</a>) the inquiry is of no consequence for our present purpose.
+There certainly are cases in which the effect follows without any
+interval perceptible by our faculties: and when there is an interval, we
+cannot tell by how many intermediate links imperceptible to us that
+interval may really be filled up. But even granting that an effect may
+commence simultaneously with its cause, the view I have taken of
+causation is in no way practically affected. Whether the cause and its
+effect be necessarily successive or not, the beginning of a phenomenon
+is what implies a cause, and causation is the law of the succession of
+phenomena. If these axioms be granted, we can afford, though I see no
+necessity for doing so, to drop the words antecedent and consequent as
+applied to cause and effect. I have no objection to define a cause, the
+assemblage of phenomena, which occurring, some other phenomenon
+invariably commences, or has its origin. Whether the effect coincides in
+point of time with, or immediately follows, the hindmost of its
+conditions, is immaterial. At all events it does not precede it; and
+when we are in doubt, between two coexistent phenomena, which is cause
+and which effect, we rightly deem the question solved if we can
+ascertain which of them preceded the other.</p>
+
+
+<p><span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_V_7">� 7.</a> It continually happens that several different phenomena, which are
+not in the slightest degree dependent or conditional on one another, are
+found all to depend, as the phrase is, on one and the same agent; in
+other words, one and the same phenomenon is seen to be followed by
+several sorts of effects quite heterogeneous, but which go on
+simultaneously one with another; provided, of course, that all other
+conditions requisite for each of them also exist. Thus, the sun produces
+the celestial motions, it produces daylight, and it produces heat. The
+earth causes the fall of heavy bodies, and it also, in its capacity of a
+great magnet, causes the phenomena of the magnetic needle. A crystal of
+galena causes the sensations of hardness, of weight, of cubical form, of
+grey colour, and many others between which we can trace no
+interdependence. The purpose to which the phraseology of Properties and
+Powers is specially adapted, is the expression of this sort of cases.
+When the same phenomenon is followed (either subject or not to the
+presence of other conditions) by effects of different and dissimilar
+orders, it is usual to say that each different sort of effect is
+produced by a different property of the cause. Thus we distinguish the
+attractive or gravitative property of the earth, and its magnetic
+property: the gravitative, luminiferous, and calorific properties of the
+sun: the colour, shape, weight, and hardness of a crystal. These are
+mere phrases, which explain nothing, and add nothing to our knowledge of
+the subject; but, considered as abstract names denoting the connexion
+between the different effects produced and the object which produces
+them, they are a very powerful instrument of abridgment, and of that
+acceleration of the process of thought which abridgment accomplishes.</p>
+
+<p>This class of considerations leads to a conception which we shall find
+to be of great importance, that of a Permanent Cause, or original
+natural agent. There exist in nature a number of permanent causes, which
+have subsisted ever since the human race has been in existence, and for
+an indefinite and probably an enormous length of time previous. The sun,
+the earth, and planets, with their various constituents, air, water, and
+other distinguishable substances, whether simple or <span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span>compound, of which
+nature is made up, are such Permanent Causes. These have existed, and
+the effects or consequences which they were fitted to produce have taken
+place (as often as the other conditions of the production met,) from the
+very beginning of our experience. But we can give no account of the
+origin of the Permanent Causes themselves. Why these particular natural
+agents existed originally and no others, or why they are commingled in
+such and such proportions, and distributed in such and such a manner
+throughout space, is a question we cannot answer. More than this: we can
+discover nothing regular in the distribution itself; we can reduce it to
+no uniformity, to no law. There are no means by which, from the
+distribution of these causes or agents in one part of space, we could
+conjecture whether a similar distribution prevails in another. The
+coexistence, therefore, of Primeval Causes, ranks, to us, among merely
+casual concurrences: and all those sequences or coexistences among the
+effects of several such causes, which, though invariable while those
+causes coexist, would, if the coexistence terminated, terminate along
+with it, we do not class as cases of causation, or laws of nature: we
+can only calculate on finding these sequences or coexistences where we
+know by direct evidence, that the natural agents on the properties of
+which they ultimately depend, are distributed in the requisite manner.
+These Permanent Causes are not always objects; they are sometimes
+events, that is to say, periodical cycles of events, that being the only
+mode in which events can possess the property of permanence. Not only,
+for instance, is the earth itself a permanent cause, or primitive
+natural agent, but the earth's rotation is so too: it is a cause which
+has produced, from the earliest period, (by the aid of other necessary
+conditions,) the succession of day and night, the ebb and flow of the
+sea, and many other effects, while, as we can assign no cause (except
+conjecturally) for the rotation itself, it is entitled to be ranked as a
+primeval cause. It is, however, only the <i>origin</i> of the rotation which
+is mysterious to us: once begun, its continuance is accounted for by the
+first law of motion (that of the permanence of rectilinear motion <span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span>once
+impressed) combined with the gravitation of the parts of the earth
+towards one another.</p>
+
+<p>All phenomena without exception which begin to exist, that is, all
+except the primeval causes, are effects either immediate or remote of
+those primitive facts, or of some combination of them. There is no Thing
+produced, no event happening, in the known universe, which is not
+connected by an uniformity, or invariable sequence, with some one or
+more of the phenomena which preceded it; insomuch that it will happen
+again as often as those phenomena occur again, and as no other
+phenomenon having the character of a counteracting cause shall coexist.
+These antecedent phenomena, again, were connected in a similar manner
+with some that preceded them; and so on, until we reach, as the ultimate
+step attainable by us, either the properties of some one primeval cause,
+or the conjunction of several. The whole of the phenomena of nature were
+therefore the necessary, or in other words, the unconditional,
+consequences of some former collocation of the Permanent Causes.</p>
+
+<p>The state of the whole universe at any instant, we believe to be the
+consequence of its state at the previous instant; insomuch that one who
+knew all the agents which exist at the present moment, their collocation
+in space, and all their properties, in other words, the laws of their
+agency, could predict the whole subsequent history of the universe, at
+least unless some new volition of a power capable of controlling the
+universe should supervene.<a name="FNanchor_21_102" id="FNanchor_21_102"></a><a href="#Footnote_21_102" class="fnanchor">[21]</a> And if any particular state of the
+<span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span>entire universe could ever recur a second time, all subsequent states
+would return too, and history would, like a circulating decimal of many
+figures, periodically repeat itself:&mdash;</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">Jam redit et virgo, redeunt Saturnia regna....<br /></span>
+<span class="i0">Alter erit tum Tiphys, et altera qu� vehat Argo<br /></span>
+<span class="i0">Delectos heroas; erunt quoque altera bella,<br /></span>
+<span class="i0">Atque iterum ad Trojam magnus mittetur Achilles.<br /></span>
+</div></div>
+
+<p>And though things do not really revolve in this eternal round, the whole
+series of events in the history of the universe, past and future, is not
+the less capable, in its own nature, of being constructed <i>� priori</i> by
+any one whom we can suppose acquainted with the original distribution of
+all natural agents, and with the whole of their properties, that is, the
+laws of succession existing between them and their effects: saving the
+far more than human powers of combination and calculation which would be
+required, even in one possessing the data, for the actual performance of
+the task.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_8">� 8.</a> Since everything which occurs is determined by laws of causation
+and collocations of the original causes, it follows that the
+coexistences which are observable among effects cannot be themselves the
+subject of any similar set of laws, distinct from laws of causation.
+Uniformities there are, as well of coexistence as of succession, among
+effects; but these must in all cases be a mere result either of the
+identity or of the coexistence of their causes: if the causes did not
+coexist, neither could the effects. And these causes being also effects
+of prior causes, and these of others, until we reach the primeval
+causes, it follows that (except in the case of effects which can be
+traced immediately or remotely to one and the <span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span>same cause) the
+coexistences of phenomena can in no case be universal, unless the
+coexistences of the primeval causes to which the effects are ultimately
+traceable, can be reduced to an universal law: but we have seen that
+they cannot. There are, accordingly, no original and independent, in
+other words no unconditional, uniformities of coexistence, between
+effects of different causes; if they coexist, it is only because the
+causes have casually coexisted. The only independent and unconditional
+coexistences which are sufficiently invariable to have any claim to the
+character of laws, are between different and mutually independent
+effects of the same cause; in other words, between different properties
+of the same natural agent. This portion of the Laws of Nature will be
+treated of in the latter part of the present Book, under the name of the
+Specific Properties of Kinds.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_V_9">� 9.</a> It is proper in this place to advert to a rather ancient doctrine
+respecting causation, which has been revived during the last few years
+in many quarters, and at present gives more signs of life than any other
+theory of causation at variance with that set forth in the preceding
+pages.</p>
+
+<p>According to the theory in question, Mind, or, to speak more precisely,
+Will, is the only cause of phenomena. The type of Causation, as well as
+the exclusive source from which we derive the idea, is our own voluntary
+agency. Here, and here only (it is said) we have direct evidence of
+causation. We know that we can move our bodies. Respecting the phenomena
+of inanimate nature, we have no other direct knowledge than that of
+antecedence and sequence. But in the case of our voluntary actions, it
+is affirmed that we are conscious of power, before we have experience of
+results. An act of volition, whether followed by an effect or not, is
+accompanied by a consciousness of effort, "of force exerted, of power in
+action, which is necessarily causal, or causative." This feeling of
+energy or force, inherent in an act of will, is knowledge <i>� priori</i>;
+assurance, prior to experience, that we have the power of causing
+effects. Volition, therefore, it is asserted, is something more than an
+unconditional antecedent; <span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span>it is a cause, in a different sense from that
+in which physical phenomena are said to cause one another: it is an
+Efficient Cause. From this the transition is easy to the further
+doctrine, that Volition is the <i>sole</i> Efficient Cause of all phenomena.
+"It is inconceivable that dead force could continue unsupported for a
+moment beyond its creation. We cannot even conceive of change or
+phenomena without the energy of a mind." "The word <i>action</i>" itself,
+says another writer of the same school, "has no real significance except
+when applied to the doings of an intelligent agent. Let any one
+conceive, if he can, of any power, energy, or force, inherent in a lump
+of matter." Phenomena may have the semblance of being produced by
+physical causes, but they are in reality produced, say these writers, by
+the immediate agency of mind. All things which do not proceed from a
+human (or, I suppose, an animal) will, proceed, they say, directly from
+divine will. The earth is not moved by the combination of a centripetal
+and a projectile force; this is but a mode of speaking, which serves to
+facilitate our conceptions. It is moved by the direct volition of an
+omnipotent Being, in a path coinciding with that which we deduce from
+the hypothesis of these two forces.</p>
+
+<p>As I have so often observed, the general question of the existence of
+Efficient Causes does not fall within the limits of our subject: but a
+theory which represents them as capable of being subjects of human
+knowledge, and which passes off as efficient causes what are only
+physical or phenomenal causes, belongs as much to Logic as to
+Metaphysics, and is a fit subject for discussion here.</p>
+
+<p>To my apprehension, a volition is not an efficient, but simply a
+physical, cause. Our will causes our bodily actions in the same sense,
+and in no other, in which cold causes ice, or a spark causes an
+explosion of gunpowder. The volition, a state of our mind, is the
+antecedent; the motion of our limbs in conformity to the volition, is
+the consequent. This sequence I conceive to be not a subject of direct
+consciousness, in the sense intended by the theory. The antecedent,
+indeed, and the consequent, are subjects of consciousness. But the
+connexion between them is a subject of experience. I cannot <span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span>admit that
+our consciousness of the volition contains in itself any <i>� priori</i>
+knowledge that the muscular motion will follow. If our nerves of motion
+were paralysed, or our muscles stiff and inflexible, and had been so all
+our lives, I do not see the slightest ground for supposing that we
+should ever (unless by information from other people) have known
+anything of volition as a physical power, or been conscious of any
+tendency in feelings of our mind to produce motions of our body, or of
+other bodies. I will not undertake to say whether we should in that case
+have had the physical feeling which I suppose is meant when these
+writers speak of "consciousness of effort:" I see no reason why we
+should not; since that physical feeling is probably a state of nervous
+sensation beginning and ending in the brain, without involving the
+motory apparatus: but we certainly should not have designated it by any
+term equivalent to effort, since effort implies consciously aiming at an
+end, which we should not only in that case have had no reason to do, but
+could not even have had the idea of doing. If conscious at all of this
+peculiar sensation, we should have been conscious of it, I conceive,
+only as a kind of uneasiness, accompanying our feelings of desire.</p>
+
+<p>It is well argued by Sir William Hamilton against the theory in
+question, that it "is refuted by the consideration, that between the
+overt fact of corporeal movement of which we are cognisant, and the
+internal act of mental determination of which we are also cognisant,
+there intervenes a numerous series of intermediate agencies of which we
+have no knowledge; and, consequently, that we can have no consciousness
+of any causal connexion between the extreme links of this chain, the
+volition to move and the limb moving, as this hypothesis asserts. No one
+is immediately conscious, for example, of moving his arm through his
+volition. Previously to this ultimate movement, muscles, nerves, a
+multitude of solid and fluid parts, must be set in motion by the will,
+but of this motion we know, from consciousness, absolutely nothing. A
+person struck with paralysis is conscious of no inability in his limb to
+fulfil the determinations of his will; and it is only after having
+willed, and finding that his limbs do not obey his <span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span>volition, that he
+learns by this experience, that the external movement does not follow
+the internal act. But as the paralytic learns after the volition that
+his limbs do not obey his mind; so it is only after volition that the
+man in health learns, that his limbs do obey the mandates of his
+will."<a name="FNanchor_22_103" id="FNanchor_22_103"></a><a href="#Footnote_22_103" class="fnanchor">[22]</a></p>
+
+<p>Those against whom I am contending have never produced, and do not
+pretend to produce, any positive evidence<a name="FNanchor_23_104" id="FNanchor_23_104"></a><a href="#Footnote_23_104" class="fnanchor">[23]</a> that the power of our will
+to move our bodies would be known to us independently of experience.
+What they have to say on the subject is, that the production of physical
+events by a will seems to carry its own explanation with it, while the
+action of matter upon matter seems to require something else to explain
+it; and is even, according to them, "inconceivable" <span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span>on any other
+supposition than that some will intervenes between the apparent cause
+and its apparent effect. They thus rest their case on an appeal to the
+inherent laws of our conceptive faculty; mistaking, as I apprehend, for
+the laws of that faculty its acquired habits, grounded on the
+spontaneous tendencies of its uncultured state. The succession between
+the will to move a limb and the actual motion, is one of the most direct
+and instantaneous of all sequences which come under our observation, and
+is familiar to every moment's experience from our earliest infancy; more
+familiar than any succession of events exterior to our bodies, and
+especially more so than any other case of the apparent origination (as
+distinguished from the mere communication) of motion. Now, it is the
+natural tendency of the mind to be always attempting to facilitate its
+conception of unfamiliar facts by assimilating them to others which are
+familiar. Accordingly, our voluntary acts, being the most familiar to us
+of all cases of causation, are, in the infancy and early youth of the
+human race, spontaneously taken as the type of causation in general, and
+all phenomena are supposed to be directly produced by the will of some
+sentient being. This original Fetichism I shall not characterize in the
+words of Hume, or of any follower of Hume, but in those of a religious
+metaphysician, Dr. Reid, in order more effectually to show the unanimity
+which exists on the subject among all competent thinkers.</p>
+
+<p>"When we turn our attention to external objects, and begin to exercise
+our rational faculties about them, we find that there are some motions
+and changes in them which we have power to produce, and that there are
+many which must have some other cause. Either the objects must have life
+and active power, as we have, or they must be moved or changed by
+something that has life and active power, as external objects are moved
+by us.</p>
+
+<p>"Our first thoughts seem to be, that the objects in which we perceive
+such motion have understanding and active power as we have. 'Savages,'
+says the Abb� Raynal, 'wherever they see motion which they cannot
+account for, there they suppose a soul.' All men may be considered as
+savages in this respect, <span class="pagenum"><a name="Page_392" id="Page_392">[Pg 392]</a></span>until they are capable of instruction, and of
+using their faculties in a more perfect manner than savages do.</p>
+
+<p>"The Abb� Raynal's observation is sufficiently confirmed, both from
+fact, and from the structure of all languages.</p>
+
+<p>"Rude nations do really believe sun, moon, and stars, earth, sea, and
+air, fountains, and lakes, to have understanding and active power. To
+pay homage to them, and implore their favour, is a kind of idolatry
+natural to savages.</p>
+
+<p>"All languages carry in their structure the marks of their being formed
+when this belief prevailed. The distinction of verbs and participles
+into active and passive, which is found in all languages, must have been
+originally intended to distinguish what is really active from what is
+merely passive; and in all languages, we find active verbs applied to
+those objects, in which, according to the Abb� Raynal's observation,
+savages suppose a soul.</p>
+
+<p>"Thus we say the sun rises and sets, and comes to the meridian, the moon
+changes, the sea ebbs and flows, the winds blow. Languages were formed
+by men who believed these objects to have life and active power in
+themselves. It was therefore proper and natural to express their motions
+and changes by active verbs.</p>
+
+<p>"There is no surer way of tracing the sentiments of nations before they
+have records, than by the structure of their language, which,
+notwithstanding the changes produced in it by time, will always retain
+some signatures of the thoughts of those by whom it was invented. When
+we find the same sentiments indicated in the structure of all languages,
+those sentiments must have been common to the human species when
+languages were invented.</p>
+
+<p>"When a few, of superior intellectual abilities, find leisure for
+speculation, they begin to philosophize, and soon discover, that many of
+those objects which at first they believed to be intelligent and active
+are really lifeless and passive. This is a very important discovery. It
+elevates the mind, emancipates from many vulgar superstitions, and
+invites to further discoveries of the same kind.</p>
+
+<p>"As philosophy advances, life and activity in natural <span class="pagenum"><a name="Page_393" id="Page_393">[Pg 393]</a></span>objects retires,
+and leaves them dead and inactive. Instead of moving voluntarily, we
+find them to be moved necessarily; instead of acting, we find them to be
+acted upon; and Nature appears as one great machine, where one wheel is
+turned by another, that by a third; and how far this necessary
+succession may reach, the philosopher does not know."<a name="FNanchor_24_105" id="FNanchor_24_105"></a><a href="#Footnote_24_105" class="fnanchor">[24]</a></p>
+
+<p>There is, then, a spontaneous tendency of the intellect to account to
+itself for all cases of causation by assimilating them to the
+intentional acts of voluntary agents like itself. This is the
+instinctive philosophy of the human mind in its earliest stage, before
+it has become familiar with any other invariable sequences than those
+between its own volitions or those of other human beings and their
+voluntary acts. As the notion of fixed laws of succession among external
+phenomena gradually establishes itself, the propensity to refer all
+phenomena to voluntary agency slowly gives way before it. The
+suggestions, however, of daily life continuing to be more powerful than
+those of scientific thought, the original instinctive philosophy
+maintains its ground in the mind, underneath the growths obtained by
+cultivation, and keeps up a constant resistance to their throwing their
+roots deep into the soil. The theory against which I am contending
+derives its nourishment from that substratum. Its strength does not lie
+in argument, but in its affinity to an obstinate tendency of the infancy
+of the human mind.</p>
+
+<p>That this tendency, however, is not the result of an inherent mental
+law, is proved by superabundant evidence. The history of science, from
+its earliest dawn, shows that mankind have not been unanimous in
+thinking either that the action of matter upon matter was not
+conceivable, or that the action of mind upon matter was. To some
+thinkers, and some schools of thinkers, both in ancient and in modern
+times, this last has appeared much more inconceivable than the former.
+Sequences entirely physical and material, as soon as they had become
+sufficiently familiar to the human mind, came to be thought perfectly
+natural, and were regarded not only as needing no explanation
+themselves, but as being capable of <span class="pagenum"><a name="Page_394" id="Page_394">[Pg 394]</a></span>affording it to others, and even of
+serving as the ultimate explanation of things in general.</p>
+
+<p>One of the ablest recent supporters of the Volitional theory has
+furnished an explanation, at once historically true and philosophically
+acute, of the failure of the Greek philosophers in physical inquiry, in
+which, as I conceive, he unconsciously depicts his own state of mind.
+"Their stumbling-block was one as to the nature of the evidence they had
+to expect for their conviction.... They had not seized the idea that
+they must not expect to understand the processes of outward causes, but
+only their results: and consequently, the whole physical philosophy of
+the Greeks was an attempt to identify mentally the effect with its
+cause, to feel after some not only necessary but natural connexion,
+where they meant by natural that which would <i>per se</i> carry some
+presumption to their own mind.... They wanted to see some <i>reason</i> why
+the physical antecedent should produce this particular consequent, and
+their only attempts were in directions where they could find such
+reasons."<a name="FNanchor_25_106" id="FNanchor_25_106"></a><a href="#Footnote_25_106" class="fnanchor">[25]</a> In other words, they were not content merely to know that
+one phenomenon was always followed by another; they thought that they
+had not attained the true aim of science, unless they could perceive
+something in the nature of the one phenomenon from which it might have
+been known or presumed <i>previous to trial</i> that it would be followed by
+the other: just what the writer, who has so clearly pointed out their
+error, thinks that he perceives in the nature of the phenomenon
+Volition. And to complete the statement of the case, he should have
+added that these early speculators not only made this their aim, but
+were quite satisfied with their success in it; not only sought for
+causes which should carry in their mere statement evidence of their
+efficiency, but fully believed that they had found such causes. The
+reviewer can see plainly that this was an error, because <i>he</i> does not
+believe that there exist any relations between material phenomena which
+can account for their producing one another: but the very fact of the
+persistency <span class="pagenum"><a name="Page_395" id="Page_395">[Pg 395]</a></span>of the Greeks in this error, shows that their minds were in
+a very different state: they were able to derive from the assimilation
+of physical facts to other physical facts, the kind of mental
+satisfaction which we connect with the word explanation, and which the
+reviewer would have us think can only be found in referring phenomena to
+a will. When Thales and Hippo held that moisture was the universal
+cause, and external element, of which all other things were but the
+infinitely various sensible manifestations; when Anaximenes predicated
+the same thing of air, Pythagoras of numbers, and the like, they all
+thought that they had found a real explanation; and were content to rest
+in this explanation as ultimate. The ordinary sequences of the external
+universe appeared to them, no less than to their critic, to be
+inconceivable without the supposition of some universal agency to
+connect the antecedents with the consequents; but they did not think
+that Volition, exerted by minds, was the only agency which fulfilled
+this requirement. Moisture, or air, or numbers, carried to their minds a
+precisely similar impression of making intelligible what was otherwise
+inconceivable, and gave the same full satisfaction to the demands of
+their conceptive faculty.</p>
+
+<p>It was not the Greeks alone, who "wanted to see some reason why the
+physical antecedent should produce this particular consequent," some
+connexion "which would <i>per se</i> carry some presumption to their own
+mind." Among modern philosophers, Leibnitz laid it down as a
+self-evident principle that all physical causes without exception must
+contain in their own nature something which makes it intelligible that
+they should be able to produce the effects which they do produce. Far
+from admitting Volition as the only kind of cause which carried internal
+evidence of its own power, and as the real bond of connexion between
+physical antecedents and their consequents, he demanded some naturally
+and <i>per se</i> efficient physical antecedent as the bond of connexion
+between Volition itself and its effects. He distinctly refused to admit
+the will of God as a sufficient explanation of anything except miracles;
+and insisted upon finding something that would <span class="pagenum"><a name="Page_396" id="Page_396">[Pg 396]</a></span>account <i>better</i> for the
+phenomena of nature than a mere reference to divine volition.<a name="FNanchor_26_107" id="FNanchor_26_107"></a><a href="#Footnote_26_107" class="fnanchor">[26]</a></p>
+
+<p>Again, and conversely, the action of mind upon matter (which, we are now
+told, not only needs no explanation itself, but is the explanation of
+all other effects), has appeared to some thinkers to be itself the grand
+inconceivability. It was to get over this very difficulty that the
+Cartesians invented the system of Occasional Causes. They could not
+conceive that thoughts in a mind could produce movements in a body, or
+that bodily movements could produce thoughts. They could see no
+necessary connexion, no relation <i>� priori</i>, between a motion and a
+thought. And as the Cartesians, more than any other school of
+philosophical speculation before or since, made their own minds the
+measure of all things, and refused, on principle, to believe that Nature
+had done what they were unable to see any reason why she must do, they
+affirmed it to be impossible that a material and a mental fact could be
+causes one of another. They regarded them as mere Occasions on which the
+real agent, God, thought fit to exert his power as a Cause. When a man
+wills to move his foot, it is not his will that moves it, but God (they
+said) moves it on the occasion of his will. God, according to this
+system, is the only efficient cause, not <i>qu�</i> mind, or <i>qu�</i> endowed
+with volition, but <i>qu�</i> omnipotent. This hypothesis was, as I said,
+originally suggested by the supposed inconceivability of any real mutual
+action between Mind and Matter: but it was afterwards extended to the
+action of Matter upon Matter, for on a nicer examination they found this
+inconceivable too, and therefore, according to their logic, impossible.
+The <i>deus ex machin�</i> was ultimately called in to produce a spark on the
+occasion of a flint and steel coming together, or to break an egg on the
+occasion of its falling on the ground.</p>
+
+<p>All this, undoubtedly, shows that it is the disposition of mankind in
+general, not to be satisfied with knowing that one fact is invariably
+antecedent and another consequent, but to look out for something which
+may seem to explain their being so. But we also see that this demand may
+be completely satisfied <span class="pagenum"><a name="Page_397" id="Page_397">[Pg 397]</a></span>by an agency purely physical, provided it be
+much more familiar than that which it is invoked to explain. To Thales
+and Anaximenes, it appeared inconceivable that the antecedents which we
+see in nature, should produce the consequents; but perfectly natural
+that water, or air, should produce them. The writers whom I oppose
+declare this inconceivable, but can conceive that mind, or volition, is
+<i>per se</i> an efficient cause: while the Cartesians could not conceive
+even that, but peremptorily declared that no mode of production of any
+fact whatever was conceivable, except the direct agency of an omnipotent
+being. Thus giving additional proof of what finds new confirmation in
+every stage of the history of science: that both what persons can, and
+what they cannot, conceive, is very much an affair of accident, and
+depends altogether on their experience, and their habits of thought;
+that by cultivating the requisite associations of ideas, people may make
+themselves unable to conceive any given thing; and may make themselves
+able to conceive most things, however inconceivable these may at first
+appear: and the same facts in each person's mental history which
+determine what is or is not conceivable to him, determine also which
+among the various sequences in nature will appear to him so natural and
+plausible, as to need no other proof of their existence; to be evident
+by their own light, independent equally of experience and of
+explanation.</p>
+
+<p>By what rule is any one to decide between one theory of this description
+and another? The theorists do not direct us to any external evidence;
+they appeal each to his own subjective feelings. One says, the
+succession C, B, appears to me more natural, conceivable, and credible
+<i>per se</i>, than the succession A, B; you are therefore mistaken in
+thinking that B depends upon A; I am certain, though I can give no other
+evidence of it, that C comes in between A and B, and is the real and
+only cause of B. The other answers&mdash;the successions C, B, and A, B,
+appear to me equally natural and conceivable, or the latter more so than
+the former: A is quite capable of producing B without any other
+intervention. A third agrees with the first in being unable to conceive
+that A can produce B, but finds the sequence D, B, still more natural
+than C, B, or of nearer kin to the subject matter, and prefers his D
+theory <span class="pagenum"><a name="Page_398" id="Page_398">[Pg 398]</a></span>to the C theory. It is plain that there is no universal law
+operating here, except the law that each person's conceptions are
+governed and limited by his individual experience and habits of thought.
+We are warranted in saying of all three, what each of them already
+believes of the other two, namely, that they exalt into an original law
+of the human intellect and of outward nature, one particular sequence of
+phenomena, which appears to them more natural and more conceivable than
+other sequences, only because it is more familiar. And from this
+judgment I am unable to except the theory, that Volition is an Efficient
+Cause.</p>
+
+<p>I am unwilling to leave the subject without adverting to the additional
+fallacy contained in the corollary from this theory; in the inference
+that because Volition is an efficient cause, therefore it is the only
+cause, and the direct agent in producing even what is apparently
+produced by something else. Volitions are not known to produce anything
+directly except nervous action, for the will influences even the muscles
+only through the nerves. Though it were granted, then, that every
+phenomenon has an efficient, and not merely a phenomenal cause, and that
+volition, in the case of the peculiar phenomena which are known to be
+produced by it, is that efficient cause; are we therefore to say, with
+these writers, that since we know of no other efficient cause, and ought
+not to assume one without evidence, there <i>is</i> no other, and volition is
+the direct cause of all phenomena? A more outrageous stretch of
+inference could hardly be made. Because among the infinite variety of
+the phenomena of nature there is one, namely, a particular mode of
+action of certain nerves, which has for its cause, and as we are now
+supposing for its efficient cause, a state of our mind; and because this
+is the only efficient cause of which we are conscious, being the only
+one of which in the nature of the case we <i>can</i> be conscious, since it
+is the only one which exists within ourselves; does this justify us in
+concluding that all other phenomena must have the same kind of efficient
+cause with that one eminently special, narrow, and peculiarly human or
+animal, phenomenon? The nearest parallel to this specimen of
+generalization is suggested <span class="pagenum"><a name="Page_399" id="Page_399">[Pg 399]</a></span>by the recently revived controversy on the
+old subject of Plurality of Worlds, in which the contending parties have
+been so conspicuously successful in overthrowing one another. Here also
+we have experience only of a single case, that of the world in which we
+live, but that this is inhabited we know absolutely, and without
+possibility of doubt. Now if on this evidence any one were to infer that
+every heavenly body without exception, sun, planet, satellite, comet,
+fixed star or nebula, is inhabited, and must be so from the inherent
+constitution of things, his inference would exactly resemble that of the
+writers who conclude that because volition is the efficient cause of our
+own bodily motions, it must be the efficient cause of everything else in
+the universe. It is true there are cases in which, with acknowledged
+propriety, we generalize from a single instance to a multitude of
+instances. But they must be instances which resemble the one known
+instance, and not such as have no circumstance in common with it except
+that of being instances. I have, for example, no direct evidence that
+any creature is alive except myself: yet I attribute, with full
+assurance, life and sensation to other human beings and animals. But I
+do not conclude that all other things are alive merely because I am. I
+ascribe to certain other creatures a life like my own, because they
+manifest it by the same sort of indications by which mine is manifested.
+I find that their phenomena and mine conform to the same laws, and it is
+for this reason that I believe both to arise from a similar cause.
+Accordingly I do not extend the conclusion beyond the grounds for it.
+Earth, fire, mountains, trees, are remarkable agencies, but their
+phenomena do not conform to the same laws as my actions do, and I
+therefore do not believe earth or fire, mountains or trees, to possess
+animal life. But the supporters of the Volition Theory ask us to infer
+that volition causes everything, for no reason except that it causes one
+particular thing; although that one phenomenon, far from being a type of
+all natural phenomena, is eminently peculiar; its laws bearing scarcely
+any resemblance to those of any other phenomenon, whether of inorganic
+or of organic nature.</p>
+
+
+<p><span class="pagenum"><a name="Page_400" id="Page_400">[Pg 400]</a></span></p>
+<p class="center">NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.</p>
+
+<blockquote><p>The author of the Second Burnett Prize Essay (Dr. Tulloch), who
+has employed a considerable number of pages in controverting
+the doctrines of the preceding chapter, has somewhat surprised
+me by denying a fact, which I imagined too well known to
+require proof&mdash;that there have been philosophers who found in
+physical explanations of phenomena the same complete mental
+satisfaction which we are told is only given by volitional
+explanation, and others who denied the Volitional Theory on the
+same ground of inconceivability on which it is defended. The
+assertion of the Essayist is countersigned still more
+positively by an able reviewer of the Essay:<a name="FNanchor_27_108" id="FNanchor_27_108"></a><a href="#Footnote_27_108" class="fnanchor">[27]</a> "Two
+illustrations," says the reviewer, "are advanced by Mr. Mill:
+the case of Thales and Anaximenes, stated by him to have
+maintained, the one Moisture and the other Air to be the origin
+of all things; and that of Descartes and Leibnitz, whom he
+asserts to have found the action of Mind upon Matter the grand
+inconceivability. In counterstatement as to the first of these
+cases the author shows&mdash;what we believe now hardly admits of
+doubt&mdash;that the Greek philosophers distinctly recognised as
+beyond and above their primal material source, the <i>&#957;&#959;&#8166;&#962;</i>, or Divine Intelligence, as the efficient and originating
+Source of all: and as to the second, by proof that it was the
+<i>mode</i>, not the <i>fact</i>, of that action on matter, which was
+represented as inconceivable."</p>
+
+<p>A greater quantity of historical error has seldom been
+comprised in a single sentence. With regard to Thales, the
+assertion that he considered water as a mere material in the
+hands of <i>&#957;&#959;&#8166;&#962;</i> rests on a passage of Cicero <i>de Natur�
+Deorum</i>: and whoever will refer to any of the accurate
+historians of philosophy, will find that they treat this as a
+mere fancy of Cicero, resting on no authority, opposed to all
+the evidence; and make surmises as to the manner in which
+Cicero may have been led into the error. (See Ritter, vol. i.
+p. 211, 2nd ed.; Brandis, vol. i. pp. 118-9, 1st ed.; Preller,
+<i>Historia Philosophi� Gr�co-Roman�</i>, p. 10. "Schiefe Ansicht,
+durchaus zu verwerfen;" "augenscheinlich folgernd statt zu
+berichten;" "quibus vera sententia Thaletis plane detorquetur;"
+are the expressions of these writers.) As for Anaximenes, he,
+even according to Cicero, maintained, not that air was the
+material out of which God made the world, but that the air was
+a god: "Anaximenes a�ra deum statuit:" or according to St.
+Augustine, that it was the material out of which the gods were
+made; "non tamen ab ipsis [Diis] a�rem factum, sed ipsos ex
+a�re ortos credidit." Those who are not familiar with the
+metaphysical terminology of antiquity, must not be misled by
+finding it stated that Anaximenes attributed <i>&#968;&#965;&#967;&#8052;</i>
+(translated <i>soul</i>, or <i>life</i>) to his universal element, the
+air. The Greek philosophers acknowledged several kinds of
+<i>&#968;&#965;&#967;&#8052;</i>, the nutritive, the sensitive, and the
+intellective.<a name="FNanchor_28_109" id="FNanchor_28_109"></a><a href="#Footnote_28_109" class="fnanchor">[28]</a> Even the moderns with admitted correctness
+attribute life to plants. As far as we can make out the meaning
+of Anaximenes, he made choice of Air as the universal agent, on
+the ground that it is perpetually in motion, without any
+apparent cause external to itself: so that he conceived it as
+exercising spontaneous force, and as the <span class="pagenum"><a name="Page_401" id="Page_401">[Pg 401]</a></span>principle of life and
+activity in all things, men and gods inclusive. If this be not
+representing it as the Efficient Cause, the dispute altogether
+has no meaning.</p>
+
+<p>If either Anaximenes, or Thales, or any of their cotemporaries,
+had held the doctrine that <i>&#957;&#959;&#8166;&#962;</i> was the Efficient
+Cause, that doctrine could not have been reputed, as it was
+throughout antiquity, to have originated with Anaxagoras. The
+testimony of Aristotle, in the first book of his Metaphysics,
+is perfectly decisive with respect to these early speculations.
+After enumerating four kinds of causes, or rather four
+different meanings of the word Cause, viz. the Essence of a
+thing, the Matter of it, the Origin of Motion (Efficient
+Cause), and the End or Final Cause, he proceeds to say, that
+most of the early philosophers recognised only the second kind
+of Cause, the Matter of a thing, <i>&#964;&#8048;&#962; &#7952;&#957; &#8021;&#955;&#951;&#962;
+&#949;&#7988;&#948;&#949;&#953; &#956;&#8057;&#957;&#945;&#962;
+&#8096;&#8053;&#952;&#951;&#963;&#945;&#957; &#7936;&#961;&#967;&#8048;&#962;
+&#949;&#7990;&#957;&#945;&#953; &#960;&#8049;&#957;&#964;&#969;&#957;</i>. As his first example he
+specifies Thales, whom he describes as taking the lead in this
+view of the subject, <i>&#8001; &#964;&#8134;&#962; &#964;&#959;&#953;&#945;&#973;&#964;&#951;&#962;
+&#7936;&#961;&#967;&#951;&#947;&#8056;&#962; &#966;&#953;&#955;&#959;&#963;&#959;&#966;&#8055;&#945;&#962;</i>, and goes on to Hippon, Anaximenes, Diogenes (of
+Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.
+Anaxagoras, however, (he proceeds to say,) taught a different
+doctrine, as we know, and it is <i>alleged</i> that Hermotimus of
+Clazomen� taught it before him. Anaxagoras represented, that
+even if these various theories of the universal material were
+true, there would be need of some other cause to account for
+the transformations of the material, since the material cannot
+originate its own changes: <i>&#959;&#8016; &#947;&#8048;&#961; &#948;&#8052; &#964;&#8057;
+&#947;&#949; &#8017;&#960;&#959;&#954;&#949;&#8055;&#956;&#949;&#957;&#959;&#957;
+&#945;&#8016;&#964;&#8056; &#960;&#959;&#953;&#949;&#8150;
+&#956;&#949;&#964;&#945;&#946;&#8049;&#955;&#955;&#949;&#953;&#957; &#7953;&#945;&#8166;&#964;&#959;;
+&#955;&#8051;&#947;&#969;
+&#948;' &#959;&#7990;&#959;&#957; &#959;&#8020;&#964;&#949; &#964;&#8056;
+&#958;&#8059;&#955;&#959;&#957; &#959;&#8020;&#964;&#949; &#8005;
+&#967;&#945;&#955;&#954;&#8056;&#962; &#945;&#7988;&#964;&#953;&#959;&#962; &#964;&#959;&#8166;
+&#956;&#949;&#964;&#945;&#946;&#8049;&#955;&#955;&#949;&#953;&#957; &#8051;&#954;&#8049;&#964;&#949;&#961;&#959;&#957;
+&#945;&#8016;&#964;&#8182;&#957;,
+&#959;&#8016;&#948;&#8050; &#960;&#959;&#953;&#949;&#8150; &#964;&#8056; &#956;&#7953;&#957; &#958;&#8059;&#955;&#959;&#957;
+&#954;&#955;&#8055;&#957;&#951;&#957; &#8005; &#948;&#8051;
+&#967;&#945;&#955;&#954;&#8056;&#962; &#7936;&#957;&#948;&#961;&#953;&#8049;&#957;&#964;&#945;,
+&#7936;&#955;&#955;' &#7953;&#964;&#949;&#961;&#959;&#957; &#964;&#953; &#964;&#8134;&#962;
+&#956;&#949;&#964;&#945;&#946;&#959;&#955;&#8134;&#962; &#945;&#7988;&#964;&#953;&#959;&#957;</i>, viz., the other kind of cause, <i>&#8005;&#952;&#949;&#957; &#7969; &#7936;&#961;&#967;&#8052;
+&#964;&#8134;&#962; &#954;&#953;&#957;&#8053;&#963;&#949;&#969;&#962;</i>&mdash;an Efficient Cause. Aristotle
+expresses great approbation of this doctrine (which he says
+made its author appear the only sober man among persons raving,
+<i>&#959;&#7990;&#959;&#957; &#957;&#8053;&#966;&#969;&#957; &#7952;&#966;&#8049;&#957;&#951;
+&#960;&#945;&#961;' &#949;&#7984;&#954;&#8134; &#955;&#8051;&#947;&#959;&#957;&#964;&#945;&#962;
+&#964;&#959;&#8166;&#962; &#960;&#961;&#8057;&#964;&#949;&#961;&#959;&#957;</i>);
+but while describing the influence which it exercised over
+subsequent speculation, he remarks that the philosophers
+against whom this, as he thinks, insuperable difficulty was
+urged, had not felt it to be any difficulty: <i>&#959;&#8016;&#948;&#8050;&#957; &#7952;&#948;&#965;&#963;&#967;&#949;&#961;&#8049;&#957;&#945;&#957;
+&#7952;&#957; &#7953;&#945;&#965;&#964;&#959;&#8150;&#962;</i>. It is surely unnecessary to say more
+in proof of the matter of fact which Dr. Tulloch and his
+reviewer deny.</p>
+
+<p>Having pointed out what he thinks the error of these early
+speculators in not recognising the need of an efficient cause,
+Aristotle goes on to mention two other efficient causes to
+which they might have had recourse, instead of intelligence:
+<i>&#964;&#8059;&#967;&#951;</i>, chance, and <i>&#964;&#8056; &#945;&#8016;&#964;&#959;&#956;&#8049;&#964;&#959;&#957;</i>, spontaneity.
+He indeed puts these aside as not sufficiently worthy causes
+for the order in the universe, <i>&#959;&#8016;&#948;' &#945;&#8022; &#964;&#8183; &#945;&#8016;&#964;&#959;&#956;&#8049;&#964;&#8179;
+&#954;&#945;&#8054; &#964;&#8135; &#964;&#8059;&#967;&#8131; &#964;&#959;&#963;&#959;&#8166;&#964;&#959;&#957;
+&#7952;&#960;&#953;&#964;&#961;&#8051;&#968;&#945;&#953; &#960;&#961;&#8118;&#947;&#956;&#945;
+&#954;&#945;&#955;&#8182;&#962; &#949;&#7990;&#967;&#949;&#957;</i>: but he does
+not reject them as incapable of producing any effect, but only
+as incapable of producing <i>that</i> effect. He himself recognises
+<i>&#964;&#8059;&#967;&#951;</i> and <i>&#964;&#8056; &#945;&#8016;&#964;&#959;&#956;&#8049;&#964;&#959;&#957;</i> as co-ordinate agents
+with Mind in producing the phenomena of the universe; the
+department allotted to them being composed of all the classes
+of phenomena which are not supposed to follow any uniform law.
+By thus including Chance among efficient causes, Aristotle fell
+into an error which philosophy has now outgrown, but which is
+by no means so alien to the spirit even of modern speculation
+as it may at first sight appear. Up to quite a recent period
+philosophers went on ascribing, and many of them have not yet
+ceased to ascribe, a real existence to <span class="pagenum"><a name="Page_402" id="Page_402">[Pg 402]</a></span>the results of
+abstraction. Chance could make out as good a title to that
+dignity as many other of the mind's abstract creations: it had
+had a name given to it, and why should it not be a reality? As
+for <i>&#964;&#8056; &#945;&#8016;&#964;&#959;&#956;&#8049;&#964;&#959;&#957;</i>, it is recognised even yet as one of
+the modes of origination of phenomena, by all those thinkers
+who maintain what is called the Freedom of the Will. The same
+self-determining power which that doctrine attributes to
+volitions, was supposed by the ancients to be possessed also by
+some other natural phenomena: a circumstance which throws
+considerable light on more than one of the supposed invincible
+necessities of belief. I have introduced it here, because this
+belief of Aristotle, or rather of the Greek philosophers
+generally, is as fatal as the doctrines of Thales and the Ionic
+school, to the theory that the human mind is compelled by its
+constitution to conceive volition as the origin of all force,
+and the efficient cause of all phenomena.<a name="FNanchor_29_110" id="FNanchor_29_110"></a><a href="#Footnote_29_110" class="fnanchor">[29]</a></p>
+
+<p>With regard to the modern philosophers (Leibnitz and the
+Cartesians) whom I had cited as having maintained that the
+action of mind upon matter, so far from <span class="pagenum"><a name="Page_403" id="Page_403">[Pg 403]</a></span>being the only
+conceivable origin of material phenomena, is itself
+inconceivable; the attempt to rebut this argument by asserting
+that the mode, not the fact, of the action of mind on matter
+was represented as inconceivable, is an abuse of the privilege
+of writing confidently about authors without reading them: for
+any knowledge whatever of Leibnitz would have taught those who
+thus speak of him, that the inconceivability of the mode, and
+the impossibility of the thing, were in his mind convertible
+expressions. What was his famous Principle of the Sufficient
+Reason, the very corner stone of his philosophy, from which the
+Preestablished Harmony, the doctrine of Monads, and all the
+opinions most characteristic of Leibnitz, were corollaries? It
+was, that nothing exists, the existence of which is not capable
+of being proved and explained <i>� priori</i>; the proof and
+explanation in the case of contingent facts being derived from
+the nature of their causes; which could not be the causes
+unless there was something in their nature showing them to be
+capable of producing those particular effects. And this
+"something" which accounts for the production of physical
+effects, he was able to find in many physical causes, but could
+not find it in any finite minds, which therefore he
+unhesitatingly asserted to be incapable of producing any
+physical effects whatever. "On ne saurait concevoir," he says,
+"une action r�ciproque de la mati�re et de l'intelligence l'une
+sur l'autre," and there is therefore (he contends) no choice
+but between the Occasional Causes of the Cartesians, and his
+own Preestablished Harmony, according to which there is no more
+connexion between our volitions and our muscular actions than
+there is between two clocks which are wound up to strike at the
+same instant. But he felt no similar difficulty as to physical
+causes: and throughout his speculations, as in the passage I
+have already cited respecting gravitation, he distinctly
+refuses to consider as part of the order of nature any fact
+which is not explicable from the nature of its physical cause.</p>
+
+<p>With regard to the Cartesians (not Descartes; I did not make
+that mistake, though the reviewer of Dr. Tulloch's Essay
+attributes it to me) I take a passage almost at random from
+Malebranche, who is the best known of the Cartesians, and,
+though not the inventor of the system of Occasional Causes, is
+its principal expositor. In Part 2, chap. 3, of his Sixth Book,
+having first said that matter cannot have the power of moving
+itself, he proceeds to argue that neither can mind have the
+power of moving it. "Quand on examine l'id�e que l'on a de tous
+les esprits finis, on ne voit point de liaison n�cessaire entre
+leur volont� et le mouvement de quelque corps que ce soit, on
+voit au contraire qu'il n'y en a point, et qu'il n'y en peut
+avoir;" (there is nothing in the idea of finite mind which can
+account for its causing the motion of a body;) "on doit aussi
+conclure, si on veut raisonner selon ses lumi�res, qu'il n'y a
+aucun esprit cr�� qui puisse remuer quelque corps que ce soit
+comme cause v�ritable ou principale, de m�me que l'on a dit
+qu'aucun corps ne se pouvait remuer soi-m�me:" thus the idea of
+Mind is according to him as incompatible as the idea of Matter
+with the exercise of active force. But when, he continues, we
+consider not a created but a Divine Mind, the case is altered;
+for the idea of a Divine Mind includes omnipotence; and the
+idea of omnipotence does contain the idea of being able to move
+bodies. Thus it is the nature of omnipotence which renders the
+motion of bodies even by the divine mind credible or
+conceivable, while, so far as depended on the mere nature of
+mind, it would have been inconceivable and <span class="pagenum"><a name="Page_404" id="Page_404">[Pg 404]</a></span>incredible. If
+Malebranche had not believed in an omnipotent being, he would
+have held all action of mind on body to be a demonstrated
+impossibility.<a name="FNanchor_30_111" id="FNanchor_30_111"></a><a href="#Footnote_30_111" class="fnanchor">[30]</a></p>
+
+<p>A doctrine more precisely the reverse of the Volitional theory
+of causation cannot well be imagined. The volitional theory is,
+that we know by intuition or by direct experience the action of
+our own mental volitions on matter; that we may hence infer all
+other action upon matter to be that of volition, and might thus
+know, without any other evidence, that matter is under the
+government of a divine mind. Leibnitz and the Cartesians, on
+the contrary, maintain that our volitions do not and cannot act
+upon matter, and that it is only the existence of an
+all-governing Being, and that Being omnipotent, which can
+account for the sequence between our volitions and our bodily
+actions. When we consider that each of these two theories,
+which, as theories of causation, stand at the opposite extremes
+of possible divergence from one another, invokes not only as
+its evidence, but as its sole evidence, the absolute
+inconceivability of any theory but itself, we are enabled to
+measure the worth of this kind of evidence; and when we find
+the Volitional theory entirely built upon the assertion that by
+our mental constitution we are compelled to recognise our
+volitions as efficient causes, and then find other thinkers
+maintaining that we know that they are not, and cannot be such
+causes, and cannot conceive them to be so, I think we have a
+right to say, that this supposed law of our mental constitution
+does not exist.</p>
+
+<p>Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this,
+that Leibnitz and the Cartesians were Theists, and believed the
+will of God to be an efficient cause. Doubtless they did, and
+the Cartesians even believed, though Leibnitz did not, that it
+is the only such cause. Dr. Tulloch mistakes the nature of the
+question. I was not writing on Theism, as Dr. Tulloch is, but
+against a particular theory of causation, which if it be
+unfounded, can give no effective support to Theism or to
+anything else. I found it asserted that volition is the only
+efficient cause, on the ground that no other efficient cause is
+conceivable. To this assertion I oppose the instances of
+Leibnitz and of the Cartesians, who affirmed with equal
+positiveness that volition as an efficient cause is itself not
+conceivable, and that omnipotence, which renders all things
+conceivable, can alone take away the impossibility. This I
+thought, and think, a conclusive answer to the argument on
+which this theory of causation avowedly depends. But I
+certainly did not imagine that Theism was bound up with that
+theory; nor expected to be charged with denying Leibnitz and
+the Cartesians to be Theists because I denied that they held
+the theory. </p></blockquote>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_405" id="Page_405">[Pg 405]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_VI" id="BOOK_III_CHAPTER_VI"></a>CHAPTER VI.<br />
+
+ON THE COMPOSITION OF CAUSES.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VI_1">� 1.</a> To complete the general notion of causation on which the rules of
+experimental inquiry into the laws of nature must be founded, one
+distinction still remains to be pointed out: a distinction so radical,
+and of so much importance, as to require a chapter to itself.</p>
+
+<p>The preceding discussions have rendered us familiar with the case in
+which several agents, or causes, concur as conditions to the production
+of an effect: a case, in truth, almost universal, there being very few
+effects to the production of which no more than one agent contributes.
+Suppose, then, that two different agents, operating jointly, are
+followed, under a certain set of collateral conditions, by a given
+effect. If either of these agents, instead of being joined with the
+other, had operated alone, under the same set of conditions in all other
+respects, some effect would probably have followed; which would have
+been different from the joint effect of the two, and more or less
+dissimilar to it. Now, if we happen to know what would be the effect of
+each cause when acting separately from the other, we are often able to
+arrive deductively, or <i>� priori</i>, at a correct prediction of what will
+arise from their conjunct agency. To enable us to do this, it is only
+necessary that the same law which expresses the effect of each cause
+acting by itself, shall also correctly express the part due to that
+cause, of the effect which follows from the two together. This condition
+is realized in the extensive and important class of phenomena commonly
+called mechanical, namely the phenomena of the communication of motion
+(or of pressure, which is tendency to motion) from one body to another.
+In this important class of cases of causation, one cause never, properly
+speaking, defeats or <span class="pagenum"><a name="Page_406" id="Page_406">[Pg 406]</a></span>frustrates another; both have their full effect.
+If a body is propelled in two directions by two forces, one tending to
+drive it to the north and the other to the east, it is caused to move in
+a given time exactly as far in both directions as the two forces would
+separately have carried it; and is left precisely where it would have
+arrived if it had been acted upon first by one of the two forces, and
+afterwards by the other. This law of nature is called, in dynamics, the
+principle of the Composition of Forces: and in imitation of that
+well-chosen expression, I shall give the name of the Composition of
+Causes to the principle which is exemplified in all cases in which the
+joint effect of several causes is identical with the sum of their
+separate effects.</p>
+
+<p>This principle, however, by no means prevails in all departments of the
+field of nature. The chemical combination of two substances produces, as
+is well known, a third substance with properties entirely different from
+those of either of the two substances separately, or both of them taken
+together. Not a trace of the properties of hydrogen or of oxygen is
+observable in those of their compound, water. The taste of sugar of lead
+is not the sum of the tastes of its component elements, acetic acid and
+lead or its oxide; nor is the colour of blue vitriol a mixture of the
+colours of sulphuric acid and copper. This explains why mechanics is a
+deductive or demonstrative science, and chemistry not. In the one, we
+can compute the effects of all combinations of causes, whether real or
+hypothetical, from the laws which we know to govern those causes when
+acting separately; because they continue to observe the same laws when
+in combination which they observed when separate: whatever would have
+happened in consequence of each cause taken by itself, happens when they
+are together, and we have only to cast up the results. Not so in the
+phenomena which are the peculiar subject of the science of chemistry.
+There, most of the uniformities to which the causes conformed when
+separate, cease altogether when they are conjoined; and we are not, at
+least in the present state of our knowledge, able to foresee what result
+will follow <span class="pagenum"><a name="Page_407" id="Page_407">[Pg 407]</a></span>from any new combination, until we have tried the specific
+experiment.</p>
+
+<p>If this be true of chemical combinations, it is still more true of those
+far more complex combinations of elements which constitute organized
+bodies; and in which those extraordinary new uniformities arise, which
+are called the laws of life. All organized bodies are composed of parts
+similar to those composing inorganic nature, and which have even
+themselves existed in an inorganic state; but the phenomena of life,
+which result from the juxtaposition of those parts in a certain manner,
+bear no analogy to any of the effects which would be produced by the
+action of the component substances considered as mere physical agents.
+To whatever degree we might imagine our knowledge of the properties of
+the several ingredients of a living body to be extended and perfected,
+it is certain that no mere summing up of the separate actions of those
+elements will ever amount to the action of the living body itself. The
+tongue, for instance, is, like all other parts of the animal frame,
+composed of gelatine, fibrin, and other products of the chemistry of
+digestion, but from no knowledge of the properties of those substances
+could we ever predict that it could taste, unless gelatine or fibrin
+could themselves taste; for no elementary fact can be in the conclusion,
+which was not in the premises.</p>
+
+<p>There are thus two different modes of the conjunct action of causes;
+from which arise two modes of conflict, or mutual interference, between
+laws of nature. Suppose, at a given point of time and space, two or more
+causes, which, if they acted separately, would produce effects contrary,
+or at least conflicting with each other; one of them tending to undo,
+wholly or partially, what the other tends to do. Thus, the expansive
+force of the gases generated by the ignition of gunpowder tends to
+project a bullet towards the sky, while its gravity tends to make it
+fall to the ground. A stream running into a reservoir at one end tends
+to fill it higher and higher, while a drain at the other extremity tends
+to empty it. Now, in such cases as these, even if the two causes which
+are in joint action exactly annul one another, still the laws of both
+<span class="pagenum"><a name="Page_408" id="Page_408">[Pg 408]</a></span>are fulfilled; the effect is the same as if the drain had been open for
+half an hour first,<a name="FNanchor_31_112" id="FNanchor_31_112"></a><a href="#Footnote_31_112" class="fnanchor">[31]</a> and the stream had flowed in for as long
+afterwards. Each agent produced the same amount of effect as if it had
+acted separately, though the contrary effect which was taking place
+during the same time obliterated it as fast as it was produced. Here
+then are two causes, producing by their joint operation an effect which
+at first seems quite dissimilar to those which they produce separately,
+but which on examination proves to be really the sum of those separate
+effects. It will be noticed that we here enlarge the idea of the sum of
+two effects, so as to include what is commonly called their difference,
+but which is in reality the result of the addition of opposites; a
+conception to which mankind are indebted for that admirable extension of
+the algebraical calculus, which has so vastly increased its powers as an
+instrument of discovery, by introducing into its reasonings (with the
+sign of subtraction prefixed, and under the name of Negative Quantities)
+every description whatever of positive phenomena, provided they are of
+such a quality in reference to those previously introduced, that to add
+the one is equivalent to subtracting an equal quantity of the other.</p>
+
+<p>There is, then, one mode of the mutual interference of laws of nature,
+in which, even when the concurrent causes annihilate each other's
+effects, each exerts its full efficacy according to its own law, its law
+as a separate agent. But in the other description of cases, the agencies
+which are brought together cease entirely, and a totally different set
+of phenomena arise: as in the experiment of two liquids which, when
+mixed in certain proportions, instantly become, not a larger amount of
+liquid, but a solid mass.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VI_2">� 2.</a> This difference between the case in which the joint effect of
+causes is the sum of their separate effects, and the <span class="pagenum"><a name="Page_409" id="Page_409">[Pg 409]</a></span>case in which it
+is heterogeneous to them; between laws which work together without
+alteration, and laws which, when called upon to work together, cease and
+give place to others; is one of the fundamental distinctions in nature.
+The former case, that of the Composition of Causes, is the general one;
+the other is always special and exceptional. There are no objects which
+do not, as to some of their phenomena, obey the principle of the
+Composition of Causes; none that have not some laws which are rigidly
+fulfilled in every combination into which the objects enter. The weight
+of a body, for instance, is a property which it retains in all the
+combinations in which it is placed. The weight of a chemical compound,
+or of an organized body, is equal to the sum of the weights of the
+elements which compose it. The weight either of the elements or of the
+compound will vary, if they be carried farther from their centre of
+attraction, or brought nearer to it; but whatever affects the one
+affects the other. They always remain precisely equal. So again, the
+component parts of a vegetable or animal substance do not lose their
+mechanical and chemical properties as separate agents, when, by a
+peculiar mode of juxtaposition, they, as an aggregate whole, acquire
+physiological or vital properties in addition. Those bodies continue, as
+before, to obey mechanical and chemical laws, in so far as the operation
+of those laws is not counteracted by the new laws which govern them as
+organized beings. When, in short, a concurrence of causes takes place
+which calls into action new laws bearing no analogy to any that we can
+trace in the separate operation of the causes, the new laws, while they
+supersede one portion of the previous laws, may coexist with another
+portion, and may even compound the effect of those previous laws with
+their own.</p>
+
+<p>Again, laws which were themselves generated in the second mode, may
+generate others in the first. Though there are laws which, like those of
+chemistry and physiology, owe their existence to a breach of the
+principle of Composition of Causes, it does not follow that these
+peculiar, or as they might be termed, <i>heteropathic</i> laws, are not
+capable of composition with one another. The causes which by one
+combination have <span class="pagenum"><a name="Page_410" id="Page_410">[Pg 410]</a></span>had their laws altered, may carry their new laws with
+them unaltered into their ulterior combinations. And hence there is no
+reason to despair of ultimately raising chemistry and physiology to the
+condition of deductive sciences; for though it is impossible to deduce
+all chemical and physiological truths from the laws or properties of
+simple substances or elementary agents, they may possibly be deducible
+from laws which commence when these elementary agents are brought
+together into some moderate number of not very complex combinations. The
+Laws of Life will never be deducible from the mere laws of the
+ingredients, but the prodigiously complex Facts of Life may all be
+deducible from comparatively simple laws of life; which laws (depending
+indeed on combinations, but on comparatively simple combinations, of
+antecedents) may, in more complex circumstances, be strictly compounded
+with one another, and with the physical and chemical laws of the
+ingredients. The details of the vital phenomena, even now, afford
+innumerable exemplifications of the Composition of Causes; and in
+proportion as these phenomena are more accurately studied, there appears
+more reason to believe that the same laws which operate in the simpler
+combinations of circumstances do, in fact, continue to be observed in
+the more complex. This will be found equally true in the phenomena of
+mind; and even in social and political phenomena, the results of the
+laws of mind. It is in the case of chemical phenomena that the least
+progress has yet been made in bringing the special laws under general
+ones from which they may be deduced; but there are even in chemistry
+many circumstances to encourage the hope that such general laws will
+hereafter be discovered. The different actions of a chemical compound
+will never, undoubtedly, be found to be the sums of the actions of its
+separate elements; but there may exist, between the properties of the
+compound and those of its elements, some constant relation, which, if
+discoverable by a sufficient induction, would enable us to foresee the
+sort of compound which will result from a new combination before we have
+actually tried it, and to judge of what sort of elements some new
+substance is compounded before we have analysed <span class="pagenum"><a name="Page_411" id="Page_411">[Pg 411]</a></span>it. The law of definite
+proportions, first discovered in its full generality by Dalton, is a
+complete solution of this problem in one, though but a secondary aspect,
+that of quantity: and in respect to quality, we have already some
+partial generalizations sufficient to indicate the possibility of
+ultimately proceeding farther. We can predicate some common properties
+of the kind of compounds which result from the combination, in each of
+the small number of possible proportions, of any acid whatever with any
+base. We have also the curious law, discovered by Berthollet, that two
+soluble salts mutually decompose one another whenever the new
+combinations which result produce an insoluble compound, or one less
+soluble than the two former. Another uniformity is that called the law
+of isomorphism; the identity of the crystalline forms of substances
+which possess in common certain peculiarities of chemical composition.
+Thus it appears that even heteropathic laws, such laws of combined
+agency as are not compounded of the laws of the separate agencies, are
+yet, at least in some cases, derived from them according to a fixed
+principle. There may, therefore, be laws of the generation of laws from
+others dissimilar to them; and in chemistry, these undiscovered laws of
+the dependence of the properties of the compound on the properties of
+its elements, may, together with the laws of the elements themselves,
+furnish the premises by which the science is perhaps destined one day to
+be rendered deductive.</p>
+
+<p>It would seem, therefore, that there is no class of phenomena in which
+the Composition of Causes does not obtain: that as a general rule,
+causes in combination produce exactly the same effects as when acting
+singly: but that this rule, though general, is not universal: that in
+some instances, at some particular points in the transition from
+separate to united action, the laws change, and an entirely new set of
+effects are either added to, or take the place of, those which arise
+from the separate agency of the same causes: the laws of these new
+effects being again susceptible of composition, to an indefinite extent,
+like the laws which they superseded.</p>
+
+
+<p><span class="pagenum"><a name="Page_412" id="Page_412">[Pg 412]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_VI_3">� 3.</a> That effects are proportional to their causes is laid down by some
+writers as an axiom in the theory of causation; and great use is
+sometimes made of this principle in reasonings respecting the laws of
+nature, though it is incumbered with many difficulties and apparent
+exceptions, which much ingenuity has been expended in showing not to be
+real ones. This proposition, in so far as it is true, enters as a
+particular case into the general principle of the Composition of Causes;
+the causes compounded being, in this instance, homogeneous; in which
+case, if in any, their joint effect might be expected to be identical
+with the sum of their separate effects. If a force equal to one hundred
+weight will raise a certain body along an inclined plane, a force equal
+to two hundred weight will raise two bodies exactly similar, and thus
+the effect is proportional to the cause. But does not a force equal to
+two hundred weight actually contain in itself two forces each equal to
+one hundred weight, which, if employed apart, would separately raise the
+two bodies in question? The fact, therefore, that when exerted jointly
+they raise both bodies at once, results from the Composition of Causes,
+and is a mere instance of the general fact that mechanical forces are
+subject to the law of Composition. And so in every other case which can
+be supposed. For the doctrine of the proportionality of effects to their
+causes cannot of course be applicable to cases in which the augmentation
+of the cause alters the <i>kind</i> of effect; that is, in which the surplus
+quantity superadded to the cause does not become compounded with it, but
+the two together generate an altogether new phenomenon. Suppose that the
+application of a certain quantity of heat to a body merely increases its
+bulk, that a double quantity melts it, and a triple quantity decomposes
+it: these three effects being heterogeneous, no ratio, whether
+corresponding or not to that of the quantities of heat applied, can be
+established between them. Thus the supposed axiom of the proportionality
+of effects to their causes fails at the precise point where the
+principle of the Composition of Causes also fails; viz., where the
+concurrence of causes is such as to determine a change in the properties
+of the body generally, and render it subject to new <span class="pagenum"><a name="Page_413" id="Page_413">[Pg 413]</a></span>laws, more or less
+dissimilar to those to which it conformed in its previous state. The
+recognition, therefore, of any such law of proportionality, is
+superseded by the more comprehensive principle, in which as much of it
+as is true is implicitly asserted.</p>
+
+<p>The general remarks on causation, which seemed necessary as an
+introduction to the theory of the inductive process, may here terminate.
+That process is essentially an inquiry into cases of causation. All the
+uniformities which exist in the succession of phenomena, and most of the
+uniformities in their coexistence, are either, as we have seen,
+themselves laws of causation, or consequences resulting from, and
+corollaries capable of being deduced from, such laws. If we could
+determine what causes are correctly assigned to what effects, and what
+effects to what causes, we should be virtually acquainted with the whole
+course of nature. All those uniformities which are mere results of
+causation, might then be explained and accounted for; and every
+individual fact or event might be predicted, provided we had the
+requisite data, that is, the requisite knowledge of the circumstances
+which, in the particular instance, preceded it.</p>
+
+<p>To ascertain, therefore, what are the laws of causation which exist in
+nature; to determine the effect of every cause, and the causes of all
+effects,&mdash;is the main business of Induction; and to point out how this
+is done is the chief object of Inductive Logic.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_414" id="Page_414">[Pg 414]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_VII" id="BOOK_III_CHAPTER_VII"></a>CHAPTER VII.<br />
+
+OF OBSERVATION AND EXPERIMENT.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VII_1">� 1.</a> It results from the preceding exposition, that the process of
+ascertaining what consequents, in nature, are invariably connected with
+what antecedents, or in other words what phenomena are related to each
+other as causes and effects, is in some sort a process of analysis. That
+every fact which begins to exist has a cause, and that this cause must
+be found somewhere among the facts which immediately preceded the
+occurrence, may be taken for certain. The whole of the present facts are
+the infallible result of all past facts, and more immediately of all the
+facts which existed at the moment previous. Here, then, is a great
+sequence, which we know to be uniform. If the whole prior state of the
+entire universe could again recur, it would again be followed by the
+present state. The question is, how to resolve this complex uniformity
+into the simpler uniformities which compose it, and assign to each
+portion of the vast antecedent the portion of the consequent which is
+attendant on it.</p>
+
+<p>This operation, which we have called analytical, inasmuch as it is the
+resolution of a complex whole into the component elements, is more than
+a merely mental analysis. No mere contemplation of the phenomena, and
+partition of them by the intellect alone, will of itself accomplish the
+end we have now in view. Nevertheless, such a mental partition is an
+indispensable first step. The order of nature, as perceived at a first
+glance, presents at every instant a chaos followed by another chaos. We
+must decompose each chaos into single facts. We must learn to see in the
+chaotic antecedent a multitude of distinct antecedents, in the chaotic
+consequent a multitude of distinct consequents. This, supposing it done,
+<span class="pagenum"><a name="Page_415" id="Page_415">[Pg 415]</a></span>will not of itself tell us on which of the antecedents each consequent
+is invariably attendant. To determine that point, we must endeavour to
+effect a separation of the facts from one another, not in our minds
+only, but in nature. The mental analysis, however, must take place
+first. And every one knows that in the mode of performing it, one
+intellect differs immensely from another. It is the essence of the act
+of observing; for the observer is not he who merely sees the thing which
+is before his eyes, but he who sees what parts that thing is composed
+of. To do this well is a rare talent. One person, from inattention, or
+attending only in the wrong place, overlooks half of what he sees:
+another sets down much more than he sees, confounding it with what he
+imagines, or with what he infers; another takes note of the <i>kind</i> of
+all the circumstances, but being inexpert in estimating their degree,
+leaves the quantity of each vague and uncertain; another sees indeed the
+whole, but makes such an awkward division of it into parts, throwing
+things into one mass which require to be separated, and separating
+others which might more conveniently be considered as one, that the
+result is much the same, sometimes even worse, than if no analysis had
+been attempted at all. It would be possible to point out what qualities
+of mind, and modes of mental culture, fit a person for being a good
+observer: that, however, is a question not of Logic, but of the Theory
+of Education, in the most enlarged sense of the term. There is not
+properly an Art of Observing. There may be rules for observing. But
+these, like rules for inventing, are properly instructions for the
+preparation of one's own mind; for putting it into the state in which it
+will be most fitted to observe, or most likely to invent. They are,
+therefore, essentially rules of self-education, which is a different
+thing from Logic. They do not teach how to do the thing, but how to make
+ourselves capable of doing it. They are an art of strengthening the
+limbs, not an art of using them.</p>
+
+<p>The extent and minuteness of observation which may be requisite, and the
+degree of decomposition to which it may be necessary to carry the mental
+analysis, depend on the particular purpose in view. To ascertain the
+state of the whole <span class="pagenum"><a name="Page_416" id="Page_416">[Pg 416]</a></span>universe at any particular moment is impossible, but
+would also be useless. In making chemical experiments, we do not think
+it necessary to note the position of the planets; because experience has
+shown, as a very superficial experience is sufficient to show, that in
+such cases that circumstance is not material to the result: and,
+accordingly, in the ages when men believed in the occult influences of
+the heavenly bodies, it might have been unphilosophical to omit
+ascertaining the precise condition of those bodies at the moment of the
+experiment. As to the degree of minuteness of the mental subdivision; if
+we were obliged to break down what we observe into its very simplest
+elements, that is, literally into single facts, it would be difficult to
+say where we should find them: we can hardly ever affirm that our
+divisions of any kind have reached the ultimate unit. But this too is
+fortunately unnecessary. The only object of the mental separation is to
+suggest the requisite physical separation, so that we may either
+accomplish it ourselves, or seek for it in nature; and we have done
+enough when we have carried the subdivision as far as the point at which
+we are able to see what observations or experiments we require. It is
+only essential, at whatever point our mental decomposition of facts may
+for the present have stopped, that we should hold ourselves ready and
+able to carry it farther as occasion requires, and should not allow the
+freedom of our discriminating faculty to be imprisoned by the swathes
+and bands of ordinary classification; as was the case with all early
+speculative inquirers, not excepting the Greeks, to whom it seldom
+occurred that what was called by one abstract name might, in reality, be
+several phenomena, or that there was a possibility of decomposing the
+facts of the universe into any elements but those which ordinary
+language already recognised.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VII_2">� 2.</a> The different antecedents and consequents, being, then, supposed to
+be, so far as the case requires, ascertained and discriminated from one
+another; we are to inquire which is connected with which. In every
+instance which comes under our observation, there are many antecedents
+and many <span class="pagenum"><a name="Page_417" id="Page_417">[Pg 417]</a></span>consequents. If those antecedents could not be severed from
+one another except in thought, or if those consequents never were found
+apart, it would be impossible for us to distinguish (<i>� posteriori</i> at
+least) the real laws, or to assign to any cause its effect, or to any
+effect its cause. To do so, we must be able to meet with some of the
+antecedents apart from the rest, and observe what follows from them; or
+some of the consequents, and observe by what they are preceded. We must,
+in short, follow the Baconian rule of <i>varying the circumstances</i>. This
+is, indeed, only the first rule of physical inquiry, and not, as some
+have thought, the sole rule; but it is the foundation of all the rest.</p>
+
+<p>For the purpose of varying the circumstances, we may have recourse
+(according to a distinction commonly made) either to observation or to
+experiment; we may either <i>find</i> an instance in nature, suited to our
+purposes, or, by an artificial arrangement of circumstances, <i>make</i> one.
+The value of the instance depends on what it is in itself, not on the
+mode in which it is obtained: its employment for the purposes of
+induction depends on the same principles in the one case and in the
+other; as the uses of money are the same whether it is inherited or
+acquired. There is, in short, no difference in kind, no real logical
+distinction, between the two processes of investigation. There are,
+however, practical distinctions to which it is of considerable
+importance to advert.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VII_3">� 3.</a> The first and most obvious distinction between Observation and
+Experiment is, that the latter is an immense extension of the former. It
+not only enables us to produce a much greater number of variations in
+the circumstances than nature spontaneously offers, but also, in
+thousands of cases, to produce the precise <i>sort</i> of variation which we
+are in want of for discovering the law of the phenomenon; a service
+which nature, being constructed on a quite different scheme from that of
+facilitating our studies, is seldom so friendly as to bestow upon us.
+For example, in order to ascertain what principle in the atmosphere
+enables it to sustain life, the variation we require is that a living
+animal should be immersed <span class="pagenum"><a name="Page_418" id="Page_418">[Pg 418]</a></span>in each component element of the atmosphere
+separately. But nature does not supply either oxygen or azote in a
+separate state. We are indebted to artificial experiment for our
+knowledge that it is the former, and not the latter, which supports
+respiration; and for our knowledge of the very existence of the two
+ingredients.</p>
+
+<p>Thus far the advantage of experimentation over simple observation is
+universally recognised: all are aware that it enables us to obtain
+innumerable combinations of circumstances which are not to be found in
+nature, and so add to nature's experiments a multitude of experiments of
+our own. But there is another superiority (or, as Bacon would have
+expressed it, another prerogative) of instances artificially obtained
+over spontaneous instances,&mdash;of our own experiments over even the same
+experiments when made by nature,&mdash;which is not of less importance, and
+which is far from being felt and acknowledged in the same degree.</p>
+
+<p>When we can produce a phenomenon artificially, we can take it, as it
+were, home with us, and observe it in the midst of circumstances with
+which in all other respects we are accurately acquainted. If we desire
+to know what are the effects of the cause A, and are able to produce A
+by means at our disposal, we can generally determine at our own
+discretion, so far as is compatible with the nature of the phenomenon A,
+the whole of the circumstances which shall be present along with it: and
+thus, knowing exactly the simultaneous state of everything else which is
+within the reach of A's influence, we have only to observe what
+alteration is made in that state by the presence of A.</p>
+
+<p>For example, by the electric machine we can produce in the midst of
+known circumstances, the phenomena which nature exhibits on a grander
+scale in the form of lightning and thunder. Now let any one consider
+what amount of knowledge of the effects and laws of electric agency
+mankind could have obtained from the mere observation of thunder-storms,
+and compare it with that which they have gained, and may expect to gain,
+from electrical and galvanic experiments. This example is the more
+striking, now that we have <span class="pagenum"><a name="Page_419" id="Page_419">[Pg 419]</a></span>reason to believe that electric action is of
+all natural phenomena (except heat) the most pervading and universal,
+which, therefore, it might antecedently have been supposed could stand
+least in need of artificial means of production to enable it to be
+studied; while the fact is so much the contrary, that without the
+electric machine, the Leyden jar, and the voltaic battery, we probably
+should never have suspected the existence of electricity as one of the
+great agents in nature; the few electric phenomena we should have known
+of would have continued to be regarded either as supernatural, or as a
+sort of anomalies and eccentricities in the order of the universe.</p>
+
+<p>When we have succeeded in insulating the phenomenon which is the subject
+of inquiry, by placing it among known circumstances, we may produce
+further variations of circumstances to any extent, and of such kinds as
+we think best calculated to bring the laws of the phenomenon into a
+clear light. By introducing one well-defined circumstance after another
+into the experiment, we obtain assurance of the manner in which the
+phenomenon behaves under an indefinite variety of possible
+circumstances. Thus, chemists, after having obtained some
+newly-discovered substance in a pure state, (that is, having made sure
+that there is nothing present which can interfere with and modify its
+agency,) introduce various other substances, one by one, to ascertain
+whether it will combine with them, or decompose them, and with what
+result; and also apply heat, or electricity, or pressure, to discover
+what will happen to the substance under each of these circumstances.</p>
+
+<p>But if, on the other hand, it is out of our power to produce the
+phenomenon, and we have to seek for instances in which nature produces
+it, the task before us is very different. Instead of being able to
+choose what the concomitant circumstances shall be, we now have to
+discover what they are; which, when we go beyond the simplest and most
+accessible cases, it is next to impossible to do, with any precision and
+completeness. Let us take, as an exemplification of a phenomenon which
+we have no means of fabricating artificially, a human mind. Nature
+produces many; but the consequence <span class="pagenum"><a name="Page_420" id="Page_420">[Pg 420]</a></span>of our not being able to produce
+them by art is, that in every instance in which we see a human mind
+developing itself, or acting upon other things, we see it surrounded and
+obscured by an indefinite multitude of unascertainable circumstances,
+rendering the use of the common experimental methods almost delusive. We
+may conceive to what extent this is true, if we consider, among other
+things, that whenever nature produces a human mind, she produces, in
+close connexion with it, a body; that is, a vast complication of
+physical facts, in no two cases perhaps exactly similar, and most of
+which (except the mere structure, which we can examine in a sort of
+coarse way after it has ceased to act), are radically out of the reach
+of our means of exploration. If, instead of a human mind, we suppose the
+subject of investigation to be a human society or State, all the same
+difficulties recur in a greatly augmented degree.</p>
+
+<p>We have thus already come within sight of a conclusion, which the
+progress of the inquiry will, I think, bring before us with the clearest
+evidence: namely, that in the sciences which deal with phenomena in
+which artificial experiments are impossible (as in the case of
+astronomy), or in which they have a very limited range (as in mental
+philosophy, social science, and even physiology), induction from direct
+experience is practised at a disadvantage in most cases equivalent to
+impracticability: from which it follows that the methods of those
+sciences, in order to accomplish anything worthy of attainment, must be
+to a great extent, if not principally, deductive. This is already known
+to be the case with the first of the sciences we have mentioned,
+astronomy; that it is not generally recognised as true of the others, is
+probably one of the reasons why they are not in a more advanced state.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VII_4">� 4.</a> If what is called pure observation is at so great a disadvantage,
+compared with artificial experimentation, in one department of the
+direct exploration of phenomena, there is another branch in which the
+advantage is all on the side of the former.</p>
+
+<p>Inductive inquiry having for its object to ascertain what <span class="pagenum"><a name="Page_421" id="Page_421">[Pg 421]</a></span>causes are
+connected with what effects, we may begin this search at either end of
+the road which leads from the one point to the other: we may either
+inquire into the effects of a given cause, or into the causes of a given
+effect. The fact that light blackens chloride of silver might have been
+discovered either by experiments on light, trying what effect it would
+produce on various substances, or by observing that portions of the
+chloride had repeatedly become black, and inquiring into the
+circumstances. The effect of the urali poison might have become known
+either by administering it to animals, or by examining how it happened
+that the wounds which the Indians of Guiana inflict with their arrows
+prove so uniformly mortal. Now it is manifest from the mere statement of
+the examples, without any theoretical discussion, that artificial
+experimentation is applicable only to the former of these modes of
+investigation. We can take a cause, and try what it will produce: but we
+cannot take an effect, and try what it will be produced by. We can only
+watch till we see it produced, or are enabled to produce it by accident.</p>
+
+<p>This would be of little importance, if it always depended on our choice
+from which of the two ends of the sequence we would undertake our
+inquiries. But we have seldom any option. As we can only travel from the
+known to the unknown, we are obliged to commence at whichever end we are
+best acquainted with. If the agent is more familiar to us than its
+effects, we watch for, or contrive, instances of the agent, under such
+varieties of circumstances as are open to us, and observe the result.
+If, on the contrary, the conditions on which a phenomenon depends are
+obscure, but the phenomenon itself familiar, we must commence our
+inquiry from the effect. If we are struck with the fact that chloride of
+silver has been blackened, and have no suspicion of the cause, we have
+no resource but to compare instances in which the fact has chanced to
+occur, until by that comparison we discover that in all those instances
+the substances had been exposed to light. If we knew nothing of the
+Indian arrows but their fatal effect, accident alone could turn our
+attention to experiments on the urali; in the regular course of
+investigation, we could only <span class="pagenum"><a name="Page_422" id="Page_422">[Pg 422]</a></span>inquire, or try to observe, what had been
+done to the arrows in particular instances.</p>
+
+<p>Wherever, having nothing to guide us to the cause, we are obliged to set
+out from the effect, and to apply the rule of varying the circumstances
+to the consequents, not the antecedents, we are necessarily destitute of
+the resource of artificial experimentation. We cannot, at our choice,
+obtain consequents, as we can antecedents, under any set of
+circumstances compatible with their nature. There are no means of
+producing effects but through their causes, and by the supposition the
+causes of the effect in question are not known to us. We have therefore
+no expedient but to study it where it offers itself spontaneously. If
+nature happens to present us with instances sufficiently varied in their
+circumstances, and if we are able to discover, either among the
+proximate antecedents or among some other order of antecedents,
+something which is always found when the effect is found, however
+various the circumstances, and never found when it is not; we may
+discover, by mere observation without experiment, a real uniformity in
+nature.</p>
+
+<p>But though this is certainly the most favourable case for sciences of
+pure observation, as contrasted with those in which artificial
+experiments are possible, there is in reality no case which more
+strikingly illustrates the inherent imperfection of direct induction
+when not founded on experimentation. Suppose that, by a comparison of
+cases of the effect, we have found an antecedent which appears to be,
+and perhaps is, invariably connected with it: we have not yet proved
+that antecedent to be the cause, until we have reversed the process, and
+produced the effect by means of that antecedent. If we can produce the
+antecedent artificially, and if, when we do so, the effect follows, the
+induction is complete; that antecedent is the cause of that
+consequent.<a name="FNanchor_32_113" id="FNanchor_32_113"></a><a href="#Footnote_32_113" class="fnanchor">[32]</a> But we have then added <span class="pagenum"><a name="Page_423" id="Page_423">[Pg 423]</a></span>the evidence of experiment to
+that of simple observation. Until we had done so, we had only proved
+<i>invariable</i> antecedence within the limits of experience, but not
+<i>unconditional</i> antecedence, or causation. Until it had been shown by
+the actual production of the antecedent under known circumstances, and
+the occurrence thereupon of the consequent, that the antecedent was
+really the condition on which it depended; the uniformity of succession
+which was proved to exist between them might, for aught we knew, be
+(like the succession of day and night) not a case of causation at all;
+both antecedent and consequent might be successive stages of the effect
+of an ulterior cause. Observation, in short, without experiment
+(supposing no aid from deduction) can ascertain sequences and
+coexistences, but cannot prove causation.</p>
+
+<p>In order to see these remarks verified by the actual state of the
+sciences, we have only to think of the condition of natural history. In
+zoology, for example, there is an immense number of uniformities
+ascertained, some of coexistence, others of succession, to many of
+which, notwithstanding considerable variations of the attendant
+circumstances, we know not any exception: but the antecedents, for the
+most part, are such as we cannot artificially produce; or if we can, it
+is only by setting in motion the exact process by which nature produces
+them; and this being to us a mysterious process, of which the main
+circumstances are not only unknown but unobservable, we do not succeed
+in obtaining the antecedents under known circumstances. What is the
+result? That on this vast subject, which affords so much and such varied
+scope for observation, we have made most scanty progress in ascertaining
+any laws of causation. We know not with certainty, in the case of most
+of the phenomena that we find conjoined, which is the condition of the
+other; which is cause, and which effect, or whether either of them is
+so, or they are not rather conjunct effects of causes yet to be
+discovered, complex results of laws hitherto unknown.</p>
+
+<p>Although some of the foregoing observations may be, in technical
+strictness of arrangement, premature in this place, it seemed that a few
+general remarks on the difference between <span class="pagenum"><a name="Page_424" id="Page_424">[Pg 424]</a></span>sciences of mere observation
+and sciences of experimentation, and the extreme disadvantage under
+which directly inductive inquiry is necessarily carried on in the
+former, were the best preparation for discussing the methods of direct
+induction; a preparation rendering superfluous much that must otherwise
+have been introduced, with some inconvenience, into the heart of that
+discussion. To the consideration of these methods we now proceed.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_425" id="Page_425">[Pg 425]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_VIII" id="BOOK_III_CHAPTER_VIII"></a>CHAPTER VIII.<br />
+
+OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_1">� 1.</a> The simplest and most obvious modes of singling out from among the
+circumstances which precede or follow a phenomenon, those with which it
+is really connected by an invariable law, are two in number. One is, by
+comparing together different instances in which the phenomenon occurs.
+The other is, by comparing instances in which the phenomenon does occur,
+with instances in other respects similar in which it does not. These two
+methods may be respectively denominated, the Method of Agreement, and
+the Method of Difference.</p>
+
+<p>In illustrating these methods, it will be necessary to bear in mind the
+twofold character of inquiries into the laws of phenomena; which may be
+either inquiries into the cause of a given effect, or into the effects
+or properties of a given cause. We shall consider the methods in their
+application to either order of investigation, and shall draw our
+examples equally from both.</p>
+
+<p>We shall denote antecedents by the large letters of the alphabet, and
+the consequents corresponding to them by the small. Let A, then, be an
+agent or cause, and let the object of our inquiry be to ascertain what
+are the effects of this cause. If we can either find, or produce, the
+agent A in such varieties of circumstances, that the different cases
+have no circumstance in common except A; then whatever effect we find to
+be produced in all our trials, is indicated as the effect of A. Suppose,
+for example, that A is tried along with B and C, and that the effect is
+<i>a b c</i>; and suppose that A is next tried with D and E, but without B
+and C, and that the effect is <i>a d e</i>. Then we may reason thus: <i>b</i> and
+<i>c</i> are not effects of A, for they were not produced by it in the second
+experiment; nor <span class="pagenum"><a name="Page_426" id="Page_426">[Pg 426]</a></span>are <i>d</i> and <i>e</i>, for they were not produced in the
+first. Whatever is really the effect of A must have been produced in
+both instances; now this condition is fulfilled by no circumstance
+except <i>a</i>. The phenomenon <i>a</i> cannot have been the effect of B or C,
+since it was produced where they were not; nor of D or E, since it was
+produced where they were not. Therefore it is the effect of A.</p>
+
+<p>For example, let the antecedent A be the contact of an alkaline
+substance and an oil. This combination being tried under several
+varieties of circumstances, resembling each other in nothing else, the
+results agree in the production of a greasy and detersive or saponaceous
+substance: it is therefore concluded that the combination of an oil and
+an alkali causes the production of a soap. It is thus we inquire, by the
+Method of Agreement, into the effect of a given cause.</p>
+
+<p>In a similar manner we may inquire into the cause of a given effect. Let
+<i>a</i> be the effect. Here, as shown in the last chapter, we have only the
+resource of observation without experiment: we cannot take a phenomenon
+of which we know not the origin, and try to find its mode of production
+by producing it: if we succeeded in such a random trial it could only be
+by accident. But if we can observe <i>a</i> in two different combinations, <i>a
+b c</i>, and <i>a d e</i>; and if we know, or can discover, that the antecedent
+circumstances in these cases respectively were A B C and A D E; we may
+conclude by a reasoning similar to that in the preceding example, that A
+is the antecedent connected with the consequent <i>a</i> by a law of
+causation. B and C, we may say, cannot be causes of <i>a</i>, since on its
+second occurrence they were not present; nor are D and E, for they were
+not present on its first occurrence. A, alone of the five circumstances,
+was found among the antecedents of <i>a</i> in both instances.</p>
+
+<p>For example, let the effect <i>a</i> be crystallization. We compare instances
+in which bodies are known to assume crystalline structure, but which
+have no other point of agreement; and we find them to have one, and as
+far as we can observe, only one, antecedent in common: the deposition of
+a solid matter from a liquid state, either a state of fusion or of
+solution. We conclude, <span class="pagenum"><a name="Page_427" id="Page_427">[Pg 427]</a></span>therefore, that the solidification of a
+substance from a liquid state is an invariable antecedent of its
+crystallization.</p>
+
+<p>In this example we may go farther, and say, it is not only the
+invariable antecedent but the cause; or at least the proximate event
+which completes the cause. For in this case we are able, after detecting
+the antecedent A, to produce it artificially, and by finding that <i>a</i>
+follows it, verify the result of our induction. The importance of thus
+reversing the proof was strikingly manifested when by keeping a phial of
+water charged with siliceous particles undisturbed for years, a chemist
+(I believe Dr. Wollaston) succeeded in obtaining crystals of quartz: and
+in the equally interesting experiment in which Sir James Hall produced
+artificial marble, by the cooling of its materials from fusion under
+immense pressure: two admirable examples of the light which may be
+thrown upon the most secret processes of nature by well-contrived
+interrogation of her.</p>
+
+<p>But if we cannot artificially produce the phenomenon A, the conclusion
+that it is the cause of <i>a</i> remains subject to very considerable doubt.
+Though an invariable, it may not be the unconditional antecedent of <i>a</i>,
+but may precede it as day precedes night or night day. This uncertainty
+arises from the impossibility of assuring ourselves that A is the <i>only</i>
+immediate antecedent common to both the instances. If we could be
+certain of having ascertained all the invariable antecedents, we might
+be sure that the unconditional invariable antecedent, or cause, must be
+found somewhere among them. Unfortunately it is hardly ever possible to
+ascertain all the antecedents, unless the phenomenon is one which we can
+produce artificially. Even then, the difficulty is merely lightened, not
+removed: men knew how to raise water in pumps long before they adverted
+to what was really the operating circumstance in the means they
+employed, namely, the pressure of the atmosphere on the open surface of
+the water. It is, however, much easier to analyse completely a set of
+arrangements made by ourselves, than the whole complex mass of the
+agencies which nature happens to be exerting at the moment of the
+production of a given phenomenon. <span class="pagenum"><a name="Page_428" id="Page_428">[Pg 428]</a></span>We may overlook some of the material
+circumstances in an experiment with an electrical machine; but we shall,
+at the worst, be better acquainted with them than with those of a
+thunder-storm.</p>
+
+<p>The mode of discovering and proving laws of nature, which we have now
+examined, proceeds on the following axiom: Whatever circumstances can be
+excluded, without prejudice to the phenomenon, or can be absent
+notwithstanding its presence, is not connected with it in the way of
+causation. The casual circumstances being thus eliminated, if only one
+remains, that one is the cause which we are in search of: if more than
+one, they either are, or contain among them, the cause; and so, <i>mutatis
+mutandis</i>, of the effect. As this method proceeds by comparing different
+instances to ascertain in what they agree, I have termed it the Method
+of Agreement: and we may adopt as its regulating principle the following
+canon:&mdash;</p>
+
+<p class="center"><span class="smcap">First Canon.</span></p>
+
+<p><i>If two or more instances of the phenomenon under investigation have
+only one circumstance in common, the circumstance in which alone all the
+instances agree, is the cause (or effect) of the given phenomenon.</i></p>
+
+<p>Quitting for the present the Method of Agreement, to which we shall
+almost immediately return, we proceed to a still more potent instrument
+of the investigation of nature, the Method of Difference.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_2">� 2.</a> In the Method of Agreement, we endeavoured to obtain instances
+which agreed in the given circumstance but differed in every other: in
+the present method we require, on the contrary, two instances resembling
+one another in every other respect, but differing in the presence or
+absence of the phenomenon we wish to study. If our object be to discover
+the effects of an agent A, we must procure A in some set of ascertained
+circumstances, as A B C, and having noted the effects produced, compare
+them with the effect of the remaining circumstances B C, when A is
+absent. If the effect of A B C is <i>a b c</i>, and the effect of B C, <i>b c</i>,
+it is <span class="pagenum"><a name="Page_429" id="Page_429">[Pg 429]</a></span>evident that the effect of A is <i>a</i>. So again, if we begin at the
+other end, and desire to investigate the cause of an effect <i>a</i>, we must
+select an instance, as <i>a b c</i>, in which the effect occurs, and in which
+the antecedents were A B C, and we must look out for another instance in
+which the remaining circumstances, <i>b c</i>, occur without <i>a</i>. If the
+antecedents, in that instance, are B C, we know that the cause of <i>a</i>
+must be A: either A alone, or A in conjunction with some of the other
+circumstances present.</p>
+
+<p>It is scarcely necessary to give examples of a logical process to which
+we owe almost all the inductive conclusions we draw in daily life. When
+a man is shot through the heart, it is by this method we know that it
+was the gun-shot which killed him: for he was in the fulness of life
+immediately before, all circumstances being the same, except the wound.</p>
+
+<p>The axioms implied in this method are evidently the following. Whatever
+antecedent cannot be excluded without preventing the phenomenon, is the
+cause, or a condition, of that phenomenon: Whatever consequent can be
+excluded, with no other difference in the antecedents than the absence
+of a particular one, is the effect of that one. Instead of comparing
+different instances of a phenomenon, to discover in what they agree,
+this method compares an instance of its occurrence with an instance of
+its non-occurrence, to discover in what they differ. The canon which is
+the regulating principle of the Method of Difference may be expressed as
+follows:</p>
+
+<p class="center"><span class="smcap">Second Canon.</span></p>
+
+<p><i>If an instance in which the phenomenon under investigation occurs, and
+an instance in which it does not occur, have every circumstance in
+common save one, that one occurring only in the former; the circumstance
+in which alone the two instances differ, is the effect, or the cause, or
+an indispensable part of the cause, of the phenomenon.</i></p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_3">� 3.</a> The two methods which we have now stated have many features of
+resemblance, but there are also many distinctions <span class="pagenum"><a name="Page_430" id="Page_430">[Pg 430]</a></span>between them. Both
+are methods of <i>elimination</i>. This term (employed in the theory of
+equations to denote the process by which one after another of the
+elements of a question is excluded, and the solution made to depend on
+the relation between the remaining elements only) is well suited to
+express the operation, analogous to this, which has been understood
+since the time of Bacon to be the foundation of experimental inquiry:
+namely, the successive exclusion of the various circumstances which are
+found to accompany a phenomenon in a given instance, in order to
+ascertain what are those among them which can be absent consistently
+with the existence of the phenomenon. The Method of Agreement stands on
+the ground that whatever can be eliminated, is not connected with the
+phenomenon by any law. The Method of Difference has for its foundation,
+that whatever cannot be eliminated, is connected with the phenomenon by
+a law.</p>
+
+<p>Of these methods, that of Difference is more particularly a method of
+artificial experiment; while that of Agreement is more especially the
+resource employed where experimentation is impossible. A few reflections
+will prove the fact, and point out the reason of it.</p>
+
+<p>It is inherent in the peculiar character of the Method of Difference,
+that the nature of the combinations which it requires is much more
+strictly defined than in the Method of Agreement. The two instances
+which are to be compared with one another must be exactly similar, in
+all circumstances except the one which we are attempting to investigate:
+they must be in the relation of A B C and B C, or of <i>a b c</i> and <i>b c</i>.
+It is true that this similarity of circumstances needs not extend to
+such as are already known to be immaterial to the result. And in the
+case of most phenomena we learn at once, from the commonest experience,
+that most of the coexistent phenomena of the universe may be either
+present or absent without affecting the given phenomenon; or, if
+present, are present indifferently when the phenomenon does not happen
+and when it does. Still, even limiting the identity which is required
+between the two instances, A B C and B C, to such circumstances as are
+not already known to be indifferent; it is <span class="pagenum"><a name="Page_431" id="Page_431">[Pg 431]</a></span>very seldom that nature
+affords two instances, of which we can be assured that they stand in
+this precise relation to one another. In the spontaneous operations of
+nature there is generally such complication and such obscurity, they are
+mostly either on so overwhelmingly large or on so inaccessibly minute a
+scale, we are so ignorant of a great part of the facts which really take
+place, and even those of which we are not ignorant are so multitudinous,
+and therefore so seldom exactly alike in any two cases, that a
+spontaneous experiment, of the kind required by the Method of
+Difference, is commonly not to be found. When, on the contrary, we
+obtain a phenomenon by an artificial experiment, a pair of instances
+such as the method requires is obtained almost as a matter of course,
+provided the process does not last a long time. A certain state of
+surrounding circumstances existed before we commenced the experiment;
+this is B C. We then introduce A; say, for instance, by merely bringing
+an object from another part of the room, before there has been time for
+any change in the other elements. It is, in short (as M. Comte
+observes), the very nature of an experiment, to introduce into the
+pre-existing state of circumstances a change perfectly definite. We
+choose a previous state of things with which we are well acquainted, so
+that no unforeseen alteration in that state is likely to pass
+unobserved; and into this we introduce, as rapidly as possible, the
+phenomenon which we wish to study; so that in general we are entitled to
+feel complete assurance that the pre-existing state, and the state which
+we have produced, differ in nothing except the presence or absence of
+that phenomenon. If a bird is taken from a cage, and instantly plunged
+into carbonic acid gas, the experimentalist may be fully assured (at all
+events after one or two repetitions) that no circumstance capable of
+causing suffocation had supervened in the interim, except the change
+from immersion in the atmosphere to immersion in carbonic acid gas.
+There is one doubt, indeed, which may remain in some cases of this
+description; the effect may have been produced not by the change, but by
+the means employed to produce the change. The possibility, however, of
+this last supposition generally admits of <span class="pagenum"><a name="Page_432" id="Page_432">[Pg 432]</a></span>being conclusively tested by
+other experiments. It thus appears that in the study of the various
+kinds of phenomena which we can, by our voluntary agency, modify or
+control, we can in general satisfy the requisitions of the Method of
+Difference; but that by the spontaneous operations of nature those
+requisitions are seldom fulfilled.</p>
+
+<p>The reverse of this is the case with the Method of Agreement. We do not
+here require instances of so special and determinate a kind. Any
+instances whatever, in which nature presents us with a phenomenon, may
+be examined for the purposes of this method; and if all such instances
+agree in anything, a conclusion of considerable value is already
+attained. We can seldom, indeed, be sure that the one point of agreement
+is the only one; but this ignorance does not, as in the Method of
+Difference, vitiate the conclusion; the certainty of the result, as far
+as it goes, is not affected. We have ascertained one invariable
+antecedent or consequent, however many other invariable antecedents or
+consequents may still remain unascertained. If A B C, A D E, A F G, are
+all equally followed by <i>a</i>, then <i>a</i> is an invariable consequent of A.
+If <i>a b c</i>, <i>a d e</i>, <i>a f g</i>, all number A among their antecedents, then
+A is connected as an antecedent, by some invariable law, with <i>a</i>. But
+to determine whether this invariable antecedent is a cause, or this
+invariable consequent an effect, we must be able, in addition, to
+produce the one by means of the other; or, at least, to obtain that
+which alone constitutes our assurance of having produced anything,
+namely, an instance in which the effect, <i>a</i>, has come into existence,
+with no other change in the pre-existing circumstances than the addition
+of A. And this, if we can do it, is an application of the Method of
+Difference, not of the Method of Agreement.</p>
+
+<p>It thus appears to be by the Method of Difference alone that we can
+ever, in the way of direct experience, arrive with certainty at causes.
+The Method of Agreement leads only to laws of phenomena (as some writers
+call them, but improperly, since laws of causation are also laws of
+phenomena): that is, to uniformities, which either are not laws of
+causation, or in which the question of causation must for the present
+<span class="pagenum"><a name="Page_433" id="Page_433">[Pg 433]</a></span>remain undecided. The Method of Agreement is chiefly to be resorted to,
+as a means of suggesting applications of the Method of Difference (as in
+the last example the comparison of A B C, A D E, A F G, suggested that A
+was the antecedent on which to try the experiment whether it could
+produce <i>a</i>); or as an inferior resource, in case the Method of
+Difference is impracticable; which, as we before showed, generally
+arises from the impossibility of artificially producing the phenomena.
+And hence it is that the Method of Agreement, though applicable in
+principle to either case, is more emphatically the method of
+investigation on those subjects where artificial experimentation is
+impossible: because on those it is, generally, our only resource of a
+directly inductive nature; while, in the phenomena which we can produce
+at pleasure, the Method of Difference generally affords a more
+efficacious process, which will ascertain causes as well as mere laws.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_4">� 4.</a> There are, however, many cases in which, though our power of
+producing the phenomenon is complete, the Method of Difference either
+cannot be made available at all, or not without a previous employment of
+the Method of Agreement. This occurs when the agency by which we can
+produce the phenomenon is not that of one single antecedent, but a
+combination of antecedents, which we have no power of separating from
+each other, and exhibiting apart. For instance, suppose the subject of
+inquiry to be the cause of the double refraction of light. We can
+produce this phenomenon at pleasure, by employing any one of the many
+substances which are known to refract light in that peculiar manner. But
+if, taking one of those substances, as Iceland spar for example, we wish
+to determine on which of the properties of Iceland spar this remarkable
+phenomenon depends, we can make no use, for that purpose, of the Method
+of Difference; for we cannot find another substance precisely resembling
+Iceland spar except in some one property. The only mode, therefore, of
+prosecuting this inquiry is that afforded by the Method of Agreement; by
+which, in fact, through a comparison of all the known substances which
+have the property of doubly <span class="pagenum"><a name="Page_434" id="Page_434">[Pg 434]</a></span>refracting light, it was ascertained that
+they agree in the circumstance of being crystalline substances; and
+though the converse does not hold, though all crystalline substances
+have not the property of double refraction, it was concluded, with
+reason, that there is a real connexion between these two properties;
+that either crystalline structure, or the cause which gives rise to that
+structure, is one of the conditions of double refraction.</p>
+
+<p>Out of this employment of the Method of Agreement arises a peculiar
+modification of that method, which is sometimes of great avail in the
+investigation of nature. In cases similar to the above, in which it is
+not possible to obtain the precise pair of instances which our second
+canon requires&mdash;instances agreeing in every antecedent except A, or in
+every consequent except <i>a</i>; we may yet be able, by a double employment
+of the Method of Agreement, to discover in what the instances which
+contain A or <i>a</i>, differ from those which do not.</p>
+
+<p>If we compare various instances in which <i>a</i> occurs, and find that they
+all have in common the circumstance A, and (as far as can be observed)
+no other circumstance, the Method of Agreement, so far, bears testimony
+to a connexion between A and <i>a</i>. In order to convert this evidence of
+connexion into proof of causation by the direct Method of Difference, we
+ought to be able, in some one of these instances, as for example A B C,
+to leave out A, and observe whether by doing so, <i>a</i> is prevented. Now
+supposing (what is often the case) that we are not able to try this
+decisive experiment; yet, provided we can by any means discover what
+would be its result if we could try it, the advantage will be the same.
+Suppose, then, that as we previously examined a variety of instances in
+which <i>a</i> occurred, and found them to agree in containing A, so we now
+observe a variety of instances in which <i>a</i> does not occur, and find
+them agree in not containing A; which establishes, by the Method of
+Agreement, the same connexion between the absence of A and the absence
+of <i>a</i>, which was before established between their presence. As, then,
+it had been shown that whenever A is present <i>a</i> is present, so it being
+now shown that when A is taken away <i>a</i> is removed along with it, we
+<span class="pagenum"><a name="Page_435" id="Page_435">[Pg 435]</a></span>have by the one proposition A B C, <i>a b c</i>, by the other B C, <i>b c</i>,
+the positive and negative instances which the Method of Difference
+requires.</p>
+
+<p>This method may be called the Indirect Method of Difference, or the
+Joint Method of Agreement and Difference; and consists in a double
+employment of the Method of Agreement, each proof being independent of
+the other, and corroborating it. But it is not equivalent to a proof by
+the direct Method of Difference. For the requisitions of the Method of
+Difference are not satisfied, unless we can be quite sure either that
+the instances affirmative of <i>a</i> agree in no antecedent whatever but A,
+or that the instances negative of <i>a</i> agree in nothing but the negation
+of A. Now if it were possible, which it never is, to have this
+assurance, we should not need the joint method; for either of the two
+sets of instances separately would then be sufficient to prove
+causation. This indirect method, therefore, can only be regarded as a
+great extension and improvement of the Method of Agreement, but not as
+participating in the more cogent nature of the Method of Difference. The
+following may be stated as its canon:&mdash;</p>
+
+<p class="center"><span class="smcap">Third Canon.</span></p>
+
+<p><i>If two or more instances in which the phenomenon occurs have only one
+circumstance in common, while two or more instances in which it does not
+occur have nothing in common save the absence of that circumstance; the
+circumstance in which alone the two sets of instances differ, is the
+effect, or the cause, or an indispensable part of the cause, of the
+phenomenon.</i></p>
+
+<p>We shall presently see that the Joint Method of Agreement and Difference
+constitutes, in another respect not yet adverted to, an improvement upon
+the common Method of Agreement, namely, in being unaffected by a
+characteristic imperfection of that method, the nature of which still
+remains to be pointed out. But as we cannot enter into this exposition
+without introducing a new element of complexity into this long and
+intricate discussion, I shall postpone it to a subsequent chapter, and
+shall at once proceed to a statement of two other methods, which will
+complete the enumeration of <span class="pagenum"><a name="Page_436" id="Page_436">[Pg 436]</a></span>the means which mankind possess for
+exploring the laws of nature by specific observation and experience.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_5">� 5.</a> The first of these has been aptly denominated the Method of
+Residues. Its principle is very simple. Subducting from any given
+phenomenon all the portions which, by virtue of preceding inductions,
+can be assigned to known causes, the remainder will be the effect of the
+antecedents which had been overlooked, or of which the effect was as yet
+an unknown quantity.</p>
+
+<p>Suppose, as before, that we have the antecedents A B C, followed by the
+consequents <i>a b c</i>, and that by previous inductions (founded, we will
+suppose, on the Method of Difference) we have ascertained the causes of
+some of these effects, or the effects of some of these causes; and are
+thence apprised that the effect of A is <i>a</i>, and that the effect of B is
+<i>b</i>. Subtracting the sum of these effects from the total phenomenon,
+there remains <i>c</i>, which now, without any fresh experiments, we may know
+to be the effect of C. This Method of Residues is in truth a peculiar
+modification of the Method of Difference. If the instance A B C, <i>a b
+c</i>, could have been compared with a single instance A B, <i>a b</i>, we
+should have proved C to be the cause of <i>c</i>, by the common process of
+the Method of Difference. In the present case, however, instead of a
+single instance A B, we have had to study separately the causes A and B,
+and to infer from the effects which they produce separately, what effect
+they must produce in the case A B C where they act together. Of the two
+instances, therefore, which the Method of Difference requires,&mdash;the one
+positive, the other negative,&mdash;the negative one, or that in which the
+given phenomenon is absent, is not the direct result of observation and
+experiment, but has been arrived at by deduction. As one of the forms of
+the Method of Difference, the Method of Residues partakes of its
+rigorous certainty, provided the previous inductions, those which gave
+the effects of A and B, were obtained by the same infallible method, and
+provided we are certain that C is the <i>only</i> antecedent to which the
+residual phenomenon <i>c</i> can be referred; the only agent of <span class="pagenum"><a name="Page_437" id="Page_437">[Pg 437]</a></span>which we had
+not already calculated and subducted the effect. But as we can never be
+quite certain of this, the evidence derived from the Method of Residues
+is not complete unless we can obtain C artificially and try it
+separately, or unless its agency, when once suggested, can be accounted
+for, and proved deductively from known laws.</p>
+
+<p>Even with these reservations, the Method of Residues is one of the most
+important among our instruments of discovery. Of all the methods of
+investigating laws of nature, this is the most fertile in unexpected
+results; often informing us of sequences in which neither the cause nor
+the effect were sufficiently conspicuous to attract of themselves the
+attention of observers. The agent C may be an obscure circumstance, not
+likely to have been perceived unless sought for, nor likely to have been
+sought for until attention had been awakened by the insufficiency of the
+obvious causes to account for the whole of the effect. And <i>c</i> may be so
+disguised by its intermixture with <i>a</i> and <i>b</i>, that it would scarcely
+have presented itself spontaneously as a subject of separate study. Of
+these uses of the method, we shall presently cite some remarkable
+examples. The canon of the Method of Residues is as follows:&mdash;</p>
+
+<p class="center"><span class="smcap">Fourth Canon.</span></p>
+
+<p><i>Subduct from any phenomenon such part as is known by previous
+inductions to be the effect of certain antecedents, and the residue of
+the phenomenon is the effect of the remaining antecedents.</i></p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_6">� 6.</a> There remains a class of laws which it is impracticable to
+ascertain by any of the three methods which I have attempted to
+characterize; namely, the laws of those Permanent Causes, or
+indestructible natural agents, which it is impossible either to exclude
+or to isolate; which we can neither hinder from being present, nor
+contrive that they shall be present alone. It would appear at first
+sight that we could by no means separate the effects of these agents
+from the effects of those other phenomena with which they cannot be
+prevented from coexisting. In respect, indeed, to most of the permanent
+causes, no such difficulty exists; since though we cannot <span class="pagenum"><a name="Page_438" id="Page_438">[Pg 438]</a></span>eliminate
+them as coexisting facts, we can eliminate them as influencing agents,
+by simply trying our experiment in a local situation beyond the limits
+of their influence. The pendulum, for example, has its oscillations
+disturbed by the vicinity of a mountain: we remove the pendulum to a
+sufficient distance from the mountain, and the disturbance ceases: from
+these data we can determine by the Method of Difference, the amount of
+effect due to the mountain; and beyond a certain distance everything
+goes on precisely as it would do if the mountain exercised no influence
+whatever, which, accordingly, we, with sufficient reason, conclude to be
+the fact.</p>
+
+<p>The difficulty, therefore, in applying the methods already treated of to
+determine the effects of Permanent Causes, is confined to the cases in
+which it is impossible for us to get out of the local limits of their
+influence. The pendulum can be removed from the influence of the
+mountain, but it cannot be removed from the influence of the earth: we
+cannot take away the earth from the pendulum, nor the pendulum from the
+earth, to ascertain whether it would continue to vibrate if the action
+which the earth exerts upon it were withdrawn. On what evidence, then,
+do we ascribe its vibrations to the earth's influence? Not on any
+sanctioned by the Method of Difference; for one of the two instances,
+the negative instance, is wanting. Nor by the Method of Agreement; for
+though all pendulums agree in this, that during their oscillations the
+earth is always present, why may we not as well ascribe the phenomenon
+to the sun, which is equally a coexistent fact in all the experiments?
+It is evident that to establish even so simple a fact of causation as
+this, there was required some method over and above those which we have
+yet examined.</p>
+
+<p>As another example, let us take the phenomenon Heat. Independently of
+all hypothesis as to the real nature of the agency so called, this fact
+is certain, that we are unable to exhaust any body of the whole of its
+heat. It is equally certain, that no one ever perceived heat not
+emanating from a body. Being unable, then, to separate Body and Heat, we
+cannot effect such a variation of circumstances as the foregoing <span class="pagenum"><a name="Page_439" id="Page_439">[Pg 439]</a></span>three
+methods require; we cannot ascertain, by those methods, what portion of
+the phenomena exhibited by any body is due to the heat contained in it.
+If we could observe a body with its heat, and the same body entirely
+divested of heat, the Method of Difference would show the effect due to
+the heat, apart from that due to the body. If we could observe heat
+under circumstances agreeing in nothing but heat, and therefore not
+characterized also by the presence of a body, we could ascertain the
+effects of heat, from an instance of heat with a body and an instance of
+heat without a body, by the Method of Agreement; or we could determine
+by the Method of Difference what effect was due to the body, when the
+remainder which was due to the heat would be given by the Method of
+Residues. But we can do none of these things; and without them the
+application of any of the three methods to the solution of this problem
+would be illusory. It would be idle, for instance, to attempt to
+ascertain the effect of heat by subtracting from the phenomena exhibited
+by a body, all that is due to its other properties; for as we have never
+been able to observe any bodies without a portion of heat in them,
+effects due to that heat might form a part of the very results, which we
+were affecting to subtract in order that the effect of heat might be
+shown by the residue.</p>
+
+<p>If, therefore, there were no other methods of experimental investigation
+than these three, we should be unable to determine the effects due to
+heat as a cause. But we have still a resource. Though we cannot exclude
+an antecedent altogether, we may be able to produce, or nature may
+produce for us, some modification in it. By a modification is here
+meant, a change in it, not amounting to its total removal. If some
+modification in the antecedent A is always followed by a change in the
+consequent <i>a</i>, the other consequents <i>b</i> and <i>c</i> remaining the same; or
+<i>vice vers�</i>, if every change in <i>a</i> is found to have been preceded by
+some modification in A, none being observable in any of the other
+antecedents; we may safely conclude that <i>a</i> is, wholly or in part, an
+effect traceable to A, or at least in some way connected with it through
+causation. For example, in the case of heat, though we cannot <span class="pagenum"><a name="Page_440" id="Page_440">[Pg 440]</a></span>expel it
+altogether from any body, we can modify it in quantity, we can increase
+or diminish it; and doing so, we find by the various methods of
+experimentation or observation already treated of, that such increase or
+diminution of heat is followed by expansion or contraction of the body.
+In this manner we arrive at the conclusion, otherwise unattainable by
+us, that one of the effects of heat is to enlarge the dimensions of
+bodies; or what is the same thing in other words, to widen the distances
+between their particles.</p>
+
+<p>A change in a thing, not amounting to its total removal, that is, a
+change which leaves it still the same thing it was, must be a change
+either in its quantity, or in some of its variable relations to other
+things, of which variable relations the principal is its position in
+space. In the previous example, the modification which was produced in
+the antecedent was an alteration in its quantity. Let us now suppose the
+question to be, what influence the moon exerts on the surface of the
+earth. We cannot try an experiment in the absence of the moon, so as to
+observe what terrestrial phenomena her annihilation would put an end to;
+but when we find that all the variations in the <i>position</i> of the moon
+are followed by corresponding variations in the time and place of high
+water, the place being always either the part of the earth which is
+nearest to, or that which is most remote from, the moon, we have ample
+evidence that the moon is, wholly or partially, the cause which
+determines the tides. It very commonly happens, as it does in this
+instance, that the variations of an effect are correspondent, or
+analogous, to those of its cause; as the moon moves farther towards the
+east, the high water point does the same: but this is not an
+indispensable condition; as may be seen in the same example, for along
+with that high water point there is at the same instant another high
+water point diametrically opposite to it, and which, therefore, of
+necessity, moves towards the west, as the moon, followed by the nearer
+of the tide waves, advances towards the east: and yet both these motions
+are equally effects of the moon's motion.</p>
+
+<p>That the oscillations of the pendulum are caused by the earth, is proved
+by similar evidence. Those oscillations take <span class="pagenum"><a name="Page_441" id="Page_441">[Pg 441]</a></span>place between equidistant
+points on the two sides of a line, which, being perpendicular to the
+earth, varies with every variation in the earth's position, either in
+space or relatively to the object. Speaking accurately, we only know by
+the method now characterized, that all terrestrial bodies tend to the
+earth, and not to some unknown fixed point lying in the same direction.
+In every twenty-four hours, by the earth's rotation, the line drawn from
+the body at right angles to the earth coincides successively with all
+the radii of a circle, and in the course of six months the place of that
+circle varies by nearly two hundred millions of miles; yet in all these
+changes of the earth's position, the line in which bodies tend to fall
+continues to be directed towards it: which proves that terrestrial
+gravity is directed to the earth, and not, as was once fancied by some,
+to a fixed point of space.</p>
+
+<p>The method by which these results were obtained, may be termed the
+Method of Concomitant Variations: it is regulated by the following
+canon:&mdash;</p>
+
+<p class="center"><span class="smcap">Fifth Canon.</span></p>
+
+<p><i>Whatever phenomenon varies in any manner whenever another phenomenon
+varies in some particular manner, is either a cause or an effect of that
+phenomenon, or is connected with it through some fact of causation.</i></p>
+
+<p>The last clause is subjoined, because it by no means follows when two
+phenomena accompany each other in their variations, that the one is
+cause and the other effect. The same thing may, and indeed must happen,
+supposing them to be two different effects of a common cause: and by
+this method alone it would never be possible to ascertain which of the
+suppositions is the true one. The only way to solve the doubt would be
+that which we have so often adverted to, viz. by endeavouring to
+ascertain whether we can produce the one set of variations by means of
+the other. In the case of heat, for example, by increasing the
+temperature of a body we increase its bulk, but by increasing its bulk
+we do not increase its temperature; on the contrary, (as in the
+rarefaction of air under the receiver of an air-pump,) we generally
+diminish it: therefore heat is not <span class="pagenum"><a name="Page_442" id="Page_442">[Pg 442]</a></span>an effect, but a cause, of increase
+of bulk. If we cannot ourselves produce the variations, we must
+endeavour, though it is an attempt which is seldom successful, to find
+them produced by nature in some case in which the pre-existing
+circumstances are perfectly known to us.</p>
+
+<p>It is scarcely necessary to say, that in order to ascertain the uniform
+concomitance of variations in the effect with variations in the cause,
+the same precautions must be used as in any other case of the
+determination of an invariable sequence. We must endeavour to retain all
+the other antecedents unchanged, while that particular one is subjected
+to the requisite series of variations; or in other words, that we may be
+warranted in inferring causation from concomitance of variations, the
+concomitance itself must be proved by the Method of Difference.</p>
+
+<p>It might at first appear that the Method of Concomitant Variations
+assumes a new axiom, or law of causation in general, namely, that every
+modification of the cause is followed by a change in the effect. And it
+does usually happen that when a phenomenon A causes a phenomenon <i>a</i>,
+any variation in the quantity or in the various relations of A, is
+uniformly followed by a variation in the quantity or relations of <i>a</i>.
+To take a familiar instance, that of gravitation. The sun causes a
+certain tendency to motion in the earth; here we have cause and effect;
+but that tendency is <i>towards</i> the sun, and therefore varies in
+direction as the sun varies in the relation of position; and moreover
+the tendency varies in intensity, in a certain numerical correspondence
+to the sun's distance from the earth, that is, according to another
+relation of the sun. Thus we see that there is not only an invariable
+connexion between the sun and the earth's gravitation, but that two of
+the relations of the sun, its position with respect to the earth and its
+distance from the earth, are invariably connected as antecedents with
+the quantity and direction of the earth's gravitation. The cause of the
+earth's gravitating at all, is simply the sun; but the cause of its
+gravitating with a given intensity and in a given direction, is the
+existence of the sun in a given direction and at a given distance. It is
+not <span class="pagenum"><a name="Page_443" id="Page_443">[Pg 443]</a></span>strange that a modified cause, which is in truth a different cause,
+should produce a different effect.</p>
+
+<p>Although it is for the most part true that a modification of the cause
+is followed by a modification of the effect, the Method of Concomitant
+Variations does not, however, presuppose this as an axiom. It only
+requires the converse proposition; that anything on whose modifications,
+modifications of an effect are invariably consequent, must be the cause
+(or connected with the cause) of that effect; a proposition, the truth
+of which is evident; for if the thing itself had no influence on the
+effect, neither could the modifications of the thing have any influence.
+If the stars have no power over the fortunes of mankind, it is implied
+in the very terms, that the conjunctions or oppositions of different
+stars can have no such power.</p>
+
+<p>Although the most striking applications of the Method of Concomitant
+Variations take place in the cases in which the Method of Difference,
+strictly so called, is impossible, its use is not confined to those
+cases; it may often usefully follow after the Method of Difference, to
+give additional precision to a solution which that has found. When by
+the Method of Difference it has first been ascertained that a certain
+object produces a certain effect, the Method of Concomitant Variations
+may be usefully called in, to determine according to what law the
+quantity or the different relations of the effect follow those of the
+cause.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_VIII_7">� 7.</a> The case in which this method admits of the most extensive
+employment, is that in which the variations of the cause are variations
+of quantity. Of such variations we may in general affirm with safety,
+that they will be attended not only with variations, but with similar
+variations, of the effect: the proposition, that more of the cause is
+followed by more of the effect, being a corollary from the principle of
+the Composition of Causes, which, as we have seen, is the general rule
+of causation; cases of the opposite description, in which causes change
+their properties on being conjoined with one another, being, on the
+contrary, special and exceptional. Suppose, <span class="pagenum"><a name="Page_444" id="Page_444">[Pg 444]</a></span>then, that when A changes
+in quantity, <i>a</i> also changes in quantity, and in such a manner that we
+can trace the numerical relation which the changes of the one bear to
+such changes of the other as take place within our limits of
+observation. We may then, with certain precautions, safely conclude that
+the same numerical relation will hold beyond those limits. If, for
+instance, we find that when A is double, <i>a</i> is double; that when A is
+treble or quadruple, <i>a</i> is treble or quadruple; we may conclude that if
+A were a half or a third, <i>a</i> would be a half or a third, and finally,
+that if A were annihilated, <i>a</i> would be annihilated, and that <i>a</i> is
+wholly the effect of A, or wholly the effect of the same cause with A.
+And so with any other numerical relation according to which A and <i>a</i>
+would vanish simultaneously; as for instance, if <i>a</i> were proportional
+to the square of A. If, on the other hand, <i>a</i> is not wholly the effect
+of A, but yet varies when A varies, it is probably a mathematical
+function not of A alone, but of A and something else: its changes, for
+example, may be such as would occur if part of it remained constant, or
+varied on some other principle, and the remainder varied in some
+numerical relation to the variations of A. In that case, when A
+diminishes, <i>a</i> will be seen to approach not towards zero, but towards
+some other limit: and when the series of variations is such as to
+indicate what that limit is, if constant, or the law of its variation if
+variable, the limit will exactly measure how much of <i>a</i> is the effect
+of some other and independent cause, and the remainder will be the
+effect of A (or of the cause of A).</p>
+
+<p>These conclusions, however, must not be drawn without certain
+precautions. In the first place, the possibility of drawing them at all,
+manifestly supposes that we are acquainted not only with the variations,
+but with the absolute quantities both of A and <i>a</i>. If we do not know
+the total quantities, we cannot, of course, determine the real numerical
+relation according to which those quantities vary. It is therefore an
+error to conclude, as some have concluded, that because increase of heat
+expands bodies, that is, increases the distance between their particles,
+therefore the distance is wholly the effect of heat, and that if we
+could entirely exhaust the <span class="pagenum"><a name="Page_445" id="Page_445">[Pg 445]</a></span>body of its heat, the particles would be in
+complete contact. This is no more than a guess, and of the most
+hazardous sort, not a legitimate induction: for since we neither know
+how much heat there is in any body, nor what is the real distance
+between any two of its particles, we cannot judge whether the
+contraction of the distance does or does not follow the diminution of
+the quantity of heat according to such a numerical relation that the two
+quantities would vanish simultaneously.</p>
+
+<p>In contrast with this, let us consider a case in which the absolute
+quantities are known; the case contemplated in the first law of motion;
+viz. that all bodies in motion continue to move in a straight line with
+uniform velocity until acted upon by some new force. This assertion is
+in open opposition to first appearances; all terrestrial objects, when
+in motion, gradually abate their velocity and at last stop; which
+accordingly the ancients, with their <i>inductio per enumerationem
+simplicem</i>, imagined to be the law. Every moving body, however,
+encounters various obstacles, as friction, the resistance of the
+atmosphere, &amp;c., which we know by daily experience to be causes capable
+of destroying motion. It was suggested that the whole of the retardation
+might be owing to these causes. How was this inquired into? If the
+obstacles could have been entirely removed, the case would have been
+amenable to the Method of Difference. They could not be removed, they
+could only be diminished, and the case, therefore, admitted only of the
+Method of Concomitant Variations. This accordingly being employed, it
+was found that every diminution of the obstacles diminished the
+retardation of the motion: and inasmuch as in this case (unlike the case
+of heat) the total quantities both of the antecedent and of the
+consequent were known; it was practicable to estimate, with an approach
+to accuracy, both the amount of the retardation and the amount of the
+retarding causes, or resistances, and to judge how near they both were
+to being exhausted; and it appeared that the effect dwindled as rapidly,
+and at each step was as far on the road towards annihilation, as the
+cause was. The simple oscillation of a weight suspended from a fixed
+point, and moved a little out of the perpendicular, which in ordinary
+circumstances <span class="pagenum"><a name="Page_446" id="Page_446">[Pg 446]</a></span>lasts but a few minutes, was prolonged in Borda's
+experiments to more than thirty hours, by diminishing as much as
+possible the friction at the point of suspension, and by making the body
+oscillate in a space exhausted as nearly as possible of its air. There
+could therefore be no hesitation in assigning the whole of the
+retardation of motion to the influence of the obstacles; and since,
+after subducting this retardation from the total phenomenon, the
+remainder was an uniform velocity, the result was the proposition known
+as the first law of motion.</p>
+
+<p>There is also another characteristic uncertainty affecting the inference
+that the law of variation which the quantities observe within our limits
+of observation, will hold beyond those limits. There is of course, in
+the first instance, the possibility that beyond the limits, and in
+circumstances therefore of which we have no direct experience, some
+counteracting cause might develop itself; either a new agent, or a new
+property of the agents concerned, which lies dormant in the
+circumstances we are able to observe. This is an element of uncertainty
+which enters largely into all our predictions of effects; but it is not
+peculiarly applicable to the Method of Concomitant Variations. The
+uncertainty, however, of which I am about to speak, is characteristic of
+that method; especially in the cases in which the extreme limits of our
+observation are very narrow, in comparison with the possible variations
+in the quantities of the phenomena. Any one who has the slightest
+acquaintance with mathematics, is aware that very different laws of
+variation may produce numerical results which differ but slightly from
+one another within narrow limits; and it is often only when the absolute
+amounts of variation are considerable, that the difference between the
+results given by one law and by another becomes appreciable. When,
+therefore, such variations in the quantity of the antecedents as we have
+the means of observing, are small in comparison with the total
+quantities, there is much danger lest we should mistake the numerical
+law, and be led to miscalculate the variations which would take place
+beyond the limits; a miscalculation which would vitiate any conclusion
+respecting <span class="pagenum"><a name="Page_447" id="Page_447">[Pg 447]</a></span>the dependence of the effect upon the cause, that could be
+founded on those variations. Examples are not wanting of such mistakes.
+"The formul�," says Sir John Herschel,<a name="FNanchor_33_114" id="FNanchor_33_114"></a><a href="#Footnote_33_114" class="fnanchor">[33]</a> "which have been empirically
+deduced for the elasticity of steam, (till very recently,) and those for
+the resistance of fluids, and other similar subjects," when relied on
+beyond the limits of the observations from which they were deduced,
+"have almost invariably failed to support the theoretical structures
+which have been erected on them."</p>
+
+<p>In this uncertainty, the conclusion we may draw from the concomitant
+variations of <i>a</i> and A, to the existence of an invariable and exclusive
+connexion between them, or to the permanency of the same numerical
+relation between their variations when the quantities are much greater
+or smaller than those which we have had the means of observing, cannot
+be considered to rest on a complete induction. All that in such a case
+can be regarded as proved on the subject of causation is, that there is
+some connexion between the two phenomena; that A, or something which can
+influence A, must be <i>one</i> of the causes which collectively determine
+<i>a</i>. We may, however, feel assured that the relation which we have
+observed to exist between the variations of A and <i>a</i>, will hold true in
+all cases which fall between the same extreme limits; that is, wherever
+the utmost increase or diminution in which the result has been found by
+observation to coincide with the law, is not exceeded.</p>
+
+<p>The four methods which it has now been attempted to describe, are the
+only possible modes of experimental inquiry&mdash;of direct induction <i>�
+posteriori</i>, as distinguished from deduction: at least, I know not, nor
+am able to imagine, any others. And even of these, the Method of
+Residues, as we have seen, is not independent of deduction; though, as
+it also requires specific experience, it may, without impropriety, be
+included among methods of direct observation and experiment.</p>
+
+<p>These, then, with such assistance as can be obtained from <span class="pagenum"><a name="Page_448" id="Page_448">[Pg 448]</a></span>Deduction,
+compose the available resources of the human mind for ascertaining the
+laws of the succession of phenomena. Before proceeding to point out
+certain circumstances, by which the employment of these methods is
+subjected to an immense increase of complication and of difficulty, it
+is expedient to illustrate the use of the methods, by suitable examples
+drawn from actual physical investigations. These, accordingly, will form
+the subject of the succeeding chapter.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_449" id="Page_449">[Pg 449]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_IX" id="BOOK_III_CHAPTER_IX"></a>CHAPTER IX.<br />
+
+MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_1">� 1.</a> I shall select, as a first example, an interesting speculation of
+one of the most eminent of theoretical chemists, Baron Liebig. The
+object in view, is to ascertain the immediate cause of the death
+produced by metallic poisons.</p>
+
+<p>Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
+introduced into the animal organism, except in the smallest doses,
+destroy life. These facts have long been known, as insulated truths of
+the lowest order of generalization; but it was reserved for Liebig, by
+an apt employment of the first two of our methods of experimental
+inquiry, to connect these truths together by a higher induction,
+pointing out what property, common to all these deleterious substances,
+is the really operating cause of their fatal effect.</p>
+
+<p>When solutions of these substances are placed in sufficiently close
+contact with many animal products, albumen, milk, muscular fibre, and
+animal membranes, the acid or salt leaves the water in which it was
+dissolved, and enters into combination with the animal substance: which
+substance, after being thus acted upon, is found to have lost its
+tendency to spontaneous decomposition, or putrefaction.</p>
+
+<p>Observation also shows, in cases where death has been produced by these
+poisons, that the parts of the body with which the poisonous substances
+have been brought into contact, do not afterwards putrefy.</p>
+
+<p>And, finally, when the poison has been supplied in too small a quantity
+to destroy life, eschars are produced, that is, certain superficial
+portions of the tissues are destroyed, which are afterwards thrown off
+by the reparative process taking place in the healthy parts.</p>
+
+<p><span class="pagenum"><a name="Page_450" id="Page_450">[Pg 450]</a></span></p><p>These three sets of instances admit of being treated according to the
+Method of Agreement. In all of them the metallic compounds are brought
+into contact with the substances which compose the human or animal body;
+and the instances do not seem to agree in any other circumstance. The
+remaining antecedents are as different, and even opposite, as they could
+possibly be made; for in some the animal substances exposed to the
+action of the poisons are in a state of life, in others only in a state
+of organization, in others not even in that. And what is the result
+which follows in all the cases? The conversion of the animal substance
+(by combination with the poison) into a chemical compound, held together
+by so powerful a force as to resist the subsequent action of the
+ordinary causes of decomposition. Now, organic life (the necessary
+condition of sensitive life) consisting in a continual state of
+decomposition and recomposition of the different organs and tissues;
+whatever incapacitates them for this decomposition destroys life. And
+thus the proximate cause of the death produced by this description of
+poisons, is ascertained, as far as the Method of Agreement can ascertain
+it.</p>
+
+<p>Let us now bring our conclusion to the test of the Method of Difference.
+Setting out from the cases already mentioned, in which the antecedent is
+the presence of substances forming with the tissues a compound incapable
+of putrefaction, (and <i>� fortiori</i> incapable of the chemical actions
+which constitute life,) and the consequent is death, either of the whole
+organism, or of some portion of it; let us compare with these cases
+other cases, as much resembling them as possible, but in which that
+effect is not produced. And, first, "many insoluble basic salts of
+arsenious acid are known not to be poisonous. The substance called
+alkargen, discovered by Bunsen, which contains a very large quantity of
+arsenic, and approaches very closely in composition to the organic
+arsenious compounds found in the body, has not the slightest injurious
+action upon the organism." Now when these substances are brought into
+contact with the tissues in any way, they do not combine with them; they
+do not arrest <span class="pagenum"><a name="Page_451" id="Page_451">[Pg 451]</a></span>their progress to decomposition. As far, therefore, as
+these instances go, it appears that when the effect is absent, it is by
+reason of the absence of that antecedent which we had already good
+ground for considering as the proximate cause.</p>
+
+<p>But the rigorous conditions of the Method of Difference are not yet
+satisfied; for we cannot be sure that these unpoisonous bodies agree
+with the poisonous substances in every property, except the particular
+one, of entering into a difficultly decomposable compound with the
+animal tissues. To render the method strictly applicable, we need an
+instance, not of a different substance, but of one of the very same
+substances, in circumstances which would prevent it from forming, with
+the tissues, the sort of compound in question; and then, if death does
+not follow, our case is made out. Now such instances are afforded by the
+antidotes to these poisons. For example, in case of poisoning by
+arsenious acid, if hydrated peroxide of iron is administered, the
+destructive agency is instantly checked. Now this peroxide is known to
+combine with the acid, and form a compound, which, being insoluble,
+cannot act at all on animal tissues. So, again, sugar is a well-known
+antidote to poisoning by salts of copper; and sugar reduces those salts
+either into metallic copper, or into the red suboxide, neither of which
+enters into combination with animal matter. The disease called painter's
+colic, so common in manufactories of white lead, is unknown where the
+workmen are accustomed to take, as a preservative, sulphuric acid
+lemonade (a solution of sugar rendered acid by sulphuric acid). Now
+diluted sulphuric acid has the property of decomposing all compounds of
+lead with organic matter, or of preventing them from being formed.</p>
+
+<p>There is another class of instances, of the nature required by the
+Method of Difference, which seem at first sight to conflict with the
+theory. Soluble salts of silver, such for instance as the nitrate, have
+the same stiffening antiseptic effect on decomposing animal substances
+as corrosive sublimate and the most deadly metallic poisons; and when
+applied to the external parts of the body, the nitrate is a powerful
+<span class="pagenum"><a name="Page_452" id="Page_452">[Pg 452]</a></span>caustic; depriving those parts of all active vitality, and causing them
+to be thrown off by the neighbouring living structures, in the form of
+an eschar. The nitrate and the other salts of silver ought, then, it
+would seem, if the theory be correct, to be poisonous; yet they may be
+administered internally with perfect impunity. From this apparent
+exception arises the strongest confirmation which the theory has yet
+received. Nitrate of silver, in spite of its chemical properties, does
+not poison when introduced into the stomach; but in the stomach, as in
+all animal liquids, there is common salt; and in the stomach there is
+also free muriatic acid. These substances operate as natural antidotes,
+combining with the nitrate, and if its quantity is not too great,
+immediately converting it into chloride of silver; a substance very
+slightly soluble, and therefore incapable of combining with the tissues,
+although to the extent of its solubility it has a medicinal influence,
+though an entirely different class of organic actions.</p>
+
+<p>The preceding instances have afforded an induction of a high order of
+conclusiveness, illustrative of the two simplest of our four methods;
+though not rising to the maximum of certainty which the Method of
+Difference, in its most perfect exemplification, is capable of
+affording. For (let us not forget) the positive instance and the
+negative one which the rigour of that method requires, ought to differ
+only in the presence or absence of one single circumstance. Now, in the
+preceding argument, they differ in the presence or absence not of a
+single <i>circumstance</i>, but of a single <i>substance</i>: and as every
+substance has innumerable properties, there is no knowing what number of
+real differences are involved in what is nominally and apparently only
+one difference. It is conceivable that the antidote, the peroxide of
+iron for example, may counteract the poison through some other of its
+properties than that of forming an insoluble compound with it; and if
+so, the theory would fall to the ground, so far as it is supported by
+that instance. This source of uncertainty, which is a serious hindrance
+to all extensive generalizations in chemistry, is however reduced in the
+present case to almost the lowest degree <span class="pagenum"><a name="Page_453" id="Page_453">[Pg 453]</a></span>possible, when we find that
+not only one substance, but many substances, possess the capacity of
+acting as antidotes to metallic poisons, and that all these agree in the
+property of forming insoluble compounds with the poisons, while they
+cannot be ascertained to agree in any other property whatsoever. We have
+thus, in favour of the theory, all the evidence which can be obtained by
+what we termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference; the evidence of which, though it never can
+amount to that of the Method of Difference properly so called, may
+approach indefinitely near to it.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_2">� 2.</a> Let the object be<a name="FNanchor_34_115" id="FNanchor_34_115"></a><a href="#Footnote_34_115" class="fnanchor">[34]</a> to ascertain the law of what is termed
+<i>induced</i> electricity; to find under what conditions any electrified
+body, whether positively or negatively electrified, gives rise to a
+contrary electric state in some other body adjacent to it.</p>
+
+<p>The most familiar exemplification of the phenomenon to be investigated
+is the following. Around the prime conductors of an electrical machine,
+the atmosphere to some distance, or any conducting surface suspended in
+that atmosphere, is found to be in an electric condition opposite to
+that of the prime conductor itself. Near and around the positive prime
+conductor there is negative electricity, and near and around the
+negative prime conductor there is positive electricity. When pith balls
+are brought near to either of the conductors, they become electrified
+with the opposite electricity to it; either receiving a share from the
+already electrified atmosphere by conduction, or acted upon by the
+direct inductive influence of the conductor itself: they are then
+attracted by the conductor to which they are in opposition; or, if
+withdrawn in their electrified state, <span class="pagenum"><a name="Page_454" id="Page_454">[Pg 454]</a></span>they will be attracted by any
+other oppositely charged body. In like manner the hand, if brought near
+enough to the conductor, receives or gives an electric discharge; now we
+have no evidence that a charged conductor can be suddenly discharged
+unless by the approach of a body oppositely electrified. In the case,
+therefore, of the electric machine, it appears that the accumulation of
+electricity in an insulated conductor is always accompanied by the
+excitement of the contrary electricity in the surrounding atmosphere,
+and in every conductor placed near the former conductor. It does not
+seem possible, in this case, to produce one electricity by itself.</p>
+
+<p>Let us now examine all the other instances which we can obtain,
+resembling this instance in the given consequent, namely, the evolution
+of an opposite electricity in the neighbourhood of an electrified body.
+As one remarkable instance we have the Leyden jar; and after the
+splendid experiments of Faraday in complete and final establishment of
+the substantial identity of magnetism and electricity, we may cite the
+magnet, both the natural and the electro-magnet, in neither of which it
+is possible to produce one kind of electricity by itself, or to charge
+one pole without charging an opposite pole with the contrary electricity
+at the same time. We cannot have a magnet with one pole: if we break a
+natural loadstone into a thousand pieces, each piece will have its two
+oppositely electrified poles complete within itself. In the voltaic
+circuit, again, we cannot have one current without its opposite. In the
+ordinary electric machine, the glass cylinder or plate, and the rubber,
+acquire opposite electricities.</p>
+
+<p>From all these instances, treated by the Method of Agreement, a general
+law appears to result. The instances embrace all the known modes in
+which a body can become charged with electricity; and in all of them
+there is found, as a concomitant or consequent, the excitement of the
+opposite electric state in some other body or bodies. It seems to follow
+that the two facts are invariably connected, and that the excitement of
+electricity in any body has for one of its necessary conditions the
+possibility of a simultaneous excitement of the opposite electricity in
+some neighbouring body.</p>
+
+<p><span class="pagenum"><a name="Page_455" id="Page_455">[Pg 455]</a></span></p><p>As the two contrary electricities can only be produced together, so
+they can only cease together. This may be shown by an application of the
+Method of Difference to the example of the Leyden jar. It needs scarcely
+be here remarked that in the Leyden jar, electricity can be accumulated
+and retained in considerable quantity, by the contrivance of having two
+conducting surfaces of equal extent, and parallel to each other through
+the whole of that extent, with a non-conducting substance such as glass
+between them. When one side of the jar is charged positively, the other
+is charged negatively, and it was by virtue of this fact that the Leyden
+jar served just now as an instance in our employment of the Method of
+Agreement. Now it is impossible to discharge one of the coatings unless
+the other can be discharged at the same time. A conductor held to the
+positive side cannot convey away any electricity unless an equal
+quantity be allowed to pass from the negative side: if one coating be
+perfectly insulated, the charge is safe. The dissipation of one must
+proceed <i>pari passu</i> with that of the other.</p>
+
+<p>The law thus strongly indicated admits of corroboration by the Method of
+Concomitant Variations. The Leyden jar is capable of receiving a much
+higher charge than can ordinarily be given to the conductor of an
+electrical machine. Now in the case of the Leyden jar, the metallic
+surface which receives the induced electricity is a conductor exactly
+similar to that which receives the primary charge, and is therefore as
+susceptible of receiving and retaining the one electricity, as the
+opposite surface of receiving and retaining the other; but in the
+machine, the neighbouring body which is to be oppositely electrified is
+the surrounding atmosphere, or any body casually brought near to the
+conductor; and as these are generally much inferior in their capacity of
+becoming electrified, to the conductor itself, their limited power
+imposes a corresponding limit to the capacity of the conductor for being
+charged. As the capacity of the neighbouring body for supporting the
+opposition increases, a higher charge becomes possible: and to this
+appears to be owing the great superiority of the Leyden jar.</p>
+
+<p><span class="pagenum"><a name="Page_456" id="Page_456">[Pg 456]</a></span></p><p>A further and most decisive confirmation by the Method of Difference,
+is to be found in one of Faraday's experiments in the course of his
+researches on the subject of induced electricity.</p>
+
+<p>Since common or machine electricity, and voltaic electricity, may be
+considered for the present purpose to be identical, Faraday wished to
+know whether, as the prime conductor develops opposite electricity upon
+a conductor in its vicinity, so a voltaic current running along a wire
+would induce an opposite current upon another wire laid parallel to it
+at a short distance. Now this case is similar to the cases previously
+examined, in every circumstance except the one to which we have ascribed
+the effect. We found in the former instances that whenever electricity
+of one kind was excited in one body, electricity of the opposite kind
+must be excited in a neighbouring body. But in Faraday's experiment this
+indispensable opposition exists within the wire itself. From the nature
+of a voltaic charge, the two opposite currents necessary to the
+existence of each other are both accommodated in one wire; and there is
+no need of another wire placed beside it to contain one of them, in the
+same way as the Leyden jar must have a positive and a negative surface.
+The exciting cause can and does produce all the effect which its laws
+require, independently of any electric excitement of a neighbouring
+body. Now the result of the experiment with the second wire was, that no
+opposite current was produced. There was an instantaneous effect at the
+closing and breaking of the voltaic circuit; electric inductions
+appeared when the two wires were moved to and from one another; but
+these are phenomena of a different class. There was no induced
+electricity in the sense in which this is predicated of the Leyden jar;
+there was no sustained current running up the one wire while an opposite
+current ran down the neighbouring wire; and this alone would have been a
+true parallel case to the other.</p>
+
+<p>It thus appears by the combined evidence of the Method of Agreement, the
+Method of Concomitant Variations, and the most rigorous form of the
+Method of Difference, that neither of the two kinds of electricity can
+be excited without an equal <span class="pagenum"><a name="Page_457" id="Page_457">[Pg 457]</a></span>excitement of the other and opposite kind:
+that both are effects of the same cause; that the possibility of the one
+is a condition of the possibility of the other, and the quantity of the
+one an impassable limit to the quantity of the other. A scientific
+result of considerable interest in itself, and illustrating those three
+methods in a manner both characteristic and easily intelligible.<a name="FNanchor_35_116" id="FNanchor_35_116"></a><a href="#Footnote_35_116" class="fnanchor">[35]</a></p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_3">� 3.</a> Our third example shall be extracted from Sir John Herschel's
+<i>Discourse on the Study of Natural Philosophy</i>, a work replete with
+happily-selected exemplifications of inductive processes from almost
+every department of physical science, and in which alone, of all books
+which I have met with, the four methods of induction are distinctly
+recognised, though not so clearly characterized and defined, nor their
+correlation so fully shown, as has appeared to me desirable. The present
+example is described by Sir John Herschel as "one of the most beautiful
+specimens" which can be cited "of inductive experimental inquiry lying
+within a moderate compass;" the theory of dew, first promulgated by the
+late Dr. Wells, and now universally adopted by scientific authorities.
+The passages in inverted commas are extracted verbatim from the
+Discourse.<a name="FNanchor_36_117" id="FNanchor_36_117"></a><a href="#Footnote_36_117" class="fnanchor">[36]</a></p>
+
+<p>"Suppose <i>dew</i> were the phenomenon proposed, whose cause we would know.
+In the first place" we must determine precisely what we mean by dew:
+what the fact really is, whose <span class="pagenum"><a name="Page_458" id="Page_458">[Pg 458]</a></span>cause we desire to investigate. "We must
+separate dew from rain, and the moisture of fogs, and limit the
+application of the term to what is really meant, which is the
+spontaneous appearance of moisture on substances exposed in the open air
+when no rain or <i>visible</i> wet is falling." This answers to a preliminary
+operation which will be characterized in the ensuing book, treating of
+operations subsidiary to induction.<a name="FNanchor_37_118" id="FNanchor_37_118"></a><a href="#Footnote_37_118" class="fnanchor">[37]</a></p>
+
+<p>"Now, here we have analogous phenomena in the moisture which bedews a
+cold metal or stone when we breathe upon it; that which appears on a
+glass of water fresh from the well in hot weather; that which appears on
+the inside of windows when sudden rain or hail chills the external air;
+that which runs down our walls when, after a long frost, a warm moist
+thaw comes on." Comparing these cases, we find that they all contain the
+phenomenon which was proposed as the subject of investigation. Now "all
+these instances agree in one point, the coldness of the object dewed, in
+comparison with the air in contact with it." But there still remains the
+most important case of all, that of nocturnal dew: does the same
+circumstance exist in this case? "Is it a fact that the object dewed is
+colder than the air? Certainly not, one would at first be inclined to
+say; for what is to <i>make</i> it so? But ... the experiment is easy: we
+have only to lay a thermometer in contact with the dewed substance, and
+hang one at a little distance above it, out of reach of its influence.
+The experiment has been therefore made, the question has been asked, and
+the answer has been invariably in the affirmative. Whenever an object
+contracts dew, it <i>is</i> colder than the air."</p>
+
+<p>Here then is a complete application of the Method of Agreement,
+establishing the fact of an invariable connexion between the deposition
+of dew on a surface, and the coldness of that surface compared with the
+external air. But which of these is cause, and which effect? or are they
+both effects of something else? On this subject the Method of Agreement
+can afford us no light: we must call in a more potent method. <span class="pagenum"><a name="Page_459" id="Page_459">[Pg 459]</a></span>"We must
+collect more facts, or, which comes to the same thing, vary the
+circumstances; since every instance in which the circumstances differ is
+a fresh fact: and especially, we must note the contrary or negative
+cases, <i>i.e.</i> where no dew is produced:" a comparison between instances
+of dew and instances of no dew, being the condition necessary to bring
+the Method of Difference into play.</p>
+
+<p>"Now, first, no dew is produced on the surface of polished metals, but
+it <i>is</i> very copiously on glass, both exposed with their faces upwards,
+and in some cases the under side of a horizontal plate of glass is also
+dewed." Here is an instance in which the effect is produced, and another
+instance in which it is not produced; but we cannot yet pronounce, as
+the canon of the Method of Difference requires, that the latter instance
+agrees with the former in all its circumstances except one; for the
+differences between glass and polished metals are manifold, and the only
+thing we can as yet be sure of is, that the cause of dew will be found
+among the circumstances by which the former substance is distinguished
+from the latter. But if we could be sure that glass, and the various
+other substances on which dew is deposited, have only one quality in
+common, and that polished metals and the other substances on which dew
+is not deposited have also nothing in common but the one circumstance,
+of not having the one quality which the others have; the requisitions of
+the Method of Difference would be completely satisfied, and we should
+recognise, in that quality of the substances, the cause of dew. This,
+accordingly, is the path of inquiry which is next to be pursued.</p>
+
+<p>"In the cases of polished metal and polished glass, the contrast shows
+evidently that the <i>substance</i> has much to do with the phenomenon;
+therefore let the substance <i>alone</i> be diversified as much as possible,
+by exposing polished surfaces of various kinds. This done, a <i>scale of
+intensity</i> becomes obvious. Those polished substances are found to be
+most strongly dewed which conduct heat worst; while those which conduct
+well, resist dew most effectually." The complication increases; here is
+the Method of Concomitant Variations called to our assistance; and no
+other method was practicable <span class="pagenum"><a name="Page_460" id="Page_460">[Pg 460]</a></span>on this occasion; for the quality of
+conducting heat could not be excluded, since all substances conduct heat
+in some degree. The conclusion obtained is, that <i>c�teris paribus</i> the
+deposition of dew is in some proportion to the power which the body
+possesses of resisting the passage of heat; and that this, therefore,
+(or something connected with this,) must be at least one of the causes
+which assist in producing the deposition of dew on the surface.</p>
+
+<p>"But if we expose rough surfaces instead of polished, we sometimes find
+this law interfered with. Thus, roughened iron, especially if painted
+over or blackened, becomes dewed sooner than varnished paper; the kind
+of <i>surface</i>, therefore, has a great influence. Expose, then, the <i>same</i>
+material in very diversified states as to surface," (that is, employ the
+Method of Difference to ascertain concomitance of variations,) "and
+another scale of intensity becomes at once apparent; those <i>surfaces</i>
+which <i>part with their heat</i> most readily by radiation, are found to
+contract dew most copiously." Here, therefore, are the requisites for a
+second employment of the Method of Concomitant Variations; which in this
+case also is the only method available, since all substances radiate
+heat in some degree or other. The conclusion obtained by this new
+application of the method is, that <i>c�teris paribus</i> the deposition of
+dew is also in some proportion to the power of radiating heat; and that
+the quality of doing this abundantly (or some cause on which that
+quality depends) is another of the causes which promote the deposition
+of dew on the substance.</p>
+
+<p>"Again, the influence ascertained to exist of <i>substance</i> and <i>surface</i>
+leads us to consider that of <i>texture</i>: and here, again, we are
+presented on trial with remarkable differences, and with a third scale
+of intensity, pointing out substances of a close firm texture, such as
+stones, metals, &amp;c., as unfavourable, but those of a loose one, as
+cloth, velvet, wool, eider-down, cotton, &amp;c., as eminently favourable to
+the contraction of dew." The Method of Concomitant Variations is here,
+for the third time, had recourse to; and, as before, from necessity,
+since the texture of no substance is absolutely firm or absolutely
+loose. Looseness of texture, therefore, or something which is the cause
+<span class="pagenum"><a name="Page_461" id="Page_461">[Pg 461]</a></span>of that quality, is another circumstance which promotes the deposition
+of dew; but this third cause resolves itself into the first, viz. the
+quality of resisting the passage of heat: for substances of loose
+texture "are precisely those which are best adapted for clothing, or for
+impeding the free passage of heat from the skin into the air, so as to
+allow their outer surfaces to be very cold, while they remain warm
+within;" and this last is, therefore, an induction (from fresh
+instances) simply <i>corroborative</i> of a former induction.</p>
+
+<p>It thus appears that the instances in which much dew is deposited, which
+are very various, agree in this, and, so far as we are able to observe,
+in this only, that they either radiate heat rapidly or conduct it
+slowly: qualities between which there is no other circumstance of
+agreement, than that by virtue of either, the body tends to lose heat
+from the surface more rapidly than it can be restored from within. The
+instances, on the contrary, in which no dew, or but a small quantity of
+it, is formed, and which are also extremely various, agree (as far as we
+can observe) in nothing except in <i>not</i> having this same property. We
+seem, therefore, to have detected the characteristic difference between
+the substances on which dew is produced, and those on which it is not
+produced. And thus have been realized the requisitions of what we have
+termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference. The example afforded of this indirect method,
+and of the manner in which the data are prepared for it by the Methods
+of Agreement and of Concomitant Variations, is the most important of all
+the illustrations of induction afforded by this interesting speculation.</p>
+
+<p>We might now consider the question, on what the deposition of dew
+depends, to be completely solved, if we could be quite sure that the
+substances on which dew is produced differ from those on which it is
+not, in <i>nothing</i> but in the property of losing heat from the surface
+faster than the loss can be repaired from within. And though we never
+can have that complete certainty, this is not of so much importance as
+might at first be supposed; for we have, at all events, ascertained
+<span class="pagenum"><a name="Page_462" id="Page_462">[Pg 462]</a></span>that even if there be any other quality hitherto unobserved which is
+present in all the substances which contract dew, and absent in those
+which do not, this other property must be one which, in all that great
+number of substances, is present or absent exactly where the property of
+being a better radiator than conductor is present or absent; an extent
+of coincidence which affords a strong presumption of a community of
+cause, and a consequent invariable coexistence between the two
+properties; so that the property of being a better radiator than
+conductor, if not itself the cause, almost certainly always accompanies
+the cause, and, for purposes of prediction, no error is likely to be
+committed by treating it as if it were really such.</p>
+
+<p>Reverting now to an earlier stage of the inquiry, let us remember that
+we had ascertained that, in every instance where dew is formed, there is
+actual coldness of the surface below the temperature of the surrounding
+air; but we were not sure whether this coldness was the cause of dew, or
+its effect. This doubt we are now able to resolve. We have found that,
+in every such instance, the substance is one which, by its own
+properties or laws, would, if exposed in the night, become colder than
+the surrounding air. The coldness therefore being accounted for
+independently of the dew, while it is proved that there is a connexion
+between the two, it must be the dew which depends on the coldness; or in
+other words, the coldness is the cause of the dew.</p>
+
+<p>This law of causation, already so amply established, admits, however, of
+efficient additional corroboration in no less than three ways. First, by
+deduction from the known laws of aqueous vapour when diffused through
+air or any other gas; and though we have not yet come to the Deductive
+Method, we will not omit what is necessary to render this speculation
+complete. It is known by direct experiment that only a limited quantity
+of water can remain suspended in the state of vapour at each degree of
+temperature, and that this maximum grows less and less as the
+temperature diminishes. From this it follows, deductively, that if there
+is already as much vapour suspended as the air will contain at its
+existing temperature, <span class="pagenum"><a name="Page_463" id="Page_463">[Pg 463]</a></span>any lowering of that temperature will cause a
+portion of the vapour to be condensed, and become water. But, again, we
+know deductively, from the laws of heat, that the contact of the air
+with a body colder than itself, will necessarily lower the temperature
+of the stratum of air immediately applied to its surface; and will
+therefore cause it to part with a portion of its water, which
+accordingly will, by the ordinary laws of gravitation or cohesion,
+attach itself to the surface of the body, thereby constituting dew. This
+deductive proof, it will have been seen, has the advantage of at once
+proving causation as well as coexistence; and it has the additional
+advantage that it also accounts for the exceptions to the occurrence of
+the phenomenon, the cases in which, although the body is colder than the
+air, yet no dew is deposited; by showing that this will necessarily be
+the case when the air is so under-supplied with aqueous vapour,
+comparatively to its temperature, that even when somewhat cooled by the
+contact of the colder body, it can still continue to hold in suspension
+all the vapour which was previously suspended in it: thus in a very dry
+summer there are no dews, in a very dry winter no hoar frost. Here,
+therefore, is an additional condition of the production of dew, which
+the methods we previously made use of failed to detect, and which might
+have remained still undetected, if recourse had not been had to the plan
+of deducing the effect from the ascertained properties of the agents
+known to be present.</p>
+
+<p>The second corroboration of the theory is by direct experiment,
+according to the canon of the Method of Difference. We can, by cooling
+the surface of any body, find in all cases some temperature, (more or
+less inferior to that of the surrounding air, according to its
+hygrometric condition,) at which dew will begin to be deposited. Here,
+too, therefore, the causation is directly proved. We can, it is true,
+accomplish this only on a small scale; but we have ample reason to
+conclude that the same operation, if conducted in Nature's great
+laboratory, would equally produce the effect.</p>
+
+<p>And, finally, even on that great scale we are able to verify the result.
+The case is one of those rare cases, as we have <span class="pagenum"><a name="Page_464" id="Page_464">[Pg 464]</a></span>shown them to be, in
+which nature works the experiment for us in the same manner in which we
+ourselves perform it; introducing into the previous state of things a
+single and perfectly definite new circumstance, and manifesting the
+effect so rapidly that there is not time for any other material change
+in the pre-existing circumstances. "It is observed that dew is never
+copiously deposited in situations much screened from the open sky, and
+not at all in a cloudy night; but <i>if the clouds withdraw even for a few
+minutes, and leave a clear opening, a deposition of dew presently
+begins</i>, and goes on increasing.... Dew formed in clear intervals will
+often even evaporate again when the sky becomes thickly overcast." The
+proof, therefore, is complete, that the presence or absence of an
+uninterrupted communication with the sky causes the deposition or
+non-deposition of dew. Now, since a clear sky is nothing but the absence
+of clouds, and it is a known property of clouds, as of all other bodies
+between which and any given object nothing intervenes but an elastic
+fluid, that they tend to raise or keep up the superficial temperature of
+the object by radiating heat to it, we see at once that the
+disappearance of clouds will cause the surface to cool; so that Nature,
+in this case, produces a change in the antecedent by definite and known
+means, and the consequent follows accordingly: a natural experiment
+which satisfies the requisitions of the Method of Difference.<a name="FNanchor_38_119" id="FNanchor_38_119"></a><a href="#Footnote_38_119" class="fnanchor">[38]</a></p>
+
+<p><span class="pagenum"><a name="Page_465" id="Page_465">[Pg 465]</a></span></p><p>The accumulated proof of which the Theory of Dew has been found
+susceptible, is a striking instance of the fulness of assurance which
+the inductive evidence of laws of causation may attain, in cases in
+which the invariable sequence is by no means obvious to a superficial
+view.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_4">� 4.</a> The admirable physiological investigations of Dr. Brown-S�quard
+afford brilliant examples of the application of the Inductive Methods to
+a class of inquiries in which, for reasons which will presently be
+given, direct induction takes place under peculiar difficulties and
+disadvantages. As one of the most apt instances I select his speculation
+(in the Proceedings of the Royal Society for May 16, 1861) on the
+relations between muscular irritability, cadaveric rigidity, and
+putrefaction.</p>
+
+<p>The law which Dr. Brown-S�quard's investigation tends to establish, is
+the following:&mdash;"The greater the degree of muscular irritability at the
+time of death, the later the cadaveric rigidity sets in, and the longer
+it lasts, and the later also putrefaction appears, and the slower it
+progresses." One would say at first sight that the method here required
+must be that of Concomitant Variations. But this is a delusive
+appearance, arising from the circumstance that the conclusion to be
+tested is itself a fact of concomitant variation. For the establishment
+of that fact any of the Methods may be put in requisition, and it will
+be found that the fourth Method, though really employed, has only a
+subordinate place in this particular investigation.</p>
+
+<p>The evidences by which Dr. Brown-S�quard establishes the law may be
+enumerated as follows:&mdash;</p>
+
+<p>1st. Paralysed muscles have greater irritability than healthy muscles.
+Now, paralysed muscles are later in assuming the cadaveric rigidity than
+healthy muscles, the rigidity <span class="pagenum"><a name="Page_466" id="Page_466">[Pg 466]</a></span>lasts longer, and putrefaction sets in
+later and proceeds more slowly.</p>
+
+<p>Both these propositions had to be proved by experiment; and for the
+experiments which prove them, science is also indebted to Dr.
+Brown-S�quard. The former of the two&mdash;that paralysed muscles have
+greater irritability than healthy muscles&mdash;he ascertained in various
+ways, but most decisively by "comparing the duration of irritability in
+a paralysed muscle and in the corresponding healthy one of the opposite
+side, while they are both submitted to the same excitation." He "often
+found in experimenting in that way, that the paralysed muscle remained
+irritable twice, three times, or even four times as long as the healthy
+one." This is a case of induction by the Method of Difference. The two
+limbs, being those of the same animal, were presumed to differ in no
+circumstance material to the case except the paralysis, to the presence
+and absence of which, therefore, the difference in the muscular
+irritability was to be attributed. This assumption of complete
+resemblance in all material circumstances save one, evidently could not
+be safely made in any one pair of experiments, because the two legs of
+any given animal might be accidentally in very different pathological
+conditions; but if, besides taking pains to avoid any such difference,
+the experiment was repeated sufficiently often in different animals to
+exclude the supposition that any abnormal circumstance could be present
+in them all, the conditions of the Method of Difference were adequately
+secured.</p>
+
+<p>In the same manner in which Dr. Brown-S�quard proved that paralysed
+muscles have greater irritability, he also proved the correlative
+proposition respecting cadaveric rigidity and putrefaction. Having, by
+section of the roots of the sciatic nerve, and again of a lateral half
+of the spinal cord, produced paralysis in one hind leg of an animal
+while the other remained healthy, he found that not only did muscular
+irritability last much longer in the paralysed limb, but rigidity set in
+later and ended later, and putrefaction began later and was less rapid
+than on the healthy side. This is a common case <span class="pagenum"><a name="Page_467" id="Page_467">[Pg 467]</a></span>of the Method of
+Difference, requiring no comment. A further and very important
+corroboration was obtained by the same method. When the animal was
+killed, not shortly after the section of the nerve, but a month later,
+the effect was reversed; rigidity set in sooner, and lasted a shorter
+time, than in the healthy muscles. But after this lapse of time, the
+paralysed muscles, having been kept by the paralysis in a state of rest,
+had lost a great part of their irritability, and instead of more, had
+become less irritable than those on the healthy side. This gives the A B
+C, a b c, and B C, b c, of the Method of Difference. One antecedent,
+increased irritability, being changed, and the other circumstances being
+the same, the consequence did not follow; and moreover, when a new
+antecedent, contrary to the first, was supplied, it was followed by a
+contrary consequent. This instance is attended with the special
+advantage, of proving that the retardation and prolongation of the
+rigidity do not depend directly on the paralysis, since that was the
+same in both the instances; but specifically on one effect of the
+paralysis, namely, the increased irritability; since they ceased when it
+ceased, and were reversed when it was reversed.</p>
+
+<p>2ndly. Diminution of the temperature of muscles before death increases
+their irritability. But diminution of their temperature also retards
+cadaveric rigidity and putrefaction.</p>
+
+<p>Both these truths were first made known by Dr. Brown-S�quard himself,
+through experiments which conclude according to the Method of
+Difference. There is nothing in the nature of the process requiring
+specific analysis.</p>
+
+<p>3rdly. Muscular exercise, prolonged to exhaustion, diminishes the
+muscular irritability. This is a well-known truth, dependent on the most
+general laws of muscular action, and proved by experiments under the
+Method of Difference, constantly repeated. Now it has been shown by
+observation that overdriven cattle, if killed before recovery from their
+fatigue, become rigid and putrefy in a surprisingly short time. A
+similar fact has been observed in the case of animals hunted to death;
+cocks killed during or shortly after a fight; and soldiers slain in the
+field of battle. These various cases agree <span class="pagenum"><a name="Page_468" id="Page_468">[Pg 468]</a></span>in no circumstance, directly
+connected with the muscles, except that these have just been subjected
+to exhausting exercise. Under the canon, therefore, of the Method of
+Agreement, it may be inferred that there is a connexion between the two
+facts. The Method of Agreement, indeed, as has been shown, is not
+competent to prove causation. The present case, however, is already
+known to be a case of causation, it being certain that the state of the
+body after death must somehow depend upon its state at the time of
+death. We are therefore warranted in concluding that the single
+circumstance in which all the instances agree, is the part of the
+antecedent which is the cause of that particular consequent.</p>
+
+<p>4thly. In proportion as the nutrition of muscles is in a good state,
+their irritability is high. This fact also rests on the general evidence
+of the laws of physiology, grounded on many familiar applications of the
+Method of Difference. Now, in the case of those who die from accident or
+violence, with their muscles in a good state of nutrition, the muscular
+irritability continues long after death, rigidity sets in late, and
+persists long without the putrefactive change. On the contrary, in cases
+of disease in which nutrition has been diminished for a long time before
+death, all these effects are reversed. These are the conditions of the
+Joint Method of Agreement and Difference. The cases of retarded and long
+continued rigidity here in question, agree only in being preceded by a
+high state of nutrition of the muscles; the cases of rapid and brief
+rigidity agree only in being preceded by a low state of muscular
+nutrition; a connexion is therefore inductively proved between the
+degree of the nutrition, and the slowness and prolongation of the
+rigidity.</p>
+
+<p>5thly. Convulsions, like exhausting exercise, but in a still greater
+degree, diminish the muscular irritability. Now, when death follows
+violent and prolonged convulsions, as in tetanus, hydrophobia, some
+cases of cholera, and certain poisons, rigidity sets in very rapidly,
+and after a very brief duration, gives place to putrefaction. This is
+another example of the Method of Agreement, of the same character with
+No. 3.</p>
+
+<p><span class="pagenum"><a name="Page_469" id="Page_469">[Pg 469]</a></span></p><p>6thly. The series of instances which we shall take last, is of a more
+complex character, and requires a more minute analysis.</p>
+
+<p>It has long been observed that in some cases of death by lightning,
+cadaveric rigidity either does not take place at all, or is of such
+extremely brief duration as to escape notice, and that in these cases
+putrefaction is very rapid. In other cases, however, the usual cadaveric
+rigidity appears. There must be some difference in the cause, to account
+for this difference in the effect. Now "death by lightning may be the
+result of, 1st, a syncope by fright, or in consequence of a direct or
+reflex influence of lightning on the par vagum; 2ndly, hemorrhage in or
+around the brain, or in the lungs, the pericardium, &amp;c.; 3rdly,
+concussion, or some other alteration in the brain;" none of which
+phenomena have any known property capable of accounting for the
+suppression, or almost suppression, of the cadaveric rigidity. But the
+cause of death may also be that the lightning produces "a violent
+convulsion of every muscle in the body," of which, if of sufficient
+intensity, the known effect would be that "muscular irritability ceases
+almost at once." If Dr. Brown-S�quard's generalization is a true law,
+these will be the very cases in which rigidity is so much abridged as to
+escape notice; and the cases in which, on the contrary, rigidity takes
+place as usual, will be those in which the stroke of lightning operates
+in some of the other modes which have been enumerated. How, then, is
+this brought to the test? By experiments not on lightning, which cannot
+be commanded at pleasure, but on the same natural agency in a manageable
+form, that of artificial galvanism. Dr. Brown-S�quard galvanized the
+entire bodies of animals immediately after death. Galvanism cannot
+operate in any of the modes in which the stroke of lightning may have
+operated, except the single one of producing muscular convulsions. If,
+therefore, after the bodies have been galvanized, the duration of
+rigidity is much shortened and putrefaction much accelerated, it is
+reasonable to ascribe the same effects when produced by lightning, to
+the property which galvanism shares with lightning, and not to those
+which it does not. Now this Dr. Brown-S�quard <span class="pagenum"><a name="Page_470" id="Page_470">[Pg 470]</a></span>found to be the fact. The
+galvanic experiment was tried with charges of very various degrees of
+strength; and the more powerful the charge, the shorter was found to be
+the duration of rigidity, and the more speedy and rapid the
+putrefaction. In the experiment in which the charge was strongest, and
+the muscular irritability most promptly destroyed, the rigidity only
+lasted fifteen minutes. On the principle, therefore, of the Method of
+Concomitant Variations, it maybe inferred that the duration of the
+rigidity depends on the degree of the irritability; and that if the
+charge had been as much stronger than Dr. Brown-S�quard's strongest, as
+a stroke of lightning must be stronger than any electric shock which we
+can produce artificially, the rigidity would have been shortened in a
+corresponding ratio, and might have disappeared altogether. This
+conclusion having been arrived at, the case of an electric shock,
+whether natural or artificial, becomes an instance in addition to all
+those already ascertained, of correspondence between the irritability of
+the muscle and the duration of rigidity.</p>
+
+<p>All these instances are summed up in the following statement:&mdash;"That
+when the degree of muscular irritability at the time of death is
+considerable, either in consequence of a good state of nutrition, as in
+persons who die in full health from an accidental cause, or in
+consequence of rest, as in cases of paralysis, or on account of the
+influence of cold, cadaveric rigidity in all these cases sets in late
+and lasts long, and putrefaction appears late, and progresses slowly:"
+but "that when the degree of muscular irritability at the time of death
+is slight, either in consequence of a bad state of nutrition, or of
+exhaustion from over-exertion, or from convulsions caused by disease or
+poison, cadaveric rigidity sets in and ceases soon, and putrefaction
+appears and progresses quickly." These facts present, in all their
+completeness, the conditions of the Joint Method of Agreement and
+Difference. Early and brief rigidity takes place in cases which agree
+only in the circumstance of a low state of muscular irritability.
+Rigidity begins late and lasts long in cases which agree only in the
+contrary circumstance, of a muscular irritability high and unusually
+prolonged. It follows that there is a connexion through causation
+between the degree of muscular irritability after death, and the
+tardiness <span class="pagenum"><a name="Page_471" id="Page_471">[Pg 471]</a></span>and prolongation of the cadaveric rigidity. This
+investigation places in a strong light the value and efficacy of the
+Joint Method. For, as we have already seen, the defect of that Method
+is, that like the Method of Agreement, of which it is only an improved
+form, it cannot prove causation. But in the present case (as in one of
+the steps in the argument which led up to it) causation is already
+proved; since there could never be any doubt that the rigidity
+altogether, and the putrefaction which follows it, are caused by the
+fact of death: the observations and experiments on which this rests are
+too familiar to need analysis, and fall under the Method of Difference.
+It being, therefore, beyond doubt that the aggregate antecedent, the
+death, is the actual cause of the whole train of consequents, whatever
+of the circumstances attending the death can be shown to be followed in
+all its variations by variations in the effect under investigation, must
+be the particular feature of the fact of death on which that effect
+depends. The degree of muscular irritability at the time of death
+fulfils this condition. The only point that could be brought into
+question, would be whether the effect depended on the irritability
+itself, or on something which always accompanied the irritability: and
+this doubt is set at rest by establishing, as the instances do, that by
+whatever cause the high or low irritability is produced, the effect
+equally follows; and cannot, therefore, depend upon the causes of
+irritability, nor upon the other effects of those causes, which are as
+various as the causes themselves; but upon the irritability, solely.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_5">� 5.</a> The last two examples will have conveyed to any one by whom they
+have been duly followed, so clear a conception of the use and practical
+management of three of the four methods of experimental inquiry, as to
+supersede the necessity of any further exemplification of them. The
+remaining method, that of Residues, not having found a place in any of
+the preceding investigations, I shall quote from Sir John Herschel some
+examples of that method, with the remarks by which they are introduced.</p>
+
+<p>"It is by this process, in fact, that science, in its present advanced
+state, is chiefly promoted. Most of the phenomena <span class="pagenum"><a name="Page_472" id="Page_472">[Pg 472]</a></span>which Nature presents
+are very complicated; and when the effects of all known causes are
+estimated with exactness, and subducted, the residual facts are
+constantly appearing in the form of phenomena altogether new, and
+leading to the most important conclusions.</p>
+
+<p>"For example: the return of the comet predicted by Professor Encke, a
+great many times in succession, and the general good agreement of its
+calculated with its observed place during any one of its periods of
+visibility, would lead us to say that its gravitation towards the sun
+and planets is the sole and sufficient cause of all the phenomena of its
+orbitual motion; but when the effect of this cause is strictly
+calculated and subducted from the observed motion, there is found to
+remain behind a <i>residual phenomenon</i>, which would never have been
+otherwise ascertained to exist, which is a small anticipation of the
+time of its reappearance, or a diminution of its periodic time, which
+cannot be accounted for by gravity, and whose cause is therefore to be
+inquired into. Such an anticipation would be caused by the resistance of
+a medium disseminated through the celestial regions; and as there are
+other good reasons for believing this to be a <i>vera causa</i>," (an
+actually existing antecedent,) "it has therefore been ascribed to such a
+resistance.<a name="FNanchor_39_120" id="FNanchor_39_120"></a><a href="#Footnote_39_120" class="fnanchor">[39]</a></p>
+
+<p>"M. Arago, having suspended a magnetic needle by a silk thread, and set
+it in vibration, observed, that it came much sooner to a state of rest
+when suspended over a plate of copper, than when no such plate was
+beneath it. Now, in both cases there were two <i>ver� caus�</i>" (antecedents
+known to exist) "why it <i>should</i> come at length to rest, viz. the
+resistance of the air, which opposes, and at length destroys, all
+motions performed in it; and the want of perfect mobility in the silk
+thread. But the effect of these causes being exactly known by the
+observation made in the absence of the copper, and being thus allowed
+for and subducted, a residual phenomenon appeared, in the fact that a
+retarding influence was <span class="pagenum"><a name="Page_473" id="Page_473">[Pg 473]</a></span>exerted by the copper itself; and this fact,
+once ascertained, speedily led to the knowledge of an entirely new and
+unexpected class of relations." This example belongs, however, not to
+the Method of Residues but to the Method of Difference, the law being
+ascertained by a direct comparison of the results of two experiments,
+which differed in nothing but the presence or absence of the plate of
+copper. To have made it exemplify the Method of Residues, the effect of
+the resistance of the air and that of the rigidity of the silk should
+have been calculated <i>� priori</i>, from the laws obtained by separate and
+foregone experiments.</p>
+
+<p>"Unexpected and peculiarly striking confirmations of inductive laws
+frequently occur in the form of residual phenomena, in the course of
+investigations of a widely different nature from those which gave rise
+to the inductions themselves. A very elegant example may be cited in the
+unexpected confirmation of the law of the development of heat in elastic
+fluids by compression, which is afforded by the phenomena of sound. The
+inquiry into the cause of sound had led to conclusions respecting its
+mode of propagation, from which its velocity in the air could be
+precisely calculated. The calculations were performed; but, when
+compared with fact, though the agreement was quite sufficient to show
+the general correctness of the cause and mode of propagation assigned,
+yet the <i>whole</i> velocity could not be shown to arise from this theory.
+There was still a residual velocity to be accounted for, which placed
+dynamical philosophers for a long time in great dilemma. At length
+Laplace struck on the happy idea, that this might arise from the <i>heat</i>
+developed in the act of that condensation which necessarily takes place
+at every vibration by which sound is conveyed. The matter was subjected
+to exact calculation, and the result was at once the complete
+explanation of the residual phenomenon, and a striking confirmation of
+the general law of the development of heat by compression, under
+circumstances beyond artificial imitation."</p>
+
+<p>"Many of the new elements of chemistry have been detected in the
+investigation of residual phenomena. Thus Arfwedson discovered lithia by
+perceiving an excess of weight <span class="pagenum"><a name="Page_474" id="Page_474">[Pg 474]</a></span>in the sulphate produced from a small
+portion of what he considered as magnesia present in a mineral he had
+analysed. It is on this principle, too, that the small concentrated
+residues of great operations in the arts are almost sure to be the
+lurking places of new chemical ingredients: witness iodine, brome,
+selenium, and the new metals accompanying platina in the experiments of
+Wollaston and Tennant. It was a happy thought of Glauber to examine what
+everybody else threw away."<a name="FNanchor_40_121" id="FNanchor_40_121"></a><a href="#Footnote_40_121" class="fnanchor">[40]</a></p>
+
+<p>"Almost all the greatest discoveries in Astronomy," says the same
+author,<a name="FNanchor_41_122" id="FNanchor_41_122"></a><a href="#Footnote_41_122" class="fnanchor">[41]</a> "have resulted from the consideration of residual phenomena
+of a quantitative or numerical kind.... It was thus that the grand
+discovery of the precession of the equinoxes resulted as a residual
+phenomenon, from the imperfect explanation of the return of the seasons
+by the return of the sun to the same apparent place among the fixed
+stars. Thus, also, aberration and nutation resulted as residual
+phenomena from that portion of the changes of the apparent places of the
+fixed stars which was left unaccounted for by precession. And thus again
+the apparent proper motions of the stars are the observed residues of
+their apparent movements outstanding and unaccounted for by strict
+calculation of the effects of precession, nutation, and aberration. The
+nearest approach which human theories can make to perfection is to
+diminish this residue, this <i>caput mortuum</i> of observation, as it may be
+considered, as much as practicable, and, if possible, to reduce it to
+nothing, either by showing that something has been neglected in our
+estimation of known causes, or by reasoning upon it as a new fact, and
+on the principle of the inductive philosophy ascending from the effect
+to its cause or causes."</p>
+
+<p>The disturbing effects mutually produced by the earth and planets upon
+each other's motions were first brought to light as residual phenomena,
+by the difference which appeared between the observed places of those
+bodies, and the places calculated on a consideration solely of their
+gravitation <span class="pagenum"><a name="Page_475" id="Page_475">[Pg 475]</a></span>towards the sun. It was this which determined astronomers
+to consider the law of gravitation as obtaining between all bodies
+whatever, and therefore between all particles of matter; their first
+tendency having been to regard it as a force acting only between each
+planet or satellite and the central body to whose system it belonged.
+Again, the catastrophists, in geology, be their opinion right or wrong,
+support it on the plea, that after the effect of all causes now in
+operation has been allowed for, there remains in the existing
+constitution of the earth a large residue of facts, proving the
+existence at former periods either of other forces, or of the same
+forces in a much greater degree of intensity. To add one more example:
+those who assert, what no one has shown any real ground for believing,
+that there is in one human individual, one sex, or one race of mankind
+over another, an inherent and inexplicable superiority in mental
+faculties, could only substantiate their proposition by subtracting from
+the differences of intellect which we in fact see, all that can be
+traced by known laws either to the ascertained differences of physical
+organization, or to the differences which have existed in the outward
+circumstances in which the subjects of the comparison have hitherto been
+placed. What these causes might fail to account for, would constitute a
+residual phenomenon, which and which alone would be evidence of an
+ulterior original distinction, and the measure of its amount. But the
+assertors of such supposed differences have not provided themselves with
+these necessary logical conditions of the establishment of their
+doctrine.</p>
+
+<p>The spirit of the Method of Residues being, it is hoped, sufficiently
+intelligible from these examples, and the other three methods having
+already been so fully exemplified, we may here close our exposition of
+the four methods, considered as employed in the investigation of the
+simpler and more elementary order of the combinations of phenomena.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_IX_6">� 6.</a> Dr. Whewell has expressed a very unfavourable opinion of the
+utility of the Four Methods, as well as of the <span class="pagenum"><a name="Page_476" id="Page_476">[Pg 476]</a></span>aptness of the examples
+by which I have attempted to illustrate them. His words are these:&mdash;<a name="FNanchor_42_123" id="FNanchor_42_123"></a><a href="#Footnote_42_123" class="fnanchor">[42]</a></p>
+
+<p>"Upon these methods, the obvious thing to remark is, that they take for
+granted the very thing which is most difficult to discover, the
+reduction of the phenomena to formul� such as are here presented to us.
+When we have any set of complex facts offered to us; for instance, those
+which were offered in the cases of discovery which I have
+mentioned,&mdash;the facts of the planetary paths, of falling bodies, of
+refracted rays, of cosmical motions, of chemical analysis; and when, in
+any of these cases, we would discover the law of nature which governs
+them, or, if any one chooses so to term it, the feature in which all the
+cases agree, where are we to look for our A, B, C, and <i>a</i>, <i>b</i>, <i>c</i>?
+Nature does not present to us the cases in this form; and how are we to
+reduce them to this form? You say, <i>when</i> we find the combination of A B
+C with <i>a b c</i> and A B D with <i>a b d</i>, then we may draw our inference.
+Granted; but when and where are we to find such combinations? Even now
+that the discoveries are made, who will point out to us what are the A,
+B, C, and <i>a</i>, <i>b</i>, <i>c</i> elements of the cases which have just been
+enumerated? Who will tell us which of the methods of inquiry those
+historically real and successful inquiries exemplify? Who will carry
+these formul� through the history of the sciences, as they have really
+grown up; and show us that these four methods have been operative in
+their formation; or that any light is thrown upon the steps of their
+progress by reference to these formul�?"</p>
+
+<p>He adds that, in this work, the methods have not been applied "to a
+large body of conspicuous and undoubted examples of discovery, extending
+along the whole history of science;" which ought to have been done in
+order that the methods might be shown to possess the "advantage" (which
+he claims as belonging to his own) of being those "by which all great
+discoveries in science have really been made."&mdash;(p. 277.)</p>
+
+<p><span class="pagenum"><a name="Page_477" id="Page_477">[Pg 477]</a></span></p><p>There is a striking similarity between the objections here made against
+Canons of Induction, and what was alleged, in the last century, by as
+able men as Dr. Whewell, against the acknowledged Canon of
+Ratiocination. Those who protested against the Aristotelian Logic said
+of the Syllogism, what Dr. Whewell says of the Inductive Methods, that
+it "takes for granted the very thing which is most difficult to
+discover, the reduction of the argument to formul� such as are here
+presented to us." The grand difficulty, they said, is to obtain your
+syllogism, not to judge of its correctness when obtained. On the matter
+of fact, both they and Dr. Whewell are right. The greatest difficulty in
+both cases is first that of obtaining the evidence, and next, of
+reducing it to the form which tests its conclusiveness. But if we try to
+reduce it without knowing <i>to what</i>, we are not likely to make much
+progress. It is a more difficult thing to solve a geometrical problem,
+than to judge whether a proposed solution is correct: but if people were
+not able to judge of the solution when found, they would have little
+chance of finding it. And it cannot be pretended that to judge of an
+induction when found, is perfectly easy, is a thing for which aids and
+instruments are superfluous; for erroneous inductions, false inferences
+from experience, are quite as common, on some subjects much commoner,
+than true ones. The business of Inductive Logic is to provide rules and
+models (such as the Syllogism and its rules are for ratiocination) to
+which if inductive arguments conform, those arguments are conclusive,
+and not otherwise. This is what the Four Methods profess to be, and what
+I believe they are universally considered to be by experimental
+philosophers, who had practised all of them long before any one sought
+to reduce the practice to theory.</p>
+
+<p>The assailants of the Syllogism had also anticipated Dr. Whewell in the
+other branch of his argument. They said that no discoveries were ever
+made by syllogism; and Dr. Whewell says, or seems to say, that none were
+ever made by the four Methods of Induction. To the former objectors,
+Archbishop Whately very pertinently answered, that their argument, if
+good at all, was good against the reasoning process <span class="pagenum"><a name="Page_478" id="Page_478">[Pg 478]</a></span>altogether; for
+whatever cannot be reduced to syllogism, is not reasoning. And Dr.
+Whewell's argument, if good at all, is good against all inferences from
+experience. In saying that no discoveries were ever made by the four
+Methods, he affirms that none were ever made by observation and
+experiment; for assuredly if any were, it was by processes reducible to
+one or other of those methods.</p>
+
+<p>This difference between us accounts for the dissatisfaction which my
+examples give him; for I did not select them with a view to satisfy any
+one who required to be convinced that observation and experiment are
+modes of acquiring knowledge: I confess that in the choice of them I
+thought only of illustration, and of facilitating the <i>conception</i> of
+the Methods by concrete instances. If it had been my object to justify
+the processes themselves as means of investigation, there would have
+been no need to look far off, or make use of recondite or complicated
+instances. As a specimen of a truth ascertained by the Method of
+Agreement, I might have chosen the proposition "Dogs bark." This dog,
+and that dog, and the other dog, answer to A B C, A D E, A F G. The
+circumstance of being a dog, answers to A. Barking answers to <i>a</i>. As a
+truth made known by the Method of Difference, "Fire burns" might have
+sufficed. Before I touch the fire I am not burnt; this is B C; I touch
+it, and am burnt; this is A B C, <i>a</i> B C.</p>
+
+<p>Such familiar experimental processes are not regarded as inductions by
+Dr. Whewell; but they are perfectly homogeneous with those by which,
+even on his own showing, the pyramid of science is supplied with its
+base. In vain he attempts to escape from this conclusion by laying the
+most arbitrary restrictions on the choice of examples admissible as
+instances of Induction: they must neither be such as are still matter of
+discussion (p. 265), nor must any of them be drawn from mental and
+social subjects (p. 269), nor from ordinary observation and practical
+life (pp. 241-247). They must be taken exclusively from the
+generalizations by which scientific thinkers have ascended to great and
+comprehensive laws of natural phenomena. Now it is seldom possible, in
+these complicated <span class="pagenum"><a name="Page_479" id="Page_479">[Pg 479]</a></span>inquiries, to go much beyond the initial steps,
+without calling in the instrument of Deduction, and the temporary aid of
+hypotheses; as I myself, in common with Dr. Whewell, have maintained
+against the purely empirical school. Since therefore such cases could
+not conveniently be selected to illustrate the principles of mere
+observation and experiment, Dr. Whewell is misled by their absence into
+representing the Experimental Methods as serving no purpose in
+scientific investigation; forgetting that if those methods had not
+supplied the first generalizations, there would have been no materials
+for his own conception of Induction to work upon.</p>
+
+<p>His challenge, however, to point out which of the four methods are
+exemplified in certain important cases of scientific inquiry, is easily
+answered. "The planetary paths," as far as they are a case of induction
+at all,<a name="FNanchor_43_124" id="FNanchor_43_124"></a><a href="#Footnote_43_124" class="fnanchor">[43]</a> fall under the Method of Agreement. The law of "falling
+bodies," namely that they describe spaces proportional to the squares of
+the times, was historically a deduction from the first law of motion;
+but the experiments by which it was verified, and by which it might have
+been discovered, were examples of the Method of Agreement; and the
+apparent variation from the true law, caused by the resistance of the
+air, was cleared up by experiments <i>in vacuo</i>, constituting an
+application of the Method of Difference. The law of "refracted rays"
+(the constancy of the ratio between the sines of incidence and of
+refraction for each refracting substance) was ascertained by direct
+measurement, and therefore by the Method of Agreement. The "cosmical
+motions" were determined by highly complex processes of thought, in
+which Deduction was predominant, but the Methods of Agreement and of
+Concomitant Variations had a large part in establishing the empirical
+laws. Every case without exception of "chemical analysis" constitutes a
+well-marked example of the Method of Difference. To any one acquainted
+with the subjects&mdash;to Dr. Whewell himself, there would not be the
+smallest difficulty in setting out "the A B C and <i>a b c</i> elements" of
+these cases.</p>
+
+<p><span class="pagenum"><a name="Page_480" id="Page_480">[Pg 480]</a></span></p><p>If discoveries are ever made by observation and experiment without
+Deduction, the four methods are methods of discovery: but even if they
+were not methods of discovery, it would not be the less true that they
+are the sole methods of Proof; and in that character, even the results
+of deduction are amenable to them. The great generalizations which begin
+as Hypotheses, must end by being proved, and are in reality (as will be
+shown hereafter) proved, by the Four Methods. Now it is with Proof, as
+such, that Logic is principally concerned. This distinction has indeed
+no chance of finding favour with Dr. Whewell; for it is the peculiarity
+of his system, not to recognise, in cases of Induction, any necessity
+for proof. If, after assuming an hypothesis and carefully collating it
+with facts, nothing is brought to light inconsistent with it, that is,
+if experience does not <i>disprove</i> it, he is content: at least until a
+simpler hypothesis, equally consistent with experience, presents itself.
+If this be Induction, doubtless there is no necessity for the four
+methods. But to suppose that it is so, appears to me a radical
+misconception of the nature of the evidence of physical truths.</p>
+
+<p>So real and practical is the need of a test for induction, similar to
+the syllogistic test of ratiocination, that inferences which bid
+defiance to the most elementary notions of inductive logic are put forth
+without misgiving by persons eminent in physical science, as soon as
+they are off the ground on which they are conversant with the facts, and
+not reduced to judge only by the arguments; and as for educated persons
+in general, it may be doubted if they are better judges of a good or a
+bad induction than they were before Bacon wrote. The improvement in the
+results of thinking has seldom extended to the processes; or has
+reached, if any process, that of investigation only, not that of proof.
+A knowledge of many laws of nature has doubtless been arrived at, by
+framing hypotheses and finding that the facts corresponded to them; and
+many errors have been got rid of by coming to a knowledge of facts which
+were inconsistent with them, but not by discovering that the mode of
+thought which led to the errors was itself faulty, and might have been
+known to be such independently <span class="pagenum"><a name="Page_481" id="Page_481">[Pg 481]</a></span>of the facts which disproved the
+specific conclusion. Hence it is, that while the thoughts of mankind
+have on many subjects worked themselves practically right, the thinking
+power remains as weak as ever: and on all subjects on which the facts
+which would check the result are not accessible, as in what relates to
+the invisible world, and even, as has been seen lately, to the visible
+world of the planetary regions, men of the greatest scientific
+acquirements argue as pitiably as the merest ignoramus. For though they
+have made many sound inductions, they have not learnt from them (and Dr.
+Whewell thinks there is no necessity that they should learn) the
+principles of inductive <i>evidence</i>.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_482" id="Page_482">[Pg 482]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_X" id="BOOK_III_CHAPTER_X"></a>CHAPTER X.<br />
+
+OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_1">� 1.</a> In the preceding exposition of the four methods of observation and
+experiment, by which we contrive to distinguish among a mass of
+coexistent phenomena the particular effect due to a given cause, or the
+particular cause which gave birth to a given effect; it has been
+necessary to suppose, in the first instance, for the sake of
+simplification, that this analytical operation is encumbered by no other
+difficulties than what are essentially inherent in its nature; and to
+represent to ourselves, therefore, every effect, on the one hand as
+connected exclusively with a single cause, and on the other hand as
+incapable of being mixed and confounded with any other coexistent
+effect. We have regarded <i>a b c d e</i>, the aggregate of the phenomena
+existing at any moment, as consisting of dissimilar facts, <i>a</i>, <i>b</i>,
+<i>c</i>, <i>d</i>, and <i>e</i>, for each of which one, and only one, cause needs be
+sought; the difficulty being only that of singling out this one cause
+from the multitude of antecedent circumstances, A, B, C, D, and E. The
+cause indeed may not be simple; it may consist of an assemblage of
+conditions; but we have supposed that there was only one possible
+assemblage of conditions, from which the given effect could result.</p>
+
+<p>If such were the fact, it would be comparatively an easy task to
+investigate the laws of nature. But the supposition does not hold, in
+either of its parts. In the first place, it is not true that the same
+phenomenon is always produced by the same cause: the effect <i>a</i> may
+sometimes arise from A, sometimes from B. And, secondly, the effects of
+different causes are often not dissimilar, but homogeneous, and marked
+out by no assignable boundaries from one another: A and B <span class="pagenum"><a name="Page_483" id="Page_483">[Pg 483]</a></span>may produce
+not <i>a</i> and <i>b</i>, but different portions of an effect <i>a</i>. The obscurity
+and difficulty of the investigation of the laws of phenomena is
+singularly increased by the necessity of adverting to these two
+circumstances; Intermixture of Effects, and Plurality of Causes. To the
+latter, being the simpler of the two considerations, we shall first
+direct our attention.</p>
+
+<p>It is not true, then, that one effect must be connected with only one
+cause, or assemblage of conditions; that each phenomenon can be produced
+only in one way. There are often several independent modes in which the
+same phenomenon could have originated. One fact may be the consequent in
+several invariable sequences; it may follow, with equal uniformity, any
+one of several antecedents, or collections of antecedents. Many causes
+may produce motion: many causes may produce some kinds of sensation:
+many causes may produce death. A given effect may really be produced by
+a certain cause, and yet be perfectly capable of being produced without
+it.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_2">� 2.</a> One of the principal consequences of this fact of Plurality of
+Causes is, to render the first of the inductive methods, that of
+Agreement, uncertain. To illustrate that method, we supposed two
+instances, A B C followed by <i>a b c</i>, and A D E followed by <i>a d e</i>.
+From these instances it might apparently be concluded that A is an
+invariable antecedent of <i>a</i>, and even that it is the unconditional
+invariable antecedent, or cause, if we could be sure that there is no
+other antecedent common to the two cases. That this difficulty may not
+stand in the way, let us suppose the two cases positively ascertained to
+have no antecedent in common except A. The moment, however, that we let
+in the possibility of a plurality of causes, the conclusion fails. For
+it involves a tacit supposition, that <i>a</i> must have been produced in
+both instances by the same cause. If there can possibly have been two
+causes, those two may, for example, be C and E: the one may have been
+the cause of <i>a</i> in the former of the instances, the other in the
+latter, A having no influence in either case.</p>
+
+<p>Suppose, for example, that two great artists, or great philosophers,
+<span class="pagenum"><a name="Page_484" id="Page_484">[Pg 484]</a></span>that two extremely selfish, or extremely generous characters, were
+compared together as to the circumstances of their education and
+history, and the two cases were found to agree only in one circumstance:
+would it follow that this one circumstance was the cause of the quality
+which characterized both those individuals? Not at all; for the causes
+which may produce any type of character are innumerable; and the two
+persons might equally have agreed in their character, though there had
+been no manner of resemblance in their previous history.</p>
+
+<p>This, therefore, is a characteristic imperfection of the Method of
+Agreement; from which imperfection the Method of Difference is free. For
+if we have two instances, A B C and B C, of which B C gives <i>b c</i>, and A
+being added converts it into <i>a b c</i>, it is certain that in this
+instance at least, A was either the cause of <i>a</i>, or an indispensable
+portion of its cause, even though the cause which produces it in other
+instances may be altogether different. Plurality of Causes, therefore,
+not only does not diminish the reliance due to the Method of Difference,
+but does not even render a greater number of observations or experiments
+necessary: two instances, the one positive and the other negative, are
+still sufficient for the most complete and rigorous induction. Not so,
+however, with the Method of Agreement. The conclusions which that
+yields, when the number of instances compared is small, are of no real
+value, except as, in the character of suggestions, they may lead either
+to experiments bringing them to the test of the Method of Difference, or
+to reasonings which may explain and verify them deductively.</p>
+
+<p>It is only when the instances, being indefinitely multiplied and varied,
+continue to suggest the same result, that this result acquires any high
+degree of independent value. If there are but two instances, A B C and A
+D E, though these instances have no antecedent in common except A, yet
+as the effect may possibly have been produced in the two cases by
+different causes, the result is at most only a slight probability in
+favour of A; there may be causation, but it is almost equally probable
+that there was only a coincidence. But the <span class="pagenum"><a name="Page_485" id="Page_485">[Pg 485]</a></span>oftener we repeat the
+observation, varying the circumstances, the more we advance towards a
+solution of this doubt. For if we try A F G, A H K, &amp;c., all unlike one
+another except in containing the circumstance A, and if we find the
+effect <i>a</i> entering into the result in all these cases, we must suppose
+one of two things, either that it is caused by A, or that it has as many
+different causes as there are instances. With each addition, therefore,
+to the number of instances, the presumption is strengthened in favour of
+A. The inquirer, of course, will not neglect, if an opportunity present
+itself, to exclude A from some one of these combinations, from A H K for
+instance, and by trying H K separately, appeal to the Method of
+Difference in aid of the Method of Agreement. By the Method of
+Difference alone can it be ascertained that A is the cause of <i>a</i>; but
+that it is either the cause, or another effect of the same cause, may be
+placed beyond any reasonable doubt by the Method of Agreement, provided
+the instances are very numerous, as well as sufficiently various.</p>
+
+<p>After how great a multiplication, then, of varied instances, all
+agreeing in no other antecedent except A, is the supposition of a
+plurality of causes sufficiently rebutted, and the conclusion that <i>a</i>
+is connected with A divested of the characteristic imperfection, and
+reduced to a virtual certainty? This is a question which we cannot be
+exempted from answering: but the consideration of it belongs to what is
+called the Theory of Probability, which will form the subject of a
+chapter hereafter. It is seen, however, at once, that the conclusion
+does amount to a practical certainty after a sufficient number of
+instances, and that the method, therefore, is not radically vitiated by
+the characteristic imperfection. The result of these considerations is
+only, in the first place, to point out a new source of inferiority in
+the Method of Agreement as compared with other modes of investigation,
+and new reasons for never resting contented with the results obtained by
+it, without attempting to confirm them either by the Method of
+Difference, or by connecting them deductively with some law or laws
+already ascertained by that superior method. And, in the second place,
+we learn from this the true theory of the value of mere <i>number</i> <span class="pagenum"><a name="Page_486" id="Page_486">[Pg 486]</a></span>of
+instances in inductive inquiry. The Plurality of Causes is the only
+reason why mere number is of any importance. The tendency of
+unscientific inquirers is to rely too much on number, without analysing
+the instances; without looking closely enough into their nature, to
+ascertain what circumstances are or are not eliminated by means of them.
+Most people hold their conclusions with a degree of assurance
+proportioned to the mere <i>mass</i> of the experience on which they appear
+to rest; not considering that by the addition of instances to instances,
+all of the same kind, that is, differing from one another only in points
+already recognised as immaterial, nothing whatever is added to the
+evidence of the conclusion. A single instance eliminating some
+antecedent which existed in all the other cases, is of more value than
+the greatest multitude of instances which are reckoned by their number
+alone. It is necessary, no doubt, to assure ourselves, by repetition of
+the observation or experiment, that no error has been committed
+concerning the individual facts observed; and until we have assured
+ourselves of this, instead of varying the circumstances, we cannot too
+scrupulously repeat the same experiment or observation without any
+change. But when once this assurance has been obtained, the
+multiplication of instances which do not exclude any more circumstances
+is entirely useless, provided there have been already enough to exclude
+the supposition of Plurality of Causes.</p>
+
+<p>It is of importance to remark, that the peculiar modification of the
+Method of Agreement, which, as partaking in some degree of the nature of
+the Method of Difference, I have called the Joint Method of Agreement
+and Difference, is not affected by the characteristic imperfection now
+pointed out. For, in the joint method, it is supposed not only that the
+instances in which <i>a</i> is, agree only in containing A, but also that the
+instances in which <i>a</i> is not, agree only in not containing A. Now, if
+this be so, A must be not only the cause of <i>a</i>, but the only possible
+cause: for if there were another, as for example B, then in the
+instances in which <i>a</i> is not, B must have been absent as well as A, and
+it would not be true that these instances agree <i>only</i> in not containing
+A. This, therefore, <span class="pagenum"><a name="Page_487" id="Page_487">[Pg 487]</a></span>constitutes an immense advantage of the joint
+method over the simple Method of Agreement. It may seem, indeed, that
+the advantage does not belong so much to the joint method, as to one of
+its two premises, (if they may be so called,) the negative premise. The
+Method of Agreement, when applied to negative instances, or those in
+which a phenomenon does <i>not</i> take place, is certainly free from the
+characteristic imperfection which affects it in the affirmative case.
+The negative premise, it might therefore be supposed, could be worked as
+a simple case of the Method of Agreement, without requiring an
+affirmative premise to be joined with it. But though this is true in
+principle, it is generally altogether impossible to work the Method of
+Agreement by negative instances without positive ones: it is so much
+more difficult to exhaust the field of negation than that of
+affirmation. For instance, let the question be, what is the cause of the
+transparency of bodies; with what prospect of success could we set
+ourselves to inquire directly in what the multifarious substances which
+are <i>not</i> transparent, agree? But we might hope much sooner to seize
+some point of resemblance among the comparatively few and definite
+species of objects which <i>are</i> transparent; and this being attained, we
+should quite naturally be put upon examining whether the <i>absence</i> of
+this one circumstance be not precisely the point in which all opaque
+substances will be found to resemble.</p>
+
+<p>The Joint Method of Agreement and Difference, therefore, or, as I have
+otherwise called it, the Indirect Method of Difference (because, like
+the Method of Difference properly so called, it proceeds by ascertaining
+how and in what the cases where the phenomenon is present, differ from
+those in which it is absent) is, after the Direct Method of Difference,
+the most powerful of the remaining instruments of inductive
+investigation; and in the sciences which depend on pure observation,
+with little or no aid from experiment, this method, so well exemplified
+in the speculation on the cause of dew, is the primary resource, so far
+as direct appeals to experience are concerned.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_3">� 3.</a> We have thus far treated Plurality of Causes only as <span class="pagenum"><a name="Page_488" id="Page_488">[Pg 488]</a></span>a possible
+supposition, which, until removed, renders our inductions uncertain; and
+have only considered by what means, where the plurality does not really
+exist, we may be enabled to disprove it. But we must also consider it as
+a case actually occurring in nature, and which, as often as it does
+occur, our methods of induction ought to be capable of ascertaining and
+establishing. For this, however, there is required no peculiar method.
+When an effect is really producible by two or more causes, the process
+for detecting them is in no way different from that by which we discover
+single causes. They may (first) be discovered as separate sequences, by
+separate sets of instances. One set of observations or experiments shows
+that the sun is a cause of heat, another that friction is a source of
+it, another that percussion, another that electricity, another that
+chemical action is such a source. Or (secondly) the plurality may come
+to light in the course of collating a number of instances, when we
+attempt to find some circumstance in which they all agree, and fail in
+doing so. We find it impossible to trace, in all the cases in which the
+effect is met with, any common circumstance. We find that we can
+eliminate <i>all</i> the antecedents; that no one of them is present in all
+the instances, no one of them indispensable to the effect. On closer
+scrutiny, however, it appears that though no one is always present, one
+or other of several always is. If, on further analysis, we can detect in
+these any common element, we may be able to ascend from them to some one
+cause which is the really operative circumstance in them all. Thus it is
+now thought that in the production of heat by friction, percussion,
+chemical action, &amp;c., the ultimate source is one and the same. But if
+(as continually happens) we cannot take this ulterior step, the
+different antecedents must be set down provisionally as distinct causes,
+each sufficient of itself to produce the effect.</p>
+
+<p>We here close our remarks on the Plurality of Causes, and proceed to the
+still more peculiar and more complex case of the Intermixture of
+Effects, and the interference of causes with one another: a case
+constituting the principal part of the complication and difficulty of
+the study of nature; and <span class="pagenum"><a name="Page_489" id="Page_489">[Pg 489]</a></span>with which the four only possible methods of
+directly inductive investigation by observation and experiment, are for
+the most part, as will appear presently, quite unequal to cope. The
+instrument of Deduction alone is adequate to unravel the complexities
+proceeding from this source; and the four methods have little more in
+their power than to supply premises for, and a verification of, our
+deductions.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_4">� 4.</a> A concurrence of two or more causes, not separately producing each
+its own effect, but interfering with or modifying the effects of one
+another, takes place, as has already been explained, in two different
+ways. In the one, which is exemplified by the joint operation of
+different forces in mechanics, the separate effects of all the causes
+continue to be produced, but are compounded with one another, and
+disappear in one total. In the other, illustrated by the case of
+chemical action, the separate effects cease entirely, and are succeeded
+by phenomena altogether different, and governed by different laws.</p>
+
+<p>Of these cases the former is by far the more frequent, and this case it
+is which, for the most part, eludes the grasp of our experimental
+methods. The other and exceptional case is essentially amenable to them.
+When the laws of the original agents cease entirely, and a phenomenon
+makes its appearance, which, with reference to those laws, is quite
+heterogeneous; when, for example, two gaseous substances, hydrogen and
+oxygen, on being brought together, throw off their peculiar properties,
+and produce the substance called water; in such cases the new fact may
+be subjected to experimental inquiry, like any other phenomenon; and the
+elements which are said to compose it may be considered as the mere
+agents of its production; the conditions on which it depends, the facts
+which make up its cause.</p>
+
+<p>The <i>effects</i> of the new phenomenon, the <i>properties</i> of water, for
+instance, are as easily found by experiment as the effects of any other
+cause. But to discover the <i>cause</i> of it, that is, the particular
+conjunction of agents from which it results, is often difficult enough.
+In the first place, the origin and <span class="pagenum"><a name="Page_490" id="Page_490">[Pg 490]</a></span>actual production of the phenomenon
+are most frequently inaccessible to our observation. If we could not
+have learned the composition of water until we found instances in which
+it was actually produced from oxygen and hydrogen, we should have been
+forced to wait until the casual thought struck some one of passing an
+electric spark through a mixture of the two gases, or inserting a
+lighted taper into it, merely to try what would happen. Besides, many
+substances, though they can be analysed, cannot by any known artificial
+means be recompounded. Further, even if we could have ascertained, by
+the Method of Agreement, that oxygen and hydrogen were both present when
+water is produced, no experimentation on oxygen and hydrogen separately,
+no knowledge of their laws, could have enabled us deductively to infer
+that they would produce water. We require a specific experiment on the
+two combined.</p>
+
+<p>Under these difficulties, we should generally have been indebted for our
+knowledge of the causes of this class of effects, not to any inquiry
+directed specifically towards that end, but either to accident, or to
+the gradual progress of experimentation on the different combinations of
+which the producing agents are susceptible; if it were not for a
+peculiarity belonging to effects of this description, that they often,
+under some particular combination of circumstances, reproduce their
+causes. If water results from the juxtaposition of hydrogen and oxygen
+whenever this can be made sufficiently close and intimate, so, on the
+other hand, if water itself be placed in certain situations, hydrogen
+and oxygen are reproduced from it: an abrupt termination is put to the
+new laws, and the agents reappear separately with their own properties
+as at first. What is called chemical analysis is the process of
+searching for the causes of a phenomenon among its effects, or rather
+among the effects produced by the action of some other causes upon it.</p>
+
+<p>Lavoisier, by heating mercury to a high temperature in a close vessel
+containing air, found that the mercury increased in weight, and became
+what was then called red precipitate, while the air, on being examined
+after the experiment, proved <span class="pagenum"><a name="Page_491" id="Page_491">[Pg 491]</a></span>to have lost weight, and to have become
+incapable of supporting life or combustion. When red precipitate was
+exposed to a still greater heat, it became mercury again, and gave off a
+gas which did support life and flame. Thus the agents which by their
+combination produced red precipitate, namely the mercury and the gas,
+reappear as effects resulting from that precipitate when acted upon by
+heat. So, if we decompose water by means of iron filings, we produce two
+effects, rust and hydrogen: now rust is already known by experiments
+upon the component substances, to be an effect of the union of iron and
+oxygen: the iron we ourselves supplied, but the oxygen must have been
+produced from the water. The result therefore is that water has
+disappeared, and hydrogen and oxygen have appeared in its stead: or in
+other words, the original laws of these gaseous agents, which had been
+suspended by the superinduction of the new laws called the properties of
+water, have again started into existence, and the causes of water are
+found among its effects.</p>
+
+<p>Where two phenomena, between the laws or properties of which considered
+in themselves no connexion can be traced, are thus reciprocally cause
+and effect, each capable in its turn of being produced from the other,
+and each, when it produces the other, ceasing itself to exist (as water
+is produced from oxygen and hydrogen, and oxygen and hydrogen are
+reproduced from water); this causation of the two phenomena by one
+another, each being generated by the other's destruction, is properly
+transformation. The idea of chemical composition is an idea of
+transformation, but of a transformation which is incomplete; since we
+consider the oxygen and hydrogen to be present in the water <i>as</i> oxygen
+and hydrogen, and capable of being discovered in it if our senses were
+sufficiently keen: a supposition (for it is no more) grounded solely on
+the fact, that the weight of the water is the sum of the separate
+weights of the two ingredients. If there had not been this exception to
+the entire disappearance, in the compound, of the laws of the separate
+ingredients; if the combined agents had not, in this one particular of
+weight, preserved their own laws, and produced a joint result equal to
+the sum of their separate <span class="pagenum"><a name="Page_492" id="Page_492">[Pg 492]</a></span>results; we should never, probably, have had
+the notion now implied by the words chemical composition: and, in the
+facts of water produced from hydrogen and oxygen, and hydrogen and
+oxygen produced from water, as the transformation would have been
+complete, we should have seen only a transformation.</p>
+
+<p>The very promising generalization now commonly known as the Conservation
+or Persistence of Force, bears a close resemblance to what the
+conception of chemical composition would become, if divested of the one
+circumstance which now distinguishes it from simple transformation. It
+has long been known that heat is capable of producing electricity, and
+electricity heat; that mechanical motion in numerous cases produces and
+is produced by them both; and so of all other physical forces. It has of
+late become the general belief of scientific inquirers that mechanical
+force, electricity, magnetism, heat, light, and chemical action (to
+which has subsequently been added vital action) are not so much causes
+of one another as convertible into one another; and they are now
+generally spoken of as forms of one and the same force, varying only in
+its manifestations. This doctrine may be admitted, without by any means
+implying that Force is a real entity, a Thing in itself, distinct from
+all its phenomenal manifestations to our organs. Supposing the doctrine
+true, the several kinds of phenomena which it identifies in respect of
+their origin would nevertheless remain different facts; facts which
+would be causes of one another&mdash;reciprocally causes and effects, which
+is the first element in the form of causation properly called
+transformation. What the doctrine contains more than this, is, that in
+each of these cases of reciprocal causation, the causes are reproduced
+without alteration in quantity. This is what takes place in the
+transformations of matter: when water has been converted into hydrogen
+and oxygen, these can be reconverted into precisely the same quantity of
+water from which they were produced. To establish a corresponding law in
+regard to Force, it has to be proved that heat is capable of being
+converted into electricity, electricity into chemical action, chemical
+action into mechanical force, and mechanical force back again into the
+exact quantity of heat which was originally expended; and so <span class="pagenum"><a name="Page_493" id="Page_493">[Pg 493]</a></span>through
+all the interchanges. Were this proved, it would establish what
+constitutes transformation, as distinguished from the simple fact of
+reciprocal causation. The fact in issue is simply the quantitative
+equivalence of all these natural agencies; whereby a given quantity of
+any one is convertible into, and interchangeable with, a given, and
+always the same, quantity of any other: this, no less, but also no more.
+It cannot yet be said that the law has been fully proved of any case,
+except that of interchange between heat and mechanical motion. It does
+seem to be ascertained, not only that these two are convertible into
+each other, but that after any number of conversions the original
+quantities reappear without addition or diminution, like the original
+quantities of hydrogen and oxygen after passing through the condition of
+water. If the same thing comes to be proved true of all the other
+forces, in relation to these two and to one another, the law of
+Conservation will be established; and it will be a legitimate mode of
+expressing the fact, to speak of Force, as we already speak of Matter,
+as indestructible. But Force will not the less remain, to the
+philosopher, a mere abstraction of the mind. All that will have been
+proved is, that in the phenomena of Nature, nothing actually ceases
+without generating a calculable, and always the same, quantity of some
+other natural phenomenon, which again, when it ceases, will in its turn
+either generate a calculable, and always the same, quantity of some
+third phenomenon, or reproduce the original quantity of the first.</p>
+
+<p>In these cases, where the heteropathic effect (as we called it in a
+former chapter)<a name="FNanchor_44_125" id="FNanchor_44_125"></a><a href="#Footnote_44_125" class="fnanchor">[44]</a> is but a transformation of its cause, or in other
+words, where the effect and its cause are reciprocally such, and
+mutually convertible into each other; the problem of finding the cause
+resolves itself into the far easier one of finding an effect, which is
+the kind of inquiry that admits of being prosecuted by direct
+experiment. But there are other cases of heteropathic effects to which
+this mode of investigation is not applicable. Take, for instance, the
+heteropathic laws of mind; that portion of the phenomena of our mental
+nature which are analogous to chemical rather than to dynamical
+<span class="pagenum"><a name="Page_494" id="Page_494">[Pg 494]</a></span>phenomena; as when a complex passion is formed by the coalition of
+several elementary impulses, or a complex emotion by several simple
+pleasures or pains, of which it is the result without being the
+aggregate, or in any respect homogeneous with them. The product, in
+these cases, is generated by its various factors; but the factors cannot
+be reproduced from the product; just as a youth can grow into an old
+man, but an old man cannot grow into a youth. We cannot ascertain from
+what simple feelings any of our complex states of mind are generated, as
+we ascertain the ingredients of a chemical compound, by making it, in
+its turn, generate them. We can only, therefore, discover these laws by
+the slow process of studying the simple feelings themselves, and
+ascertaining synthetically, by experimenting on the various combinations
+of which they are susceptible, what they, by their mutual action upon
+one another, are capable of generating.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_5">� 5.</a> It might have been supposed that the other, and apparently simpler
+variety of the mutual interference of causes, where each cause continues
+to produce its own proper effect according to the same laws to which it
+conforms in its separate state, would have presented fewer difficulties
+to the inductive inquirer than that of which we have just finished the
+consideration. It presents, however, so far as direct induction apart
+from deduction is concerned, infinitely greater difficulties. When a
+concurrence of causes gives rise to a new effect, bearing no relation to
+the separate effects of those causes, the resulting phenomenon stands
+forth undisguised, inviting attention to its peculiarity, and presenting
+no obstacle to our recognising its presence or absence among any number
+of surrounding phenomena. It admits therefore of being easily brought
+under the canons of Induction, provided instances can be obtained such
+as those canons require: and the non-occurrence of such instances, or
+the want of means to produce them artificially, is the real and only
+difficulty in such investigations; a difficulty not logical, but in some
+sort physical. It is otherwise with cases of what, in a preceding
+chapter, has been denominated the Composition of Causes. There, the
+effects of <span class="pagenum"><a name="Page_495" id="Page_495">[Pg 495]</a></span>the separate causes do not terminate and give place to
+others, thereby ceasing to form any part of the phenomenon to be
+investigated; on the contrary, they still take place, but are
+intermingled with, and disguised by, the homogeneous and closely allied
+effects of other causes. They are no longer <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, <i>e</i>,
+existing side by side, and continuing to be separately discernible; they
+are + <i>a</i>, - <i>a</i>, 1/2 <i>b</i>, - <i>b</i>, 2 <i>b</i>, &amp;c., some of which cancel one
+another, while many others do not appear distinguishably, but merge in
+one sum: forming altogether a result, between which and the causes
+whereby it was produced there is often an insurmountable difficulty in
+tracing by observation any fixed relation whatever.</p>
+
+<p>The general idea of the Composition of Causes has been seen to be, that
+though two or more laws interfere with one another, and apparently
+frustrate or modify one another's operation, yet in reality all are
+fulfilled, the collective effect being the exact sum of the effects of
+the causes taken separately. A familiar instance is that of a body kept
+in equilibrium by two equal and contrary forces. One of the forces if
+acting alone would carry the body in a given time a certain distance to
+the west, the other if acting alone would carry it exactly as far
+towards the east; and the result is the same as if it had been first
+carried to the west as far as the one force would carry it, and then
+back towards the east as far as the other would carry it, that is,
+precisely the same distance; being ultimately left where it was found at
+first.</p>
+
+<p>All laws of causation are liable to be in this manner counteracted, and
+seemingly frustrated, by coming into conflict with other laws, the
+separate result of which is opposite to theirs, or more or less
+inconsistent with it. And hence, with almost every law, many instances
+in which it really is entirely fulfilled, do not, at first sight, appear
+to be cases of its operation at all. It is so in the example just
+adduced: a force, in mechanics, means neither more nor less than a cause
+of motion, yet the sum of the effects of two causes of motion may be
+rest. Again, a body solicited by two forces in directions making an
+angle with one another, moves in the diagonal; and it seems a paradox to
+say that motion in the diagonal <span class="pagenum"><a name="Page_496" id="Page_496">[Pg 496]</a></span>is the sum of two motions in two other
+lines. Motion, however, is but change of place, and at every instant the
+body is in the exact place it would have been in if the forces had acted
+during alternate instants instead of acting in the same instant; (saving
+that if we suppose two forces to act successively which are in truth
+simultaneous, we must of course allow them double the time.) It is
+evident, therefore, that each force has had, during each instant, all
+the effect which belonged to it; and that the modifying influence which
+one of two concurrent causes is said to exercise with respect to the
+other, may be considered as exerted not over the action of the cause
+itself, but over the effect after it is completed. For all purposes of
+predicting, calculating, or explaining their joint result, causes which
+compound their effects may be treated as if they produced simultaneously
+each of them its own effect, and all these effects coexisted visibly.</p>
+
+<p>Since the laws of causes are as really fulfilled when the causes are
+said to be counteracted by opposing causes, as when they are left to
+their own undisturbed action, we must be cautious not to express the
+laws in such terms as would render the assertion of their being
+fulfilled in those cases a contradiction. If, for instance, it were
+stated as a law of nature that a body to which a force is applied moves
+in the direction of the force, with a velocity proportioned to the force
+directly, and to its own mass inversely; when in point of fact some
+bodies to which a force is applied do not move at all, and those which
+do move (at least in the region of our earth) are, from the very first,
+retarded by the action of gravity and other resisting forces, and at
+last stopped altogether; it is clear that the general proposition,
+though it would be true under a certain hypothesis, would not express
+the facts as they actually occur. To accommodate the expression of the
+law to the real phenomena, we must say, not that the object moves, but
+that it <i>tends</i> to move, in the direction and with the velocity
+specified. We might, indeed, guard our expression in a different mode,
+by saying that the body moves in that manner unless prevented, or except
+in so far as prevented, by some counteracting <span class="pagenum"><a name="Page_497" id="Page_497">[Pg 497]</a></span>cause. But the body does
+not only move in that manner unless counteracted; it <i>tends</i> to move in
+that manner even when counteracted; it still exerts, in the original
+direction, the same energy of movement as if its first impulse had been
+undisturbed, and produces, by that energy, an exactly equivalent
+quantity of effect. This is true even when the force leaves the body as
+it found it, in a state of absolute rest; as when we attempt to raise a
+body of three tons weight with a force equal to one ton. For if, while
+we are applying this force, wind or water or any other agent supplies an
+additional force just exceeding two tons, the body will be raised; thus
+proving that the force we applied exerted its full effect, by
+neutralizing an equivalent portion of the weight which it was
+insufficient altogether to overcome. And if while we are exerting this
+force of one ton upon the object in a direction contrary to that of
+gravity, it be put into a scale and weighed, it will be found to have
+lost a ton of its weight, or in other words, to press downwards with a
+force only equal to the difference of the two forces.</p>
+
+<p>These facts are correctly indicated by the expression <i>tendency</i>. All
+laws of causation, in consequence of their liability to be counteracted,
+require to be stated in words affirmative of tendencies only, and not of
+actual results. In those sciences of causation which have an accurate
+nomenclature, there are special words which signify a tendency to the
+particular effect with which the science is conversant; thus <i>pressure</i>,
+in mechanics, is synonymous with tendency to motion, and forces are not
+reasoned on as causing actual motion, but as exerting pressure. A
+similar improvement in terminology would be very salutary in many other
+branches of science.</p>
+
+<p>The habit of neglecting this necessary element in the precise expression
+of the laws of nature, has given birth to the popular prejudice that all
+general truths have exceptions; and much unmerited distrust has thence
+accrued to the conclusions of science, when they have been submitted to
+the judgment of minds insufficiently disciplined and cultivated. The
+rough generalizations suggested by common observation <span class="pagenum"><a name="Page_498" id="Page_498">[Pg 498]</a></span>usually have
+exceptions; but principles of science, or in other words, laws of
+causation, have not. "What is thought to be an exception to a
+principle," (to quote words used on a different occasion,) "is always
+some other and distinct principle cutting into the former; some other
+force which impinges<a name="FNanchor_45_126" id="FNanchor_45_126"></a><a href="#Footnote_45_126" class="fnanchor">[45]</a> against the first force, and deflects it from
+its direction. There are not a law and an exception to that law, the law
+acting in ninety-nine cases, and the exception in one. There are two
+laws, each possibly acting in the whole hundred cases, and bringing
+about a common effect by their conjunct operation. If the force which,
+being the less conspicuous of the two, is called the <i>disturbing</i> force,
+prevails sufficiently over the other force in some one case, to
+constitute that case what is commonly called an exception, the same
+disturbing force probably acts as a modifying cause in many other cases
+which no one will call exceptions.</p>
+
+<p>"Thus if it were stated to be a law of nature that all heavy bodies fall
+to the ground, it would probably be said that the resistance of the
+atmosphere, which prevents a balloon from falling, constitutes the
+balloon an exception to that pretended law of nature. But the real law
+is, that all heavy bodies <i>tend</i> to fall; and to this there is no
+exception, not even the sun and moon; for even they, as every astronomer
+knows, tend towards the earth, with a force exactly equal to that with
+which the earth tends towards them. The resistance of the atmosphere
+might, in the particular case of the balloon, from a misapprehension of
+what the law of gravitation is, be said to <i>prevail over</i> the law; but
+its disturbing effect is quite as real in every other case, since though
+it does not prevent, it retards the fall of all bodies whatever. The
+rule, and the so-called exception, do not divide the cases between them;
+each of them is a comprehensive rule extending to all cases. To call one
+of these concurrent principles an exception to the other, is
+superficial, and contrary to the correct principles <span class="pagenum"><a name="Page_499" id="Page_499">[Pg 499]</a></span>of nomenclature and
+arrangement. An effect of precisely the same kind, and arising from the
+same cause, ought not to be placed in two different categories, merely
+as there does or does not exist another cause preponderating over
+it."<a name="FNanchor_46_127" id="FNanchor_46_127"></a><a href="#Footnote_46_127" class="fnanchor">[46]</a></p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_6">� 6.</a> We have now to consider according to what method these complex
+effects, compounded of the effects of many causes, are to be studied;
+how we are enabled to trace each effect to the concurrence of causes in
+which it originated, and ascertain the conditions of its recurrence&mdash;the
+circumstances in which it may be expected again to occur. The conditions
+of a phenomenon which arises from a composition of causes, may be
+investigated either deductively or experimentally.</p>
+
+<p>The case, it is evident, is naturally susceptible of the deductive mode
+of investigation. The law of an effect of this description is a result
+of the laws of the separate causes on the combination of which it
+depends, and is therefore in itself capable of being deduced from these
+laws. This is called the method <i>� priori</i>. The other, or <i>� posteriori</i>
+method, professes to proceed according to the canons of experimental
+inquiry. Considering the whole assemblage of concurrent causes which
+produced the phenomenon, as one single cause, it attempts to ascertain
+the cause in the ordinary manner, by a comparison of instances. This
+second method subdivides itself into two different varieties. If it
+merely collates instances of the effect, it is a method of pure
+observation. If it operates upon the causes, and tries different
+combinations of them, in hopes of ultimately hitting the precise
+combination which will produce the given total effect, it is a method of
+experiment.</p>
+
+<p>In order more completely to clear up the nature of each of these three
+methods, and determine which of them deserves the preference, it will be
+expedient (conformably to a favourite maxim of Lord Chancellor Eldon, to
+which, though it has often incurred philosophical ridicule, a deeper
+philosophy will not refuse its sanction) to "clothe them in
+circumstances." <span class="pagenum"><a name="Page_500" id="Page_500">[Pg 500]</a></span>We shall select for this purpose a case which as yet
+furnishes no very brilliant example of the success of any of the three
+methods, but which is all the more suited to illustrate the difficulties
+inherent in them. Let the subject of inquiry be, the conditions of
+health and disease in the human body; or (for greater simplicity) the
+conditions of recovery from a given disease; and in order to narrow the
+question still more, let it be limited, in the first instance, to this
+one inquiry: Is, or is not some particular medicament (mercury, for
+instance) a remedy for the given disease.</p>
+
+<p>Now, the deductive method would set out from known properties of
+mercury, and known laws of the human body, and by reasoning from these,
+would attempt to discover whether mercury will act upon the body when in
+the morbid condition supposed, in such a manner as to restore health.
+The experimental method would simply administer mercury in as many cases
+as possible, noting the age, sex, temperament, and other peculiarities
+of bodily constitution, the particular form or variety of the disease,
+the particular stage of its progress, &amp;c., remarking in which of these
+cases it produced a salutary effect, and with what circumstances it was
+on those occasions combined. The method of simple observation would
+compare instances of recovery, to find whether they agreed in having
+been preceded by the administration of mercury; or would compare
+instances of recovery with instances of failure, to find cases which,
+agreeing in all other respects, differed only in the fact that mercury
+had been administered, or that it had not.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_7">� 7.</a> That the last of these three modes of investigation is applicable
+to the case, no one has ever seriously contended. No conclusions of
+value on a subject of such intricacy, ever were obtained in that way.
+The utmost that could result would be a vague general impression for or
+against the efficacy of mercury, of no avail for guidance unless
+confirmed by one of the other two methods. Not that the results, which
+this method strives to obtain, would not be of the utmost possible value
+if they could be obtained. If all the cases of recovery <span class="pagenum"><a name="Page_501" id="Page_501">[Pg 501]</a></span>which presented
+themselves, in an examination extending to a great number of instances,
+were cases in which mercury had been administered, we might generalize
+with confidence from this experience, and should have obtained a
+conclusion of real value. But no such basis for generalization can we,
+in a case of this description, hope to obtain. The reason is that which
+we have spoken of as constituting the characteristic imperfection of the
+Method of Agreement; Plurality of Causes. Supposing even that mercury
+does tend to cure the disease, so many other causes, both natural and
+artificial, also tend to cure it, that there are sure to be abundant
+instances of recovery in which mercury has not been administered:
+unless, indeed, the practice be to administer it in all cases; on which
+supposition it will equally be found in the cases of failure.</p>
+
+<p>When an effect results from the union of many causes, the share which
+each has in the determination of the effect cannot in general be great:
+and the effect is not likely, even in its presence or absence, still
+less in its variations, to follow, even approximately, any one of the
+causes. Recovery from a disease is an event to which, in every case,
+many influences must concur. Mercury may be one such influence; but from
+the very fact that there are many other such, it will necessarily happen
+that although mercury is administered, the patient, for want of other
+concurring influences, will often not recover, and that he often will
+recover when it is not administered, the other favourable influences
+being sufficiently powerful without it. Neither, therefore, will the
+instances of recovery agree in the administration of mercury, nor will
+the instances of failure agree in its non-administration. It is much if,
+by multiplied and accurate returns from hospitals and the like, we can
+collect that there are rather more recoveries and rather fewer failures
+when mercury is administered than when it is not; a result of very
+secondary value even as a guide to practice, and almost worthless as a
+contribution to the theory of the subject.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_X_8">� 8.</a> The inapplicability of the method of simple observation to
+ascertain the conditions of effects dependent on <span class="pagenum"><a name="Page_502" id="Page_502">[Pg 502]</a></span>many concurring
+causes, being thus recognised; we shall next inquire whether any greater
+benefit can be expected from the other branch of the <i>� posteriori</i>
+method, that which proceeds by directly trying different combinations of
+causes, either artificially produced or found in nature, and taking
+notice what is their effect: as, for example, by actually trying the
+effect of mercury, in as many different circumstances as possible. This
+method differs from the one which we have just examined, in turning our
+attention directly to the causes or agents, instead of turning it to the
+effect, recovery from the disease. And since, as a general rule, the
+effects of causes are far more accessible to our study than the causes
+of effects, it is natural to think that this method has a much better
+chance of proving successful than the former.</p>
+
+<p>The method now under consideration is called the Empirical Method; and
+in order to estimate it fairly, we must suppose it to be completely, not
+incompletely, empirical. We must exclude from it everything which
+partakes of the nature not of an experimental but of a deductive
+operation. If for instance we try experiments with mercury upon a person
+in health, in order to ascertain the general laws of its action upon the
+human body, and then reason from these laws to determine how it will act
+upon persons affected with a particular disease, this may be a really
+effectual method, but this is deduction. The experimental method does
+not derive the law of a complex case from the simpler laws which
+conspire to produce it, but makes its experiments directly upon the
+complex case. We must make entire abstraction of all knowledge of the
+simpler tendencies, the <i>modi operandi</i> of mercury in detail. Our
+experimentation must aim at obtaining a direct answer to the specific
+question, Does or does not mercury tend to cure the particular disease?</p>
+
+<p>Let us see, therefore, how far the case admits of the observance of
+those rules of experimentation, which it is found necessary to observe
+in other cases. When we devise an experiment to ascertain the effect of
+a given agent, there are certain precautions which we never, if we can
+help it, omit. In the first place, we introduce the agent into the midst
+of a <span class="pagenum"><a name="Page_503" id="Page_503">[Pg 503]</a></span>set of circumstances which we have exactly ascertained. It needs
+hardly be remarked how far this condition is from being realized in any
+case connected with the phenomena of life; how far we are from knowing
+what are all the circumstances which pre-exist in any instance in which
+mercury is administered to a living being. This difficulty, however,
+though insuperable in most cases, may not be so in all; there are
+sometimes concurrences of many causes, in which we yet know accurately
+what the causes are. Moreover, the difficulty may be attenuated by
+sufficient multiplication of experiments, in circumstances rendering it
+improbable that any of the unknown causes should exist in them all. But
+when we have got clear of this obstacle, we encounter another still more
+serious. In other cases, when we intend to try an experiment, we do not
+reckon it enough that there be no circumstance in the case the presence
+of which is unknown to us. We require also that none of the
+circumstances which we do know, shall have effects susceptible of being
+confounded with those of the agent whose properties we wish to study. We
+take the utmost pains to exclude all causes capable of composition with
+the given cause; or if forced to let in any such causes, we take care to
+make them such that we can compute and allow for their influence, so
+that the effect of the given cause may, after the subduction of those
+other effects, be apparent as a residual phenomenon.</p>
+
+<p>These precautions are inapplicable to such cases as we are now
+considering. The mercury of our experiment being tried with an unknown
+multitude (or even let it be a known multitude) of other influencing
+circumstances, the mere fact of their being influencing circumstances
+implies that they disguise the effect of the mercury, and preclude us
+from knowing whether it has any effect or not. Unless we already knew
+what and how much is owing to every other circumstance, (that is, unless
+we suppose the very problem solved which we are considering the means of
+solving,) we cannot tell that those other circumstances may not have
+produced the whole of the effect, independently or even in spite of the
+mercury. The Method of Difference, in the ordinary mode of its use,
+namely by <span class="pagenum"><a name="Page_504" id="Page_504">[Pg 504]</a></span>comparing the state of things following the experiment with
+the state which preceded it, is thus, in the case of intermixture of
+effects, entirely unavailing; because other causes than that whose
+effect we are seeking to determine, have been operating during the
+transition. As for the other mode of employing the Method of Difference,
+namely by comparing, not the same case at two different periods, but
+different cases, this in the present instance is quite chimerical. In
+phenomena so complicated it is questionable if two cases, similar in all
+respects but one, ever occurred; and were they to occur, we could not
+possibly know that they were so exactly similar.</p>
+
+<p>Anything like a scientific use of the method of experiment, in these
+complicated cases, is therefore out of the question. We can in the most
+favourable cases only discover, by a succession of trials, that a
+certain cause is <i>very often</i> followed by a certain effect. For, in one
+of these conjunct effects, the portion which is determined by any one of
+the influencing agents, is generally, as we before remarked, but small;
+and it must be a more potent cause than most, if even the tendency which
+it really exerts is not thwarted by other tendencies in nearly as many
+cases as it is fulfilled.</p>
+
+<p>If so little can be done by the experimental method to determine the
+conditions of an effect of many combined causes, in the case of medical
+science; still less is this method applicable to a class of phenomena
+more complicated than even those of physiology, the phenomena of
+politics and history. There, Plurality of Causes exists in almost
+boundless excess, and effects are, for the most part, inextricably
+interwoven with one another. To add to the embarrassment, most of the
+inquiries in political science relate to the production of effects of a
+most comprehensive description, such as the public wealth, public
+security, public morality, and the like: results liable to be affected
+directly or indirectly either in <i>plus</i> or in <i>minus</i> by nearly every
+fact which exists, or event which occurs, in human society. The vulgar
+notion, that the safe methods on political subjects are those of
+Baconian induction&mdash;that the true guide is not general reasoning, but
+specific experience&mdash;will one day be quoted as among the most
+unequivocal marks of a low state <span class="pagenum"><a name="Page_505" id="Page_505">[Pg 505]</a></span>of the speculative faculties in any
+age in which it is accredited. Nothing can be more ludicrous than the
+sort of parodies on experimental reasoning which one is accustomed to
+meet with, not in popular discussion only, but in grave treatises, when
+the affairs of nations are the theme. "How," it is asked, "can an
+institution be bad, when the country has prospered under it?" "How can
+such or such causes have contributed to the prosperity of one country,
+when another has prospered without them?" Whoever makes use of an
+argument of this kind, not intending to deceive, should be sent back to
+learn the elements of some one of the more easy physical sciences. Such
+reasoners ignore the fact of Plurality of Causes in the very case which
+affords the most signal example of it. So little could be concluded, in
+such a case, from any possible collation of individual instances, that
+even the impossibility, in social phenomena, of making artificial
+experiments, a circumstance otherwise so prejudicial to directly
+inductive inquiry, hardly affords, in this case, additional reason of
+regret. For even if we could try experiments upon a nation or upon the
+human race, with as little scruple as M. Magendie tried them on dogs and
+rabbits, we should never succeed in making two instances identical in
+every respect except the presence or absence of some one definite
+circumstance. The nearest approach to an experiment in the philosophical
+sense, which takes place in politics, is the introduction of a new
+operative element into national affairs by some special and assignable
+measure of government, such as the enactment or repeal of a particular
+law. But where there are so many influences at work, it requires some
+time for the influence of any new cause upon national phenomena to
+become apparent; and as the causes operating in so extensive a sphere
+are not only infinitely numerous, but in a state of perpetual
+alteration, it is always certain that before the effect of the new cause
+becomes conspicuous enough to be a subject of induction, so many of the
+other influencing circumstances will have changed as to vitiate the
+experiment.</p>
+
+<p>Two, therefore, of the three possible methods for the study of phenomena
+resulting from the composition of many causes, <span class="pagenum"><a name="Page_506" id="Page_506">[Pg 506]</a></span>being, from the very
+nature of the case, inefficient and illusory, there remains only the
+third,&mdash;that which considers the causes separately, and infers the
+effect from the balance of the different tendencies which produce it: in
+short, the deductive, or <i>� priori</i> method. The more particular
+consideration of this intellectual process requires a chapter to itself.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_507" id="Page_507">[Pg 507]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_XI" id="BOOK_III_CHAPTER_XI"></a>CHAPTER XI.<br />
+
+OF THE DEDUCTIVE METHOD.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XI_1">� 1.</a> The mode of investigation which, from the proved inapplicability of
+direct methods of observation and experiment, remains to us as the main
+source of the knowledge we possess or can acquire respecting the
+conditions, and laws of recurrence, of the more complex phenomena, is
+called, in its most general expression, the Deductive Method; and
+consists of three operations: the first, one of direct induction; the
+second, of ratiocination; the third, of verification.</p>
+
+<p>I call the first step in the process an inductive operation, because
+there must be a direct induction as the basis of the whole; though in
+many particular investigations the place of the induction may be
+supplied by a prior deduction; but the premises of this prior deduction
+must have been derived from induction.</p>
+
+<p>The problem of the Deductive Method is, to find the law of an effect,
+from the laws of the different tendencies of which it is the joint
+result. The first requisite, therefore, is to know the laws of those
+tendencies; the law of each of the concurrent causes: and this supposes
+a previous process of observation or experiment upon each cause
+separately; or else a previous deduction, which also must depend for its
+ultimate premises on observation or experiment. Thus, if the subject be
+social or historical phenomena, the premises of the Deductive Method
+must be the laws of the causes which determine that class of phenomena;
+and those causes are human actions, together with the general outward
+circumstances under the influence of which mankind are placed, and which
+constitute man's position on the earth. The Deductive Method, applied to
+social phenomena, must begin, therefore, by investigating, or must
+suppose to have been already investigated, the laws of human <span class="pagenum"><a name="Page_508" id="Page_508">[Pg 508]</a></span>action,
+and those properties of outward things by which the actions of human
+beings in society are determined. Some of these general truths will
+naturally be obtained by observation and experiment, others by
+deduction: the more complex laws of human action, for example, may be
+deduced from the simpler ones; but the simple or elementary laws will
+always, and necessarily, have been obtained by a directly inductive
+process.</p>
+
+<p>To ascertain, then, the laws of each separate cause which takes a share
+in producing the effect, is the first desideratum of the Deductive
+Method. To know what the causes are, which must be subjected to this
+process of study, may or may not be difficult. In the case last
+mentioned, this first condition is of easy fulfilment. That social
+phenomena depend on the acts and mental impressions of human beings,
+never could have been a matter of any doubt, however imperfectly it may
+have been known either by what laws those impressions and actions are
+governed, or to what social consequences their laws naturally lead.
+Neither, again, after physical science had attained a certain
+development, could there be any real doubt where to look for the laws on
+which the phenomena of life depend, since they must be the mechanical
+and chemical laws of the solid and fluid substances composing the
+organized body and the medium in which it subsists, together with the
+peculiar vital laws of the different tissues constituting the organic
+structure. In other cases, really far more simple than these, it was
+much less obvious in what quarter the causes were to be looked for: as
+in the case of the celestial phenomena. Until, by combining the laws of
+certain causes, it was found that those laws explained all the facts
+which experience had proved concerning the heavenly motions, and led to
+predictions which it always verified, mankind never knew that those
+<i>were</i> the causes. But whether we are able to put the question before,
+or not until after, we have become capable of answering it, in either
+case it must be answered; the laws of the different causes must be
+ascertained, before we can proceed to deduce from them the conditions of
+the effect.</p>
+
+<p>The mode of ascertaining those laws neither is, nor can be, <span class="pagenum"><a name="Page_509" id="Page_509">[Pg 509]</a></span>any other
+than the fourfold method of experimental inquiry, already discussed. A
+few remarks on the application of that method to cases of the
+Composition of Causes, are all that is requisite.</p>
+
+<p>It is obvious that we cannot expect to find the law of a tendency, by an
+induction from cases in which the tendency is counteracted. The laws of
+motion could never have been brought to light from the observation of
+bodies kept at rest by the equilibrium of opposing forces. Even where
+the tendency is not, in the ordinary sense of the word, counteracted,
+but only modified, by having its effects compounded with the effects
+arising from some other tendency or tendencies, we are still in an
+unfavourable position for tracing, by means of such cases, the law of
+the tendency itself. It would have been scarcely possible to discover
+the law that every body in motion tends to continue moving in a straight
+line, by an induction from instances in which the motion is deflected
+into a curve, by being compounded with the effect of an accelerating
+force. Notwithstanding the resources afforded in this description of
+cases by the Method of Concomitant Variations, the principles of a
+judicious experimentation prescribe that the law of each of the
+tendencies should be studied, if possible, in cases in which that
+tendency operates alone, or in combination with no agencies but those of
+which the effect can, from previous knowledge, be calculated and allowed
+for.</p>
+
+<p>Accordingly, in the cases, unfortunately very numerous and important, in
+which the causes do not suffer themselves to be separated and observed
+apart, there is much difficulty in laying down with due certainty the
+inductive foundation necessary to support the deductive method. This
+difficulty is most of all conspicuous in the case of physiological
+phenomena; it being seldom possible to separate the different agencies
+which collectively compose an organized body, without destroying the
+very phenomena which it is our object to investigate:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">&mdash;following life, in creatures we dissect,<br /></span>
+<span class="i0">We lose it, in the moment we detect.<br /></span>
+</div></div>
+
+<p>And for this reason I am inclined to the opinion, that physiology
+<span class="pagenum"><a name="Page_510" id="Page_510">[Pg 510]</a></span>(greatly and rapidly progressive as it now is) is embarrassed by
+greater natural difficulties, and is probably susceptible of a less
+degree of ultimate perfection, than even the social science; inasmuch as
+it is possible to study the laws and operations of one human mind apart
+from other minds, much less imperfectly than we can study the laws of
+one organ or tissue of the human body apart from the other organs or
+tissues.</p>
+
+<p>It has been judiciously remarked that pathological facts, or, to speak
+in common language, diseases in their different forms and degrees,
+afford in the case of physiological investigation the most valuable
+equivalent to experimentation properly so called; inasmuch as they often
+exhibit to us a definite disturbance in some one organ or organic
+function, the remaining organs and functions being, in the first
+instance at least, unaffected. It is true that from the perpetual
+actions and reactions which are going on among all parts of the organic
+economy, there can be no prolonged disturbance in any one function
+without ultimately involving many of the others; and when once it has
+done so, the experiment for the most part loses its scientific value.
+All depends on observing the early stages of the derangement; which,
+unfortunately, are of necessity the least marked. If, however, the
+organs and functions not disturbed in the first instance, become
+affected in a fixed order of succession, some light is thereby thrown
+upon the action which one organ exercises over another: and we
+occasionally obtain a series of effects which we can refer with some
+confidence to the original local derangement; but for this it is
+necessary that we should know that the original derangement <i>was</i> local.
+If it was what is termed constitutional, that is, if we do not know in
+what part of the animal economy it took its rise, or the precise nature
+of the disturbance which took place in that part, we are unable to
+determine which of the various derangements was cause and which effect;
+which of them were produced by one another, and which by the direct,
+though perhaps tardy, action of the original cause.</p>
+
+<p>Besides natural pathological facts, we can produce pathological facts
+artificially; we can try experiments, even in the <span class="pagenum"><a name="Page_511" id="Page_511">[Pg 511]</a></span>popular sense of the
+term, by subjecting the living being to some external agent, such as the
+mercury of our former example, or the section of a nerve to ascertain
+the functions of different parts of the nervous system. As this
+experimentation is not intended to obtain a direct solution of any
+practical question, but to discover general laws, from which afterwards
+the conditions of any particular effect may be obtained by deduction;
+the best cases to select are those of which the circumstances can be
+best ascertained: and such are generally not those in which there is any
+practical object in view. The experiments are best tried, not in a state
+of disease, which is essentially a changeable state, but in the
+condition of health, comparatively a fixed state. In the one, unusual
+agencies are at work, the results of which we have no means of
+predicting; in the other, the course of the accustomed physiological
+phenomena would, it may generally be presumed, remain undisturbed, were
+it not for the disturbing cause which we introduce.</p>
+
+<p>Such, with the occasional aid of the Method of Concomitant Variations,
+(the latter not less incumbered than the more elementary methods by the
+peculiar difficulties of the subject,) are our inductive resources for
+ascertaining the laws of the causes considered separately, when we have
+it not in our power to make trial of them in a state of actual
+separation. The insufficiency of these resources is so glaring, that no
+one can be surprised at the backward state of the science of physiology;
+in which indeed our knowledge of causes is so imperfect, that we can
+neither explain, nor could without specific experience have predicted,
+many of the facts which are certified to us by the most ordinary
+observation. Fortunately, we are much better informed as to the
+empirical laws of the phenomena, that is, the uniformities respecting
+which we cannot yet decide whether they are cases of causation, or mere
+results of it. Not only has the order in which the facts of organization
+and life successively manifest themselves, from the first germ of
+existence to death, been found to be uniform, and very accurately
+ascertainable; but, by a great application of the Method of Concomitant
+Variations to the entire facts of <span class="pagenum"><a name="Page_512" id="Page_512">[Pg 512]</a></span>comparative anatomy and physiology,
+the characteristic organic structure corresponding to each class of
+functions has been determined with considerable precision. Whether these
+organic conditions are the whole of the conditions, and in many cases
+whether they are conditions at all, or mere collateral effects of some
+common cause, we are quite ignorant: nor are we ever likely to know,
+unless we could construct an organized body, and try whether it would
+live.</p>
+
+<p>Under such disadvantages do we, in cases of this description, attempt
+the initial, or inductive step, in the application of the Deductive
+Method to complex phenomena. But such, fortunately, is not the common
+case. In general, the laws of the causes on which the effect depends may
+be obtained by an induction from comparatively simple instances, or, at
+the worst, by deduction from the laws of simpler causes, so obtained. By
+simple instances are meant, of course, those in which the action of each
+cause was not intermixed or interfered with, or not to any great extent,
+by other causes whose laws were unknown. And only when the induction
+which furnished the premises to the Deductive method rested on such
+instances, has the application of such a method to the ascertainment of
+the laws of a complex effect, been attended with brilliant results.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XI_2">� 2.</a> When the laws of the causes have been ascertained, and the first
+stage of the great logical operation now under discussion satisfactorily
+accomplished, the second part follows; that of determining from the laws
+of the causes, what effect any given combination of those causes will
+produce. This is a process of calculation, in the wider sense of the
+term; and very often involves processes of calculation in the narrowest
+sense. It is a ratiocination; and when our knowledge of the causes is so
+perfect, as to extend to the exact numerical laws which they observe in
+producing their effects, the ratiocination may reckon among its premises
+the theorems of the science of number, in the whole immense extent of
+that science. Not only are the most advanced truths of mathematics often
+required to enable us to compute an effect, the numerical law <span class="pagenum"><a name="Page_513" id="Page_513">[Pg 513]</a></span>of which
+we already know; but, even by the aid of those most advanced truths, we
+can go but a little way. In so simple a case as the common problem of
+three bodies gravitating towards one another, with a force directly as
+their mass and inversely as the square of the distance, all the
+resources of the calculus have not hitherto sufficed to obtain any
+general solution but an approximate one. In a case a little more
+complex, but still one of the simplest which arise in practice, that of
+the motion of a projectile, the causes which affect the velocity and
+range (for example) of a cannon-ball may be all known and estimated; the
+force of the gunpowder, the angle of elevation, the density of the air,
+the strength and direction of the wind; but it is one of the most
+difficult of mathematical problems to combine all these, so as to
+determine the effect resulting from their collective action.</p>
+
+<p>Besides the theorems of number, those of geometry also come in as
+premises, where the effects take place in space, and involve motion and
+extension, as in mechanics, optics, acoustics, astronomy. But when the
+complication increases, and the effects are under the influence of so
+many and such shifting causes as to give no room either for fixed
+numbers, or for straight lines and regular curves, (as in the case of
+physiological, to say nothing of mental and social phenomena,) the laws
+of number and extension are applicable, if at all, only on that large
+scale on which precision of details becomes unimportant. Although these
+laws play a conspicuous part in the most striking examples of the
+investigation of nature by the Deductive Method, as for example in the
+Newtonian theory of the celestial motions, they are by no means an
+indispensable part of every such process. All that is essential in it is
+reasoning from a general law to a particular case, that is, determining
+by means of the particular circumstances of that case, what result is
+required in that instance to fulfil the law. Thus in the Torricellian
+experiment, if the fact that air has weight had been previously known,
+it would have been easy, without any numerical data, to deduce from the
+general law of equilibrium, that the mercury would stand in the tube at
+such a height that the column of mercury would exactly <span class="pagenum"><a name="Page_514" id="Page_514">[Pg 514]</a></span>balance a column
+of the atmosphere of equal diameter; because, otherwise, equilibrium
+would not exist.</p>
+
+<p>By such ratiocinations from the separate laws of the causes, we may, to
+a certain extent, succeed in answering either of the following
+questions: Given a certain combination of causes, what effect will
+follow? and, What combination of causes, if it existed, would produce a
+given effect? In the one case, we determine the effect to be expected in
+any complex circumstances of which the different elements are known: in
+the other case we learn, according to what law&mdash;under what antecedent
+conditions&mdash;a given complex effect will occur.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XI_3">� 3.</a> But (it may here be asked) are not the same arguments by which the
+methods of direct observation and experiment were set aside as illusory
+when applied to the laws of complex phenomena, applicable with equal
+force against the Method of Deduction? When in every single instance a
+multitude, often an unknown multitude, of agencies, are clashing and
+combining, what security have we that in our computation <i>� priori</i> we
+have taken all these into our reckoning? How many must we not generally
+be ignorant of? Among those which we know, how probable that some have
+been overlooked; and, even were all included, how vain the pretence of
+summing up the effects of many causes, unless we know accurately the
+numerical law of each,&mdash;a condition in most cases not to be fulfilled;
+and even when fulfilled, to make the calculation transcends, in any but
+very simple cases, the utmost power of mathematical science with all its
+most modern improvements.</p>
+
+<p>These objections have real weight, and would be altogether unanswerable,
+if there were no test by which, when we employ the Deductive Method, we
+might judge whether an error of any of the above descriptions had been
+committed or not. Such a test however there is: and its application
+forms, under the name of Verification, the third essential component
+part of the Deductive Method; without which all the results it can give
+have little other value than that of conjecture. To <span class="pagenum"><a name="Page_515" id="Page_515">[Pg 515]</a></span>warrant reliance on
+the general conclusions arrived at by deduction, these conclusions must
+be found, on careful comparison, to accord with the results of direct
+observation wherever it can be had. If, when we have experience to
+compare with them, this experience confirms them, we may safely trust to
+them in other cases of which our specific experience is yet to come. But
+if our deductions have led to the conclusion that from a particular
+combination of causes a given effect would result, then in all known
+cases where that combination can be shown to have existed, and where the
+effect has not followed, we must be able to show (or at least to make a
+probable surmise) what frustrated it: if we cannot, the theory is
+imperfect, and not yet to be relied upon. Nor is the verification
+complete, unless some of the cases in which the theory is borne out by
+the observed result, are of at least equal complexity with any other
+cases in which its application could be called for.</p>
+
+<p>If direct observation and collation of instances have furnished us with
+any empirical laws of the effect (whether true in all observed cases, or
+only true for the most part), the most effectual verification of which
+the theory could be susceptible would be, that it led deductively to
+those empirical laws; that the uniformities, whether complete or
+incomplete, which were observed to exist among the phenomena, were
+accounted for by the laws of the causes&mdash;were such as could not but
+exist if those be really the causes by which the phenomena are produced.
+Thus it was very reasonably deemed an essential requisite of any true
+theory of the causes of the celestial motions, that it should lead by
+deduction to Kepler's laws: which, accordingly, the Newtonian theory
+did.</p>
+
+<p>In order, therefore, to facilitate the verification of theories obtained
+by deduction, it is important that as many as possible of the empirical
+laws of the phenomena should be ascertained, by a comparison of
+instances, conformably to the Method of Agreement: as well as (it must
+be added) that the phenomena themselves should be described, in the most
+comprehensive as well as accurate manner possible; by collecting from
+the observation of parts, the simplest possible <span class="pagenum"><a name="Page_516" id="Page_516">[Pg 516]</a></span>correct expressions for
+the corresponding wholes: as when the series of the observed places of a
+planet was first expressed by a circle, then by a system of epicycles,
+and subsequently by an ellipse.</p>
+
+<p>It is worth remarking, that complex instances which would have been of
+no use for the discovery of the simple laws into which we ultimately
+analyse their phenomena, nevertheless, when they have served to verify
+the analysis, become additional evidence of the laws themselves.
+Although we could not have got at the law from complex cases, still when
+the law, got at otherwise, is found to be in accordance with the result
+of a complex case, that case becomes a new experiment on the law, and
+helps to confirm what it did not assist to discover. It is a new trial
+of the principle in a different set of circumstances; and occasionally
+serves to eliminate some circumstance not previously excluded, and the
+exclusion of which might require an experiment impossible to be
+executed. This was strikingly conspicuous in the example formerly
+quoted, in which the difference between the observed and the calculated
+velocity of sound was ascertained to result from the heat extricated by
+the condensation which takes place in each sonorous vibration. This was
+a trial, in new circumstances, of the law of the development of heat by
+compression; and it added materially to the proof of the universality of
+that law. Accordingly any law of nature is deemed to have gained in
+point of certainty, by being found to explain some complex case which
+had not previously been thought of in connexion with it; and this indeed
+is a consideration to which it is the habit of scientific inquirers to
+attach rather too much value than too little.</p>
+
+<p>To the Deductive Method, thus characterized in its three constituent
+parts, Induction, Ratiocination, and Verification, the human mind is
+indebted for its most conspicuous triumphs in the investigation of
+nature. To it we owe all the theories by which vast and complicated
+phenomena are embraced under a few simple laws, which, considered as the
+laws of those great phenomena, could never have been detected by their
+direct study. We may form some conception of <span class="pagenum"><a name="Page_517" id="Page_517">[Pg 517]</a></span>what the method has done
+for us, from the case of the celestial motions; one of the simplest
+among the greater instances of the Composition of Causes, since (except
+in a few cases not of primary importance) each of the heavenly bodies
+may be considered, without material inaccuracy, to be never at one time
+influenced by the attraction of more than two bodies, the sun and one
+other planet or satellite; making, with the reaction of the body itself,
+and the force generated by the body's own motion and acting in the
+direction of the tangent, only four different agents on the concurrence
+of which the motions of that body depend; a much smaller number, no
+doubt, than that by which any other of the great phenomena of nature is
+determined or modified. Yet how could we ever have ascertained the
+combination of forces on which the motions of the earth and planets are
+dependent, by merely comparing the orbits or velocities of different
+planets, or the different velocities or positions of the same planet?
+Notwithstanding the regularity which manifests itself in those motions,
+in a degree so rare among the effects of a concurrence of causes; and
+although the periodical recurrence of exactly the same effect, affords
+positive proof that all the combinations of causes which occur at all,
+recur periodically; we should not have known what the causes were, if
+the existence of agencies precisely similar on our own earth had not,
+fortunately, brought the causes themselves within the reach of
+experimentation under simple circumstances. As we shall have occasion to
+analyse, further on, this great example of the Method of Deduction, we
+shall not occupy any time with it here, but shall proceed to that
+secondary application of the Deductive Method, the result of which is
+not to prove laws of phenomena, but to explain them.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_518" id="Page_518">[Pg 518]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_XII" id="BOOK_III_CHAPTER_XII"></a>CHAPTER XII.<br />
+
+OF THE EXPLANATION OF LAWS OF NATURE.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_1">� 1.</a> The deductive operation by which we derive the law of an effect
+from the laws of the causes, the concurrence of which gives rise to it,
+may be undertaken either for the purpose of discovering the law, or of
+explaining a law already discovered. The word <i>explanation</i> occurs so
+continually and holds so important a place in philosophy, that a little
+time spent in fixing the meaning of it will be profitably employed.</p>
+
+<p>An individual fact is said to be explained, by pointing out its cause,
+that is, by stating the law or laws of causation, of which its
+production is an instance. Thus, a conflagration is explained, when it
+is proved to have arisen from a spark falling into the midst of a heap
+of combustibles. And in a similar manner, a law or uniformity in nature
+is said to be explained, when another law or laws are pointed out, of
+which that law itself is but a case, and from which it could be deduced.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_2">� 2.</a> There are three distinguishable sets of circumstances in which a
+law of causation may be explained from, or, as it also is often
+expressed, resolved into, other laws.</p>
+
+<p>The first is the case already so fully considered; an intermixture of
+laws, producing a joint effect equal to the sum of the effects of the
+causes taken separately. The law of the complex effect is explained, by
+being resolved into the separate laws of the causes which contribute to
+it. Thus, the law of the motion of a planet is resolved into the law of
+the acquired force, which tends to produce an uniform motion in the
+tangent, and the law of the centripetal force <span class="pagenum"><a name="Page_519" id="Page_519">[Pg 519]</a></span>which tends to produce an
+accelerating motion towards the sun; the real motion being a compound of
+the two.</p>
+
+<p>It is necessary here to remark, that in this resolution of the law of a
+complex effect, the laws of which it is compounded are not the only
+elements. It is resolved into the laws of the separate causes, together
+with the fact of their coexistence. The one is as essential an
+ingredient as the other; whether the object be to discover the law of
+the effect, or only to explain it. To deduce the laws of the heavenly
+motions, we require not only to know the law of a rectilineal and that
+of a gravitative force, but the existence of both these forces in the
+celestial regions, and even their relative amount. The complex laws of
+causation are thus resolved into two distinct kinds of elements: the
+one, simpler laws of causation, the other (in the aptly selected
+expression of Dr. Chalmers) collocations; the collocations consisting in
+the existence of certain agents or powers, in certain circumstances of
+place and time. We shall hereafter have occasion to return to this
+distinction, and to dwell on it at such length as dispenses with the
+necessity of further insisting on it here. The first mode, then, of the
+explanation of Laws of Causation, is when the law of an effect is
+resolved into the various tendencies of which it is the result, together
+with the laws of those tendencies.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_3">� 3.</a> A second case is when, between what seemed the cause and what was
+supposed to be its effect, further observation detects an intermediate
+link; a fact caused by the antecedent, and in its turn causing the
+consequent; so that the cause at first assigned is but the remote cause,
+operating through the intermediate phenomenon. A seemed the cause of C,
+but it subsequently appeared that A was only the cause of B, and that it
+is B which was the cause of C. For example: mankind were aware that the
+act of touching an outward object caused a sensation. It was
+subsequently discovered, that after we have touched the object, and
+before we experience the sensation, some change takes place in a kind of
+thread called a nerve, which extends from our outward organs to the
+brain. Touching the object, therefore, is only the remote cause of our
+<span class="pagenum"><a name="Page_520" id="Page_520">[Pg 520]</a></span>sensation; that is, not the cause, properly speaking, but the cause of
+the cause;&mdash;the real cause of the sensation is the change in the state
+of the nerve. Future experience may not only give us more knowledge than
+we now have of the particular nature of this change, but may also
+interpolate another link: between the contact (for example) of the
+object with our outward organs, and the production of the change of
+state in the nerve, there may take place some electric phenomenon; or
+some phenomenon of a nature not resembling the effects of any known
+agency. Hitherto, however, no such intermediate link has been
+discovered; and the touch of the object must be considered,
+provisionally, as the proximate cause of the affection of the nerve. The
+sequence, therefore, of a sensation of touch on contact with an object,
+is ascertained not to be an ultimate law; it is resolved, as the phrase
+is, into two other laws,&mdash;the law, that contact with an object produces
+an affection of the nerve; and the law, that an affection of the nerve
+produces sensation.</p>
+
+<p>To take another example: the more powerful acids corrode or blacken
+organic compounds. This is a case of causation, but of remote causation;
+and is said to be explained when it is shown that there is an
+intermediate link, namely, the separation of some of the chemical
+elements of the organic structure from the rest, and their entering into
+combination with the acid. The acid causes this separation of the
+elements, and the separation of the elements causes the disorganization,
+and often the charring of the structure. So, again, chlorine extracts
+colouring matters, (whence its efficacy in bleaching,) and purifies the
+air from infection. This law is resolved into the two following laws.
+Chlorine has a powerful affinity for bases of all kinds, particularly
+metallic bases and hydrogen. Such bases are essential elements of
+colouring matters and contagious compounds: which substances, therefore,
+are decomposed and destroyed by chlorine.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_4">� 4.</a> It is of importance to remark, that when a sequence of phenomena is
+thus resolved into other laws, they are always laws more general than
+itself. The law that A is followed by <span class="pagenum"><a name="Page_521" id="Page_521">[Pg 521]</a></span>C, is less general than either of
+the laws which connect B with C and A with B. This will appear from very
+simple considerations.</p>
+
+<p>All laws of causation are liable to be counteracted or frustrated, by
+the non-fulfilment of some negative condition: the tendency, therefore,
+of B to produce C may be defeated. Now the law that A produces B, is
+equally fulfilled whether B is followed by C or not; but the law that A
+produces C by means of B, is of course only fulfilled when B is really
+followed by C, and is therefore less general than the law that A
+produces B. It is also less general than the law that B produces C. For
+B may have other causes besides A; and as A produces C only by means of
+B, while B produces C whether it has itself been produced by A or by
+anything else, the second law embraces a greater number of instances,
+covers as it were a greater space of ground, than the first.</p>
+
+<p>Thus, in our former example, the law that the contact of an object
+causes a change in the state of the nerve, is more general than the law
+that contact with an object causes sensation, since, for aught we know,
+the change in the nerve may equally take place when, from a
+counteracting cause, as for instance, strong mental excitement, the
+sensation does not follow; as in a battle, where wounds are sometimes
+received without any consciousness of receiving them. And again, the law
+that change in the state of a nerve produces sensation, is more general
+than the law that contact with an object produces sensation; since the
+sensation equally follows the change in the nerve when not produced by
+contact with an object, but by some other cause; as in the well-known
+case, when a person who has lost a limb, feels the same sensation which
+he has been accustomed to call a pain in the limb.</p>
+
+<p>Not only are the laws of more immediate sequence into which the law of a
+remote sequence is resolved, laws of greater generality than that law
+is, but (as a consequence of, or rather as implied in, their greater
+generality) they are more to be relied on; there are fewer chances of
+their being ultimately found not to be universally true. From the moment
+when the sequence of A and C is shown not to be immediate, but to
+<span class="pagenum"><a name="Page_522" id="Page_522">[Pg 522]</a></span>depend on an intervening phenomenon, then, however constant and
+invariable the sequence of A and C has hitherto been found,
+possibilities arise of its failure, exceeding those which can affect
+either of the more immediate sequences, A, B, and B, C. The tendency of
+A to produce C may be defeated by whatever is capable of defeating
+either the tendency of A to produce B, or the tendency of B to produce
+C; it is therefore twice as liable to failure as either of those more
+elementary tendencies; and the generalization that A is always followed
+by C, is twice as likely to be found erroneous. And so of the converse
+generalization, that C is always preceded and caused by A; which will be
+erroneous not only if there should happen to be a second immediate mode
+of production of C itself, but moreover if there be a second mode of
+production of B, the immediate antecedent of C in the sequence.</p>
+
+<p>The resolution of the one generalization into the other two, not only
+shows that there are possible limitations of the former, from which its
+two elements are exempt, but shows also where these are to be looked
+for. As soon as we know that B intervenes between A and C, we also know
+that if there be cases in which the sequence of A and C does not hold,
+these are most likely to be found by studying the effects or the
+conditions of the phenomenon B.</p>
+
+<p>It appears, then, that in the second of the three modes in which a law
+may be resolved into other laws, the latter are more general, that is,
+extend to more cases, and are also less likely to require limitation
+from subsequent experience, than the law which they serve to explain.
+They are more nearly unconditional; they are defeated by fewer
+contingencies; they are a nearer approach to the universal truth of
+nature. The same observations are still more evidently true with regard
+to the first of the three modes of resolution. When the law of an effect
+of combined causes is resolved into the separate laws of the causes, the
+nature of the case implies that the law of the effect is less general
+than the law of any of the causes, since it only holds when they are
+combined; while the law of any one of the causes holds good both then,
+and also when that cause acts apart from the rest. It is also manifest
+that <span class="pagenum"><a name="Page_523" id="Page_523">[Pg 523]</a></span>the complex law is liable to be oftener unfulfilled than any one
+of the simpler laws of which it is the result, since every contingency
+which defeats any of the laws prevents so much of the effect as depends
+on it, and thereby defeats the complex law. The mere rusting, for
+example, of some small part of a great machine, often suffices entirely
+to prevent the effect which ought to result from the joint action of all
+the parts. The law of the effect of a combination of causes is always
+subject to the whole of the negative conditions which attach to the
+action of all the causes severally.</p>
+
+<p>There is another and an equally strong reason why the law of a complex
+effect must be less general than the laws of the causes which conspire
+to produce it. The same causes, acting according to the same laws, and
+differing only in the proportions in which they are combined, often
+produce effects which differ not merely in quantity, but in kind. The
+combination of a centripetal with a projectile force, in the proportions
+which obtain in all the planets and satellites of our solar system,
+gives rise to an elliptical motion; but if the ratio of the two forces
+to each other were slightly altered, it is demonstrated that the motion
+produced would be in a circle, or a parabola, or an hyperbola: and it is
+thought that in the case of some comets one of these is probably the
+fact. Yet the law of the parabolic motion would be resolvable into the
+very same simple laws into which that of the elliptical motion is
+resolved, namely, the law of the permanence of rectilineal motion, and
+the law of gravitation. If, therefore, in the course of ages, some
+circumstance were to manifest itself which, without defeating the law of
+either of those forces, should merely alter their proportion to one
+another, (such as the shock of some solid body, or even the accumulating
+effect of the resistance of the medium in which astronomers have been
+led to surmise that the motions of the heavenly bodies take place,) the
+elliptical motion might be changed into a motion in some other conic
+section; and the complex law, that the planetary motions take place in
+ellipses, would be deprived of its universality, though the discovery
+would not at all detract from the universality of the simpler laws into
+which that <span class="pagenum"><a name="Page_524" id="Page_524">[Pg 524]</a></span>complex law is resolved. The law, in short, of each of the
+concurrent causes remains the same, however their collocations may vary;
+but the law of their joint effect varies with every difference in the
+collocations. There needs no more to show how much more general the
+elementary laws must be, than any of the complex laws which are derived
+from them.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_5">� 5.</a> Besides the two modes which have been treated of, there is a third
+mode in which laws are resolved into one another; and in this it is
+self-evident that they are resolved into laws more general than
+themselves. This third mode is the <i>subsumption</i> (as it has been called)
+of one law under another: or (what comes to the same thing) the
+gathering up of several laws into one more general law which includes
+them all. The most splendid example of this operation was when
+terrestrial gravity and the central force of the solar system were
+brought together under the general law of gravitation. It had been
+proved antecedently that the earth and the other planets tend to the
+sun; and it had been known from the earliest times that terrestrial
+bodies tend towards the earth. These were similar phenomena; and to
+enable them both to be subsumed under one law, it was only necessary to
+prove that, as the effects were similar in quality, so also they, as to
+quantity, conform to the same rules. This was first shown to be true of
+the moon, which agreed with terrestrial objects not only in tending to a
+centre, but in the fact that this centre was the earth. The tendency of
+the moon towards the earth being ascertained to vary as the inverse
+square of the distance, it was deduced from this, by direct calculation,
+that if the moon were as near to the earth as terrestrial objects are,
+and the acquired force in the direction of the tangent were suspended,
+the moon would fall towards the earth through exactly as many feet in a
+second as those objects do by virtue of their weight. Hence the
+inference was irresistible, that the moon also tends to the earth by
+virtue of its weight: and that the two phenomena, the tendency of the
+moon to the earth and the tendency of terrestrial objects to the earth,
+being not <span class="pagenum"><a name="Page_525" id="Page_525">[Pg 525]</a></span>only similar in quality, but, when in the same circumstances,
+identical in quantity, are cases of one and the same law of causation.
+But the tendency of the moon to the earth, and the tendency of the earth
+and planets to the sun, were already known to be cases of the same law
+of causation: and thus the law of all these tendencies, and the law of
+terrestrial gravity, were recognised as identical, and were subsumed
+under one general law, that of gravitation.</p>
+
+<p>In a similar manner, the laws of magnetic phenomena have more recently
+been subsumed under known laws of electricity. It is thus that the most
+general laws of nature are usually arrived at: we mount to them by
+successive steps. For, to arrive by correct induction at laws which hold
+under such an immense variety of circumstances, laws so general as to be
+independent of any varieties of space or time which we are able to
+observe, requires for the most part many distinct sets of experiments or
+observations, conducted at different times and by different people. One
+part of the law is first ascertained, afterwards another part: one set
+of observations teaches us that the law holds good under some
+conditions, another that it holds good under other conditions, by
+combining which observations we find that it holds good under conditions
+much more general, or even universally. The general law, in this case,
+is literally the sum of all the partial ones; it is the recognition of
+the same sequence in different sets of instances; and may, in fact, be
+regarded as merely one step in the process of elimination. That tendency
+of bodies towards one another, which we now call gravity, had at first
+been observed only on the earth's surface, where it manifested itself
+only as a tendency of all bodies towards the earth, and might,
+therefore, be ascribed to a peculiar property of the earth itself: one
+of the circumstances, namely, the proximity of the earth, had not been
+eliminated. To eliminate this circumstance required a fresh set of
+instances in other parts of the universe: these we could not ourselves
+create; and though nature had created them for us, we were placed in
+very unfavourable circumstances for observing them. To make these
+observations, fell naturally to the lot of a different set of persons
+from those <span class="pagenum"><a name="Page_526" id="Page_526">[Pg 526]</a></span>who studied terrestrial phenomena; and had, indeed, been a
+matter of great interest at a time when the idea of explaining celestial
+facts by terrestrial laws was looked upon as the confounding of an
+indefeasible distinction. When, however, the celestial motions were
+accurately ascertained, and the deductive processes performed, from
+which it appeared that their laws and those of terrestrial gravity
+corresponded, those celestial observations became a set of instances
+which exactly eliminated the circumstance of proximity to the earth; and
+proved that in the original case, that of terrestrial objects, it was
+not the earth, as such, that caused the motion or the pressure, but the
+circumstance common to that case with the celestial instances, namely,
+the presence of some great body within certain limits of distance.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XII_6">� 6.</a> There are, then, three modes of explaining laws of causation, or,
+which is the same thing, resolving them into other laws. First, when the
+law of an effect of combined causes is resolved into the separate laws
+of the causes, together with the fact of their combination. Secondly,
+when the law which connects any two links, not proximate, in a chain of
+causation, is resolved into the laws which connect each with the
+intermediate links. Both of these are cases of resolving one law into
+two or more; in the third, two or more are resolved into one: when,
+after the law has been shown to hold good in several different classes
+of cases, we decide that what is true in each of these classes of cases,
+is true under some more general supposition, consisting of what all
+those classes of cases have in common. We may here remark that this last
+operation involves none of the uncertainties attendant on induction by
+the Method of Agreement, since we need not suppose the result to be
+extended by way of inference to any new class of cases, different from
+those by the comparison of which it was engendered.</p>
+
+<p>In all these three processes, laws are, as we have seen, resolved into
+laws more general than themselves; laws extending to all the cases which
+the former extended to, and others besides. In the first two modes they
+are also resolved <span class="pagenum"><a name="Page_527" id="Page_527">[Pg 527]</a></span>into laws more certain, in other words, more
+universally true than themselves; they are, in fact, proved not to be
+themselves laws of nature, the character of which is to be universally
+true, but <i>results</i> of laws of nature, which may be only true
+conditionally, and for the most part. No difference of this sort exists
+in the third case; since here the partial laws are, in fact, the very
+same law as the general one, and any exception to them would be an
+exception to it too.</p>
+
+<p>By all the three processes, the range of deductive science is extended;
+since the laws, thus resolved, may be thenceforth deduced
+demonstratively from the laws into which they are resolved. As already
+remarked, the same deductive process which proves a law or fact of
+causation if unknown, serves to explain it when known.</p>
+
+<p>The word explanation is here used in its philosophical sense. What is
+called explaining one law of nature by another, is but substituting one
+mystery for another; and does nothing to render the general course of
+nature other than mysterious: we can no more assign a <i>why</i> for the more
+extensive laws than for the partial ones. The explanation may substitute
+a mystery which has become familiar, and has grown to <i>seem</i> not
+mysterious, for one which is still strange. And this is the meaning of
+explanation, in common parlance. But the process with which we are here
+concerned often does the very contrary: it resolves a phenomenon with
+which we are familiar, into one of which we previously knew little or
+nothing; as when the common fact of the fall of heavy bodies was
+resolved into the tendency of all particles of matter towards one
+another. It must be kept constantly in view, therefore, that in science,
+those who speak of explaining any phenomenon mean (or should mean)
+pointing out not some more familiar, but merely some more general,
+phenomenon, of which it is a partial exemplification; or some laws of
+causation which produce it by their joint or successive action, and from
+which, therefore, its conditions may be determined deductively. Every
+such operation brings us a step nearer towards answering the question
+which was stated in a previous chapter as comprehending the whole
+problem of the investigation of nature, viz. What are the fewest
+<span class="pagenum"><a name="Page_528" id="Page_528">[Pg 528]</a></span>assumptions, which being granted, the order of nature as it exists
+would be the result? What are the fewest general propositions from which
+all the uniformities existing in nature could be deduced?</p>
+
+<p>The laws, thus explained or resolved, are sometimes said to be
+<i>accounted for</i>; but the expression is incorrect, if taken to mean
+anything more than what has been already stated. In minds not habituated
+to accurate thinking, there is often a confused notion that the general
+laws are the <i>causes</i> of the partial ones; that the law of general
+gravitation, for example, causes the phenomenon of the fall of bodies to
+the earth. But to assert this, would be a misuse of the word cause:
+terrestrial gravity is not an effect of general gravitation, but a
+<i>case</i> of it; that is, one kind of the particular instances in which
+that general law obtains. To account for a law of nature means, and can
+mean, nothing more than to assign other laws more general, together with
+collocations, which laws and collocations being supposed, the partial
+law follows without any additional supposition.</p>
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_529" id="Page_529">[Pg 529]</a></span></p>
+<h3><a name="BOOK_III_CHAPTER_XIII" id="BOOK_III_CHAPTER_XIII"></a>CHAPTER XIII.<br />
+
+MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.</h3>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_1">� 1.</a> The most striking example which the history of science presents, of
+the explanation of laws of causation and other uniformities of sequence
+among special phenomena, by resolving them into laws of greater
+simplicity and generality, is the great Newtonian generalization:
+respecting which typical instance so much having already been said, it
+is sufficient to call attention to the great number and variety of the
+special observed uniformities which are in this case accounted for,
+either as particular cases or as consequences of one very simple law of
+universal nature. The simple fact of a tendency of every particle of
+matter towards every other particle, varying inversely as the square of
+the distance, explains the fall of bodies to the earth, the revolutions
+of the planets and satellites, the motions (so far as known) of comets,
+and all the various regularities which have been observed in these
+special phenomena; such as the elliptical orbits, and the variations
+from exact ellipses; the relation between the solar distances of the
+planets and the duration of their revolutions; the precession of the
+equinoxes; the tides, and a vast number of minor astronomical truths.</p>
+
+<p>Mention has also been made in the preceding chapter of the explanation
+of the phenomena of magnetism from laws of electricity; the special laws
+of magnetic agency having been affiliated by deduction to observed laws
+of electric action, in which they have ever since been considered to be
+included as special cases. An example not so complete in itself, but
+even more fertile in consequences, having been the starting point of the
+really scientific study of physiology, is the affiliation, <span class="pagenum"><a name="Page_530" id="Page_530">[Pg 530]</a></span>commenced by
+Bichat, and carried on by subsequent biologists, of the properties of
+the bodily organs, to the elementary properties of the tissues into
+which they are anatomically decomposed.</p>
+
+<p>Another striking instance is afforded by Dalton's generalization,
+commonly known as the atomic theory. It had been known from the very
+commencement of accurate chemical observation, that any two bodies
+combine chemically with one another in only a certain number of
+proportions; but those proportions were in each case expressed by a
+percentage&mdash;so many parts (by weight) of each ingredient, in 100 of the
+compound; (say 35 and a fraction of one element, 64 and a fraction of
+the other): in which mode of statement no relation was perceived between
+the proportion in which a given element combines with one substance, and
+that in which it combines with others. The great step made by Dalton
+consisted in perceiving, that a unit of weight might be established for
+each substance, such that by supposing the substance to enter into all
+its combinations in the ratio either of that unit, or of some low
+multiple of that unit, all the different proportions, previously
+expressed by percentages, were found to result. Thus 1 being assumed as
+the unit of hydrogen, if 8 were then taken as that of oxygen, the
+combination of one unit of hydrogen with one unit of oxygen would
+produce the exact proportion of weight between the two substances which
+is known to exist in water; the combination of one unit of hydrogen with
+two units of oxygen would produce the proportion which exists in the
+other compound of the same two elements, called peroxide of hydrogen;
+and the combinations of hydrogen and of oxygen with all other
+substances, would correspond with the supposition that those elements
+enter into combination by single units, or twos, or threes, of the
+numbers assigned to them, 1 and 8, and the other substances by ones or
+twos or threes of other determinate numbers proper to each. The result
+is that a table of the equivalent numbers, or, as they are called,
+atomic weights, of all the elementary substances, comprises in itself,
+and scientifically explains, all the proportions in which any substance,
+elementary or compound, is found capable of <span class="pagenum"><a name="Page_531" id="Page_531">[Pg 531]</a></span>entering into chemical
+combination with any other substance whatever.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_2">� 2.</a> Some interesting cases of the explanation of old uniformities by
+newly ascertained laws are afforded by the researches of Professor
+Graham. That eminent chemist was the first who drew attention to the
+distinction which may be made of all substances into two classes, termed
+by him crystalloids and colloids; or rather, of all states of matter
+into the crystalloid and the colloidal states, for many substances are
+capable of existing in either. When in the colloidal state, their
+sensible properties are very different from those of the same substance
+when crystallized, or when in a state easily susceptible of
+crystallization. Colloid substances pass with extreme difficulty and
+slowness into the crystalline state, and are extremely inert in all the
+ordinary chemical relations. Substances in the colloid state are almost
+always, when combined with water, more or less viscous or gelatinous.
+The most prominent examples of the state are certain animal and
+vegetable substances, particularly gelatine, albumen, starch, the gums,
+caramel, tannin, and some others. Among substances not of organic
+origin, the most notable instances are hydrated silicic acid, and
+hydrated alumina, with other metallic peroxides of the aluminous class.</p>
+
+<p>Now it is found, that while colloidal substances are easily penetrated
+by water, and by the solutions of crystalloid substances, they are very
+little penetrable by one another: which enabled Professor Graham to
+introduce a highly effective process (termed dialysis) for separating
+the crystalloid substances contained in any liquid mixture, by passing
+them through a thin septum of colloidal matter, which does not suffer
+anything colloidal to pass, or suffers it only in very minute quantity.
+This property of colloids enabled Mr. Graham to account for a number of
+special results of observation, not previously explained.</p>
+
+<p>For instance, "while soluble crystalloids are always highly sapid,
+soluble colloids are singularly insipid," as might be expected; for, as
+the sentient extremities of the nerves of the <span class="pagenum"><a name="Page_532" id="Page_532">[Pg 532]</a></span>palate "are probably
+protected by a colloidal membrane," impermeable to other colloids, a
+colloid, when tasted, probably never reaches those nerves. Again, "it
+has been observed that vegetable gum is not digested in the stomach; the
+coats of that organ dialyse the soluble food, absorbing crystalloids,
+and rejecting all colloids." One of the mysterious processes
+accompanying digestion, the secretion of free muriatic acid by the coats
+of the stomach, obtains a probable hypothetical explanation through the
+same law. Finally, much light is thrown upon the observed phenomena of
+osmose (the passage of fluids outward and inward through animal
+membranes) by the fact that the membranes are colloidal. In consequence,
+the water and saline solutions contained in the animal body pass easily
+and rapidly through the membranes, while the substances directly
+applicable to nutrition, which are mostly colloidal, are detained by
+them.<a name="FNanchor_47_128" id="FNanchor_47_128"></a><a href="#Footnote_47_128" class="fnanchor">[47]</a></p>
+
+<p>The property which salt possesses of preserving animal substances from
+putrefaction is resolved by Liebig into two more general laws, the
+strong attraction of salt for water, and the necessity of the presence
+of water as a condition of putrefaction. The intermediate phenomenon
+which is interpolated between the remote cause and the effect, can here
+be not merely inferred but seen; for it is a familiar fact, that flesh
+upon which salt has been thrown is speedily found swimming in brine.</p>
+
+<p>The second of the two factors (as they may be termed) into which the
+preceding law has been resolved, the necessity of water to putrefaction,
+itself affords an additional example of the Resolution of Laws. The law
+itself is proved by the Method of Difference, since flesh completely
+dried and kept in a dry atmosphere does not putrefy; as we see in the
+case of dried provisions, and human bodies in very dry climates. A
+deductive explanation of this same law results from Liebig's
+speculations. The putrefaction of animal and other azotised <span class="pagenum"><a name="Page_533" id="Page_533">[Pg 533]</a></span>bodies is a
+chemical process, by which they are gradually dissipated in a gaseous
+form, chiefly in that of carbonic acid and ammonia; now to convert the
+carbon of the animal substance into carbonic acid requires oxygen, and
+to convert the azote into ammonia requires hydrogen, which are the
+elements of water. The extreme rapidity of the putrefaction of azotised
+substances, compared with the gradual decay of non-azotised bodies (such
+as wood and the like) by the action of oxygen alone, he explains from
+the general law that substances are much more easily decomposed by the
+action of two different affinities upon two of their elements, than by
+the action of only one.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_3">� 3.</a> Among the many important properties of the nervous system, which
+have either been first discovered or strikingly illustrated by Dr.
+Brown-S�quard, I select the reflex influence of the nervous system on
+nutrition and secretion. By reflex nervous action is meant, action which
+one part of the nervous system exerts over another part, without any
+intermediate action on the brain, and consequently without
+consciousness; or which, if it does pass through the brain, at least
+produces its effects independently of the will. There are many
+experiments which prove that irritation of a nerve in one part of the
+body may in this manner excite powerful action in another part; for
+example, food injected into the stomach through a divided &oelig;sophagus,
+nevertheless produces secretion of saliva; warm water injected into the
+bowels, and various other irritations of the lower intestines, have been
+found to excite secretion of the gastric juice, and so forth. The
+reality of the power being thus proved, its agency explains a great
+variety of apparently anomalous phenomena; of which I select the
+following from Dr. Brown-S�quard's <i>Lectures on the Nervous System</i>.</p>
+
+<p>The production of tears by irritation of the eye, or of the mucous
+membrane of the nose:</p>
+
+<p>The secretions of the eye and nose increased by exposure of other parts
+of the body to cold:</p>
+
+<p>Inflammation of the eye, especially when of traumatic <span class="pagenum"><a name="Page_534" id="Page_534">[Pg 534]</a></span>origin, very
+frequently excites a similar affection in the other eye, which may be
+cured by section of the intervening nerve:</p>
+
+<p>Loss of sight sometimes produced by neuralgia; and has been known to be
+at once cured by the extirpation (for instance) of a carious tooth:</p>
+
+<p>Even cataract has been produced in a healthy eye by cataract in the
+other eye, or by neuralgia, or by a wound of the frontal nerve:</p>
+
+<p>The well-known phenomenon of a sudden stoppage of the heart's action,
+and consequent death, produced by irritation of some of the nervous
+extremities: <i>e.g.</i>, by drinking very cold water; or by a blow on the
+abdomen, or other sudden excitation of the abdominal sympathetic nerve;
+though this nerve may be irritated to any extent without stopping the
+heart's action, if a section be made of the communicating nerves:</p>
+
+<p>The extraordinary effects produced on the internal organs by an
+extensive burn on the surface of the body; consisting in violent
+inflammation of the tissues of the abdomen, chest, or head: which, when
+death ensues from this kind of injury, is one of the most frequent
+causes of it:</p>
+
+<p>Paralysis and an�sthesia of one part of the body from neuralgia in
+another part; and muscular atrophy from neuralgia, even when there is no
+paralysis:</p>
+
+<p>Tetanus produced by the lesion of a nerve; Dr. Brown-S�quard thinks it
+highly probable that hydrophobia is a phenomenon of a similar nature:</p>
+
+<p>Morbid changes in the nutrition of the brain and spinal cord,
+manifesting themselves by epilepsy, chorea, hysteria, and other
+diseases, occasioned by lesion of some of the nervous extremities in
+remote places, as by worms, calculi, tumours, carious bones, and in some
+cases even by very slight irritations of the skin.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_4">� 4.</a> From the foregoing and similar instances, we may see the
+importance, when a law of nature previously unknown has been brought to
+light, or when new light has been thrown upon a known law by experiment,
+of examining all cases <span class="pagenum"><a name="Page_535" id="Page_535">[Pg 535]</a></span>which present the conditions necessary for
+bringing that law into action; a process fertile in demonstrations of
+special laws previously unsuspected, and explanations of others already
+empirically known.</p>
+
+<p>For instance, Faraday discovered by experiment, that voltaic electricity
+could be evolved from a natural magnet, provided a conducting body were
+set in motion at right angles to the direction of the magnet: and this
+he found to hold not only of small magnets, but of that great magnet,
+the earth. The law being thus established experimentally, that
+electricity is evolved, by a magnet, and a conductor moving at right
+angles to the direction of its poles, we may now look out for fresh
+instances in which these conditions meet. Wherever a conductor moves or
+revolves at right angles to the direction of the earth's magnetic poles,
+there we may expect an evolution of electricity. In the northern
+regions, where the polar direction is nearly perpendicular to the
+horizon, all horizontal motions of conductors will produce electricity;
+horizontal wheels, for example, made of metal; likewise all running
+streams will evolve a current of electricity, which will circulate round
+them; and the air thus charged with electricity may be one of the causes
+of the Aurora Borealis. In the equatorial regions, on the contrary,
+upright wheels placed parallel to the equator will originate a voltaic
+circuit, and waterfalls will naturally become electric.</p>
+
+<p>For a second example; it has been proved, chiefly by the researches of
+Professor Graham, that gases have a strong tendency to permeate animal
+membranes, and diffuse themselves through the spaces which such
+membranes inclose, notwithstanding the presence of other gases in those
+spaces. Proceeding from this general law, and reviewing a variety of
+cases in which gases lie contiguous to membranes, we are enabled to
+demonstrate or to explain the following more special laws: 1st. The
+human or animal body, when surrounded with any gas not already contained
+within the body, absorbs it rapidly; such, for instance, as the gases of
+putrefying matters: which helps to explain malaria. 2nd. The carbonic
+acid gas of effervescing drinks, evolved in the stomach, <span class="pagenum"><a name="Page_536" id="Page_536">[Pg 536]</a></span>permeates its
+membranes, and rapidly spreads through the system. 3rd. Alcohol taken
+into the stomach passes into vapour and spreads through the system with
+great rapidity; (which, combined with the high combustibility of
+alcohol, or in other words its ready combination with oxygen, may
+perhaps help to explain the bodily warmth immediately consequent on
+drinking spirituous liquors.) 4th. In any state of the body in which
+peculiar gases are formed within it, these will rapidly exhale through
+all parts of the body; and hence the rapidity with which, in certain
+states of disease, the surrounding atmosphere becomes tainted. 5th. The
+putrefaction of the interior parts of a carcase will proceed as rapidly
+as that of the exterior, from the ready passage outwards of the gaseous
+products. 6th. The exchange of oxygen and carbonic acid in the lungs is
+not prevented, but rather promoted, by the intervention of the membrane
+of the lungs and the coats of the blood-vessels between the blood and
+the air. It is necessary, however, that there should be a substance in
+the blood with which the oxygen of the air may immediately combine;
+otherwise instead of passing into the blood, it would permeate the whole
+organism: and it is necessary that the carbonic acid, as it is formed in
+the capillaries, should also find a substance in the blood with which it
+can combine; otherwise it would leave the body at all points, instead of
+being discharged through the lungs.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_5">� 5.</a> The following is a deduction which confirms, by explaining, the old
+but not undisputed empirical generalization, that soda powders weaken
+the human system. These powders, consisting of a mixture of tartaric
+acid with bicarbonate of soda, from which the carbonic acid is set free,
+must pass into the stomach as tartrate of soda. Now, neutral tartrates,
+citrates, and acetates of the alkalis are found, in their passage
+through the system, to be changed into carbonates; and to convert a
+tartrate into a carbonate requires an additional quantity of oxygen, the
+abstraction of which must lessen the oxygen destined for assimilation
+with the blood, on the <span class="pagenum"><a name="Page_537" id="Page_537">[Pg 537]</a></span>quantity of which the vigorous action of the
+human system partly depends.</p>
+
+<p>The instances of new theories agreeing with and explaining old
+empiricisms, are innumerable. All the just remarks made by experienced
+persons on human character and conduct, are so many special laws, which
+the general laws of the human mind explain and resolve. The empirical
+generalizations on which the operations of the arts have usually been
+founded, are continually justified and confirmed on the one hand, or
+corrected and improved on the other, by the discovery of the simpler
+scientific laws on which the efficacy of those operations depends. The
+effects of the rotation of crops, of the various manures, and other
+processes of improved agriculture, have been for the first time resolved
+in our own day into known laws of chemical and organic action, by Davy,
+Liebig, and others. The processes of the medical art are even now mostly
+empirical: their efficacy is concluded, in each instance, from a special
+and most precarious experimental generalization: but as science advances
+in discovering the simple laws of chemistry and physiology, progress is
+made in ascertaining the intermediate links in the series of phenomena,
+and the more general laws on which they depend; and thus, while the old
+processes are either exploded, or their efficacy, in so far as real,
+explained, better processes, founded on the knowledge of proximate
+causes, are continually suggested and brought into use.<a name="FNanchor_48_129" id="FNanchor_48_129"></a><a href="#Footnote_48_129" class="fnanchor">[48]</a> Many even of
+the truths of geometry were generalizations from experience before they
+were deduced from first principles. <span class="pagenum"><a name="Page_538" id="Page_538">[Pg 538]</a></span>The quadrature of the cycloid is
+said to have been first effected by measurement, or rather by weighing a
+cycloidal card, and comparing its weight with that of a piece of similar
+card of known dimensions.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_6">� 6.</a> To the foregoing examples from physical science, let us add another
+from mental. The following is one of the simple laws of mind: Ideas of a
+pleasurable or painful character form associations more easily and
+strongly than other ideas, that is, they become associated after fewer
+repetitions, and the association is more durable. This is an
+experimental law, grounded on the Method of Difference. By deduction
+from this law, many of the more special laws which experience shows to
+exist among particular mental phenomena may be demonstrated and
+explained:&mdash;the ease and rapidity, for instance, with which thoughts
+connected with our passions or our more cherished interests are excited,
+and the firm hold which the facts relating to them have on our memory;
+the vivid recollection we retain of minute circumstances which
+accompanied any object or event that deeply interested us, and of the
+times and places in which we have been very happy or very miserable; the
+horror with which we view the accidental instrument of any occurrence
+which shocked us, or the locality where it took place, and the pleasure
+we derive from any memorial of past enjoyment; all these effects being
+proportional to the sensibility of the individual mind, and to the
+consequent intensity of the pain or pleasure from which the association
+originated. It has been suggested by the able writer of a biographical
+sketch of Dr. Priestley in a monthly periodical,<a name="FNanchor_49_130" id="FNanchor_49_130"></a><a href="#Footnote_49_130" class="fnanchor">[49]</a> that the same
+elementary law of our mental constitution, suitably followed out, would
+explain a variety of mental phenomena previously inexplicable, and in
+particular some of the fundamental diversities of human character and
+genius. Associations being of two sorts, either between synchronous, or
+between successive impressions; and the influence of the law which
+renders associations stronger in <span class="pagenum"><a name="Page_539" id="Page_539">[Pg 539]</a></span>proportion to the pleasurable or
+painful character of the impressions, being felt with peculiar force in
+the synchronous class of associations; it is remarked by the writer
+referred to, that in minds of strong organic sensibility synchronous
+associations will be likely to predominate, producing a tendency to
+conceive things in pictures and in the concrete, richly clothed in
+attributes and circumstances, a mental habit which is commonly called
+Imagination, and is one of the peculiarities of the painter and the
+poet; while persons of more moderate susceptibility to pleasure and pain
+will have a tendency to associate facts chiefly in the order of their
+succession, and such persons, if they possess mental superiority, will
+addict themselves to history or science rather than to creative art.
+This interesting speculation the author of the present work has
+endeavoured, on another occasion, to pursue farther, and to examine how
+far it will avail towards explaining the peculiarities of the poetical
+temperament.<a name="FNanchor_50_131" id="FNanchor_50_131"></a><a href="#Footnote_50_131" class="fnanchor">[50]</a> It is at least an example which may serve, instead of
+many others, to show the extensive scope which exists for deductive
+investigation in the important and hitherto so imperfect Science of
+Mind.</p>
+
+
+<p class="newsection"><a name="BOOK_III_CHAPTER_XIII_7">� 7.</a> The copiousness with which the discovery and explanation of special
+laws of phenomena by deduction from simpler and more general ones has
+here been exemplified, was prompted by a desire to characterize clearly,
+and place in its due position of importance, the Deductive Method;
+which, in the present state of knowledge, is destined henceforth
+irrevocably to predominate in the course of scientific investigation. A
+revolution is peaceably and progressively effecting itself in
+philosophy, the reverse of that to which Bacon has attached his name.
+That great man changed the method of the sciences from deductive to
+experimental, and it is now rapidly reverting from experimental to
+deductive. But the deductions which Bacon abolished were from premises
+hastily snatched up, or arbitrarily assumed. The principles were neither
+established by legitimate canons of experimental inquiry, nor the
+results <span class="pagenum"><a name="Page_540" id="Page_540">[Pg 540]</a></span>tested by that indispensable element of a rational Deductive
+Method, verification by specific experience. Between the primitive
+method of Deduction and that which I have attempted to characterize,
+there is all the difference which exists between the Aristotelian
+physics and the Newtonian theory of the heavens.</p>
+
+<p>It would, however, be a mistake to expect that those great
+generalizations, from which the subordinate truths of the more backward
+sciences will probably at some future period be deduced by reasoning (as
+the truths of astronomy are deduced from the generalities of the
+Newtonian theory), will be found, in all, or even in most cases, among
+truths now known and admitted. We may rest assured, that many of the
+most general laws of nature are as yet entirely unthought of; and that
+many others, destined hereafter to assume the same character, are known,
+if at all, only as laws or properties of some limited class of
+phenomena; just as electricity, now recognised as one of the most
+universal of natural agencies, was once known only as a curious property
+which certain substances acquired by friction, of first attracting and
+then repelling light bodies. If the theories of heat, cohesion,
+crystallization, and chemical action, are destined, as there can be
+little doubt that they are, to become deductive, the truths which will
+then be regarded as the <i>principia</i> of those sciences would probably, if
+now announced, appear quite as novel<a name="FNanchor_51_132" id="FNanchor_51_132"></a><a href="#Footnote_51_132" class="fnanchor">[51]</a> as the law of gravitation
+appeared to the cotemporaries of Newton; possibly even more so, since
+Newton's law, after all, was but an extension of the law of weight&mdash;that
+is, of a generalization familiar from of old, and which already
+comprehended a not inconsiderable body of natural phenomena. The general
+laws of a similarly commanding character, which we still look forward to
+the discovery of, may not always find so much of their foundations
+already laid.</p>
+
+<p>These general truths will doubtless make their first appearance in the
+character of hypotheses; not proved, nor even <span class="pagenum"><a name="Page_541" id="Page_541">[Pg 541]</a></span>admitting of proof, in
+the first instance, but assumed as premises for the purpose of deducing
+from them the known laws of concrete phenomena. But this, though their
+initial, cannot be their final state. To entitle an hypothesis to be
+received as one of the truths of nature, and not as a mere technical
+help to the human faculties, it must be capable of being tested by the
+canons of legitimate induction, and must actually have been submitted to
+that test. When this shall have been done, and done successfully,
+premises will have been obtained from which all the other propositions
+of the science will thenceforth be presented as conclusions, and the
+science will, by means of a new and unexpected Induction, be rendered
+Deductive.</p>
+
+<div class="footnotes"><h3>FOOTNOTES:</h3>
+
+<div class="footnote"><p><a name="Footnote_1_82" id="Footnote_1_82"></a><a href="#FNanchor_1_82"><span class="label">[1]</span></a> Dr. Whewell thinks it improper to apply the term Induction
+to any operation not terminating in the establishment of a general
+truth. Induction, he says (<i>Philosophy of Discovery</i>, p. 245), "is not
+the same thing as experience and observation. Induction is experience or
+observation <i>consciously</i> looked at in a <i>general</i> form. This
+consciousness and generality are necessary parts of that knowledge which
+is science." And he objects (p. 241) to the mode in which the word
+Induction is employed in this work, as an undue extension of that term
+"not only to the cases in which the general induction is consciously
+applied to a particular instance, but to the cases in which the
+particular instance is dealt with by means of experience in that rude
+sense in which experience can be asserted of brutes, and in which of
+course we can in no way imagine that the law is possessed or understood
+as a general proposition." This use of the term he deems a "confusion of
+knowledge with practical tendencies."
+</p><p>
+I disclaim, as strongly as Dr. Whewell can do, the application of such
+terms as induction, inference, or reasoning, to operations performed by
+mere instinct, that is, from an animal impulse, without the exertion of
+any intelligence. But I perceive no ground for confining the use of
+those terms to cases in which the inference is drawn in the forms and
+with the precautions required by scientific propriety. To the idea of
+Science, an express recognition and distinct apprehension of general
+laws as such, is essential: but nine-tenths of the conclusions drawn
+from experience in the course of practical life, are drawn without any
+such recognition: they are direct inferences from known cases, to a case
+supposed to be similar. I have endeavoured to show that this is not only
+as legitimate an operation, but substantially the same operation, as
+that of ascending from known cases to a general proposition; except that
+the latter process has one great security for correctness which the
+former does not possess. In Science, the inference must necessarily pass
+through the intermediate stage of a general proposition, because Science
+wants its conclusions for record, and not for instantaneous use. But the
+inferences drawn for the guidance of practical affairs, by persons who
+would often be quite incapable of expressing in unexceptionable terms
+the corresponding generalizations, may and frequently do exhibit
+intellectual powers quite equal to any which have ever been displayed in
+Science: and if these inferences are not inductive, what are they? The
+limitation imposed on the term by Dr. Whewell seems perfectly arbitrary;
+neither justified by any fundamental distinction between what he
+includes and what he desires to exclude, nor sanctioned by usage, at
+least from the time of Reid and Stewart, the principal legislators (as
+far as the English language is concerned) of modern metaphysical
+terminology.</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_83" id="Footnote_2_83"></a><a href="#FNanchor_2_83"><span class="label">[2]</span></a> Supra, p. <a href="#Page_214">214</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_3_84" id="Footnote_3_84"></a><a href="#FNanchor_3_84"><span class="label">[3]</span></a> <i>Novum Organum Renovatum</i>, pp. 72, 73.</p></div>
+
+<div class="footnote"><p><a name="Footnote_4_85" id="Footnote_4_85"></a><a href="#FNanchor_4_85"><span class="label">[4]</span></a> <i>Novum Organum Renovatum</i>, p. 32.</p></div>
+
+<div class="footnote"><p><a name="Footnote_5_86" id="Footnote_5_86"></a><a href="#FNanchor_5_86"><span class="label">[5]</span></a> <i>Cours de Philosophie Positive</i>, vol. ii. p. 202.</p></div>
+
+<div class="footnote"><p><a name="Footnote_6_87" id="Footnote_6_87"></a><a href="#FNanchor_6_87"><span class="label">[6]</span></a> Dr. Whewell, in his reply, contests the distinction here
+drawn, and maintains, that not only different descriptions, but
+different explanations of a phenomenon, may all be true. Of the three
+theories respecting the motions of the heavenly bodies, he says
+(<i>Philosophy of Discovery</i>, p. 231): "Undoubtedly all these explanations
+may be true and consistent with each other, and would be so if each had
+been followed out so as to show in what manner it could be made
+consistent with the facts. And this was, in reality, in a great measure
+done. The doctrine that the heavenly bodies were moved by vortices was
+successfully modified, so that it came to coincide in its results with
+the doctrine of an inverse-quadratic centripetal force.... When this
+point was reached, the vortex was merely a machinery, well or ill
+devised, for producing such a centripetal force, and therefore did not
+contradict the doctrine of a centripetal force. Newton himself does not
+appear to have been averse to explaining gravity by impulse. So little
+is it true that if one theory be true the other must be false. The
+attempt to explain gravity by the impulse of streams of particles
+flowing through the universe in all directions, which I have mentioned
+in the <i>Philosophy</i>, is so far from being inconsistent with the
+Newtonian theory, that it is founded entirely upon it. And even with
+regard to the doctrine, that the heavenly bodies move by an inherent
+virtue; if this doctrine had been maintained in any such way that it was
+brought to agree with the facts, the inherent virtue must have had its
+laws determined; and then it would have been found that the virtue had a
+reference to the central body; and so, the 'inherent virtue' must have
+coincided in its effect with the Newtonian force; and then, the two
+explanations would agree, except so far as the word 'inherent' was
+concerned. And if such a part of an earlier theory as this word
+<i>inherent</i> indicates, is found to be untenable, it is of course rejected
+in the transition to later and more exact theories, in Inductions of
+this kind, as well as in what Mr. Mill calls Descriptions. There is,
+therefore, still no validity discoverable in the distinction which Mr.
+Mill attempts to draw between descriptions like Kepler's law of
+elliptical orbits, and other examples of induction."
+</p><p>
+If the doctrine of vortices had meant, not that vortices existed, but
+only that the planets moved <i>in the same manner</i> as if they had been
+whirled by vortices; if the hypothesis had been merely a mode of
+representing the facts, not an attempt to account for them; if, in
+short, it had been only a Description; it would, no doubt, have been
+reconcileable with the Newtonian theory. The vortices, however, were not
+a mere aid to conceiving the motions of the planets, but a supposed
+physical agent, actively impelling them; a material fact, which might be
+true or not true, but could not be both true and not true. According to
+Descartes' theory it was true, according to Newton's it was not true.
+Dr. Whewell probably means that since the phrases, centripetal and
+projectile force, do not declare the nature but only the direction of
+the forces, the Newtonian theory does not absolutely contradict any
+hypothesis which may be framed respecting the mode of their production.
+The Newtonian theory, regarded as a mere <i>description</i> of the planetary
+motions, does not; but the Newtonian theory as an <i>explanation</i> of them
+does. For in what does the explanation consist? In ascribing those
+motions to a general law which obtains between all particles of matter,
+and in identifying this with the law by which bodies fall to the ground.
+If the planets are kept in their orbits by a force which draws the
+particles composing them towards every other particle of matter in the
+solar system, they are not kept in those orbits by the impulsive force
+of certain streams of matter which whirl them round. The one explanation
+absolutely excludes the other. Either the planets are not moved by
+vortices, or they do not move by a law common to all matter. It is
+impossible that both opinions can be true. As well might it be said that
+there is no contradiction between the assertions, that a man died
+because somebody killed him, and that he died a natural death.
+</p><p>
+So, again, the theory that the planets move by a virtue inherent in
+their celestial nature, is incompatible with either of the two others:
+either that of their being moved by vortices, or that which regards them
+as moving by a property which they have in common with the earth and all
+terrestrial bodies. Dr. Whewell says that the theory of an inherent
+virtue agrees with Newton's when the word inherent is left out, which of
+course it would be (he says) if "found to be untenable." But leave that
+out, and where is the theory? The word inherent <i>is</i> the theory. When
+that is omitted, there remains nothing except that the heavenly bodies
+move by "a virtue," <i>i.e.</i> by a power of some sort; or by virtue of
+their celestial nature, which directly contradicts the doctrine that
+terrestrial bodies fall by the same law.
+</p><p>
+If Dr. Whewell is not yet satisfied, any other subject will serve
+equally well to test his doctrine. He will hardly say that there is no
+contradiction between the emission theory and the undulatory theory of
+light; or that there can be both one and two electricities; or that the
+hypothesis of the production of the higher organic forms by development
+from the lower, and the supposition of separate and successive acts of
+creation, are quite reconcileable; or that the theory that volcanoes are
+fed from a central fire, and the doctrines which ascribe them to
+chemical action at a comparatively small depth below the earth's
+surface, are consistent with one another, and all true as far as they
+go.
+</p><p>
+If different explanations of the same fact cannot both be true, still
+less, surely, can different predictions. Dr. Whewell quarrels (on what
+ground it is not necessary here to consider) with the example I had
+chosen on this point, and thinks an objection to an illustration a
+sufficient answer to a theory. Examples not liable to his objection are
+easily found, if the proposition that conflicting predictions cannot
+both be true, can be made clearer by any examples. Suppose the
+phenomenon to be a newly-discovered comet, and that one astronomer
+predicts its return once in every 300 years&mdash;another once in every 400:
+can they both be right? When Columbus predicted that by sailing
+constantly westward he should in time return to the point from which he
+set out, while others asserted that he could never do so except by
+turning back, were both he and his opponents true prophets? Were the
+predictions which foretold the wonders of railways and steamships, and
+those which averred that the Atlantic could never be crossed by steam
+navigation, nor a railway train propelled ten miles an hour, both (in
+Dr. Whewell's words) "true, and consistent with one another"?
+</p><p>
+Dr. Whewell sees no distinction between holding contradictory opinions
+on a question of fact, and merely employing different analogies to
+facilitate the conception of the same fact. The case of different
+Inductions belongs to the former class, that of different Descriptions
+to the latter.</p></div>
+
+<div class="footnote"><p><a name="Footnote_7_88" id="Footnote_7_88"></a><a href="#FNanchor_7_88"><span class="label">[7]</span></a> <i>Phil. of Discov.</i> p. 256.</p></div>
+
+<div class="footnote"><p><a name="Footnote_8_89" id="Footnote_8_89"></a><a href="#FNanchor_8_89"><span class="label">[8]</span></a> <i>Essays on the Pursuit of Truth.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_9_90" id="Footnote_9_90"></a><a href="#FNanchor_9_90"><span class="label">[9]</span></a> In the first edition a note was appended at this place,
+containing some criticism on Archbishop Whately's mode of conceiving the
+relation between Syllogism and Induction. In a subsequent issue of his
+<i>Logic</i>, the Archbishop made a reply to the criticism, which induced me
+to cancel part of the note, incorporating the remainder in the text. In
+a still later edition, the Archbishop observes in a tone of something
+like disapprobation, that the objections, "doubtless from their being
+fully answered and found untenable, were silently suppressed," and that
+hence he might appear to some of his readers to be combating a shadow.
+On this latter point, the Archbishop need give himself no uneasiness.
+His readers, I make bold to say, will fully credit his mere affirmation
+that the objections have actually been made.
+</p><p>
+But as he seems to think that what he terms the suppression of the
+objections ought not to have been made "silently," I now break that
+silence, and state exactly what it is that I suppressed, and why. I
+suppressed that alone which might be regarded as personal criticism on
+the Archbishop. I had imputed to him the having omitted to ask himself a
+particular question. I found that he had asked himself the question, and
+could give it an answer consistent with his own theory. I had also,
+within the compass of a parenthesis, hazarded some remarks on certain
+general characteristics of Archbishop Whately as a philosopher. These
+remarks, though their tone, I hope, was neither disrespectful nor
+arrogant, I felt, on reconsideration, that I was hardly entitled to
+make; least of all, when the instance which I had regarded as an
+illustration of them, failed, as I now saw, to bear them out. The real
+matter at the bottom of the whole dispute, the different view we take of
+the function of the major premise, remains exactly where it was; and so
+far was I from thinking that my opinion had been "fully answered" and
+was "untenable," that in the same edition in which I cancelled the note,
+I not only enforced the opinion by further arguments, but answered
+(though without naming him) those of the Archbishop.
+</p><p>
+For not having made this statement before, I do not think it needful to
+apologize. It would be attaching very great importance to one's smallest
+sayings, to think a formal retractation requisite every time that one
+commits an error. Nor is Archbishop Whately's well-earned fame of so
+tender a quality as to require, that in withdrawing a slight criticism
+on him I should have been bound to offer a public <i>amende</i> for having
+made it.</p></div>
+
+<div class="footnote"><p><a name="Footnote_10_91" id="Footnote_10_91"></a><a href="#FNanchor_10_91"><span class="label">[10]</span></a> But though it is a condition of the validity of every
+induction that there be uniformity in the course of nature, it is not a
+necessary condition that the uniformity should pervade all nature. It is
+enough that it pervades the particular class of phenomena to which the
+induction relates. An induction concerning the motions of the planets,
+or the properties of the magnet, would not be vitiated though we were to
+suppose that wind and weather are the sport of chance, provided it be
+assumed that astronomical and magnetic phenomena are under the dominion
+of general laws. Otherwise the early experience of mankind would have
+rested on a very weak foundation; for in the infancy of science it could
+not be known that <i>all</i> phenomena are regular in their course.
+</p><p>
+Neither would it be correct to say that every induction by which we
+infer any truth, implies the general fact of uniformity <i>as foreknown</i>,
+even in reference to the kind of phenomena concerned. It implies,
+<i>either</i> that this general fact is already known, <i>or</i> that we may now
+know it: as the conclusion, the Duke of Wellington is mortal, drawn from
+the instances A, B, and C, implies either that we have already concluded
+all men to be mortal, or that we are now entitled to do so from the same
+evidence. A vast amount of confusion and paralogism respecting the
+grounds of Induction would be dispelled by keeping in view these simple
+considerations.</p></div>
+
+<div class="footnote"><p><a name="Footnote_11_92" id="Footnote_11_92"></a><a href="#FNanchor_11_92"><span class="label">[11]</span></a> Infra, <span title="See Vol. II.">chap. xxi.</span></p></div>
+
+<div class="footnote"><p><a name="Footnote_12_93" id="Footnote_12_93"></a><a href="#FNanchor_12_93"><span class="label">[12]</span></a> Infra, <span title="See Vol. II.">chap. xxi. xxii.</span></p></div>
+
+<div class="footnote"><p><a name="Footnote_13_94" id="Footnote_13_94"></a><a href="#FNanchor_13_94"><span class="label">[13]</span></a> Dr. Whewell (<i>Phil. of Discov.</i> p. 246) will not allow
+these and similar erroneous judgments to be called inductions; inasmuch
+as such superstitious fancies "were not collected from the facts by
+seeking a law of their occurrence, but were suggested by an imagination
+of the anger of superior powers, shown by such deviations from the
+ordinary course of nature." I conceive the question to be, not in what
+manner these notions were at first suggested, but by what evidence they
+have, from time to time, been supposed to be substantiated. If the
+believers in these erroneous opinions had been put on their defence,
+they would have referred to experience: to the comet which preceded the
+assassination of Julius C�sar, or to oracles and other prophecies known
+to have been fulfilled. It is by such appeals to facts that all
+analogous superstitions, even in our day, attempt to justify themselves;
+the supposed evidence of experience is necessary to their hold on the
+mind. I quite admit that the influence of such coincidences would not be
+what it is, if strength were not lent to it by an antecedent
+presumption; but this is not peculiar to such cases; preconceived
+notions of probability form part of the explanation of many other cases
+of belief on insufficient evidence. The <i>� priori</i> prejudice does not
+prevent the erroneous opinion from being sincerely regarded as a
+legitimate conclusion from experience; though it improperly predisposes
+the mind to that interpretation of experience.
+</p><p>
+Thus much in defence of the sort of examples objected to. But it would
+be easy to produce instances, equally adapted to the purpose, and in
+which no antecedent prejudice is at all concerned. "For many ages," says
+Archbishop Whately, "all farmers and gardeners were firmly
+convinced&mdash;and convinced of their knowing it by experience&mdash;that the
+crops would never turn out good unless the seed were sown during the
+increase of the moon." This was induction, but bad induction: just as a
+vicious syllogism is reasoning, but bad reasoning.</p></div>
+
+<div class="footnote"><p><a name="Footnote_14_95" id="Footnote_14_95"></a><a href="#FNanchor_14_95"><span class="label">[14]</span></a> The assertion, that any and every one of the conditions of
+a phenomenon may be and is, on some occasions and for some purposes,
+spoken of as the cause, has been disputed by an intelligent reviewer of
+this work in the <i>Prospective Review</i> (the predecessor of the justly
+esteemed <i>National Review</i>), who maintains that "we always apply the
+word cause rather to that element in the antecedents which exercises
+<i>force</i>, and which would <i>tend</i> at all times to produce the same or a
+similar effect to that which, under certain conditions, it would
+actually produce." And he says, that "every one would feel" the
+expression, that the cause of a surprise was the sentinel's being off
+his post, to be incorrect; but that the "allurement or force which
+<i>drew</i> him off his post, might be so called, because in doing so it
+removed a resisting power which would have prevented the surprise." I
+cannot think that it would be wrong to say, that the event took place
+because the sentinel was absent, and yet right to say that it took place
+because he was bribed to be absent. Since the only direct effect of the
+bribe was his absence, the bribe could be called the remote cause of the
+surprise, only on the supposition that the absence was the proximate
+cause; nor does it seem to me that any one (who had not a theory to
+support) would use the one expression and reject the other.
+</p><p>
+The reviewer observes, that when a person dies of poison, his possession
+of bodily organs is a necessary condition, but that no one would ever
+speak of it as the cause. I admit the fact; but I believe the reason to
+be, that the occasion could never arise for so speaking of it; for when
+in the inaccuracy of common discourse we are led to speak of some one
+condition of a phenomenon as its cause, the condition so spoken of is
+always one which it is at least possible that the hearer may require to
+be informed of. The possession of bodily organs is a known condition,
+and to give that as the answer, when asked the cause of a person's
+death, would not supply the information sought. Once conceive that a
+doubt could exist as to his having bodily organs, or that he were to be
+compared with some being who had them not, and cases may be imagined in
+which it might be said that his possession of them was the cause of his
+death. If Faust and Mephistopheles together took poison, it might be
+said that Faust died because he was a human being, and had a body, while
+Mephistopheles survived because he was a spirit.
+</p><p>
+It is for the same reason that no one (as the reviewer remarks) "calls
+the cause of a leap, the muscles or sinews of the body, though they are
+necessary conditions; nor the cause of a self-sacrifice, the knowledge
+which was necessary for it; nor the cause of writing a book, that a man
+has time for it, which is a necessary condition." These conditions
+(besides that they are antecedent <i>states</i>, and not proximate antecedent
+<i>events</i>, and are therefore never the conditions in closest apparent
+proximity to the effect) are all of them so obviously implied, that it
+is hardly possible there should exist that necessity for insisting on
+them, which alone gives occasion for speaking of a single condition as
+if it were the cause. Wherever this necessity exists in regard to some
+one condition, and does not exist in regard to any other, I conceive
+that it is consistent with usage, when scientific accuracy is not aimed
+at, to apply the name cause to that one condition. If the only condition
+which can be supposed to be unknown is a negative condition, the
+negative condition may be spoken of as the cause. It might be said that
+a person died for want of medical advice: though this would not be
+likely to be said, unless the person was already understood to be ill,
+and in order to indicate that this negative circumstance was what made
+the illness fatal, and not the weakness of his constitution, or the
+original virulence of the disease. It might be said that a person was
+drowned because he could not swim; the positive condition, namely, that
+he fell into the water, being already implied in the word drowned. And
+here let me remark, that his falling into the water is in this case the
+only positive condition: all the conditions not expressly or virtually
+included in this (as that he could not swim, that nobody helped him, and
+so forth) are negative. Yet, if it were simply said that the cause of a
+man's death was falling into the water, there would be quite as great a
+sense of impropriety in the expression, as there would be if it were
+said that the cause was his inability to swim; because, though the one
+condition is positive and the other negative, it would be felt that
+neither of them was sufficient, without the other, to produce death.
+</p><p>
+With regard to the assertion that nothing is termed the cause, except
+the element which exerts active force; I wave the question as to the
+meaning of active force, and accepting the phrase in its popular sense,
+I revert to a former example, and I ask, would it be more agreeable to
+custom to say that a man fell because his foot slipped in climbing a
+ladder, or that he fell because of his weight? for his weight, and not
+the motion of his foot, was the active force which determined his fall.
+If a person walking out in a frosty day, stumbled and fell, it might be
+said that he stumbled because the ground was slippery, or because he was
+not sufficiently careful; but few people, I suppose, would say, that he
+stumbled because he walked. Yet the only active force concerned was that
+which he exerted in walking: the others were mere negative conditions;
+but they happened to be the only ones which there could be any necessity
+to state; for he walked, most likely, in exactly his usual manner, and
+the negative conditions made all the difference. Again, if a person were
+asked why the army of Xerxes defeated that of Leonidas, he would
+probably say, because they were a thousand times the number; but I do
+not think he would say, it was because they fought, though that was the
+element of active force. To borrow another example, used by Mr. Grove
+and by Mr. Baden Powell, the opening of floodgates is said to be the
+cause of the flow of water; yet the active force is exerted by the water
+itself, and opening the floodgates merely supplies a negative condition.
+The reviewer adds, "there are some conditions absolutely passive, and
+yet absolutely necessary to physical phenomena, viz. the relations of
+space and time; and to these no one ever applies the word cause without
+being immediately arrested by those who hear him." Even from this
+statement I am compelled to dissent. Few persons would feel it
+incongruous to say (for example) that a secret became known because it
+was spoken of when A. B. was within hearing; which is a condition of
+space: or that the cause why one of two particular trees is taller than
+the other, is that it has been longer planted; which is a condition of
+time.</p></div>
+
+<div class="footnote"><p><a name="Footnote_15_96" id="Footnote_15_96"></a><a href="#FNanchor_15_96"><span class="label">[15]</span></a> There are a few exceptions; for there are some properties
+of objects which seem to be purely preventive; as the property of opaque
+bodies, by which they intercept the passage of light. This, as far as we
+are able to understand it, appears an instance not of one cause
+counteracting another by the same law whereby it produces its own
+effects, but of an agency which manifests itself in no other way than in
+defeating the effects of another agency. If we knew on what other
+relations to light, or on what peculiarities of structure, opacity
+depends, we might find that this is only an apparent, not a real,
+exception to the general proposition in the text. In any case it needs
+not affect the practical application. The formula which includes all the
+negative conditions of an effect in the single one of the absence of
+counteracting causes, is not violated by such cases as this; though, if
+all counteracting agencies were of this description, there would be no
+purpose served by employing the formula, since we should still have to
+enumerate specially the negative conditions of each phenomenon, instead
+of regarding them as implicitly contained in the positive laws of the
+various other agencies in nature.</p></div>
+
+<div class="footnote"><p><a name="Footnote_16_97" id="Footnote_16_97"></a><a href="#FNanchor_16_97"><span class="label">[16]</span></a> I mean by this expression, the ultimate laws of nature
+(whatever they may be) as distinguished from the derivative laws and
+from the collocations. The diurnal revolution of the earth (for example)
+is not a part of the constitution of things, because nothing can be so
+called which might possibly be terminated or altered by natural causes.</p></div>
+
+<div class="footnote"><p><a name="Footnote_17_98" id="Footnote_17_98"></a><a href="#FNanchor_17_98"><span class="label">[17]</span></a> I use the words "straight line" for brevity and
+simplicity. In reality the line in question is not exactly straight,
+for, from the effect of refraction, we actually see the sun for a short
+interval during which the opaque mass of the earth is interposed in a
+direct line between the sun and our eyes; thus realizing, though but to
+a limited extent, the coveted desideratum of seeing round a corner.</p></div>
+
+<div class="footnote"><p><a name="Footnote_18_99" id="Footnote_18_99"></a><a href="#FNanchor_18_99"><span class="label">[18]</span></a> <i>Second Burnett Prize Essay</i>, by Principal Tulloch, p.
+25.</p></div>
+
+<div class="footnote"><p><a name="Footnote_19_100" id="Footnote_19_100"></a><a href="#FNanchor_19_100"><span class="label">[19]</span></a> <i>Letters on the Philosophy of the Human Mind</i>, First
+Series, p. 219.</p></div>
+
+<div class="footnote"><p><a name="Footnote_20_101" id="Footnote_20_101"></a><a href="#FNanchor_20_101"><span class="label">[20]</span></a> <i>Essays</i>, pp. 206-208.</p></div>
+
+<div class="footnote"><p><a name="Footnote_21_102" id="Footnote_21_102"></a><a href="#FNanchor_21_102"><span class="label">[21]</span></a> To the universality which mankind are agreed in ascribing
+to the Law of Causation, there is one claim of exception, one disputed
+case, that of the Human Will; the determinations of which, a large class
+of metaphysicians are not willing to regard as following the causes
+called motives, according to as strict laws as those which they suppose
+to exist in the world of mere matter. This controverted point will
+undergo a special examination when we come to treat particularly of the
+Logic of the Moral Sciences (<span title="See Vol. II.">Book vi. ch. 2</span>). In the mean time I may
+remark that these metaphysicians, who, it must be observed, ground the
+main part of their objection on the supposed repugnance of the doctrine
+in question to our consciousness, seem to me to mistake the fact which
+consciousness testifies against. What is really in contradiction to
+consciousness, they would, I think, on strict self-examination, find to
+be, the application to human actions and volitions of the ideas involved
+in the common use of the term Necessity; which I agree with them in
+objecting to. But if they would consider that by saying that a person's
+actions <i>necessarily</i> follow from his character, all that is really
+meant (for no more is meant in any case whatever of causation) is that
+he invariably <i>does</i> act in conformity to his character, and that any
+one who thoroughly knew his character would certainly predict how he
+would act in any supposable case; they probably would not find this
+doctrine either contrary to their experience or revolting to their
+feelings. And no more than this is contended for by any one but an
+Asiatic fatalist.</p></div>
+
+<div class="footnote"><p><a name="Footnote_22_103" id="Footnote_22_103"></a><a href="#FNanchor_22_103"><span class="label">[22]</span></a> <i>Lectures on Metaphysics</i>, vol. ii. Lect. xxxix. pp.
+391-2.
+</p><p>
+I regret that I cannot invoke the authority of Sir William Hamilton in
+favour of my own opinions on Causation, as I can against the particular
+theory which I am now combating. But that acute thinker has a theory of
+Causation peculiar to himself, which has never yet, as far as I know,
+been analytically examined, but which, I venture to think, admits of as
+complete refutation as any one of the false or insufficient
+psychological theories which strew the ground in such numbers under his
+potent metaphysical scythe. (Since examined and controverted in the
+sixteenth chapter of <i>An Examination of Sir William Hamilton's
+Philosophy</i>).</p></div>
+
+<div class="footnote"><p><a name="Footnote_23_104" id="Footnote_23_104"></a><a href="#FNanchor_23_104"><span class="label">[23]</span></a> Unless we are to consider as such the following statement,
+by one of the writers quoted in the text: "In the case of mental
+exertion, the result to be accomplished is preconsidered or meditated,
+and is therefore known <i>� priori</i>, or before experience."&mdash;(Bowen's
+<i>Lowell Lectures on the Application of Metaphysical and Ethical Science
+to the Evidence of Religion</i>, Boston, 1849.) This is merely saying that
+when we will a thing we have an idea of it. But to have an idea of what
+we wish to happen, does not imply a prophetic knowledge that it will
+happen. Perhaps it will be said that the <i>first time</i> we exerted our
+will, when we had of course no experience of any of the powers residing
+in us, we nevertheless must already have known that we possessed them,
+since we cannot will that which we do not believe to be in our power.
+But the impossibility is perhaps in the words only, and not in the
+facts; for we may <i>desire</i> what we do not know to be in our power; and
+finding by experience that our bodies move according to our <i>desire</i>, we
+may then, and only then, pass into the more complicated mental state
+which is termed will.
+</p><p>
+After all, even if we had an instinctive knowledge that our actions
+would follow our will, this, as Brown remarks, would prove nothing as to
+the nature of Causation. Our knowing, previous to experience, that an
+antecedent will be followed by a certain consequent, would not prove the
+relation between them to be anything more than antecedence and
+consequence.</p></div>
+
+<div class="footnote"><p><a name="Footnote_24_105" id="Footnote_24_105"></a><a href="#FNanchor_24_105"><span class="label">[24]</span></a> Reid's <i>Essays on the Active Powers</i>, Essay iv. ch. 3.</p></div>
+
+<div class="footnote"><p><a name="Footnote_25_106" id="Footnote_25_106"></a><a href="#FNanchor_25_106"><span class="label">[25]</span></a> <i>Prospective Review</i> for February 1850.</p></div>
+
+<div class="footnote"><p><a name="Footnote_26_107" id="Footnote_26_107"></a><a href="#FNanchor_26_107"><span class="label">[26]</span></a> Vide supra, <a href="#TNpage396">p. 270, note</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_27_108" id="Footnote_27_108"></a><a href="#FNanchor_27_108"><span class="label">[27]</span></a> <i>Westminster Review</i> for October 1855.</p></div>
+
+<div class="footnote"><p><a name="Footnote_28_109" id="Footnote_28_109"></a><a href="#FNanchor_28_109"><span class="label">[28]</span></a> See the whole doctrine in Aristotle <i>de Anim�</i>: where the
+<i>&#952;&#961;&#949;&#960;&#964;&#953;&#954;&#8052; &#968;&#965;&#967;&#8052;</i> is treated as exactly equivalent to <i>&#952;&#961;&#949;&#960;&#964;&#953;&#954;&#8052; &#948;&#8059;&#957;&#945;&#956;&#953;&#962;</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_29_110" id="Footnote_29_110"></a><a href="#FNanchor_29_110"><span class="label">[29]</span></a> It deserves notice that the parts of nature, which
+Aristotle regards as presenting evidence of design, are the
+Uniformities: the phenomena in so far as reducible to law. <i>&#932;&#8059;&#967;&#951;</i> and <i>&#964;&#8056; &#945;&#8016;&#964;&#959;&#956;&#8049;&#964;&#959;&#957;</i> satisfy him as explanations of the
+variable element in phenomena, but their occurring according to a fixed
+rule can only, to his conceptions, be accounted for by an Intelligent
+Will. The common, or what may be called the instinctive, religious
+interpretation of nature, is the reverse of this. The events in which
+men spontaneously see the hand of a supernatural being, are those which
+cannot, as they think, be reduced to a physical law. What they can
+distinctly connect with physical causes, and especially what they can
+predict, though of course ascribed to an Author of Nature if they
+already recognise such an author, might be conceived, they think, to
+arise from a blind fatality, and in any case do not appear to them to
+bear so obviously the mark of a divine will. And this distinction has
+been countenanced by eminent writers on Natural Theology, in particular
+by Dr. Chalmers: who thinks that though design is present everywhere,
+the irresistible evidence of it is to be found not in the <i>laws</i> of
+nature but in the collocations, <i>i.e.</i> in the part of nature in which it
+is impossible to trace any law. A few properties of dead matter might,
+he thinks, conceivably account for the regular and invariable succession
+of effects and causes; but that the different kinds of matter have been
+so placed as to promote beneficent ends, is what he regards as the proof
+of a Divine Providence. Mr. Baden Powell, in his Essay entitled
+"Philosophy of Creation," has returned to the point of view of Aristotle
+and the ancients, and vigorously reasserts the doctrine that the
+indication of design in the universe is not special adaptations, but
+Uniformity and Law, these being the evidences of mind, and not what
+appears to us to be a provision for our uses. While I decline to express
+any opinion here on this <i>vexata qu�stio</i>, I ought not to mention Mr.
+Powell's volume without the acknowledgment due to the philosophic spirit
+which pervades generally the three Essays composing it, forming in the
+case of one of them (the "Unity of Worlds") an honourable contrast with
+the other dissertations, so far as they have come under my notice, which
+have appeared on either side of that controversy.</p></div>
+
+<div class="footnote"><p><a name="Footnote_30_111" id="Footnote_30_111"></a><a href="#FNanchor_30_111"><span class="label">[30]</span></a> In the words of Fontenelle, another celebrated Cartesian,
+"les philosophes aussi bien que le peuple avaient cru que l'�me et le
+corps agissaient r�ellement et physiquement l'un sur l'autre. Descartes
+vint, qui prouva que leur nature ne permettait point cette sorte de
+communication v�ritable, et qu'ils n'en pouvaient avoir qu'une
+apparente, dont Dieu �tait le M�diateur."&mdash;<i>&OElig;uvres de Fontenelle</i>,
+ed. 1767, tom. v. p. 534.</p></div>
+
+<div class="footnote"><p><a name="Footnote_31_112" id="Footnote_31_112"></a><a href="#FNanchor_31_112"><span class="label">[31]</span></a> I omit, for simplicity, to take into account the effect,
+in this latter case, of the diminution of pressure, in diminishing the
+flow of water through the drain; which evidently in no way affects the
+truth or applicability of the principle, since when the two causes act
+simultaneously the conditions of that diminution of pressure do not
+arise.</p></div>
+
+<div class="footnote"><p><a name="Footnote_32_113" id="Footnote_32_113"></a><a href="#FNanchor_32_113"><span class="label">[32]</span></a> Unless, indeed, the consequent was generated not by the
+antecedent, but by the means employed to produce the antecedent. As,
+however, these means are under our power, there is so far a probability
+that they are also sufficiently within our knowledge, to enable us to
+judge whether that could be the case or not.</p></div>
+
+<div class="footnote"><p><a name="Footnote_33_114" id="Footnote_33_114"></a><a href="#FNanchor_33_114"><span class="label">[33]</span></a> <i>Discourse on the Study of Natural Philosophy</i>, p. 179.</p></div>
+
+<div class="footnote"><p><a name="Footnote_34_115" id="Footnote_34_115"></a><a href="#FNanchor_34_115"><span class="label">[34]</span></a> For this speculation, as for many other of my scientific
+illustrations, I am indebted to Professor Bain, of Aberdeen, who has
+since, in his profound treatises entitled "The Senses and the
+Intellect," and "The Emotions and the Will," carried the analytic
+investigation of the mental phenomena according to the methods of
+physical science, to the most advanced point which it has yet reached,
+and has worthily inscribed his name among the successive constructors of
+an edifice to which Hartley, Brown, and James Mill had each contributed
+their part.</p></div>
+
+<div class="footnote"><p><a name="Footnote_35_116" id="Footnote_35_116"></a><a href="#FNanchor_35_116"><span class="label">[35]</span></a> This view of the necessary coexistence of opposite
+excitements involves a great extension of the original doctrine of two
+electricities. The early theorists assumed that, when amber was rubbed,
+the amber was made positive and the rubber negative to the same degree;
+but it never occurred to them to suppose that the existence of the amber
+charge was dependent on an opposite charge in the bodies with which the
+amber was contiguous, while the existence of the negative charge on the
+rubber was equally dependent on a contrary state of the surfaces that
+might accidentally be confronted with it; that, in fact, in a case of
+electrical excitement by friction, four charges were the minimum that
+could exist. But this double electrical action is essentially implied in
+the explanation now universally adopted in regard to the phenomena of
+the common electric machine.</p></div>
+
+<div class="footnote"><p><a name="Footnote_36_117" id="Footnote_36_117"></a><a href="#FNanchor_36_117"><span class="label">[36]</span></a> Pp. 159-162.</p></div>
+
+<div class="footnote"><p><a name="Footnote_37_118" id="Footnote_37_118"></a><a href="#FNanchor_37_118"><span class="label">[37]</span></a> Infra, <span title="See Vol. II.">book iv. ch. ii.</span> On Abstraction.</p></div>
+
+<div class="footnote"><p><a name="Footnote_38_119" id="Footnote_38_119"></a><a href="#FNanchor_38_119"><span class="label">[38]</span></a> I must, however, remark, that this example, which seems to
+militate against the assertion we made of the comparative
+inapplicability of the Method of Difference to cases of pure
+observation, is really one of those exceptions which, according to a
+proverbial expression, prove the general rule. For in this case, in
+which Nature, in her experiment, seems to have imitated the type of the
+experiments made by man, she has only succeeded in producing the
+likeness of man's most imperfect experiments; namely, those in which,
+though he succeeds in producing the phenomenon, he does so by employing
+complex means, which he is unable perfectly to analyse, and can form
+therefore no sufficient judgment what portion of the effects may be due,
+not to the supposed cause, but to some unknown agency of the means by
+which that cause was produced. In the natural experiment which we are
+speaking of, the means used was the clearing off a canopy of clouds; and
+we certainly do not know sufficiently in what this process consists, or
+on what it depends, to be certain <i>� priori</i> that it might not operate
+upon the deposition of dew independently of any thermometric effect at
+the earth's surface. Even, therefore, in a case so favourable as this to
+Nature's experimental talents, her experiment is of little value except
+in corroboration of a conclusion already attained through other means.</p></div>
+
+<div class="footnote"><p><a name="Footnote_39_120" id="Footnote_39_120"></a><a href="#FNanchor_39_120"><span class="label">[39]</span></a> In his subsequent work, <i>Outlines of Astronomy</i> (� 570),
+Sir John Herschel suggests another possible explanation of the
+acceleration of the revolution of a comet.</p></div>
+
+<div class="footnote"><p><a name="Footnote_40_121" id="Footnote_40_121"></a><a href="#FNanchor_40_121"><span class="label">[40]</span></a> Discourse, pp. 156-8, and 171.</p></div>
+
+<div class="footnote"><p><a name="Footnote_41_122" id="Footnote_41_122"></a><a href="#FNanchor_41_122"><span class="label">[41]</span></a> <i>Outlines of Astronomy</i>, � 856.</p></div>
+
+<div class="footnote"><p><a name="Footnote_42_123" id="Footnote_42_123"></a><a href="#FNanchor_42_123"><span class="label">[42]</span></a> <i>Philosophy of Discovery</i>, pp. 263, 264.</p></div>
+
+<div class="footnote"><p><a name="Footnote_43_124" id="Footnote_43_124"></a><a href="#FNanchor_43_124"><span class="label">[43]</span></a> See, on this point, the <a href="#BOOK_III_CHAPTER_II">second chapter of the present
+Book</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_44_125" id="Footnote_44_125"></a><a href="#FNanchor_44_125"><span class="label">[44]</span></a> Ante, <a href="#BOOK_III_CHAPTER_VII_1">ch. vii. � 1</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_45_126" id="Footnote_45_126"></a><a href="#FNanchor_45_126"><span class="label">[45]</span></a> It seems hardly necessary to say that the word <i>impinge</i>,
+as a general term to express collision of forces, is here used by a
+figure of speech, and not as expressive of any theory respecting the
+nature of force.</p></div>
+
+<div class="footnote"><p><a name="Footnote_46_127" id="Footnote_46_127"></a><a href="#FNanchor_46_127"><span class="label">[46]</span></a> <i>Essays on some Unsettled Questions of Political Economy</i>,
+Essay V.</p></div>
+
+<div class="footnote"><p><a name="Footnote_47_128" id="Footnote_47_128"></a><a href="#FNanchor_47_128"><span class="label">[47]</span></a> <i>Vide</i> Memoir by Thomas Graham, F.R.S., Master of the
+Mint, "On Liquid Diffusion Applied to Analysis," in the <i>Philosophical
+Transactions</i> for 1862, reprinted in the <i>Journal of the Chemical
+Society</i>, and also separately as a pamphlet.</p></div>
+
+<div class="footnote"><p><a name="Footnote_48_129" id="Footnote_48_129"></a><a href="#FNanchor_48_129"><span class="label">[48]</span></a> It was an old generalization in surgery, that tight
+bandaging had a tendency to prevent or dissipate local inflammation.
+This sequence, being, in the progress of physiological knowledge,
+resolved into more general laws, led to the important surgical invention
+made by Dr. Arnott, the treatment of local inflammation and tumours by
+means of an equable pressure, produced by a bladder partially filled
+with air. The pressure, by keeping back the blood from the part,
+prevents the inflammation, or the tumour, from being nourished: in the
+case of inflammation, it removes the stimulus, which the organ is unfit
+to receive; in the case of tumours, by keeping back the nutritive fluid,
+it causes the absorption of matter to exceed the supply, and the
+diseased mass is gradually absorbed and disappears.</p></div>
+
+<div class="footnote"><p><a name="Footnote_49_130" id="Footnote_49_130"></a><a href="#FNanchor_49_130"><span class="label">[49]</span></a> Since acknowledged and reprinted in Mr. Martineau's
+<i>Miscellanies</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_50_131" id="Footnote_50_131"></a><a href="#FNanchor_50_131"><span class="label">[50]</span></a> <i>Dissertations and Discussions</i>, vol. i., fourth paper.</p></div>
+
+<div class="footnote"><p><a name="Footnote_51_132" id="Footnote_51_132"></a><a href="#FNanchor_51_132"><span class="label">[51]</span></a> Written before the rise of the new views respecting the
+relation of heat to mechanical force; but confirmed rather than
+contradicted by them.</p></div>
+</div>
+
+
+<p class="center">END OF VOL. I.</p>
+
+
+
+
+<p class="center">
+LONDON:<br />
+SAVILL, EDWARDS AND CO., PRINTERS, CHANDOS STREET,<br />
+COVENT GARDEN.
+</p>
+
+
+<hr class="chap" />
+<h2><a name="Transcribers_Notes" id="Transcribers_Notes"></a>Transcriber's Notes</h2>
+
+
+<p>Spelling irregularities where there was no obviously preferred version
+were left as is. Variants include: "alkalies" and "alkalis;" "apprise"
+and "apprize;" "coexistent" and "co-existent" (along with derivatives);
+"coextensive" and "co-extensive;" "e. g." and "e.g."; "encumbered" and
+"incumbered;" "formul�" and "formulas;" "i. e." and "i.e."; "nonentity"
+and "non-entity;" "recal" and "recall" (and derivatives); "rectilinear"
+and "rectilineal;" "stopt" and "stopped."</p>
+
+<p>Volume I. contains "&#964;&#959; &#8004;&#957;," while Volume II. spells it
+"&#964;&#8056; &#8004;&#957;." The spellings were left as is, in each case.</p>
+
+<p>Changed "3" to "4" on page xiii: "4. &mdash;and from descriptions."</p>
+
+<p>Inserted missing page number, "167," for Chapter VIII, section 7 on page
+xiii.</p>
+
+<p>Moved the semi-colon inside the quotation marks in the footnote on page
+14: "the Science of the Formal Laws of Thought;".</p>
+
+<p>Changed "sub-divisions" to "subdivisions" on page 59: "three
+subdivisions."</p>
+
+<p>Changed "pre-supposed" to "presupposed" on page 75: "they are
+presupposed."</p>
+
+<p>In the footnote to page 122, changed the Greek character upsilon with
+dasia and oxia to upsilon with psili and oxia, making the
+transliteration "deuterai ousiai."</p>
+
+<p>Changed "he" to "be" on page 189: "to which it may be reduced."</p>
+
+<p>Changed "cb." to "ch." in footnote on page 227: "Theory of Reasoning,
+ch. iv."</p>
+
+<p>Changed "reconcilable" to "reconcileable" on page 240: "not easily
+reconcileable."</p>
+
+<p>Preserved the hyphen in "counter-acting" on page 280. Usually this is
+spelled without the hyphen, but this instance is in a quotation.</p>
+
+<p>Moved parenthesis that was after "to" to before it on page 321: "(to
+return to a former example)."</p>
+
+<p>Put "i.e." in italics on page 335: "<i>i.e.</i> by a power of some sort."</p>
+
+<p>Changed "paralyzed" to "paralysed" on page 389: "nerves of motion were
+paralysed."</p>
+
+<p><a name="TNpage396" id="TNpage396"></a>The footnote from page 396 refers to the footnote on page 270.
+There is no such footnote. The intent may be to refer to the <a href="#Footnote_28_63">footnote
+on page 268</a>. However, the text was not changed.</p>
+
+<p>Added the dropped "w" in "which" on page 420: "which the progress of the
+inquiry."</p>
+
+<p>Changed "developes" to "develops" on page 456: "the prime conductor
+develops."</p>
+
+<p>Removed the additional period at the end of the footnote on page 457:
+"Pp. 159-162."</p>
+
+<p>Added the dropped "l" to "essential" on page 515: "an essential
+requisite."</p>
+
+<p>Removed extra opening quotation mark before "gum" on page 532:
+"vegetable gum is not digested."</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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+Inductive, by John Stuart Mill
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+The Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A System of Logic: Ratiocinative and Inductive
+       7th Edition, Vol. I
+
+Author: John Stuart Mill
+
+Release Date: February 27, 2011 [EBook #35420]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL 1 ***
+
+
+
+
+Produced by David Clarke, Stephen H. Sentoff and the Online
+Distributed Proofreading Team at https://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+VOL. I.
+
+
+
+
+A
+SYSTEM OF LOGIC
+
+RATIOCINATIVE AND INDUCTIVE
+
+BEING A CONNECTED VIEW OF THE
+PRINCIPLES OF EVIDENCE
+AND THE
+METHODS OF SCIENTIFIC INVESTIGATION
+
+BY
+
+JOHN STUART MILL
+
+
+IN TWO VOLUMES
+
+VOL. I.
+
+SEVENTH EDITION
+
+
+LONDON:
+LONGMANS, GREEN, READER, AND DYER
+
+MDCCCLXVIII
+
+
+
+
+PREFACE TO THE FIRST EDITION.
+
+
+This book makes no pretence of giving to the world a new theory of the
+intellectual operations. Its claim to attention, if it possess any, is
+grounded on the fact that it is an attempt not to supersede, but to
+embody and systematize, the best ideas which have been either
+promulgated on its subject by speculative writers, or conformed to by
+accurate thinkers in their scientific inquiries.
+
+To cement together the detached fragments of a subject, never yet
+treated as a whole; to harmonize the true portions of discordant
+theories, by supplying the links of thought necessary to connect them,
+and by disentangling them from the errors with which they are always
+more or less interwoven; must necessarily require a considerable amount
+of original speculation. To other originality than this, the present
+work lays no claim. In the existing state of the cultivation of the
+sciences, there would be a very strong presumption against any one who
+should imagine that he had effected a revolution in the theory of the
+investigation of truth, or added any fundamentally new process to the
+practice of it. The improvement which remains to be effected in the
+methods of philosophizing (and the author believes that they have much
+need of improvement) can only consist in performing, more systematically
+and accurately, operations with which, at least in their elementary
+form, the human intellect in some one or other of its employments is
+already familiar.
+
+In the portion of the work which treats of Ratiocination, the author has
+not deemed it necessary to enter into technical details which may be
+obtained in so perfect a shape from the existing treatises on what is
+termed the Logic of the Schools. In the contempt entertained by many
+modern philosophers for the syllogistic art, it will be seen that he by
+no means participates; though the scientific theory on which its defence
+is usually rested appears to him erroneous: and the view which he has
+suggested of the nature and functions of the Syllogism may, perhaps,
+afford the means of conciliating the principles of the art with as much
+as is well grounded in the doctrines and objections of its assailants.
+
+The same abstinence from details could not be observed in the First
+Book, on Names and Propositions; because many useful principles and
+distinctions which were contained in the old Logic, have been gradually
+omitted from the writings of its later teachers; and it appeared
+desirable both to revive these, and to reform and rationalize the
+philosophical foundation on which they stood. The earlier chapters of
+this preliminary Book will consequently appear, to some readers,
+needlessly elementary and scholastic. But those who know in what
+darkness the nature of our knowledge, and of the processes by which it
+is obtained, is often involved by a confused apprehension of the import
+of the different classes of Words and Assertions, will not regard these
+discussions as either frivolous, or irrelevant to the topics considered
+in the later Books.
+
+On the subject of Induction, the task to be performed was that of
+generalizing the modes of investigating truth and estimating evidence,
+by which so many important and recondite laws of nature have, in the
+various sciences, been aggregated to the stock of human knowledge. That
+this is not a task free from difficulty may be presumed from the fact,
+that even at a very recent period, eminent writers (among whom it is
+sufficient to name Archbishop Whately, and the author of a celebrated
+article on Bacon in the _Edinburgh Review_) have not scrupled to
+pronounce it impossible.[1] The author has endeavoured to combat their
+theory in the manner in which Diogenes confuted the sceptical reasonings
+against the possibility of motion; remembering that Diogenes' argument
+would have been equally conclusive, though his individual perambulations
+might not have extended beyond the circuit of his own tub.
+
+Whatever may be the value of what the author has succeeded in effecting
+on this branch of his subject, it is a duty to acknowledge that for much
+of it he has been indebted to several important treatises, partly
+historical and partly philosophical, on the generalities and processes
+of physical science, which have been published within the last few
+years. To these treatises, and to their authors, he has endeavoured to
+do justice in the body of the work. But as with one of these writers,
+Dr. Whewell, he has occasion frequently to express differences of
+opinion, it is more particularly incumbent on him in this place to
+declare, that without the aid derived from the facts and ideas contained
+in that gentleman's _History of the Inductive Sciences_, the
+corresponding portion of this work would probably not have been written.
+
+The concluding Book is an attempt to contribute towards the solution of
+a question, which the decay of old opinions, and the agitation that
+disturbs European society to its inmost depths, render as important in
+the present day to the practical interests of human life, as it must at
+all times be to the completeness of our speculative knowledge: viz.
+Whether moral and social phenomena are really exceptions to the general
+certainty and uniformity of the course of nature; and how far the
+methods, by which so many of the laws of the physical world have been
+numbered among truths irrevocably acquired and universally assented to,
+can be made instrumental to the formation of a similar body of received
+doctrine in moral and political science.
+
+
+
+
+PREFACE TO THE THIRD AND FOURTH EDITIONS.
+
+
+Several criticisms, of a more or less controversial character, on this
+work, have appeared since the publication of the second edition; and Dr.
+Whewell has lately published a reply to those parts of it in which some
+of his opinions were controverted.[2]
+
+I have carefully reconsidered all the points on which my conclusions
+have been assailed. But I have not to announce a change of opinion on
+any matter of importance. Such minor oversights as have been detected,
+either by myself or by my critics, I have, in general silently,
+corrected: but it is not to be inferred that I agree with the objections
+which have been made to a passage, in every instance in which I have
+altered or cancelled it. I have often done so, merely that it might not
+remain a stumbling-block, when the amount of discussion necessary to
+place the matter in its true light would have exceeded what was suitable
+to the occasion.
+
+To several of the arguments which have been urged against me, I have
+thought it useful to reply with some degree of minuteness; not from any
+taste for controversy, but because the opportunity was favourable for
+placing my own conclusions, and the grounds of them, more clearly and
+completely before the reader. Truth, on these subjects, is militant, and
+can only establish itself by means of conflict. The most opposite
+opinions can make a plausible show of evidence while each has the
+statement of its own case; and it is only possible to ascertain which of
+them is in the right, after hearing and comparing what each can say
+against the other, and what the other can urge in its defence.
+
+Even the criticisms from which I most dissent have been of great service
+to me, by showing in what places the exposition most needed to be
+improved, or the argument strengthened. And I should have been well
+pleased if the book had undergone a much greater amount of attack; as in
+that case I should probably have been enabled to improve it still more
+than I believe I have now done.
+
+       *       *       *       *       *
+
+In the subsequent editions, the attempt to improve the work by additions
+and corrections, suggested by criticism or by thought, has been
+continued. In the present (seventh) edition, a few further corrections
+have been made, but no material additions.
+
+FOOTNOTES:
+
+[1] In the later editions of Archbishop Whately's _Logic_, he states his
+meaning to be, not that "rules" for the ascertainment of truths by
+inductive investigation cannot be laid down, or that they may not be "of
+eminent service," but that they "must always be comparatively vague and
+general, and incapable of being built up into a regular demonstrative
+theory like that of the Syllogism." (Book IV. ch. iv. Sec. 3.) And he
+observes, that to devise a system for this purpose, capable of being
+"brought into a scientific form," would be an achievement which "he must
+be more sanguine than scientific who expects." (Book IV. ch. ii. Sec. 4.)
+To effect this, however, being the express object of the portion of the
+present work which treats of Induction, the words in the text are no
+overstatement of the difference of opinion between Archbishop Whately
+and me on the subject.
+
+[2] Now forming a chapter in his volume on _The Philosophy of
+Discovery_.
+
+
+
+
+CONTENTS
+OF
+THE FIRST VOLUME.
+
+
+  INTRODUCTION.
+
+
+  Sec. 1. A definition at the commencement of a subject must be
+       provisional                                                    1
+
+    2. Is logic the art and science of reasoning?                     2
+
+    3. Or the art and science of the pursuit of truth?                3
+
+    4. Logic is concerned with inferences, not with intuitive truths  5
+
+    5. Relation of logic to the other sciences                        8
+
+    6. Its utility, how shown                                        10
+
+    7. Definition of logic stated and illustrated                    11
+
+
+  BOOK I.
+
+  OF NAMES AND PROPOSITIONS.
+
+
+  CHAPTER I. _Of the Necessity of commencing with an
+  Analysis of Language._
+
+  Sec. 1. Theory of names, why a necessary part of logic                17
+
+    2. First step in the analysis of Propositions                    18
+
+    3. Names must be studied before Things                           21
+
+
+  CHAPTER II. _Of Names._
+
+  Sec. 1. Names are names of things, not of our ideas                   23
+
+    2. Words which are not names, but parts of names                 24
+
+    3. General and Singular names                                    26
+
+    4. Concrete and Abstract                                         29
+
+    5. Connotative and Non-connotative                               31
+
+    6. Positive and Negative                                         42
+
+    7. Relative and Absolute                                         44
+
+    8. Univocal and AEquivocal                                        47
+
+
+  CHAPTER III. _Of the Things denoted by Names._
+
+  Sec. 1. Necessity of an enumeration of Nameable Things. The
+       Categories of Aristotle                                       49
+
+    2. Ambiguity of the most general names                           51
+
+    3. Feelings, or states of consciousness                          54
+
+    4. Feelings must be distinguished from their physical
+       antecedents. Perceptions, what                                56
+
+    5. Volitions, and Actions, what                                  58
+
+    6. Substance and Attribute                                       59
+
+    7. Body                                                          61
+
+    8. Mind                                                          67
+
+    9. Qualities                                                     69
+
+   10. Relations                                                     72
+
+   11. Resemblance                                                   74
+
+   12. Quantity                                                      78
+
+   13. All attributes of bodies are grounded on states of
+       consciousness                                                 79
+
+   14. So also all attributes of mind                                80
+
+   15. Recapitulation                                                81
+
+
+  CHAPTER IV. _Of Propositions._
+
+  Sec. 1. Nature and office of the copula                               85
+
+    2. Affirmative and Negative propositions                         87
+
+    3. Simple and Complex                                            89
+
+    4. Universal, Particular, and Singular                           93
+
+
+  CHAPTER V. _Of the Import of Propositions._
+
+  Sec. 1. Doctrine that a proposition is the expression of a relation
+       between two ideas                                             96
+
+    2. Doctrine that it is the expression of a relation between the
+       meanings of two names                                         99
+
+    3. Doctrine that it consists in referring something to, or
+       excluding something from, a class                            103
+
+    4. What it really is                                            107
+
+    5. It asserts (or denies) a sequence, a coexistence, a simple
+       existence, a causation                                       110
+
+    6. --or a resemblance                                           112
+
+    7. Propositions of which the terms are abstract                 115
+
+
+  CHAPTER VI. _Of Propositions merely Verbal._
+
+  Sec. 1. Essential and Accidental propositions                        119
+
+    2. All essential propositions are identical propositions        120
+
+    3. Individuals have no essences                                 124
+
+    4. Real propositions, how distinguished from verbal             126
+
+    5. Two modes of representing the import of a Real proposition   127
+
+
+  CHAPTER VII. _Of the Nature of Classification, and
+  the Five Predicables._
+
+  Sec. 1. Classification, how connected with Naming                    129
+
+    2. The Predicables, what                                        131
+
+    3. Genus and Species                                            131
+
+    4. Kinds have a real existence in nature                        134
+
+    5. Differentia                                                  139
+
+    6. Differentiae for general purposes, and differentiae for
+       special or technical purposes                                141
+
+    7. Proprium                                                     144
+
+    8. Accidens                                                     146
+
+
+  CHAPTER VIII. _Of Definition._
+
+  Sec. 1. A definition, what                                           148
+
+    2. Every name can be defined, whose meaning is susceptible
+       of analysis                                                  150
+
+    3. Complete, how distinguished from incomplete definitions      152
+
+    4. --and from descriptions                                      154
+
+    5. What are called definitions of Things, are definitions of
+       Names with an implied assumption of the existence of
+       Things corresponding to them                                 157
+
+    6. --even when such things do not in reality exist              165
+
+    7. Definitions, though of names only, must be grounded on
+       knowledge of the corresponding Things                        167
+
+
+  BOOK II.
+
+  OF REASONING.
+
+
+  CHAPTER I. _Of Inference, or Reasoning, in general._
+
+  Sec. 1. Retrospect of the preceding book                             175
+
+    2. Inferences improperly so called                              177
+
+    3. Inferences proper, distinguished into inductions and
+       ratiocinations                                               181
+
+
+  CHAPTER II. _Of Ratiocination, or Syllogism._
+
+  Sec. 1. Analysis of the Syllogism                                    184
+
+    2. The _dictum de omni_ not the foundation of reasoning,
+       but a mere identical proposition                             191
+
+    3. What is the really fundamental axiom of Ratiocination        196
+
+    4. The other form of the axiom                                  199
+
+
+  CHAPTER III. _Of the Functions, and Logical Value, of the
+  Syllogism._
+
+  Sec. 1. Is the syllogism a _petitio principii_?                      202
+
+    2. Insufficiency of the common theory                           203
+
+    3. All inference is from particulars to particulars             205
+
+    4. General propositions are a record of such inferences, and
+       the rules of the syllogism are rules for the interpretation
+       of the record                                                214
+
+    5. The syllogism not the type of reasoning, but a test of it    218
+
+    6. The true type, what                                          222
+
+    7. Relation between Induction and Deduction                     226
+
+    8. Objections answered                                          227
+
+    9. Of Formal Logic, and its relation to the Logic of Truth      231
+
+
+  CHAPTER IV. _Of Trains of Reasoning, and Deductive
+  Sciences._
+
+  Sec. 1. For what purpose trains of reasoning exist                   234
+
+    2. A train of reasoning is a series of inductive inferences     234
+
+    3. --from particulars to particulars through marks of marks     237
+
+    4. Why there are deductive sciences                             240
+
+    5. Why other sciences still remain experimental                 244
+
+    6. Experimental sciences may become deductive by the progress
+       of experiment                                                246
+
+    7. In what manner this usually takes place                      247
+
+
+  CHAPTER V. _Of Demonstration, and Necessary Truths._
+
+  Sec. 1. The Theorems of geometry are necessary truths only in
+       the sense of necessarily following from hypotheses           251
+
+    2. Those hypotheses are real facts with some of their
+       circumstances exaggerated or omitted                         255
+
+    3. Some of the first principles of geometry are axioms, and
+       these are not hypothetical                                   256
+
+    4. --but are experimental truths                                258
+
+    5. An objection answered                                        261
+
+    6. Dr. Whewell's opinions on axioms examined                    264
+
+
+  CHAPTER VI. _The same Subject continued._
+
+  Sec. 1. All deductive sciences are inductive                         281
+
+    2. The propositions of the science of number are not verbal,
+       but generalizations from experience                          284
+
+    3. In what sense hypothetical                                   289
+
+    4. The characteristic property of demonstrative science is to
+       be hypothetical                                              290
+
+    5. Definition of demonstrative evidence                         292
+
+
+  CHAPTER VII. _Examination of some Opinions opposed to
+  the preceding doctrines._
+
+  Sec. 1. Doctrine of the Universal Postulate                          294
+
+    2. The test of inconceivability does not represent the
+       aggregate of past experience                                 296
+
+    3. --nor is implied in every process of thought                 299
+
+    4. Sir W. Hamilton's opinion on the Principles of
+       Contradiction and Excluded Middle                            306
+
+
+  BOOK III.
+
+  OF INDUCTION.
+
+
+  CHAPTER I. _Preliminary Observations on Induction in general._
+
+  Sec. 1. Importance of an Inductive Logic                             313
+
+    2. The logic of science is also that of business and life       314
+
+
+  CHAPTER II. _Of Inductions improperly so called._
+
+  Sec. 1. Inductions distinguished from verbal transformations         319
+
+    2. --from inductions, falsely so called, in mathematics         321
+
+    3. --and from descriptions                                      323
+
+    4. Examination of Dr. Whewell's theory of Induction             326
+
+    5. Further illustration of the preceding remarks                336
+
+
+  CHAPTER III. _On the Ground of Induction._
+
+  Sec. 1. Axiom of the uniformity of the course of nature              341
+
+    2. Not true in every sense. Induction _per enumerationem
+       simplicem_                                                   346
+
+    3. The question of Inductive Logic stated                       348
+
+
+  CHAPTER IV. _Of Laws of Nature._
+
+  Sec. 1. The general regularity in nature is a tissue of partial
+       regularities, called laws                                    351
+
+    2. Scientific induction must be grounded on previous
+       spontaneous inductions                                       355
+
+    3. Are there any inductions fitted to be a test of all others?  357
+
+
+  CHAPTER V. _Of the Law of Universal Causation._
+
+  Sec. 1. The universal law of successive phenomena is the Law of
+       Causation                                                    360
+
+    2. --_i.e._ the law that every consequent has an invariable
+       antecedent                                                   363
+
+    3. The cause of a phenomenon is the assemblage of its
+       conditions                                                   365
+
+    4. The distinction of agent and patient illusory                373
+
+    5. The cause is not the invariable antecedent, but the
+       _unconditional_ invariable antecedent                        375
+
+    6. Can a cause be simultaneous with its effect?                 380
+
+    7. Idea of a Permanent Cause, or original natural agent         383
+
+    8. Uniformities of coexistence between effects of different
+       permanent causes, are not laws                               386
+
+    9. Doctrine that volition is an efficient cause, examined       387
+
+
+  CHAPTER VI. _Of the Composition of Causes._
+
+  Sec. 1. Two modes of the conjunct action of causes, the mechanical
+       and the chemical                                             405
+
+    2. The composition of causes the general rule; the other case
+       exceptional                                                  408
+
+    3. Are effects proportional to their causes?                    412
+
+
+  CHAPTER VII. _Of Observation and Experiment._
+
+  Sec. 1. The first step of inductive inquiry is a mental analysis of
+       complex phenomena into their elements                        414
+
+    2. The next is an actual separation of those elements           416
+
+    3. Advantages of experiment over observation                    417
+
+    4. Advantages of observation over experiment                    420
+
+
+  CHAPTER VIII. _Of the Four Methods of Experimental
+  Inquiry._
+
+  Sec. 1. Method of Agreement                                          425
+
+    2. Method of Difference                                         428
+
+    3. Mutual relation of these two methods                         429
+
+    4. Joint Method of Agreement and Difference                     433
+
+    5. Method of Residues                                           436
+
+    6. Method of Concomitant Variations                             437
+
+    7. Limitations of this last method                              443
+
+
+  CHAPTER IX. _Miscellaneous Examples of the Four Methods._
+
+  Sec. 1. Liebig's theory of metallic poisons                          449
+
+    2. Theory of induced electricity                                453
+
+    3. Dr. Wells' theory of dew                                     457
+
+    4. Dr. Brown-Sequard's theory of cadaveric rigidity             465
+
+    5. Examples of the Method of Residues                           471
+
+    6. Dr. Whewell's objections to the Four Methods                 475
+
+
+  CHAPTER X. _Of Plurality of Causes; and of the Intermixture
+  of Effects._
+
+  Sec. 1. One effect may have several causes                           482
+
+    2. --which is the source of a characteristic imperfection of
+       the Method of Agreement                                      483
+
+    3. Plurality of Causes, how ascertained                         487
+
+    4. Concurrence of Causes which do not compound their effects    489
+
+    5. Difficulties of the investigation, when causes compound
+       their effects                                                494
+
+    6. Three modes of investigating the laws of complex effects     499
+
+    7. The method of simple observation inapplicable                500
+
+    8. The purely experimental method inapplicable                  501
+
+
+  CHAPTER XI. _Of the Deductive Method._
+
+  Sec. 1. First stage; ascertainment of the laws of the separate
+       causes by direct induction                                   507
+
+    2. Second stage; ratiocination from the simple laws of the
+       complex cases                                                512
+
+    3. Third stage; verification by specific experience             514
+
+
+  CHAPTER XII. _Of the Explanation of Laws of Nature._
+
+  Sec. 1. Explanation defined                                          518
+
+    2. First mode of explanation, by resolving the law of a complex
+       effect into the laws of the concurrent causes and
+       the fact of their coexistence                                518
+
+    3. Second mode; by the detection of an intermediate link in
+       the sequence                                                 519
+
+    4. Laws are always resolved into laws more general than
+       themselves                                                   520
+
+    5. Third mode; the subsumption of less general laws under
+       a more general one                                           524
+
+    6. What the explanation of a law of nature amounts to           526
+
+
+  CHAPTER XIII. _Miscellaneous Examples of the Explanation of
+  Laws of Nature._
+
+  Sec. 1. The general theories of the sciences                         529
+
+    2. Examples from chemical speculations                          531
+
+    3. Example from Dr. Brown-Sequard's researches on the
+       nervous system                                               533
+
+    4. Examples of following newly-discovered laws into their
+       complex manifestations                                       534
+
+    5. Examples of empirical generalizations, afterwards confirmed
+       and explained deductively                                    536
+
+    6. Example from mental science                                  538
+
+    7. Tendency of all the sciences to become deductive             539
+
+
+
+
+INTRODUCTION.
+
+
+Sec. 1. There is as great diversity among authors in the modes which they
+have adopted of defining logic, as in their treatment of the details of
+it. This is what might naturally be expected on any subject on which
+writers have availed themselves of the same language as a means of
+delivering different ideas. Ethics and jurisprudence are liable to the
+remark in common with logic. Almost every writer having taken a
+different view of some of the particulars which these branches of
+knowledge are usually understood to include; each has so framed his
+definition as to indicate beforehand his own peculiar tenets, and
+sometimes to beg the question in their favour.
+
+This diversity is not so much an evil to be complained of, as an
+inevitable and in some degree a proper result of the imperfect state of
+those sciences. It is not to be expected that there should be agreement
+about the definition of anything, until there is agreement about the
+thing itself. To define, is to select from among all the properties of a
+thing, those which shall be understood to be designated and declared by
+its name; and the properties must be well known to us before we can be
+competent to determine which of them are fittest to be chosen for this
+purpose. Accordingly, in the case of so complex an aggregation of
+particulars as are comprehended in anything which can be called a
+science, the definition we set out with is seldom that which a more
+extensive knowledge of the subject shows to be the most appropriate.
+Until we know the particulars themselves, we cannot fix upon the most
+correct and compact mode of circumscribing them by a general
+description. It was not until after an extensive and accurate
+acquaintance with the details of chemical phenomena, that it was found
+possible to frame a rational definition of chemistry; and the definition
+of the science of life and organization is still a matter of dispute. So
+long as the sciences are imperfect, the definitions must partake of
+their imperfection; and if the former are progressive, the latter ought
+to be so too. As much, therefore, as is to be expected from a definition
+placed at the commencement of a subject, is that it should define the
+scope of our inquiries: and the definition which I am about to offer of
+the science of logic, pretends to nothing more, than to be a statement
+of the question which I have put to myself, and which this book is an
+attempt to resolve. The reader is at liberty to object to it as a
+definition of logic; but it is at all events a correct definition of the
+subject of these volumes.
+
+
+Sec. 2. Logic has often been called the Art of Reasoning. A writer[1] who
+has done more than any other person to restore this study to the rank
+from which it had fallen in the estimation of the cultivated class in
+our own country, has adopted the above definition with an amendment; he
+has defined Logic to be the Science, as well as the Art, of reasoning;
+meaning by the former term, the analysis of the mental process which
+takes place whenever we reason, and by the latter, the rules, grounded
+on that analysis, for conducting the process correctly. There can be no
+doubt as to the propriety of the emendation. A right understanding of
+the mental process itself, of the conditions it depends on, and the
+steps of which it consists, is the only basis on which a system of
+rules, fitted for the direction of the process, can possibly be founded.
+Art necessarily presupposes knowledge; art, in any but its infant state,
+presupposes scientific knowledge: and if every art does not bear the
+name of a science, it is only because several sciences are often
+necessary to form the groundwork of a single art. So complicated are the
+conditions which govern our practical agency, that to enable one thing
+to be _done_, it is often requisite to _know_ the nature and properties
+of many things.
+
+Logic, then, comprises the science of reasoning, as well as an art,
+founded on that science. But the word Reasoning, again, like most other
+scientific terms in popular use, abounds in ambiguities. In one of its
+acceptations, it means syllogizing; or the mode of inference which may
+be called (with sufficient accuracy for the present purpose) concluding
+from generals to particulars. In another of its senses, to reason is
+simply to infer any assertion, from assertions already admitted: and in
+this sense induction is as much entitled to be called reasoning as the
+demonstrations of geometry.
+
+Writers on logic have generally preferred the former acceptation of the
+term: the latter, and more extensive signification is that in which I
+mean to use it. I do this by virtue of the right I claim for every
+author, to give whatever provisional definition he pleases of his own
+subject. But sufficient reasons will, I believe, unfold themselves as we
+advance, why this should be not only the provisional but the final
+definition. It involves, at all events, no arbitrary change in the
+meaning of the word; for, with the general usage of the English
+language, the wider signification, I believe, accords better than the
+more restricted one.
+
+
+Sec. 3. But Reasoning, even in the widest sense of which the word is
+susceptible, does not seem to comprehend all that is included, either in
+the best, or even in the most current, conception of the scope and
+province of our science. The employment of the word Logic to denote the
+theory of argumentation, is derived from the Aristotelian, or, as they
+are commonly termed, the scholastic, logicians. Yet even with them, in
+their systematic treatises, argumentation was the subject only of the
+third part: the two former treated of Terms, and of Propositions; under
+one or other of which heads were also included Definition and Division.
+By some, indeed, these previous topics were professedly introduced only
+on account of their connexion with reasoning, and as a preparation for
+the doctrine and rules of the syllogism. Yet they were treated with
+greater minuteness, and dwelt on at greater length, than was required
+for that purpose alone. More recent writers on logic have generally
+understood the term as it was employed by the able author of the Port
+Royal Logic; viz. as equivalent to the Art of Thinking. Nor is this
+acceptation confined to books, and scientific inquiries. Even in
+ordinary conversation, the ideas connected with the word Logic include
+at least precision of language, and accuracy of classification: and we
+perhaps oftener hear persons speak of a logical arrangement, or of
+expressions logically defined, than of conclusions logically deduced
+from premises. Again, a man is often called a great logician, or a man
+of powerful logic, not for the accuracy of his deductions, but for the
+extent of his command over premises; because the general propositions
+required for explaining a difficulty or refuting a sophism, copiously
+and promptly occur to him: because, in short, his knowledge, besides
+being ample, is well under his command for argumentative use. Whether,
+therefore, we conform to the practice of those who have made the subject
+their particular study, or to that of popular writers and common
+discourse, the province of logic will include several operations of the
+intellect not usually considered to fall within the meaning of the terms
+Reasoning and Argumentation.
+
+These various operations might be brought within the compass of the
+science, and the additional advantage be obtained of a very simple
+definition, if, by an extension of the term, sanctioned by high
+authorities, we were to define logic as the science which treats of the
+operations of the human understanding in the pursuit of truth. For to
+this ultimate end, naming, classification, definition, and all other
+operations over which logic has ever claimed jurisdiction, are
+essentially subsidiary. They may all be regarded as contrivances for
+enabling a person to know the truths which are needful to him, and to
+know them at the precise moment at which they are needful. Other
+purposes, indeed, are also served by these operations; for instance,
+that of imparting our knowledge to others. But, viewed with regard to
+this purpose, they have never been considered as within the province of
+the logician. The sole object of Logic is the guidance of one's own
+thoughts: the communication of those thoughts to others falls under the
+consideration of Rhetoric, in the large sense in which that art was
+conceived by the ancients; or of the still more extensive art of
+Education. Logic takes cognizance of our intellectual operations, only
+as they conduce to our own knowledge, and to our command over that
+knowledge for our own uses. If there were but one rational being in the
+universe, that being might be a perfect logician; and the science and
+art of logic would be the same for that one person as for the whole
+human race.
+
+
+Sec. 4. But, if the definition which we formerly examined included too
+little, that which is now suggested has the opposite fault of including
+too much.
+
+Truths are known to us in two ways: some are known directly, and of
+themselves; some through the medium of other truths. The former are the
+subject of Intuition, or Consciousness;[2] the latter, of Inference. The
+truths known by intuition are the original premises from which all
+others are inferred. Our assent to the conclusion being grounded on the
+truth of the premises, we never could arrive at any knowledge by
+reasoning, unless something could be known antecedently to all
+reasoning.
+
+Examples of truths known to us by immediate consciousness, are our own
+bodily sensations and mental feelings. I know directly, and of my own
+knowledge, that I was vexed yesterday, or that I am hungry to-day.
+Examples of truths which we know only by way of inference, are
+occurrences which took place while we were absent, the events recorded
+in history, or the theorems of mathematics. The two former we infer from
+the testimony adduced, or from the traces of those past occurrences
+which still exist; the latter, from the premises laid down in books of
+geometry, under the title of definitions and axioms. Whatever we are
+capable of knowing must belong to the one class or to the other; must
+be in the number of the primitive data, or of the conclusions which can
+be drawn from these.
+
+With the original data, or ultimate premises of our knowledge; with
+their number or nature, the mode in which they are obtained, or the
+tests by which they may be distinguished; logic, in a direct way at
+least, has, in the sense in which I conceive the science, nothing to do.
+These questions are partly not a subject of science at all, partly that
+of a very different science.
+
+Whatever is known to us by consciousness, is known beyond possibility of
+question. What one sees or feels, whether bodily or mentally, one cannot
+but be sure that one sees or feels. No science is required for the
+purpose of establishing such truths; no rules of art can render our
+knowledge of them more certain than it is in itself. There is no logic
+for this portion of our knowledge.
+
+But we may fancy that we see or feel what we in reality infer. A truth,
+or supposed truth, which is really the result of a very rapid inference,
+may seem to be apprehended intuitively. It has long been agreed by
+thinkers of the most opposite schools, that this mistake is actually
+made in so familiar an instance as that of the eyesight. There is
+nothing of which we appear to ourselves to be more directly conscious,
+than the distance of an object from us. Yet it has long been
+ascertained, that what is perceived by the eye, is at most nothing more
+than a variously coloured surface; that when we fancy we see distance,
+all we really see is certain variations of apparent size, and degrees of
+faintness of colour; that our estimate of the object's distance from us
+is the result partly of a rapid inference from the muscular sensations
+accompanying the adjustment of the focal distance of the eye to objects
+unequally remote from us, and partly of a comparison (made with so much
+rapidity that we are unconscious of making it) between the size and
+colour of the object as they appear at the time, and the size and colour
+of the same or of similar objects as they appeared when close at hand,
+or when their degree of remoteness was known by other evidence. The
+perception of distance by the eye, which seems so like intuition, is
+thus, in reality, an inference grounded on experience; an inference,
+too, which we learn to make; and which we make with more and more
+correctness as our experience increases; though in familiar cases it
+takes place so rapidly as to appear exactly on a par with those
+perceptions of sight which are really intuitive, our perceptions of
+colour.[3]
+
+Of the science, therefore, which expounds the operations of the human
+understanding in the pursuit of truth, one essential part is the
+inquiry: What are the facts which are the objects of intuition or
+consciousness, and what are those which we merely infer? But this
+inquiry has never been considered a portion of logic. Its place is in
+another and a perfectly distinct department of science, to which the
+name metaphysics more particularly belongs: that portion of mental
+philosophy which attempts to determine what part of the furniture of the
+mind belongs to it originally, and what part is constructed out of
+materials furnished to it from without. To this science appertain the
+great and much debated questions of the existence of matter; the
+existence of spirit, and of a distinction between it and matter; the
+reality of time and space, as things without the mind, and
+distinguishable from the objects which are said to exist in them. For in
+the present state of the discussion on these topics, it is almost
+universally allowed that the existence of matter or of spirit, of space
+or of time, is in its nature unsusceptible of being proved; and that if
+anything is known of them, it must be by immediate intuition. To the
+same science belong the inquiries into the nature of Conception,
+Perception, Memory, and Belief; all of which are operations of the
+understanding in the pursuit of truth; but with which, as phenomena of
+the mind, or with the possibility which may or may not exist of
+analysing any of them into simpler phenomena, the logician as such has
+no concern. To this science must also be referred the following, and all
+analogous questions: To what extent our intellectual faculties and our
+emotions are innate--to what extent the result of association: Whether
+God, and duty, are realities, the existence of which is manifest to us
+_a priori_ by the constitution of our rational faculty; or whether our
+ideas of them are acquired notions, the origin of which we are able to
+trace and explain; and the reality of the objects themselves a question
+not of consciousness or intuition, but of evidence and reasoning.
+
+The province of logic must be restricted to that portion of our
+knowledge which consists of inferences from truths previously known;
+whether those antecedent data be general propositions, or particular
+observations and perceptions. Logic is not the science of Belief, but
+the science of Proof, or Evidence. In so far as belief professes to be
+founded on proof, the office of logic is to supply a test for
+ascertaining whether or not the belief is well grounded. With the claims
+which any proposition has to belief on the evidence of consciousness,
+that is, without evidence in the proper sense of the word, logic has
+nothing to do.
+
+
+Sec. 5. By far the greatest portion of our knowledge, whether of general
+truths or of particular facts, being avowedly matter of inference,
+nearly the whole, not only of science, but of human conduct, is amenable
+to the authority of logic. To draw inferences has been said to be the
+great business of life. Every one has daily, hourly, and momentary need
+of ascertaining facts which he has not directly observed; not from any
+general purpose of adding to his stock of knowledge, but because the
+facts themselves are of importance to his interests or to his
+occupations. The business of the magistrate, of the military commander,
+of the navigator, of the physician, of the agriculturist, is merely to
+judge of evidence, and to act accordingly. They all have to ascertain
+certain facts, in order that they may afterwards apply certain rules,
+either devised by themselves, or prescribed for their guidance by
+others; and as they do this well or ill, so they discharge well or ill
+the duties of their several callings. It is the only occupation in
+which the mind never ceases to be engaged; and is the subject, not of
+logic, but of knowledge in general.
+
+Logic, however, is not the same thing with knowledge, though the field
+of logic is coextensive with the field of knowledge. Logic is the common
+judge and arbiter of all particular investigations. It does not
+undertake to find evidence, but to determine whether it has been found.
+Logic neither observes, nor invents, nor discovers; but judges. It is no
+part of the business of logic to inform the surgeon what appearances are
+found to accompany a violent death. This he must learn from his own
+experience and observation, or from that of others, his predecessors in
+his peculiar pursuit. But logic sits in judgment on the sufficiency of
+that observation and experience to justify his rules, and on the
+sufficiency of his rules to justify his conduct. It does not give him
+proofs, but teaches him what makes them proofs, and how he is to judge
+of them. It does not teach that any particular fact proves any other,
+but points out to what conditions all facts must conform, in order that
+they may prove other facts. To decide whether any given fact fulfils
+these conditions, or whether facts can be found which fulfil them in a
+given case, belongs exclusively to the particular art or science, or to
+our knowledge of the particular subject.
+
+It is in this sense that logic is, what Bacon so expressively called it,
+_ars artium_; the science of science itself. All science consists of
+data and conclusions from those data, of proofs and what they prove: now
+logic points out what relations must subsist between data and whatever
+can be concluded from them, between proof and everything which it can
+prove. If there be any such indispensable relations, and if these can be
+precisely determined, every particular branch of science, as well as
+every individual in the guidance of his conduct, is bound to conform to
+those relations, under the penalty of making false inferences, of
+drawing conclusions which are not grounded in the realities of things.
+Whatever has at any time been concluded justly, whatever knowledge has
+been acquired otherwise than by immediate intuition, depended on the
+observance of the laws which it is the province of logic to investigate.
+If the conclusions are just, and the knowledge real, those laws, whether
+known or not, have been observed.
+
+
+Sec. 6. We need not, therefore, seek any farther for a solution of the
+question, so often agitated, respecting the utility of logic. If a
+science of logic exists, or is capable of existing, it must be useful.
+If there be rules to which every mind consciously or unconsciously
+conforms in every instance in which it infers rightly, there seems
+little necessity for discussing whether a person is more likely to
+observe those rules, when he knows the rules, than when he is
+unacquainted with them.
+
+A science may undoubtedly be brought to a certain, not inconsiderable,
+stage of advancement, without the application of any other logic to it
+than what all persons, who are said to have a sound understanding,
+acquire empirically in the course of their studies. Mankind judged of
+evidence, and often correctly, before logic was a science, or they never
+could have made it one. And they executed great mechanical works before
+they understood the laws of mechanics. But there are limits both to what
+mechanicians can do without principles of mechanics, and to what
+thinkers can do without principles of logic. A few individuals, by
+extraordinary genius, or by the accidental acquisition of a good set of
+intellectual habits, may work without principles in the same way, or
+nearly the same way, in which they would have worked if they had been in
+possession of principles. But the bulk of mankind require either to
+understand the theory of what they are doing, or to have rules laid down
+for them by those who have understood the theory. In the progress of
+science from its easiest to its more difficult problems, each great step
+in advance has usually had either as its precursor, or as its
+accompaniment and necessary condition, a corresponding improvement in
+the notions and principles of logic received among the most advanced
+thinkers. And if several of the more difficult sciences are still in so
+defective a state; if not only so little is proved, but disputation has
+not terminated even about the little which seemed to be so; the reason
+perhaps is, that men's logical notions have not yet acquired the degree
+of extension, or of accuracy, requisite for the estimation of the
+evidence proper to those particular departments of knowledge.
+
+
+Sec. 7. Logic, then, is the science of the operations of the understanding
+which are subservient to the estimation of evidence: both the process
+itself of advancing from known truths to unknown, and all other
+intellectual operations in so far as auxiliary to this. It includes,
+therefore, the operation of Naming; for language is an instrument of
+thought, as well as a means of communicating our thoughts. It includes,
+also, Definition, and Classification. For, the use of these operations
+(putting all other minds than one's own out of consideration) is to
+serve not only for keeping our evidences and the conclusions from them
+permanent and readily accessible in the memory, but for so marshalling
+the facts which we may at any time be engaged in investigating, as to
+enable us to perceive more clearly what evidence there is, and to judge
+with fewer chances of error whether it be sufficient. These, therefore,
+are operations specially instrumental to the estimation of evidence,
+and, as such, are within the province of Logic. There are other more
+elementary processes, concerned in all thinking, such as Conception,
+Memory, and the like; but of these it is not necessary that Logic should
+take any peculiar cognizance, since they have no special connexion with
+the problem of Evidence, further than that, like all other problems
+addressed to the understanding, it presupposes them.
+
+Our object, then, will be, to attempt a correct analysis of the
+intellectual process called Reasoning or Inference, and of such other
+mental operations as are intended to facilitate this; as well as, on the
+foundation of this analysis, and _pari passu_ with it, to bring together
+or frame a set of rules or canons for testing the sufficiency of any
+given evidence to prove any given proposition.
+
+With respect to the first part of this undertaking, I do not attempt to
+decompose the mental operations in question into their ultimate
+elements. It is enough if the analysis as far as it goes is correct,
+and if it goes far enough for the practical purposes of logic considered
+as an art. The separation of a complicated phenomenon into its component
+parts is not like a connected and interdependent chain of proof. If one
+link of an argument breaks, the whole drops to the ground; but one step
+towards an analysis holds good and has an independent value, though we
+should never be able to make a second. The results which have been
+obtained by analytical chemistry are not the less valuable, though it
+should be discovered that all which we now call simple substances are
+really compounds. All other things are at any rate compounded of those
+elements: whether the elements themselves admit of decomposition, is an
+important inquiry, but does not affect the certainty of the science up
+to that point.
+
+I shall, accordingly, attempt to analyse the process of inference, and
+the processes subordinate to inference, so far only as may be requisite
+for ascertaining the difference between a correct and an incorrect
+performance of those processes. The reason for thus limiting our design,
+is evident. It has been said by objectors to logic, that we do not learn
+to use our muscles by studying their anatomy. The fact is not quite
+fairly stated; for if the action of any of our muscles were vitiated by
+local weakness, or other physical defect, a knowledge of their anatomy
+might be very necessary for effecting a cure. But we should be justly
+liable to the criticism involved in this objection, were we, in a
+treatise on logic, to carry the analysis of the reasoning process beyond
+the point at which any inaccuracy which may have crept into it must
+become visible. In learning bodily exercises (to carry on the same
+illustration) we do, and must, analyse the bodily motions so far as is
+necessary for distinguishing those which ought to be performed from
+those which ought not. To a similar extent, and no further, it is
+necessary that the logician should analyse the mental processes with
+which Logic is concerned. Logic has no interest in carrying the analysis
+beyond the point at which it becomes apparent whether the operations
+have in any individual case been rightly or wrongly performed: in the
+same manner as the science of music teaches us to discriminate between
+musical notes, and to know the combinations of which they are
+susceptible, but not what number of vibrations in a second correspond to
+each; which, though useful to be known, is useful for totally different
+purposes. The extension of Logic as a Science is determined by its
+necessities as an Art: whatever it does not need for its practical ends,
+it leaves to the larger science which may be said to correspond, not to
+any particular art, but to art in general; the science which deals with
+the constitution of the human faculties; and to which, in the part of
+our mental nature which concerns Logic, as well as in all other parts,
+it belongs to decide what are ultimate facts, and what are resolvable
+into other facts. And I believe it will be found that most of the
+conclusions arrived at in this work have no necessary connexion with any
+particular views respecting the ulterior analysis. Logic is common
+ground on which the partisans of Hartley and of Reid, of Locke and of
+Kant, may meet and join hands. Particular and detached opinions of all
+these thinkers will no doubt occasionally be controverted, since all of
+them were logicians as well as metaphysicians; but the field on which
+their principal battles have been fought, lies beyond the boundaries of
+our science.
+
+It cannot, indeed, be pretended that logical principles can be
+altogether irrelevant to those more abstruse discussions; nor is it
+possible but that the view we are led to take of the problem which logic
+proposes, must have a tendency favourable to the adoption of some one
+opinion, on these controverted subjects, rather than another. For
+metaphysics, in endeavouring to solve its own peculiar problem, must
+employ means, the validity of which falls under the cognizance of logic.
+It proceeds, no doubt, as far as possible, merely by a closer and more
+attentive interrogation of our consciousness, or more properly speaking,
+of our memory; and so far is not amenable to logic. But wherever this
+method is insufficient to attain the end of its inquiries, it must
+proceed, like other sciences, by means of evidence. Now, the moment this
+science begins to draw inferences from evidence, logic becomes the
+sovereign judge whether its inferences are well grounded, or what other
+inferences would be so.
+
+This, however, constitutes no nearer or other relation between logic
+and metaphysics, than that which exists between logic and every other
+science. And I can conscientiously affirm, that no one proposition laid
+down in this work has been adopted for the sake of establishing, or with
+any reference to its fitness for being employed in establishing,
+preconceived opinions in any department of knowledge or of inquiry on
+which the speculative world is still undecided.[4]
+
+FOOTNOTES:
+
+[1] Archbishop Whately.
+
+[2] I use these terms indiscriminately, because, for the purpose in
+view, there is no need for making any distinction between them. But
+metaphysicians usually restrict the name Intuition to the direct
+knowledge we are supposed to have of things external to our minds, and
+Consciousness to our knowledge of our own mental phenomena.
+
+[3] This important theory has of late been called in question by a
+writer of deserved reputation, Mr. Samuel Bailey; but I do not conceive
+that the grounds on which it has been admitted as an established
+doctrine for a century past, have been at all shaken by that gentleman's
+objections. I have elsewhere said what appeared to me necessary in reply
+to his arguments. (_Westminster Review_ for October 1842; reprinted in
+_Dissertations and Discussions_, vol. ii.)
+
+[4] The view taken in the text, of the definition and purpose of Logic,
+stands in marked opposition to that of the school of philosophy which,
+in this country, is represented by the writings of Sir William Hamilton
+and of his numerous pupils. Logic, as this school conceives it, is "the
+Science of the Formal Laws of Thought;" a definition framed for the
+express purpose of excluding, as irrelevant to Logic, whatever relates
+to Belief and Disbelief, or to the pursuit of truth as such, and
+restricting the science to that very limited portion of its total
+province, which has reference to the conditions, not of Truth, but of
+Consistency. What I have thought it useful to say in opposition to this
+limitation of the field of Logic, has been said at some length in a
+separate work, first published in 1865, and entitled _An Examination of
+Sir William Hamilton's Philosophy, and of the Principal Philosophical
+Questions discussed in his Writings_. For the purposes of the present
+Treatise, I am content that the justification of the larger extension
+which I give to the domain of the science, should rest on the sequel of
+the Treatise itself. Some remarks on the relation which the Logic of
+Consistency bears to the Logic of Truth, and on the place which that
+particular part occupies in the whole to which it belongs, will be found
+in the present volume (Book II. chap. iii. Sec. 9).
+
+
+
+
+BOOK I.
+
+OF NAMES AND PROPOSITIONS.
+
+
+'La scolastique, qui produisit dans la logique, comme dans la morale,
+et dans une partie de la metaphysique, une subtilite, une precision
+d'idees, dont l'habitude inconnue aux anciens, a contribue plus qu'on ne
+croit au progres de la bonne philosophie.'--CONDORCET, _Vie de Turgot_.
+
+'To the schoolmen the vulgar languages are principally indebted for what
+precision and analytic subtlety they possess.'--SIR W. HAMILTON,
+_Discussions in Philosophy_.
+
+
+
+
+CHAPTER I.
+
+OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.
+
+
+Sec. 1. It is so much the established practice of writers on logic to
+commence their treatises by a few general observations (in most cases,
+it is true, rather meagre) on Terms and their varieties, that it will,
+perhaps, scarcely be required from me in merely following the common
+usage, to be as particular in assigning my reasons, as it is usually
+expected that those should be who deviate from it.
+
+The practice, indeed, is recommended by considerations far too obvious
+to require a formal justification. Logic is a portion of the Art of
+Thinking: Language is evidently, and by the admission of all
+philosophers, one of the principal instruments or helps of thought; and
+any imperfection in the instrument, or in the mode of employing it, is
+confessedly liable, still more than in almost any other art, to confuse
+and impede the process, and destroy all ground of confidence in the
+result. For a mind not previously versed in the meaning and right use of
+the various kinds of words, to attempt the study of methods of
+philosophizing, would be as if some one should attempt to become an
+astronomical observer, having never learned to adjust the focal distance
+of his optical instruments so as to see distinctly.
+
+Since Reasoning, or Inference, the principal subject of logic, is an
+operation which usually takes place by means of words, and in
+complicated cases can take place in no other way; those who have not a
+thorough insight into the signification and purposes of words, will be
+under chances, amounting almost to certainty, of reasoning or inferring
+incorrectly. And logicians have generally felt that unless, in the very
+first stage, they removed this source of error; unless they taught their
+pupil to put away the glasses which distort the object, and to use
+those which are adapted to his purpose in such a manner as to assist,
+not perplex, his vision; he would not be in a condition to practise the
+remaining part of their discipline with any prospect of advantage.
+Therefore it is that an inquiry into language, so far as is needful to
+guard against the errors to which it gives rise, has at all times been
+deemed a necessary preliminary to the study of logic.
+
+But there is another reason, of a still more fundamental nature, why the
+import of words should be the earliest subject of the logician's
+consideration: because without it he cannot examine into the import of
+Propositions. Now this is a subject which stands on the very threshold
+of the science of logic.
+
+The object of logic, as defined in the Introductory Chapter, is to
+ascertain how we come by that portion of our knowledge (much the
+greatest portion) which is not intuitive: and by what criterion we can,
+in matters not self-evident, distinguish between things proved and
+things not proved, between what is worthy and what is unworthy of
+belief. Of the various questions which present themselves to our
+inquiring faculties, some receive an answer from direct consciousness,
+others, if resolved at all, can only be resolved by means of evidence.
+Logic is concerned with these last. But before inquiring into the mode
+of resolving questions, it is necessary to inquire what are those which
+offer themselves; what questions are conceivable; what inquiries are
+there, to which mankind have either obtained, or been able to imagine it
+possible that they should obtain, an answer. This point is best
+ascertained by a survey and analysis of Propositions.
+
+
+Sec. 2. The answer to every question which it is possible to frame, must be
+contained in a Proposition, or Assertion. Whatever can be an object of
+belief, or even of disbelief, must, when put into words, assume the form
+of a proposition. All truth and all error lie in propositions. What, by
+a convenient misapplication of an abstract term, we call a Truth, means
+simply a True Proposition; and errors are false propositions. To know
+the import of all possible propositions, would be to know all questions
+which can be raised, all matters which are susceptible of being either
+believed or disbelieved. How many kinds of inquiries can be propounded;
+how many kinds of judgments can be made; and how many kinds of
+propositions it is possible to frame with a meaning; are but different
+forms of one and the same question. Since, then, the objects of all
+Belief and of all Inquiry express themselves in propositions; a
+sufficient scrutiny of Propositions and of their varieties will apprize
+us what questions mankind have actually asked of themselves, and what,
+in the nature of answers to those questions, they have actually thought
+they had grounds to believe.
+
+Now the first glance at a proposition shows that it is formed by putting
+together two names. A proposition, according to the common simple
+definition, which is sufficient for our purpose, is, _discourse, in
+which something is affirmed or denied of something_. Thus, in the
+proposition, Gold is yellow, the quality _yellow_ is affirmed of the
+substance _gold_. In the proposition, Franklin was not born in England,
+the fact expressed by the words _born in England_ is denied of the man
+Franklin.
+
+Every proposition consists of three parts: the Subject, the Predicate,
+and the Copula. The predicate is the name denoting that which is
+affirmed or denied. The subject is the name denoting the person or thing
+which something is affirmed or denied of. The copula is the sign
+denoting that there is an affirmation or denial; and thereby enabling
+the hearer or reader to distinguish a proposition from any other kind of
+discourse. Thus, in the proposition, The earth is round, the Predicate
+is the word _round_, which denotes the quality affirmed, or (as the
+phrase is) predicated: _the earth_, words denoting the object which that
+quality is affirmed of, compose the Subject; the word _is_, which serves
+as the connecting mark between the subject and predicate, to show that
+one of them is affirmed of the other, is called the Copula.
+
+Dismissing, for the present, the copula, of which more will be said
+hereafter, every proposition, then, consists of at least two names;
+brings together two names, in a particular manner. This is already a
+first step towards what we are in quest of. It appears from this, that
+for an act of belief, _one_ object is not sufficient; the simplest act
+of belief supposes, and has something to do with, _two_ objects: two
+names, to say the least; and (since the names must be names of
+something) two _nameable things_. A large class of thinkers would cut
+the matter short by saying, two _ideas_. They would say, that the
+subject and predicate are both of them names of ideas; the idea of gold,
+for instance, and the idea of yellow; and that what takes place (or part
+of what takes place) in the act of belief, consists in bringing (as it
+is often expressed) one of these ideas under the other. But this we are
+not yet in a condition to say: whether such be the correct mode of
+describing the phenomenon, is an after consideration. The result with
+which for the present we must be contented, is, that in every act of
+belief _two_ objects are in some manner taken cognizance of; that there
+can be no belief claimed, or question propounded, which does not embrace
+two distinct (either material or intellectual) subjects of thought; each
+of them capable, or not, of being conceived by itself, but incapable of
+being believed by itself.
+
+I may say, for instance, "the sun." The word has a meaning, and suggests
+that meaning to the mind of any one who is listening to me. But suppose
+I ask him, Whether it is true: whether he believes it? He can give no
+answer. There is as yet nothing to believe, or to disbelieve. Now,
+however, let me make, of all possible assertions respecting the sun, the
+one which involves the least of reference to any object besides itself;
+let me say, "the sun exists." Here, at once, is something which a person
+can say he believes. But here, instead of only one, we find two distinct
+objects of conception: the sun is one object; existence is another. Let
+it not be said that this second conception, existence, is involved in
+the first; for the sun may be conceived as no longer existing. "The sun"
+does not convey all the meaning that is conveyed by "the sun exists:"
+"my father" does not include all the meaning of "my father exists," for
+he may be dead; "a round square" does not include the meaning of "a
+round square exists," for it does not and cannot exist. When I say "the
+sun," "my father," or a "round square," I do not call upon the hearer
+for any belief or disbelief, nor can either the one or the other be
+afforded me; but if I say, "the sun exists," "my father exists," or "a
+round square exists," I call for belief; and should, in the first of the
+three instances, meet with it; in the second, with belief or disbelief,
+as the case might be; in the third, with disbelief.
+
+
+Sec. 3. This first step in the analysis of the object of belief, which,
+though so obvious, will be found to be not unimportant, is the only one
+which we shall find it practicable to make without a preliminary survey
+of language. If we attempt to proceed further in the same path, that is,
+to analyse any further the import of Propositions; we find forced upon
+us, as a subject of previous consideration, the import of Names. For
+every proposition consists of two names; and every proposition affirms
+or denies one of these names, of the other. Now what we do, what passes
+in our mind, when we affirm or deny two names of one another, must
+depend on what they are names of; since it is with reference to that,
+and not to the mere names themselves, that we make the affirmation or
+denial. Here, therefore, we find a new reason why the signification of
+names, and the relation generally between names and the things signified
+by them, must occupy the preliminary stage of the inquiry we are engaged
+in.
+
+It may be objected that the meaning of names can guide us at most only
+to the opinions, possibly the foolish and groundless opinions, which
+mankind have formed concerning things, and that as the object of
+philosophy is truth, not opinion, the philosopher should dismiss words
+and look into things themselves, to ascertain what questions can be
+asked and answered in regard to them. This advice (which no one has it
+in his power to follow) is in reality an exhortation to discard the
+whole fruits of the labours of his predecessors, and conduct himself as
+if he were the first person who had ever turned an inquiring eye upon
+nature. What does any one's personal knowledge of Things amount to,
+after subtracting all which he has acquired by means of the words of
+other people? Even after he has learned as much as people usually do
+learn from others, will the notions of things contained in his
+individual mind afford as sufficient a basis for a _catalogue raisonne_
+as the notions which are in the minds of all mankind?
+
+In any enumeration and classification of Things, which does not set out
+from their names, no varieties of things will of course be comprehended
+but those recognised by the particular inquirer; and it will still
+remain to be established, by a subsequent examination of names, that the
+enumeration has omitted nothing which ought to have been included. But
+if we begin with names, and use them as our clue to the things, we bring
+at once before us all the distinctions which have been recognised, not
+by a single inquirer, but by all inquirers taken together. It doubtless
+may, and I believe it will, be found, that mankind have multiplied the
+varieties unnecessarily, and have imagined distinctions among things,
+where there were only distinctions in the manner of naming them. But we
+are not entitled to assume this in the commencement. We must begin by
+recognising the distinctions made by ordinary language. If some of these
+appear, on a close examination, not to be fundamental, the enumeration
+of the different kinds of realities may be abridged accordingly. But to
+impose upon the facts in the first instance the yoke of a theory, while
+the grounds of the theory are reserved for discussion in a subsequent
+stage, is not a course which a logician can reasonably adopt.
+
+
+
+
+CHAPTER II.
+
+OF NAMES.
+
+
+Sec. 1. "A name," says Hobbes,[1] "is a word taken at pleasure to serve for
+a mark which may raise in our mind a thought like to some thought we had
+before, and which being pronounced to others, may be to them a sign of
+what thought the speaker had[2] before in his mind." This simple
+definition of a name, as a word (or set of words) serving the double
+purpose of a mark to recall to ourselves the likeness of a former
+thought, and a sign to make it known to others, appears unexceptionable.
+Names, indeed, do much more than this; but whatever else they do, grows
+out of, and is the result of this: as will appear in its proper place.
+
+Are names more properly said to be the names of things, or of our ideas
+of things? The first is the expression in common use; the last is that
+of some metaphysicians, who conceived that in adopting it they were
+introducing a highly important distinction. The eminent thinker, just
+quoted, seems to countenance the latter opinion. "But seeing," he
+continues, "names ordered in speech (as is defined) are signs of our
+conceptions, it is manifest they are not signs of the things themselves;
+for that the sound of this word _stone_ should be the sign of a stone,
+cannot be understood in any sense but this, that he that hears it
+collects that he that pronounces it thinks of a stone."
+
+If it be merely meant that the conception alone, and not the thing
+itself, is recalled by the name, or imparted to the hearer, this of
+course cannot be denied. Nevertheless, there seems good reason for
+adhering to the common usage, and calling the word _sun_ the name of
+the sun, and not the name of our idea of the sun. For names are not
+intended only to make the hearer conceive what we conceive, but also to
+inform him what we believe. Now, when I use a name for the purpose of
+expressing a belief, it is a belief concerning the thing itself, not
+concerning my idea of it. When I say, "the sun is the cause of day," I
+do not mean that my idea of the sun causes or excites in me the idea of
+day; or in other words, that thinking of the sun makes me think of day.
+I mean, that a certain physical fact, which is called the sun's presence
+(and which, in the ultimate analysis, resolves itself into sensations,
+not ideas) causes another physical fact, which is called day. It seems
+proper to consider a word as the _name_ of that which we intend to be
+understood by it when we use it; of that which any fact that we assert
+of it is to be understood of; that, in short, concerning which, when we
+employ the word, we intend to give information. Names, therefore, shall
+always be spoken of in this work as the names of things themselves, and
+not merely of our ideas of things.
+
+But the question now arises, of what things? and to answer this it is
+necessary to take into consideration the different kinds of names.
+
+
+Sec. 2. It is usual, before examining the various classes into which names
+are commonly divided, to begin by distinguishing from names of every
+description, those words which are not names, but only parts of names.
+Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
+inflected cases of nouns substantive, as _me_, _him_, _John's_; and even
+adjectives, as _large_, _heavy_. These words do not express things of
+which anything can be affirmed or denied. We cannot say, Heavy fell, or
+A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
+room. Unless, indeed, we are speaking of the mere words themselves, as
+when we say, Truly is an English word, or, Heavy is an adjective. In
+that case they are complete names, viz. names of those particular
+sounds, or of those particular collections of written characters. This
+employment of a word to denote the mere letters and syllables of which
+it is composed, was termed by the schoolmen the _suppositio materialis_
+of the word. In any other sense we cannot introduce one of these words
+into the subject of a proposition, unless in combination with other
+words; as, A heavy _body_ fell, A truly _important fact_ was asserted, A
+_member_ of _parliament_ was in the room.
+
+An adjective, however, is capable of standing by itself as the predicate
+of a proposition; as when we say, Snow is white; and occasionally even
+as the subject, for we may say, White is an agreeable colour. The
+adjective is often said to be so used by a grammatical ellipsis: Snow is
+white, instead of Snow is a white object; White is an agreeable colour,
+instead of, A white colour, or, The colour white, is agreeable. The
+Greeks and Romans were allowed, by the rules of their language, to
+employ this ellipsis universally in the subject as well as in the
+predicate of a proposition. In English this cannot, generally speaking,
+be done. We may say, The earth is round; but we cannot say, Round is
+easily moved; we must say, A round object. This distinction, however, is
+rather grammatical than logical. Since there is no difference of meaning
+between _round_, and _a round object_, it is only custom which
+prescribes that on any given occasion one shall be used, and not the
+other. We shall, therefore, without scruple, speak of adjectives as
+names, whether in their own right, or as representative of the more
+circuitous forms of expression above exemplified. The other classes of
+subsidiary words have no title whatever to be considered as names. An
+adverb, or an accusative case, cannot under any circumstances (except
+when their mere letters and syllables are spoken of) figure as one of
+the terms of a proposition.
+
+Words which are not capable of being used as names, but only as parts of
+names, were called by some of the schoolmen Syncategorematic terms: from
+[Greek: syn], with, and [Greek: kategoreo], to predicate, because it was
+only _with_ some other word that they could be predicated. A word which
+could be used either as the subject or predicate of a proposition
+without being accompanied by any other word, was termed by the same
+authorities a Categorematic term. A combination of one or more
+Categorematic, and one or more Syncategorematic words, as A heavy body,
+or A court of justice, they sometimes called a _mixed_ term; but this
+seems a needless multiplication of technical expressions. A mixed term
+is, in the only useful sense of the word, Categorematic. It belongs to
+the class of what have been called many-worded names.
+
+For, as one word is frequently not a name, but only part of a name, so a
+number of words often compose one single name, and no more. These words,
+"the place which the wisdom or policy of antiquity had destined for the
+residence of the Abyssinian princes," form in the estimation of the
+logician only one name; one Categorematic term. A mode of determining
+whether any set of words makes only one name, or more than one, is by
+predicating something of it, and observing whether, by this predication,
+we make only one assertion or several. Thus, when we say, John Nokes,
+who was the mayor of the town, died yesterday--by this predication we
+make but one assertion; whence it appears that "John Nokes, who was the
+mayor of the town," is no more than one name. It is true that in this
+proposition, besides the assertion that John Nokes died yesterday, there
+is included another assertion, namely, that John Nokes was mayor of the
+town. But this last assertion was already made: we did not make it by
+adding the predicate, "died yesterday." Suppose, however, that the words
+had been, John Nokes _and_ the mayor of the town, they would have formed
+two names instead of one. For when we say, John Nokes and the mayor of
+the town died yesterday, we make two assertions; one, that John Nokes
+died yesterday; the other, that the mayor of the town died yesterday.
+
+It being needless to illustrate at any greater length the subject of
+many-worded names, we proceed to the distinctions which have been
+established among names, not according to the words they are composed
+of, but according to their signification.
+
+
+Sec. 3. All names are names of something, real or imaginary; but all things
+have not names appropriated to them individually. For some individual
+objects we require, and consequently have, separate distinguishing
+names; there is a name for every person, and for every remarkable place.
+Other objects, of which we have not occasion to speak so frequently, we
+do not designate by a name of their own; but when the necessity arises
+for naming them, we do so by putting together several words, each of
+which, by itself, might be and is used for an indefinite number of other
+objects; as when I say, _this stone_: "this" and "stone" being, each of
+them, names that may be used of many other objects besides the
+particular one meant, though the only object of which they can both be
+used at the given moment, consistently with their signification, may be
+the one of which I wish to speak.
+
+Were this the sole purpose for which names, that are common to more
+things than one, could be employed; if they only served, by mutually
+limiting each other, to afford a designation for such individual objects
+as have no names of their own; they could only be ranked among
+contrivances for economizing the use of language. But it is evident that
+this is not their sole function. It is by their means that we are
+enabled to assert _general_ propositions; to affirm or deny any
+predicate of an indefinite number of things at once. The distinction,
+therefore, between _general_ names, and _individual_ or _singular_
+names, is fundamental; and may be considered as the first grand division
+of names.
+
+A general name is familiarly defined, a name which is capable of being
+truly affirmed, in the same sense, of each of an indefinite number of
+things. An individual or singular name is a name which is only capable
+of being truly affirmed, in the same sense, of one thing.
+
+Thus, _man_ is capable of being truly affirmed of John, George, Mary,
+and other persons without assignable limit; and it is affirmed of all of
+them in the same sense; for the word man expresses certain qualities,
+and when we predicate it of those persons, we assert that they all
+possess those qualities. But _John_ is only capable of being truly
+affirmed of one single person, at least in the same sense. For though
+there are many persons who bear that name, it is not conferred upon
+them to indicate any qualities, or anything which belongs to them in
+common; and cannot be said to be affirmed of them in any _sense_ at all,
+consequently not in the same sense. "The king who succeeded William the
+Conqueror," is also an individual name. For, that there cannot be more
+than one person of whom it can be truly affirmed, is implied in the
+meaning of the words. Even "_the_ king," when the occasion or the
+context defines the individual of whom it is to be understood, may
+justly be regarded as an individual name.
+
+It is not unusual, by way of explaining what is meant by a general name,
+to say that it is the name of a _class_. But this, though a convenient
+mode of expression for some purposes, is objectionable as a definition,
+since it explains the clearer of two things by the more obscure. It
+would be more logical to reverse the proposition, and turn it into a
+definition of the word _class_: "A class is the indefinite multitude of
+individuals denoted by a general name."
+
+It is necessary to distinguish _general_ from _collective_ names. A
+general name is one which can be predicated of _each_ individual of a
+multitude; a collective name cannot be predicated of each separately,
+but only of all taken together. "The 76th regiment of foot in the
+British army," which is a collective name, is not a general but an
+individual name; for though it can be predicated of a multitude of
+individual soldiers taken jointly, it cannot be predicated of them
+severally. We may say, Jones is a soldier, and Thompson is a soldier,
+and Smith is a soldier, but we cannot say, Jones is the 76th regiment,
+and Thompson is the 76th regiment, and Smith is the 76th regiment. We
+can only say, Jones, and Thompson, and Smith, and Brown, and so forth
+(enumerating all the soldiers), are the 76th regiment.
+
+"The 76th regiment" is a collective name, but not a general one: "a
+regiment" is both a collective and a general name. General with respect
+to all individual regiments, of each of which separately it can be
+affirmed; collective with respect to the individual soldiers of whom any
+regiment is composed.
+
+
+Sec. 4. The second general division of names is into _concrete_ and
+_abstract_. A concrete name is a name which stands for a thing; an
+abstract name is a name which stands for an attribute of a thing. Thus
+_John_, _the sea_, _this table_, are names of things. _White_, also, is
+a name of a thing, or rather of things. Whiteness, again, is the name of
+a quality or attribute of those things. Man is a name of many things;
+humanity is a name of an attribute of those things. _Old_ is a name of
+things; _old age_ is a name of one of their attributes.
+
+I have used the words concrete and abstract in the sense annexed to them
+by the schoolmen, who, notwithstanding the imperfections of their
+philosophy, were unrivalled in the construction of technical language,
+and whose definitions, in logic at least, though they never went more
+than a little way into the subject, have seldom, I think, been altered
+but to be spoiled. A practice, however, has grown up in more modern
+times, which, if not introduced by Locke, has gained currency chiefly
+from his example, of applying the expression "abstract name" to all
+names which are the result of abstraction or generalization, and
+consequently to all general names, instead of confining it to the names
+of attributes. The metaphysicians of the Condillac school,--whose
+admiration of Locke, passing over the profoundest speculations of that
+truly original genius, usually fastens with peculiar eagerness upon his
+weakest points,--have gone on imitating him in this abuse of language,
+until there is now some difficulty in restoring the word to its original
+signification. A more wanton alteration in the meaning of a word is
+rarely to be met with; for the expression _general name_, the exact
+equivalent of which exists in all languages I am acquainted with, was
+already available for the purpose to which _abstract_ has been
+misappropriated, while the misappropriation leaves that important class
+of words, the names of attributes, without any compact distinctive
+appellation. The old acceptation, however, has not gone so completely
+out of use, as to deprive those who still adhere to it of all chance of
+being understood. By _abstract_, then, I shall always, in Logic, mean
+the opposite of _concrete_: by an abstract name, the name of an
+attribute; by a concrete name, the name of an object.
+
+Do abstract names belong to the class of general, or to that of singular
+names? Some of them are certainly general. I mean those which are names
+not of one single and definite attribute, but of a class of attributes.
+Such is the word _colour_, which is a name common to whiteness, redness,
+&c. Such is even the word whiteness, in respect of the different shades
+of whiteness to which it is applied in common; the word magnitude, in
+respect of the various degrees of magnitude and the various dimensions
+of space; the word weight, in respect of the various degrees of weight.
+Such also is the word _attribute_ itself, the common name of all
+particular attributes. But when only one attribute, neither variable in
+degree nor in kind, is designated by the name; as visibleness;
+tangibleness; equality; squareness; milkwhiteness; then the name can
+hardly be considered general; for though it denotes an attribute of many
+different objects, the attribute itself is always conceived as one, not
+many.[3] To avoid needless logomachies, the best course would probably
+be to consider these names as neither general nor individual, and to
+place them in a class apart.
+
+It may be objected to our definition of an abstract name, that not only
+the names which we have called abstract, but adjectives, which we have
+placed in the concrete class, are names of attributes; that _white_, for
+example, is as much the name of the colour as _whiteness_ is. But (as
+before remarked) a word ought to be considered as the name of that which
+we intend to be understood by it when we put it to its principal use,
+that is, when we employ it in predication. When we say snow is white,
+milk is white, linen is white, we do not mean it to be understood that
+snow, or linen, or milk, is a colour. We mean that they are things
+having the colour. The reverse is the case with the word whiteness; what
+we affirm to _be_ whiteness is not snow, but the colour of snow.
+Whiteness, therefore, is the name of the colour exclusively: white is a
+name of all things whatever having the colour; a name, not of the
+quality whiteness, but of every white object. It is true, this name was
+given to all those various objects on account of the quality; and we may
+therefore say, without impropriety, that the quality forms part of its
+signification; but a name can only be said to stand for, or to be a name
+of, the things of which it can be predicated. We shall presently see
+that all names which can be said to have any signification, all names by
+applying which to an individual we give any information respecting that
+individual, may be said to _imply_ an attribute of some sort; but they
+are not names of the attribute; it has its own proper abstract name.
+
+
+Sec. 5. This leads to the consideration of a third great division of names,
+into _connotative_ and _non-connotative_, the latter sometimes, but
+improperly, called _absolute_. This is one of the most important
+distinctions which we shall have occasion to point out, and one of those
+which go deepest into the nature of language.
+
+A non-connotative term is one which signifies a subject only, or an
+attribute only. A connotative term is one which denotes a subject, and
+implies an attribute. By a subject is here meant anything which
+possesses attributes. Thus John, or London, or England, are names which
+signify a subject only. Whiteness, length, virtue, signify an attribute
+only. None of these names, therefore, are connotative. But _white_,
+_long_, _virtuous_, are connotative. The word white, denotes all white
+things, as snow, paper, the foam of the sea, &c., and implies, or as it
+was termed by the schoolmen, _connotes_[4], the attribute _whiteness_.
+The word white is not predicated of the attribute, but of the subjects,
+snow, &c.; but when we predicate it of them, we imply, or connote, that
+the attribute whiteness belongs to them. The same may be said of the
+other words above cited. Virtuous, for example, is the name of a class,
+which includes Socrates, Howard, the Man of Ross, and an undefinable
+number of other individuals, past, present, and to come. These
+individuals, collectively and severally, can alone be said with
+propriety to be denoted by the word: of them alone can it properly be
+said to be a name. But it is a name applied to all of them in
+consequence of an attribute which they are supposed to possess in
+common, the attribute which has received the name of virtue. It is
+applied to all beings that are considered to possess this attribute; and
+to none which are not so considered.
+
+All concrete general names are connotative. The word _man_, for example,
+denotes Peter, Jane, John, and an indefinite number of other
+individuals, of whom, taken as a class, it is the name. But it is
+applied to them, because they possess, and to signify that they possess,
+certain attributes. These seem to be, corporeity, animal life,
+rationality, and a certain external form, which for distinction we call
+the human. Every existing thing, which possessed all these attributes,
+would be called a man; and anything which possessed none of them, or
+only one, or two, or even three of them without the fourth, would not be
+so called. For example, if in the interior of Africa there were to be
+discovered a race of animals possessing reason equal to that of human
+beings, but with the form of an elephant, they would not be called men.
+Swift's Houyhnhnms would not be so called. Or if such newly-discovered
+beings possessed the form of man without any vestige of reason, it is
+probable that some other name than that of man would be found for them.
+How it happens that there can be any doubt about the matter, will appear
+hereafter. The word _man_, therefore, signifies all these attributes,
+and all subjects which possess these attributes. But it can be
+predicated only of the subjects. What we call men, are the subjects, the
+individual Stiles and Nokes; not the qualities by which their humanity
+is constituted. The name, therefore, is said to signify the subjects
+_directly_, the attributes _indirectly_; it _denotes_ the subjects, and
+implies, or involves, or indicates, or as we shall say henceforth
+_connotes_, the attributes. It is a connotative name.
+
+Connotative names have hence been also called _denominative_, because
+the subject which they denote is denominated by, or receives a name
+from, the attribute which they connote. Snow, and other objects, receive
+the name white, because they possess the attribute which is called
+whiteness; Peter, James, and others receive the name man, because they
+possess the attributes which are considered to constitute humanity. The
+attribute, or attributes, may therefore be said to denominate those
+objects, or to give them a common name.[5]
+
+It has been seen that all concrete general names are connotative. Even
+abstract names, though the names only of attributes, may in some
+instances be justly considered as connotative; for attributes themselves
+may have attributes ascribed to them; and a word which denotes
+attributes may connote an attribute of those attributes. Of this
+description, for example, is such a word as _fault_; equivalent to _bad_
+or _hurtful quality_. This word is a name common to many attributes, and
+connotes hurtfulness, an attribute of those various attributes. When,
+for example, we say that slowness, in a horse, is a fault, we do not
+mean that the slow movement, the actual change of place of the slow
+horse, is a bad thing, but that the property or peculiarity of the
+horse, from which it derives that name, the quality of being a slow
+mover, is an undesirable peculiarity.
+
+In regard to those concrete names which are not general but individual,
+a distinction must be made.
+
+Proper names are not connotative: they denote the individuals who are
+called by them; but they do not indicate or imply any attributes as
+belonging to those individuals. When we name a child by the name Paul,
+or a dog by the name Caesar, these names are simply marks used to enable
+those individuals to be made subjects of discourse. It may be said,
+indeed, that we must have had some reason for giving them those names
+rather than any others; and this is true; but the name, once given, is
+independent of the reason. A man may have been named John, because that
+was the name of his father; a town may have been named Dartmouth,
+because it is situated at the mouth of the Dart. But it is no part of
+the signification of the word John, that the father of the person so
+called bore the same name; nor even of the word Dartmouth, to be
+situated at the mouth of the Dart. If sand should choke up the mouth of
+the river, or an earthquake change its course, and remove it to a
+distance from the town, the name of the town would not necessarily be
+changed. That fact, therefore, can form no part of the signification of
+the word; for otherwise, when the fact confessedly ceased to be true, no
+one would any longer think of applying the name. Proper names are
+attached to the objects themselves, and are not dependent on the
+continuance of any attribute of the object.
+
+But there is another kind of names, which, although they are individual
+names, that is, predicable only of one object, are really connotative.
+For, though we may give to an individual a name utterly unmeaning, which
+we call a proper name,--a word which answers the purpose of showing what
+thing it is we are talking about, but not of telling anything about it;
+yet a name peculiar to an individual is not necessarily of this
+description. It may be significant of some attribute, or some union of
+attributes, which, being possessed by no object but one, determines the
+name exclusively to that individual. "The sun" is a name of this
+description; "God," when used by a monotheist, is another. These,
+however, are scarcely examples of what we are now attempting to
+illustrate, being, in strictness of language, general, not individual
+names: for, however they may be _in fact_ predicable only of one object,
+there is nothing in the meaning of the words themselves which implies
+this: and, accordingly, when we are imagining and not affirming, we may
+speak of many suns; and the majority of mankind have believed, and still
+believe, that there are many gods. But it is easy to produce words which
+are real instances of connotative individual names. It may be part of
+the meaning of the connotative name itself, that there can exist but
+one individual possessing the attribute which it connotes: as, for
+instance, "the _only_ son of John Stiles;" "the _first_ emperor of
+Rome." Or the attribute connoted may be a connexion with some
+determinate event, and the connexion may be of such a kind as only one
+individual could have; or may at least be such as only one individual
+actually had; and this may be implied in the form of the expression.
+"The father of Socrates" is an example of the one kind (since Socrates
+could not have had two fathers); "the author of the Iliad," "the
+murderer of Henri Quatre," of the second. For, though it is conceivable
+that more persons than one might have participated in the authorship of
+the Iliad, or in the murder of Henri Quatre, the employment of the
+article _the_ implies that, in fact, this was not the case. What is here
+done by the word _the_, is done in other cases by the context: thus,
+"Caesar's army" is an individual name, if it appears from the context
+that the army meant is that which Caesar commanded in a particular
+battle. The still more general expressions, "the Roman army," or "the
+Christian army," may be individualized in a similar manner. Another case
+of frequent occurrence has already been noticed; it is the following.
+The name, being a many-worded one, may consist, in the first place, of a
+_general_ name, capable therefore in itself of being affirmed of more
+things than one, but which is, in the second place, so limited by other
+words joined with it, that the entire expression can only be predicated
+of one object, consistently with the meaning of the general term. This
+is exemplified in such an instance as the following: "the present prime
+minister of England." Prime Minister of England is a general name; the
+attributes which it connotes may be possessed by an indefinite number of
+persons: in succession however, not simultaneously; since the meaning of
+the name itself imports (among other things) that there can be only one
+such person at a time. This being the case, and the application of the
+name being afterwards limited by the article and the word _present_, to
+such individuals as possess the attributes at one indivisible point of
+time, it becomes applicable only to one individual. And as this appears
+from the meaning of the name, without any extrinsic proof, it is
+strictly an individual name.
+
+From the preceding observations it will easily be collected, that
+whenever the names given to objects convey any information, that is,
+whenever they have properly any meaning, the meaning resides not in what
+they _denote_, but in what they _connote_. The only names of objects
+which connote nothing are _proper_ names; and these have, strictly
+speaking, no signification.[6]
+
+If, like the robber in the Arabian Nights, we make a mark with chalk on
+a house to enable us to know it again, the mark has a purpose, but it
+has not properly any meaning. The chalk does not declare anything about
+the house; it does not mean, This is such a person's house, or This is a
+house which contains booty. The object of making the mark is merely
+distinction. I say to myself, All these houses are so nearly alike that
+if I lose sight of them I shall not again be able to distinguish that
+which I am now looking at, from any of the others; I must therefore
+contrive to make the appearance of this one house unlike that of the
+others, that I may hereafter know, when I see the mark--not indeed any
+attribute of the house--but simply that it is the same house which I am
+now looking at. Morgiana chalked all the other houses in a similar
+manner, and defeated the scheme: how? simply by obliterating the
+difference of appearance between that house and the others. The chalk
+was still there, but it no longer served the purpose of a distinctive
+mark.
+
+When we impose a proper name, we perform an operation in some degree
+analogous to what the robber intended in chalking the house. We put a
+mark, not indeed upon the object itself, but, so to speak, upon the idea
+of the object. A proper name is but an unmeaning mark which we connect
+in our minds with the idea of the object, in order that whenever the
+mark meets our eyes or occurs to our thoughts, we may think of that
+individual object. Not being attached to the thing itself, it does not,
+like the chalk, enable us to distinguish the object when we see it; but
+it enables us to distinguish it when it is spoken of, either in the
+records of our own experience, or in the discourse of others; to know
+that what we find asserted in any proposition of which it is the
+subject, is asserted of the individual thing with which we were
+previously acquainted.
+
+When we predicate of anything its proper name; when we say, pointing to
+a man, this is Brown or Smith, or pointing to a city, that it is York,
+we do not, merely by so doing, convey to the hearer any information
+about them, except that those are their names. By enabling him to
+identify the individuals, we may connect them with information
+previously possessed by him; by saying, This is York, we may tell him
+that it contains the Minster. But this is in virtue of what he has
+previously heard concerning York; not by anything implied in the name.
+It is otherwise when objects are spoken of by connotative names. When we
+say, The town is built of marble, we give the hearer what may be
+entirely new information, and this merely by the signification of the
+many-worded connotative name, "built of marble." Such names are not
+signs of the mere objects, invented because we have occasion to think
+and speak of those objects individually; but signs which accompany an
+attribute: a kind of livery in which the attribute clothes all objects
+which are recognised as possessing it. They are not mere marks, but
+more, that is to say, significant marks; and the connotation is what
+constitutes their significance.
+
+As a proper name is said to be the name of the one individual which it
+is predicated of, so (as well from the importance of adhering to
+analogy, as for the other reasons formerly assigned) a connotative name
+ought to be considered a name of all the various individuals which it is
+predicable of, or in other words _denotes_, and not of what it connotes.
+But by learning what things it is a name of, we do not learn the meaning
+of the name: for to the same thing we may, with equal propriety, apply
+many names, not equivalent in meaning. Thus, I call a certain man by the
+name Sophroniscus: I call him by another name, The father of Socrates.
+Both these are names of the same individual, but their meaning is
+altogether different; they are applied to that individual for two
+different purposes; the one, merely to distinguish him from other
+persons who are spoken of; the other to indicate a fact relating to him,
+the fact that Socrates was his son. I further apply to him these other
+expressions: a man, a Greek, an Athenian, a sculptor, an old man, an
+honest man, a brave man. All these are, or may be, names of
+Sophroniscus, not indeed of him alone, but of him and each of an
+indefinite number of other human beings. Each of these names is applied
+to Sophroniscus for a different reason, and by each whoever understands
+its meaning is apprised of a distinct fact or number of facts concerning
+him; but those who knew nothing about the names except that they were
+applicable to Sophroniscus, would be altogether ignorant of their
+meaning. It is even possible that I might know every single individual
+of whom a given name could be with truth affirmed, and yet could not be
+said to know the meaning of the name. A child knows who are its brothers
+and sisters, long before it has any definite conception of the nature of
+the facts which are involved in the signification of those words.
+
+In some cases it is not easy to decide precisely how much a particular
+word does or does not connote; that is, we do not exactly know (the case
+not having arisen) what degree of difference in the object would
+occasion a difference in the name. Thus, it is clear that the word man,
+besides animal life and rationality, connotes also a certain external
+form; but it would be impossible to say precisely what form; that is, to
+decide how great a deviation from the form ordinarily found in the
+beings whom we are accustomed to call men, would suffice in a
+newly-discovered race to make us refuse them the name of man.
+Rationality, also, being a quality which admits of degrees, it has never
+been settled what is the lowest degree of that quality which would
+entitle any creature to be considered a human being. In all such cases,
+the meaning of the general name is so far unsettled and vague; mankind
+have not come to any positive agreement about the matter. When we come
+to treat of Classification, we shall have occasion to show under what
+conditions this vagueness may exist without practical inconvenience; and
+cases will appear in which the ends of language are better promoted by
+it than by complete precision; in order that, in natural history for
+instance, individuals or species of no very marked character may be
+ranged with those more strongly characterized individuals or species to
+which, in all their properties taken together, they bear the nearest
+resemblance.
+
+But this partial uncertainty in the connotation of names can only be
+free from mischief when guarded by strict precautions. One of the chief
+sources, indeed, of lax habits of thought, is the custom of using
+connotative terms without a distinctly ascertained connotation, and with
+no more precise notion of their meaning than can be loosely collected
+from observing what objects they are used to denote. It is in this
+manner that we all acquire, and inevitably so, our first knowledge of
+our vernacular language. A child learns the meaning of the words _man_,
+or _white_, by hearing them applied to a variety of individual objects,
+and finding out, by a process of generalization and analysis which he
+could not himself describe, what those different objects have in common.
+In the case of these two words the process is so easy as to require no
+assistance from culture; the objects called human beings, and the
+objects called white, differing from all others by qualities of a
+peculiarly definite and obvious character. But in many other cases,
+objects bear a general resemblance to one another, which leads to their
+being familiarly classed together under a common name, while, without
+more analytic habits than the generality of mankind possess, it is not
+immediately apparent what are the particular attributes, upon the
+possession of which in common by them all, their general resemblance
+depends. When this is the case, people use the name without any
+recognised connotation, that is, without any precise meaning; they talk,
+and consequently think, vaguely, and remain contented to attach only the
+same degree of significance to their own words, which a child three
+years old attaches to the words brother and sister. The child at least
+is seldom puzzled by the starting up of new individuals, on whom he is
+ignorant whether or not to confer the title; because there is usually an
+authority close at hand competent to solve all doubts. But a similar
+resource does not exist in the generality of cases; and new objects are
+continually presenting themselves to men, women, and children, which
+they are called upon to class _proprio motu_. They, accordingly, do this
+on no other principle than that of superficial similarity, giving to
+each new object the name of that familiar object, the idea of which it
+most readily recalls, or which, on a cursory inspection, it seems to
+them most to resemble: as an unknown substance found in the ground will
+be called, according to its texture, earth, sand, or a stone. In this
+manner, names creep on from subject to subject, until all traces of a
+common meaning sometimes disappear, and the word comes to denote a
+number of things not only independently of any common attribute, but
+which have actually no attribute in common; or none but what is shared
+by other things to which the name is capriciously refused. Even
+scientific writers have aided in this perversion of general language
+from its purpose; sometimes because, like the vulgar, they knew no
+better; and sometimes in deference to that aversion to admit new words,
+which induces mankind, on all subjects not considered technical, to
+attempt to make the original stock of names serve with but little
+augmentation to express a constantly increasing number of objects and
+distinctions, and, consequently, to express them in a manner
+progressively more and more imperfect.
+
+To what a degree this loose mode of classing and denominating objects
+has rendered the vocabulary of mental and moral philosophy unfit for the
+purposes of accurate thinking, is best known to whoever has most
+meditated on the present condition of those branches of knowledge.
+Since, however, the introduction of a new technical language as the
+vehicle of speculations on subjects belonging to the domain of daily
+discussion, is extremely difficult to effect, and would not be free from
+inconvenience even if effected, the problem for the philosopher, and one
+of the most difficult which he has to resolve, is, in retaining the
+existing phraseology, how best to alleviate its imperfections. This can
+only be accomplished by giving to every general concrete name which
+there is frequent occasion to predicate, a definite and fixed
+connotation; in order that it may be known what attributes, when we call
+an object by that name, we really mean to predicate of the object. And
+the question of most nicety is, how to give this fixed connotation to a
+name, with the least possible change in the objects which the name is
+habitually employed to denote; with the least possible disarrangement,
+either by adding or subtraction, of the group of objects which, in
+however imperfect a manner, it serves to circumscribe and hold together;
+and with the least vitiation of the truth of any propositions which are
+commonly received as true.
+
+This desirable purpose, of giving a fixed connotation where it is
+wanting, is the end aimed at whenever any one attempts to give a
+definition of a general name already in use; every definition of a
+connotative name being an attempt either merely to declare, or to
+declare and analyse, the connotation of the name. And the fact, that no
+questions which have arisen in the moral sciences have been subjects of
+keener controversy than the definitions of almost all the leading
+expressions, is a proof how great an extent the evil to which we have
+adverted has attained.
+
+Names with indeterminate connotation are not to be confounded with names
+which have more than one connotation, that is to say, ambiguous words. A
+word may have several meanings, but all of them fixed and recognised
+ones; as the word _post_, for example, or the word _box_, the various
+senses of which it would be endless to enumerate. And the paucity of
+existing names, in comparison with the demand for them, may often render
+it advisable and even necessary to retain a name in this multiplicity
+of acceptations, distinguishing these so clearly as to prevent their
+being confounded with one another. Such a word may be considered as two
+or more names, accidentally written and spoken alike.[7]
+
+
+Sec. 6. The fourth principal division of names, is into _positive_ and
+_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,
+_not-tree_, _not-good_. To every positive concrete name, a corresponding
+negative one might be framed. After giving a name to any one thing, or
+to any plurality of things, we might create a second name which should
+be a name of all things whatever, except that particular thing or
+things. These negative names are employed whenever we have occasion to
+speak collectively of all things other than some thing or class of
+things. When the positive name is connotative, the corresponding
+negative name is connotative likewise; but in a peculiar way, connoting
+not the presence but the absence of an attribute. Thus, _not-white_
+denotes all things whatever except white things; and connotes the
+attribute of not possessing whiteness. For the non-possession of any
+given attribute is also an attribute, and may receive a name as such;
+and thus negative concrete names may obtain negative abstract names to
+correspond to them.
+
+Names which are positive in form are often negative in reality, and
+others are really positive though their form is negative. The word
+_inconvenient_, for example, does not express the mere absence of
+convenience; it expresses a positive attribute, that of being the cause
+of discomfort or annoyance. So the word _unpleasant_, notwithstanding
+its negative form, does not connote the mere absence of pleasantness,
+but a less degree of what is signified by the word _painful_, which, it
+is hardly necessary to say, is positive. _Idle_, on the other hand, is a
+word which, though positive in form, expresses nothing but what would be
+signified either by the phrase _not working_, or by the phrase _not
+disposed to work_; and _sober_, either by _not drunk_ or by _not
+drunken_.
+
+There is a class of names called _privative_. A privative name is
+equivalent in its signification to a positive and a negative name taken
+together; being the name of something which has once had a particular
+attribute, or for some other reason might have been expected to have it,
+but which has it not. Such is the word _blind_, which is not equivalent
+to _not seeing_, or to _not capable of seeing_, for it would not, except
+by a poetical or rhetorical figure, be applied to stocks and stones. A
+thing is not usually said to be blind, unless the class to which it is
+most familiarly referred, or to which it is referred on the particular
+occasion, be chiefly composed of things which can see, as in the case of
+a blind man, or a blind horse; or unless it is supposed for any reason
+that it ought to see; as in saying of a man, that he rushed blindly into
+an abyss, or of philosophers or the clergy that the greater part of them
+are blind guides. The names called privative, therefore, connote two
+things: the absence of certain attributes, and the presence of others,
+from which the presence also of the former might naturally have been
+expected.
+
+
+Sec. 7. The fifth leading division of names is into _relative_ and
+_absolute_, or let us rather say, _relative_ and _non-relative_; for the
+word absolute is put upon much too hard duty in metaphysics, not to be
+willingly spared when its services can be dispensed with. It resembles
+the word _civil_ in the language of jurisprudence, which stands for the
+opposite of criminal, the opposite of ecclesiastical, the opposite of
+military, the opposite of political--in short, the opposite of any
+positive word which wants a negative.
+
+Relative names are such as father, son; ruler, subject; like; equal;
+unlike; unequal; longer, shorter; cause, effect. Their characteristic
+property is, that they are always given in pairs. Every relative name
+which is predicated of an object, supposes another object (or objects),
+of which we may predicate either that same name or another relative name
+which is said to be the _correlative_ of the former. Thus, when we call
+any person a son, we suppose other persons who must be called parents.
+When we call any event a cause, we suppose another event which is an
+effect. When we say of any distance that it is longer, we suppose
+another distance which is shorter. When we say of any object that it is
+like, we mean that it is like some other object, which is also said to
+be like the first. In this last case both objects receive the same name;
+the relative term is its own correlative.
+
+It is evident that these words, when concrete, are, like other concrete
+general names, connotative; they denote a subject, and connote an
+attribute; and each of them has or might have a corresponding abstract
+name, to denote the attribute connoted by the concrete. Thus the
+concrete _like_ has its abstract _likeness_; the concretes, father and
+son, have, or might have, the abstracts, paternity, and filiety, or
+sonship. The concrete name connotes an attribute, and the abstract name
+which answers to it denotes that attribute. But of what nature is the
+attribute? Wherein consists the peculiarity in the connotation of a
+relative name?
+
+The attribute signified by a relative name, say some, is a relation; and
+this they give, if not as a sufficient explanation, at least as the only
+one attainable. If they are asked, What then is a relation? they do not
+profess to be able to tell. It is generally regarded as something
+peculiarly recondite and mysterious. I cannot, however, perceive in what
+respect it is more so than any other attribute; indeed, it appears to me
+to be so in a somewhat less degree. I conceive, rather, that it is by
+examining into the signification of relative names, or, in other words,
+into the nature of the attribute which they connote, that a clear
+insight may best be obtained into the nature of all attributes: of all
+that is meant by an attribute.
+
+It is obvious, in fact, that if we take any two correlative names,
+_father_ and _son_ for instance, though the objects _de_noted by the
+names are different, they both, in a certain sense, connote the same
+thing. They cannot, indeed, be said to connote the same _attribute_: to
+be a father, is not the same thing as to be a son. But when we call one
+man a father, another a son, what we mean to affirm is a set of facts,
+which are exactly the same in both cases. To predicate of A that he is
+the father of B, and of B that he is the son of A, is to assert one and
+the same fact in different words. The two propositions are exactly
+equivalent: neither of them asserts more or asserts less than the
+other. The paternity of A and the filiety of B are not two facts, but
+two modes of expressing the same fact. That fact, when analysed,
+consists of a series of physical events or phenomena, in which both A
+and B are parties concerned, and from which they both derive names. What
+those names really connote, is this series of events: that is the
+meaning, and the whole meaning, which either of them is intended to
+convey. The series of events may be said to _constitute_ the relation;
+the schoolmen called it the foundation of the relation, _fundamentum
+relationis_.
+
+In this manner any fact, or series of facts, in which two different
+objects are implicated, and which is therefore predicable of both of
+them, may be either considered as constituting an attribute of the one,
+or an attribute of the other. According as we consider it in the former,
+or in the latter aspect, it is connoted by the one or the other of the
+two correlative names. _Father_ connotes the fact, regarded as
+constituting an attribute of A: _son_ connotes the same fact, as
+constituting an attribute of B. It may evidently be regarded with equal
+propriety in either light. And all that appears necessary to account for
+the existence of relative names, is, that whenever there is a fact in
+which two individuals are concerned, an attribute grounded on that fact
+may be ascribed to either of these individuals.
+
+A name, therefore, is said to be relative, when, over and above the
+object which it denotes, it implies in its signification the existence
+of another object, also deriving a denomination from the same fact which
+is the ground of the first name. Or (to express the same meaning in
+other words) a name is relative, when, being the name of one thing, its
+signification cannot be explained but by mentioning another. Or we may
+state it thus--when the name cannot be employed in discourse so as to
+have a meaning, unless the name of some other thing than what it is
+itself the name of, be either expressed or understood. These definitions
+are all, at bottom, equivalent, being modes of variously expressing this
+one distinctive circumstance--that every other attribute of an object
+might, without any contradiction, be conceived still to exist if no
+object besides that one had ever existed;[8] but those of its
+attributes which are expressed by relative names, would on that
+supposition be swept away.
+
+
+Sec. 8. Names have been further distinguished into _univocal_ and
+_aequivocal_: these, however, are not two kinds of names, but two
+different modes of employing names. A name is univocal, or applied
+univocally, with respect to all things of which it can be predicated _in
+the same sense_: it is aequivocal, or applied aequivocally, as respects
+those things of which it is predicated in different senses. It is
+scarcely necessary to give instances of a fact so familiar as the double
+meaning of a word. In reality, as has been already observed, an
+aequivocal or ambiguous word is not one name, but two names, accidentally
+coinciding in sound. _File_ meaning a steel instrument, and _file_
+meaning a line of soldiers, have no more title to be considered one
+word, because written alike, than _grease_ and _Greece_ have, because
+they are pronounced alike. They are one sound, appropriated to form two
+different words.
+
+An intermediate case is that of a name used _analogically_ or
+metaphorically; that is, a name which is predicated of two things, not
+univocally, or exactly in the same signification, but in significations
+somewhat similar, and which being derived one from the other, one of
+them may be considered the primary, and the other a secondary
+signification. As when we speak of a brilliant light and a brilliant
+achievement. The word is not applied in the same sense to the light and
+to the achievement; but having been applied to the light in its original
+sense, that of brightness to the eye, it is transferred to the
+achievement in a derivative signification, supposed to be somewhat like
+the primitive one. The word, however, is just as properly two names
+instead of one, in this case, as in that of the most perfect ambiguity.
+And one of the commonest forms of fallacious reasoning arising from
+ambiguity, is that of arguing from a metaphorical expression as if it
+were literal; that is, as if a word, when applied metaphorically, were
+the same name as when taken in its original sense: which will be seen
+more particularly in its place.
+
+
+
+
+CHAPTER III.
+
+OF THE THINGS DENOTED BY NAMES.
+
+
+Sec. 1. Looking back now to the commencement of our inquiry, let us attempt
+to measure how far it has advanced. Logic, we found, is the Theory of
+Proof. But proof supposes something provable, which must be a
+Proposition or Assertion; since nothing but a Proposition can be an
+object of belief, or therefore of proof. A Proposition is, discourse
+which affirms or denies something of some other thing. This is one step:
+there must, it seems, be two things concerned in every act of belief.
+But what are these Things? They can be no other than those signified by
+the two names, which being joined together by a copula constitute the
+Proposition. If, therefore, we knew what all names signify, we should
+know everything which in the existing state of human knowledge, is
+capable either of being made a subject of affirmation or denial, or of
+being itself affirmed or denied of a subject. We have accordingly, in
+the preceding chapter, reviewed the various kinds of Names, in order to
+ascertain what is signified by each of them. And we have now carried
+this survey far enough to be able to take an account of its results, and
+to exhibit an enumeration of all kinds of Things which are capable of
+being made predicates, or of having anything predicated of them: after
+which to determine the import of Predication, that is, of Propositions,
+can be no arduous task.
+
+The necessity of an enumeration of Existences, as the basis of Logic,
+did not escape the attention of the schoolmen, and of their master
+Aristotle, the most comprehensive, if not also the most sagacious, of
+the ancient philosophers. The Categories, or Predicaments--the former a
+Greek word, the latter its literal translation in the Latin
+language--were intended by him and his followers as an enumeration of
+all things capable of being named; an enumeration by the _summa
+genera_, _i.e._ the most extensive classes into which things could be
+distributed; which, therefore, were so many highest Predicates, one or
+other of which was supposed capable of being affirmed with truth of
+every nameable thing whatsoever. The following are the classes into
+which, according to this school of philosophy, Things in general might
+be reduced:--
+
+  [Greek: Ousia],       Substantia.
+  [Greek: Poson],       Quantitas.
+  [Greek: Poion],       Qualitas.
+  [Greek: Pros ti],     Relatio.
+  [Greek: Poiein],      Actio.
+  [Greek: Paschein],    Passio.
+  [Greek: Pou],         Ubi.
+  [Greek: Pote],        Quando.
+  [Greek: Keisthai],    Situs.
+  [Greek: Echein],      Habitus.
+
+The imperfections of this classification are too obvious to require, and
+its merits are not sufficient to reward, a minute examination. It is a
+mere catalogue of the distinctions rudely marked out by the language of
+familiar life, with little or no attempt to penetrate, by philosophic
+analysis, to the _rationale_ even of those common distinctions. Such an
+analysis, however superficially conducted, would have shown the
+enumeration to be both redundant and defective. Some objects are
+omitted, and others repeated several times under different heads. It is
+like a division of animals into men, quadrupeds, horses, asses, and
+ponies. That, for instance, could not be a very comprehensive view of
+the nature of Relation which could exclude action, passivity, and local
+situation from that category. The same observation applies to the
+categories Quando (or position in time), and Ubi (or position in space);
+while the distinction between the latter and Situs is merely verbal. The
+incongruity of erecting into a _summum genus_ the class which forms the
+tenth category is manifest. On the other hand, the enumeration takes no
+notice of anything besides substances and attributes. In what category
+are we to place sensations, or any other feelings and states of mind; as
+hope, joy, fear; sound, smell, taste; pain, pleasure; thought, judgment,
+conception, and the like? Probably all these would have been placed by
+the Aristotelian school in the categories of _actio_ and _passio_; and
+the relation of such of them as are active, to their objects, and of
+such of them as are passive, to their causes, would rightly be so
+placed; but the things themselves, the feelings or states of mind,
+wrongly. Feelings, or states of consciousness, are assuredly to be
+counted among realities, but they cannot be reckoned either among
+substances or attributes.
+
+
+Sec. 2. Before recommencing, under better auspices, the attempt made with
+such imperfect success by the great founder of the science of logic, we
+must take notice of an unfortunate ambiguity in all the concrete names
+which correspond to the most general of all abstract terms, the word
+Existence. When we have occasion for a name which shall be capable of
+denoting whatever exists, as contradistinguished from non-entity or
+Nothing, there is hardly a word applicable to the purpose which is not
+also, and even more familiarly, taken in a sense in which it denotes
+only substances. But substances are not all that exists; attributes, if
+such things are to be spoken of, must be said to exist; feelings
+certainly exist. Yet when we speak of an _object_, or of a _thing_, we
+are almost always supposed to mean a substance. There seems a kind of
+contradiction in using such an expression as that one _thing_ is merely
+an attribute of another thing. And the announcement of a Classification
+of Things would, I believe, prepare most readers for an enumeration like
+those in natural history, beginning with the great divisions of animal,
+vegetable, and mineral, and subdividing them into classes and orders.
+If, rejecting the word Thing, we endeavour to find another of a more
+general import, or at least more exclusively confined to that general
+import, a word denoting all that exists, and connoting only simple
+existence; no word might be presumed fitter for such a purpose than
+_being_: originally the present participle of a verb which in one of its
+meanings is exactly equivalent to the verb _exists_; and therefore
+suitable, even by its grammatical formation, to be the concrete of the
+abstract _existence_. But this word, strange as the fact may appear, is
+still more completely spoiled for the purpose which it seemed expressly
+made for, than the word Thing. _Being_ is, by custom, exactly synonymous
+with substance; except that it is free from a slight taint of a second
+ambiguity; being applied impartially to matter and to mind, while
+substance, though originally and in strictness applicable to both, is
+apt to suggest in preference the idea of matter. Attributes are never
+called Beings; nor are feelings. A Being is that which excites feelings,
+and which possesses attributes. The soul is called a Being; God and
+angels are called Beings; but if we were to say, extension, colour,
+wisdom, virtue, are beings, we should perhaps be suspected of thinking
+with some of the ancients, that the cardinal virtues are animals; or, at
+the least, of holding with the Platonic school the doctrine of
+self-existent Ideas, or with the followers of Epicurus that of Sensible
+Forms, which detach themselves in every direction from bodies, and by
+coming in contact with our organs, cause our perceptions. We should be
+supposed, in short, to believe that Attributes are Substances.
+
+In consequence of this perversion of the word Being, philosophers
+looking about for something to supply its place, laid their hands upon
+the word Entity, a piece of barbarous Latin, invented by the schoolmen
+to be used as an abstract name, in which class its grammatical form
+would seem to place it; but being seized by logicians in distress to
+stop a leak in their terminology, it has ever since been used as a
+concrete name. The kindred word _essence_, born at the same time and of
+the same parents, scarcely underwent a more complete transformation
+when, from being the abstract of the verb _to be_, it came to denote
+something sufficiently concrete to be enclosed in a glass bottle. The
+word Entity, since it settled down into a concrete name, has retained
+its universality of signification somewhat less impaired than any of the
+names before mentioned. Yet the same gradual decay to which, after a
+certain age, all the language of psychology seems liable, has been at
+work even here. If you call virtue an _entity_, you are indeed somewhat
+less strongly suspected of believing it to be a substance than if you
+called it a _being_; but you are by no means free from the suspicion.
+Every word which was originally intended to connote mere existence,
+seems, after a long time, to enlarge its connotation to _separate_
+existence, or existence freed from the condition of belonging to a
+substance; which condition being precisely what constitutes an
+attribute, attributes are gradually shut out; and along with them
+feelings, which in ninety-nine cases out of a hundred have no other name
+than that of the attribute which is grounded on them. Strange that when
+the greatest embarrassment felt by all who have any considerable number
+of thoughts to express, is to find a sufficient variety of precise words
+fitted to express them, there should be no practice to which even
+scientific thinkers are more addicted than that of taking valuable words
+to express ideas which are sufficiently expressed by other words already
+appropriated to them.
+
+When it is impossible to obtain good tools, the next best thing is to
+understand thoroughly the defects of those we have. I have therefore
+warned the reader of the ambiguity of the names which, for want of
+better, I am necessitated to employ. It must now be the writer's
+endeavour so to employ them as in no case to leave the meaning doubtful
+or obscure. No one of the above terms being altogether unambiguous, I
+shall not confine myself to any one, but shall employ on each occasion
+the word which seems least likely in the particular case to lead to
+misunderstanding; nor do I pretend to use either these or any other
+words with a rigorous adherence to one single sense. To do so would
+often leave us without a word to express what is signified by a known
+word in some one or other of its senses: unless authors had an unlimited
+licence to coin new words, together with (what it would be more
+difficult to assume) unlimited power of making readers understand them.
+Nor would it be wise in a writer, on a subject involving so much of
+abstraction, to deny himself the advantage derived from even an improper
+use of a term, when, by means of it, some familiar association is called
+up which brings the meaning home to the mind, as it were by a flash.
+
+The difficulty both to the writer and reader, of the attempt which must
+be made to use vague words so as to convey a precise meaning, is not
+wholly a matter of regret. It is not unfitting that logical treatises
+should afford an example of that, to facilitate which is among the most
+important uses of logic. Philosophical language will for a long time,
+and popular language still longer, retain so much of vagueness and
+ambiguity, that logic would be of little value if it did not, among its
+other advantages, exercise the understanding in doing its work neatly
+and correctly with these imperfect tools.
+
+After this preamble it is time to proceed to our enumeration. We shall
+commence with Feelings, the simplest class of nameable things; the term
+Feeling being of course understood in its most enlarged sense.
+
+
+I. FEELINGS, OR STATES OF CONSCIOUSNESS.
+
+Sec. 3. A Feeling and a State of Consciousness are, in the language of
+philosophy, equivalent expressions: everything is a feeling of which the
+mind is conscious; everything which it _feels_, or, in other words,
+which forms a part of its own sentient existence. In popular language
+Feeling is not always synonymous with State of Consciousness; being
+often taken more peculiarly for those states which are conceived as
+belonging to the sensitive, or to the emotional, phasis of our nature,
+and sometimes, with a still narrower restriction, to the emotional
+alone, as distinguished from what are conceived as belonging to the
+percipient or to the intellectual phasis. But this is an admitted
+departure from correctness of language; just as, by a popular perversion
+the exact converse of this, the word Mind is withdrawn from its rightful
+generality of signification, and restricted to the intellect. The still
+greater perversion by which Feeling is sometimes confined not only to
+bodily sensations, but to the sensations of a single sense, that of
+touch, needs not be more particularly adverted to.
+
+Feeling, in the proper sense of the term, is a genus, of which
+Sensation, Emotion, and Thought, are subordinate species. Under the word
+Thought is here to be included whatever we are internally conscious of
+when we are said to think; from the consciousness we have when we think
+of a red colour without having it before our eyes, to the most recondite
+thoughts of a philosopher or poet. Be it remembered, however, that by a
+thought is to be understood what passes in the mind itself, and not any
+object external to the mind, which the person is commonly said to be
+thinking of. He may be thinking of the sun, or of God, but the sun and
+God are not thoughts; his mental image, however, of the sun, and his
+idea of God, are thoughts; states of his mind, not of the objects
+themselves; and so also is his belief of the existence of the sun, or of
+God; or his disbelief, if the case be so. Even imaginary objects (which
+are said to exist only in our ideas) are to be distinguished from our
+ideas of them. I may think of a hobgoblin, as I may think of the loaf
+which was eaten yesterday, or of the flower which will bloom to-morrow.
+But the hobgoblin which never existed is not the same thing with my idea
+of a hobgoblin, any more than the loaf which once existed is the same
+thing with my idea of a loaf, or the flower which does not yet exist,
+but which will exist, is the same with my idea of a flower. They are
+all, not thoughts, but objects of thought; though at the present time
+all the objects are alike non-existent.
+
+In like manner, a Sensation is to be carefully distinguished from the
+object which causes the sensation; our sensation of white from a white
+object: nor is it less to be distinguished from the attribute whiteness,
+which we ascribe to the object in consequence of its exciting the
+sensation. Unfortunately for clearness and due discrimination in
+considering these subjects, our sensations seldom receive separate
+names. We have a name for the objects which produce in us a certain
+sensation: the word _white_. We have a name for the quality in those
+objects, to which we ascribe the sensation: the name _whiteness_. But
+when we speak of the sensation itself (as we have not occasion to do
+this often except in our scientific speculations), language, which
+adapts itself for the most part only to the common uses of life, has
+provided us with no single-worded or immediate designation; we must
+employ a circumlocution, and say, The sensation of white, or The
+sensation of whiteness; we must denominate the sensation either from the
+object, or from the attribute, by which it is excited. Yet the
+sensation, though it never _does_, might very well be _conceived_ to
+exist, without anything whatever to excite it. We can conceive it as
+arising spontaneously in the mind. But if it so arose, we should have no
+name to denote it which would not be a misnomer. In the case of our
+sensations of hearing we are better provided; we have the word Sound,
+and a whole vocabulary of words to denote the various kinds of sounds.
+For as we are often conscious of these sensations in the absence of any
+perceptible object, we can more easily conceive having them in the
+absence of any object whatever. We need only shut our eyes and listen to
+music, to have a conception of an universe with nothing in it except
+sounds, and ourselves hearing them: and what is easily conceived
+separately, easily obtains a separate name. But in general our names of
+sensations denote indiscriminately the sensation and the attribute.
+Thus, _colour_ stands for the sensations of white, red, &c., but also
+for the quality in the coloured object. We talk of the colours of things
+as among their _properties_.
+
+
+Sec. 4. In the case of sensations, another distinction has also to be kept
+in view, which is often confounded, and never without mischievous
+consequences. This is, the distinction between the sensation itself, and
+the state of the bodily organs which precedes the sensation, and which
+constitutes the physical agency by which it is produced. One of the
+sources of confusion on this subject is the division commonly made of
+feelings into Bodily and Mental. Philosophically speaking, there is no
+foundation at all for this distinction: even sensations are states of
+the sentient mind, not states of the body, as distinguished from it.
+What I am conscious of when I see the colour blue, is a feeling of blue
+colour, which is one thing; the picture on my retina, or the phenomenon
+of hitherto mysterious nature which takes place in my optic nerve or in
+my brain, is another thing, of which I am not at all conscious, and
+which scientific investigation alone could have apprised me of. These
+are states of my body; but the sensation of blue, which is the
+consequence of these states of body, is not a state of body: that which
+perceives and is conscious is called Mind. When sensations are called
+bodily feelings, it is only as being the class of feelings which are
+immediately occasioned by bodily states; whereas the other kinds of
+feelings, thoughts, for instance, or emotions, are immediately excited
+not by anything acting upon the bodily organs, but by sensations, or by
+previous thoughts. This, however, is a distinction not in our feelings,
+but in the agency which produces our feelings: all of them when actually
+produced are states of mind.
+
+Besides the affection of our bodily organs from without, and the
+sensation thereby produced in our minds, many writers admit a third link
+in the chain of phenomena, which they call a Perception, and which
+consists in the recognition of an external object as the exciting cause
+of the sensation. This perception, they say, is an _act_ of the mind,
+proceeding from its own spontaneous activity; while in a sensation the
+mind is passive, being merely acted upon by the outward object. And
+according to some metaphysicians, it is by an act of the mind, similar
+to perception, except in not being preceded by any sensation, that the
+existence of God, the soul, and other hyper-physical objects is
+recognised.
+
+These acts of what is termed perception, whatever be the conclusion
+ultimately come to respecting their nature, must, I conceive, take their
+place among the varieties of feelings or states of mind. In so classing
+them, I have not the smallest intention of declaring or insinuating any
+theory as to the law of mind in which these mental processes may be
+supposed to originate, or the conditions under which they may be
+legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
+suppose must be meant in an analogous case[9]) to indicate that as they
+are "_merely_ states of mind," it is superfluous to inquire into their
+distinguishing peculiarities. I abstain from the inquiry as irrelevant
+to the science of logic. In these so-called perceptions, or direct
+recognitions by the mind, of objects, whether physical or spiritual,
+which are external to itself, I can see only cases of belief; but of
+belief which claims to be intuitive, or independent of external
+evidence. When a stone lies before me, I am conscious of certain
+sensations which I receive from it; but if I say that these sensations
+come to me from an external object which I _perceive_, the meaning of
+these words is, that receiving the sensations, I intuitively _believe_
+that an external cause of those sensations exists. The laws of intuitive
+belief, and the conditions under which it is legitimate, are a subject
+which, as we have already so often remarked, belongs not to logic, but
+to the science of the ultimate laws of the human mind.
+
+To the same region of speculation belongs all that can be said
+respecting the distinction which the German metaphysicians and their
+French and English followers so elaborately draw between the _acts_ of
+the mind and its merely passive _states_; between what it receives from,
+and what it gives to, the crude materials of its experience. I am aware
+that with reference to the view which those writers take of the primary
+elements of thought and knowledge, this distinction is fundamental. But
+for the present purpose, which is to examine, not the original
+groundwork of our knowledge, but how we come by that portion of it which
+is not original; the difference between active and passive states of
+mind is of secondary importance. For us, they all are states of mind,
+they all are feelings; by which, let it be said once more, I mean to
+imply nothing of passivity, but simply that they are psychological
+facts, facts which take place in the mind, and are to be carefully
+distinguished from the external or physical facts with which they may be
+connected either as effects or as causes.
+
+
+Sec. 5. Among active states of mind, there is, however, one species which
+merits particular attention, because it forms a principal part of the
+connotation of some important classes of names. I mean _volitions_, or
+acts of the will. When we speak of sentient beings by relative names, a
+large portion of the connotation of the name usually consists of the
+actions of those beings; actions past, present, and possible or probable
+future. Take, for instance, the words Sovereign and Subject. What
+meaning do these words convey, but that of innumerable actions, done or
+to be done by the sovereign and the subjects, to or in regard to one
+another reciprocally? So with the words physician and patient, leader
+and follower, tutor and pupil. In many cases the words also connote
+actions which would be done under certain contingencies by persons other
+than those denoted: as the words mortgagor and mortgagee, obligor and
+obligee, and many other words expressive of legal relation, which
+connote what a court of justice would do to enforce the legal obligation
+if not fulfilled. There are also words which connote actions previously
+done by persons other than those denoted either by the name itself or by
+its correlative; as the word brother. From these instances, it may be
+seen how large a portion of the connotation of names consists of
+actions. Now what is an action? Not one thing, but a series of two
+things: the state of mind called a volition, followed by an effect. The
+volition or intention to produce the effect, is one thing; the effect
+produced in consequence of the intention, is another thing; the two
+together constitute the action. I form the purpose of instantly moving
+my arm; that is a state of my mind: my arm (not being tied or paralytic)
+moves in obedience to my purpose; that is a physical fact, consequent on
+a state of mind. The intention, followed by the fact, or (if we prefer
+the expression) the fact when preceded and caused by the intention, is
+called the action of moving my arm.
+
+
+Sec. 6. Of the first leading division of nameable things, viz. Feelings or
+States of Consciousness, we began by recognising three subdivisions;
+Sensations, Thoughts, and Emotions. The first two of these we have
+illustrated at considerable length; the third, Emotions, not being
+perplexed by similar ambiguities, does not require similar
+exemplification. And, finally, we have found it necessary to add to
+these three a fourth species, commonly known by the name Volitions.
+Without seeking to prejudge the metaphysical question whether any mental
+state or phenomenon can be found which is not included in one or other
+of these four species, it appears to me that the amount of illustration
+bestowed upon these may, so far as we are concerned, suffice for the
+whole genus. We shall, therefore, proceed to the two remaining classes
+of nameable things; all things which are external to the mind being
+considered as belonging either to the class of Substances or to that of
+Attributes.
+
+II. SUBSTANCES.
+
+Logicians have endeavoured to define Substance and Attribute; but their
+definitions are not so much attempts to draw a distinction between the
+things themselves, as instructions what difference it is customary to
+make in the grammatical structure of the sentence, according as we are
+speaking of substances or of attributes. Such definitions are rather
+lessons of English, or of Greek, Latin, or German, than of mental
+philosophy. An attribute, say the school logicians, must be the
+attribute _of_ something; colour, for example, must be the colour _of_
+something; goodness must be the goodness _of_ something: and if this
+something should cease to exist, or should cease to be connected with
+the attribute, the existence of the attribute would be at an end. A
+substance, on the contrary, is self-existent; in speaking about it, we
+need not put _of_ after its name. A stone is not the stone _of_
+anything; the moon is not the moon _of_ anything, but simply the moon.
+Unless, indeed, the name which we choose to give to the substance be a
+relative name; if so, it must be followed either by _of_, or by some
+other particle, implying, as that preposition does, a reference to
+something else: but then the other characteristic peculiarity of an
+attribute would fail; the _something_ might be destroyed, and the
+substance might still subsist. Thus, a father must be the father _of_
+something, and so far resembles an attribute, in being referred to
+something besides himself: if there were no child, there would be no
+father: but this, when we look into the matter, only means that we
+should not call him father. The man called father might still exist
+though there were no child, as he existed before there was a child: and
+there would be no contradiction in supposing him to exist, though the
+whole universe except himself were destroyed. But destroy all white
+substances, and where would be the attribute whiteness? Whiteness,
+without any white thing, is a contradiction in terms.
+
+This is the nearest approach to a solution of the difficulty, that will
+be found in the common treatises on logic. It will scarcely be thought
+to be a satisfactory one. If an attribute is distinguished from a
+substance by being the attribute _of_ something, it seems highly
+necessary to understand what is meant by _of_; a particle which needs
+explanation too much itself, to be placed in front of the explanation of
+anything else. And as for the self-existence of substance, it is very
+true that a substance may be conceived to exist without any other
+substance, but so also may an attribute without any other attribute: and
+we can no more imagine a substance without attributes than we can
+imagine attributes without a substance.
+
+Metaphysicians, however, have probed the question deeper, and given an
+account of Substance considerably more satisfactory than this.
+Substances are usually distinguished as Bodies or Minds. Of each of
+these, philosophers have at length provided us with a definition which
+seems unexceptionable.
+
+
+Sec. 7. A Body, according to the received doctrine of modern
+metaphysicians, may be defined, the external cause to which we ascribe
+our sensations. When I see and touch a piece of gold, I am conscious of
+a sensation of yellow colour, and sensations of hardness and weight; and
+by varying the mode of handling, I may add to these sensations many
+others completely distinct from them. The sensations are all of which I
+am directly conscious; but I consider them as produced by something not
+only existing independently of my will, but external to my bodily organs
+and to my mind. This external something I call a body.
+
+It may be asked, how come we to ascribe our sensations to any external
+cause? And is there sufficient ground for so ascribing them? It is
+known, that there are metaphysicians who have raised a controversy on
+the point; maintaining that we are not warranted in referring our
+sensations to a cause such as we understand by the word Body, or to any
+external cause whatever. Though we have no concern here with this
+controversy, nor with the metaphysical niceties on which it turns, one
+of the best ways of showing what is meant by Substance is, to consider
+what position it is necessary to take up, in order to maintain its
+existence against opponents.
+
+It is certain, then, that a part of our notion of a body consists of the
+notion of a number of sensations of our own, or of other sentient
+beings, habitually occurring simultaneously. My conception of the table
+at which I am writing is compounded of its visible form and size, which
+are complex sensations of sight; its tangible form and size, which are
+complex sensations of our organs of touch and of our muscles; its
+weight, which is also a sensation of touch and of the muscles; its
+colour, which is a sensation of sight; its hardness, which is a
+sensation of the muscles; its composition, which is another word for all
+the varieties of sensation which we receive under various circumstances
+from the wood of which it is made, and so forth. All or most of these
+various sensations frequently are, and, as we learn by experience,
+always might be, experienced simultaneously, or in many different orders
+of succession, at our own choice: and hence the thought of any one of
+them makes us think of the others, and the whole becomes mentally
+amalgamated into one mixed state of consciousness, which, in the
+language of the school of Locke and Hartley, is termed a Complex Idea.
+
+Now, there are philosophers who have argued as follows. If we conceive
+an orange to be divested of its natural colour without acquiring any new
+one; to lose its softness without becoming hard, its roundness without
+becoming square or pentagonal, or of any other regular or irregular
+figure whatever; to be deprived of size, of weight, of taste, of smell;
+to lose all its mechanical and all its chemical properties, and acquire
+no new ones; to become, in short, invisible, intangible, imperceptible
+not only by all our senses, but by the senses of all other sentient
+beings, real or possible; nothing, say these thinkers, would remain.
+For of what nature, they ask, could be the residuum? and by what token
+could it manifest its presence? To the unreflecting its existence seems
+to rest on the evidence of the senses. But to the senses nothing is
+apparent except the sensations. We know, indeed, that these sensations
+are bound together by some law; they do not come together at random, but
+according to a systematic order, which is part of the order established
+in the universe. When we experience one of these sensations, we usually
+experience the others also, or know that we have it in our power to
+experience them. But a fixed law of connexion, making the sensations
+occur together, does not, say these philosophers, necessarily require
+what is called a substratum to support them. The conception of a
+substratum is but one of many possible forms in which that connexion
+presents itself to our imagination; a mode of, as it were, realizing the
+idea. If there be such a substratum, suppose it this instant
+miraculously annihilated, and let the sensations continue to occur in
+the same order, and how would the substratum be missed? By what signs
+should we be able to discover that its existence had terminated? Should
+we not have as much reason to believe that it still existed as we now
+have? And if we should not then be warranted in believing it, how can we
+be so now? A body, therefore, according to these metaphysicians, is not
+anything intrinsically different from the sensations which the body is
+said to produce in us; it is, in short, a set of sensations, or rather,
+of possibilities of sensation, joined together according to a fixed law.
+
+The controversies to which these speculations have given rise, and the
+doctrines which have been developed in the attempt to find a conclusive
+answer to them, have been fruitful of important consequences to the
+Science of Mind. The sensations (it was answered) which we are conscious
+of, and which we receive, not at random, but joined together in a
+certain uniform manner, imply not only a law or laws of connexion, but a
+cause external to our mind, which cause, by its own laws, determines the
+laws according to which the sensations are connected and experienced.
+The schoolmen used to call this external cause by the name we have
+already employed, a _substratum_; and its attributes (as they expressed
+themselves) _inhered_, literally _stuck_, in it. To this substratum the
+name Matter is usually given in philosophical discussions. It was soon,
+however, acknowledged by all who reflected on the subject, that the
+existence of matter cannot be proved by extrinsic evidence. The answer,
+therefore, now usually made to Berkeley and his followers, is, that the
+belief is intuitive; that mankind, in all ages, have felt themselves
+compelled, by a necessity of their nature, to refer their sensations to
+an external cause: that even those who deny it in theory, yield to the
+necessity in practice, and both in speech, thought, and feeling, do,
+equally with the vulgar, acknowledge their sensations to be the effects
+of something external to them: this knowledge, therefore, it is
+affirmed, is as evidently intuitive as our knowledge of our sensations
+themselves is intuitive. And here the question merges in the fundamental
+problem of metaphysics properly so called; to which science we leave it.
+
+But although the extreme doctrine of the Idealist metaphysicians, that
+objects are nothing but our sensations and the laws which connect them,
+has not been generally adopted by subsequent thinkers; the point of most
+real importance is one on which those metaphysicians are now very
+generally considered to have made out their case: viz., that _all we
+know_ of objects is the sensations which they give us, and the order of
+the occurrence of those sensations. Kant himself, on this point, is as
+explicit as Berkeley or Locke. However firmly convinced that there
+exists an universe of "Things in themselves," totally distinct from the
+universe of phenomena, or of things as they appear to our senses; and
+even when bringing into use a technical expression (_Noumenon_) to
+denote what the thing is in itself, as contrasted with the
+_representation_ of it in our minds; he allows that this representation
+(the matter of which, he says, consists of our sensations, though the
+form is given by the laws of the mind itself) is all we know of the
+object: and that the real nature of the Thing is, and by the
+constitution of our faculties ever must remain, at least in the present
+state of existence, an impenetrable mystery to us. "Of things absolutely
+or in themselves," says Sir William Hamilton,[10] "be they external, be
+they internal, we know nothing, or know them only as incognisable; and
+become aware of their incomprehensible existence, only as this is
+indirectly and accidentally revealed to us, through certain qualities
+related to our faculties of knowledge, and which qualities, again, we
+cannot think as unconditioned, irrelative, existent in and of
+themselves. All that we know is therefore phaenomenal,--phaenomenal of the
+unknown."[11] The same doctrine is laid down in the clearest and
+strongest terms by M. Cousin, whose observations on the subject are the
+more worthy of attention, as, in consequence of the ultra-German and
+ontological character of his philosophy in other respects, they may be
+regarded as the admissions of an opponent.[12]
+
+There is not the slightest reason for believing that what we call the
+sensible qualities of the object are a type of anything inherent in
+itself, or bear any affinity to its own nature. A cause does not, as
+such, resemble its effects; an east wind is not like the feeling of
+cold, nor heat like the steam of boiling water. Why then should matter
+resemble our sensations? Why should the inmost nature of fire or water
+resemble the impressions made by those objects upon our senses?[13] Or
+on what principle are we authorized to deduce from the effects, anything
+concerning the cause, except that it is a cause adequate to produce
+those effects? It may, therefore, safely be laid down as a truth both
+obvious in itself, and admitted by all whom it is at present necessary
+to take into consideration, that, of the outward world, we know and can
+know absolutely nothing, except the sensations which we experience from
+it.[14]
+
+
+Sec. 8. Body having now been defined the external cause, and (according to
+the more reasonable opinion) the unknown external cause, to which we
+refer our sensations; it remains to frame a definition of Mind. Nor,
+after the preceding observations, will this be difficult. For, as our
+conception of a body is that of an unknown exciting cause of sensations,
+so our conception of a mind is that of an unknown recipient, or
+percipient, of them; and not of them alone, but of all our other
+feelings. As body is understood to be the mysterious something which
+excites the mind to feel, so mind is the mysterious something which
+feels and thinks. It is unnecessary to give in the case of mind, as we
+gave in the case of matter, a particular statement of the sceptical
+system by which its existence as a Thing in itself, distinct from the
+series of what are denominated its states, is called in question. But it
+is necessary to remark, that on the inmost nature (whatever be meant by
+inmost nature) of the thinking principle, as well as on the inmost
+nature of matter, we are, and with our faculties must always remain,
+entirely in the dark. All which we are aware of, even in our own minds,
+is (in the words of Mr. James Mill) a certain "thread of consciousness;"
+a series of feelings, that is, of sensations, thoughts, emotions, and
+volitions, more or less numerous and complicated. There is a something I
+call Myself, or, by another form of expression, my mind, which I
+consider as distinct from these sensations, thoughts, &c.; a something
+which I conceive to be not the thoughts, but the being that has the
+thoughts, and which I can conceive as existing for ever in a state of
+quiescence, without any thoughts at all. But what this being is, though
+it is myself, I have no knowledge, other than the series of its states
+of consciousness. As bodies manifest themselves to me only through the
+sensations of which I regard them as the causes, so the thinking
+principle, or mind, in my own nature, makes itself known to me only by
+the feelings of which it is conscious. I know nothing about myself, save
+my capacities of feeling or being conscious (including, of course,
+thinking and willing): and were I to learn anything new concerning my
+own nature, I cannot with my present faculties conceive this new
+information to be anything else, than that I have some additional
+capacities, as yet unknown to me, of feeling, thinking, or willing.
+
+Thus, then, as body is the unsentient cause to which we are naturally
+prompted to refer a certain portion of our feelings, so mind may be
+described as the sentient _subject_ (in the scholastic sense of the
+term) of all feelings; that which has or feels them. But of the nature
+of either body or mind, further than the feelings which the former
+excites, and which the latter experiences, we do not, according to the
+best existing doctrine, know anything; and if anything, logic has
+nothing to do with it, or with the manner in which the knowledge is
+acquired. With this result we may conclude this portion of our subject,
+and pass to the third and only remaining class or division of Nameable
+Things.
+
+
+III. ATTRIBUTES: AND, FIRST, QUALITIES.
+
+Sec. 9. From what has already been said of Substance, what is to be said of
+Attribute is easily deducible. For if we know not, and cannot know,
+anything of bodies but the sensations which they excite in us or in
+others, those sensations must be all that we can, at bottom, mean by
+their attributes; and the distinction which we verbally make between the
+properties of things and the sensations we receive from them, must
+originate in the convenience of discourse rather than in the nature of
+what is signified by the terms.
+
+Attributes are usually distributed under the three heads of Quality,
+Quantity, and Relation. We shall come to the two latter presently: in
+the first place we shall confine ourselves to the former.
+
+Let us take, then, as our example, one of what are termed the sensible
+qualities of objects, and let that example be whiteness. When we ascribe
+whiteness to any substance, as, for instance, snow; when we say that
+snow has the quality whiteness, what do we really assert? Simply, that
+when snow is present to our organs, we have a particular sensation,
+which we are accustomed to call the sensation of white. But how do I
+know that snow is present? Obviously by the sensations which I derive
+from it, and not otherwise. I infer that the object is present, because
+it gives me a certain assemblage or series of sensations. And when I
+ascribe to it the attribute whiteness, my meaning is only, that, of the
+sensations composing this group or series, that which I call the
+sensation of white colour is one.
+
+This is one view which may be taken of the subject. But there is also
+another and a different view. It may be said, that it is true we _know_
+nothing of sensible objects, except the sensations they excite in us;
+that the fact of our receiving from snow the particular sensation which
+is called a sensation of white, is the _ground_ on which we ascribe to
+that substance the quality whiteness; the sole proof of its possessing
+that quality. But because one thing may be the sole evidence of the
+existence of another thing, it does not follow that the two are one and
+the same. The attribute whiteness (it may be said) is not the fact of
+receiving the sensation, but something in the object itself; a _power_
+inherent in it; something _in virtue_ of which the object produces the
+sensation. And when we affirm that snow possesses the attribute
+whiteness, we do not merely assert that the presence of snow produces in
+us that sensation, but that it does so through, and by reason of, that
+power or quality.
+
+For the purposes of logic it is not of material importance which of
+these opinions we adopt. The full discussion of the subject belongs to
+the other department of scientific inquiry, so often alluded to under
+the name of metaphysics; but it may be said here, that for the doctrine
+of the existence of a peculiar species of entities called qualities, I
+can see no foundation except in a tendency of the human mind which is
+the cause of many delusions. I mean, the disposition, wherever we meet
+with two names which are not precisely synonymous, to suppose that they
+must be the names of two different things; whereas in reality they may
+be names of the same thing viewed in two different lights, or under
+different suppositions as to surrounding circumstances. Because
+_quality_ and _sensation_ cannot be put indiscriminately one for the
+other, it is supposed that they cannot both signify the same thing,
+namely, the impression or feeling with which we are affected through our
+senses by the presence of an object; though there is at least no
+absurdity in supposing that this identical impression or feeling may be
+called a sensation when considered merely in itself, and a quality when
+looked at in relation to any one of the numerous objects, the presence
+of which to our organs excites in our minds that among various other
+sensations or feelings. And if this be admissible as a supposition, it
+rests with those who contend for an entity _per se_ called a quality, to
+show that their opinion is preferable, or is anything in fact but a
+lingering remnant of the scholastic doctrine of occult causes; the very
+absurdity which Moliere so happily ridiculed when he made one of his
+pedantic physicians account for the fact that "l'opium endormit," by the
+maxim "parcequ'il a une vertu soporifique."
+
+It is evident that when the physician stated that opium had "une vertu
+soporifique," he did not account for, but merely asserted over again,
+the fact that it _endormit_. In like manner, when we say that snow is
+white because it has the quality of whiteness, we are only re-asserting
+in more technical language the fact that it excites in us the sensation
+of white. If it be said that the sensation must have some cause, I
+answer, its cause is the presence of the assemblage of phenomena which
+is termed the object. When we have asserted that as often as the object
+is present, and our organs in their normal state, the sensation takes
+place, we have stated all that we know about the matter. There is no
+need, after assigning a certain and intelligible cause, to suppose an
+occult cause besides, for the purpose of enabling the real cause to
+produce its effect. If I am asked, why does the presence of the object
+cause this sensation in me, I cannot tell: I can only say that such is
+my nature, and the nature of the object; that the fact forms a part of
+the constitution of things. And to this we must at last come, even after
+interpolating the imaginary entity. Whatever number of links the chain
+of causes and effects may consist of, how any one link produces the one
+which is next to it, remains equally inexplicable to us. It is as easy
+to comprehend that the object should produce the sensation directly and
+at once, as that it should produce the same sensation by the aid of
+something else called the _power_ of producing it.
+
+But, as the difficulties which may be felt in adopting this view of the
+subject cannot be removed without discussions transcending the bounds of
+our science, I content myself with a passing indication, and shall, for
+the purposes of logic, adopt a language compatible with either view of
+the nature of qualities. I shall say,--what at least admits of no
+dispute,--that the quality of whiteness ascribed to the object snow, is
+_grounded_ on its exciting in us the sensation of white; and adopting
+the language already used by the school logicians in the case of the
+kind of attributes called Relations, I shall term the sensation of
+white the foundation of the quality whiteness. For logical purposes the
+sensation is the only essential part of what is meant by the word; the
+only part which we ever can be concerned in proving. When that is
+proved, the quality is proved; if an object excites a sensation, it has,
+of course, the power of exciting it.
+
+
+IV. RELATIONS.
+
+Sec. 10. The _qualities_ of a body, we have said, are the attributes
+grounded on the sensations which the presence of that particular body to
+our organs excites in our minds. But when we ascribe to any object the
+kind of attribute called a Relation, the foundation of the attribute
+must be something in which other objects are concerned besides itself
+and the percipient.
+
+As there may with propriety be said to be a relation between any two
+things to which two correlative names are or may be given, we may expect
+to discover what constitutes a relation in general, if we enumerate the
+principal cases in which mankind have imposed correlative names, and
+observe what these cases have in common.
+
+What, then, is the character which is possessed in common by states of
+circumstances so heterogeneous and discordant as these: one thing _like_
+another; one thing _unlike_ another; one thing _near_ another; one thing
+_far from_ another; one thing _before_, _after_, _along with_ another;
+one thing _greater_, _equal_, _less_, than another; one thing the
+_cause_ of another, the _effect_ of another; one person the _master_,
+_servant_, _child_, _parent_, _debtor_, _creditor_, _sovereign_,
+_subject_, _attorney_, _client_, of another, and so on?
+
+Omitting, for the present, the case of Resemblance, (a relation which
+requires to be considered separately,) there seems to be one thing
+common to all these cases, and only one; that in each of them there
+exists or occurs, or has existed or occurred, or may be expected to
+exist or occur, some fact or phenomenon, into which the two things which
+are said to be related to each other, both enter as parties concerned.
+This fact, or phenomenon, is what the Aristotelian logicians called the
+_fundamentum relationis_. Thus in the relation of greater and less
+between two magnitudes, the _fundamentum relationis_ is the fact that
+one of the two magnitudes could, under certain conditions, be included
+in, without entirely filling, the space occupied by the other magnitude.
+In the relation of master and servant, the _fundamentum relationis_ is
+the fact that the one has undertaken, or is compelled, to perform
+certain services for the benefit and at the bidding of the other.
+Examples might be indefinitely multiplied; but it is already obvious
+that whenever two things are said to be related, there is some fact, or
+series of facts, into which they both enter; and that whenever any two
+things are involved in some one fact, or series of facts, we may ascribe
+to those two things a mutual relation grounded on the fact. Even if they
+have nothing in common but what is common to all things, that they are
+members of the universe, we call that a relation, and denominate them
+fellow-creatures, fellow-beings, or fellow-denizens of the universe. But
+in proportion as the fact into which the two objects enter as parts is
+of a more special and peculiar, or of a more complicated nature, so also
+is the relation grounded upon it. And there are as many conceivable
+relations as there are conceivable kinds of fact in which two things can
+be jointly concerned.
+
+In the same manner, therefore, as a quality is an attribute grounded on
+the fact that a certain sensation or sensations are produced in us by
+the object, so an attribute grounded on some fact into which the object
+enters jointly with another object, is a relation between it and that
+other object. But the fact in the latter case consists of the very same
+kind of elements as the fact in the former; namely, states of
+consciousness. In the case, for example, of any legal relation, as
+debtor and creditor, principal and agent, guardian and ward, the
+_fundamentum relationis_ consists entirely of thoughts, feelings, and
+volitions (actual or contingent), either of the persons themselves or of
+other persons concerned in the same series of transactions; as, for
+instance, the intentions which would be formed by a judge, in case a
+complaint were made to his tribunal of the infringement of any of the
+legal obligations imposed by the relation; and the acts which the judge
+would perform in consequence; acts being (as we have already seen)
+another word for intentions followed by an effect, and that effect being
+but another word for sensations, or some other feelings, occasioned
+either to the agent himself or to somebody else. There is no part of
+what the names expressive of the relation imply, that is not resolvable
+into states of consciousness; outward objects being, no doubt, supposed
+throughout as the causes by which some of those states of consciousness
+are excited, and minds as the subjects by which all of them are
+experienced, but neither the external objects nor the minds making their
+existence known otherwise than by the states of consciousness.
+
+Cases of relation are not always so complicated as those to which we
+last alluded. The simplest of all cases of relation are those expressed
+by the words antecedent and consequent, and by the word simultaneous. If
+we say, for instance, that dawn preceded sunrise, the fact in which the
+two things, dawn and sunrise, were jointly concerned, consisted only of
+the two things themselves; no third thing entered into the fact or
+phenomenon at all. Unless, indeed, we choose to call the succession of
+the two objects a third thing; but their succession is not something
+added to the things themselves; it is something involved in them. Dawn
+and sunrise announce themselves to our consciousness by two successive
+sensations. Our consciousness of the succession of these sensations is
+not a third sensation or feeling added to them; we have not first the
+two feelings, and then a feeling of their succession. To have two
+feelings at all, implies having them either successively, or else
+simultaneously. Sensations, or other feelings, being given, succession
+and simultaneousness are the two conditions, to the alternative of which
+they are subjected by the nature of our faculties; and no one has been
+able, or needs expect, to analyse the matter any farther.
+
+
+Sec. 11. In a somewhat similar position are two other sorts of relations,
+Likeness and Unlikeness. I have two sensations; we will suppose them to
+be simple ones; two sensations of white, or one sensation of white and
+another of black. I call the first two sensations _like_; the last two
+_unlike_. What is the fact or phenomenon constituting the _fundamentum_
+of this relation? The two sensations first, and then what we call a
+feeling of resemblance, or of want of resemblance. Let us confine
+ourselves to the former case. Resemblance is evidently a feeling; a
+state of the consciousness of the observer. Whether the feeling of the
+resemblance of the two colours be a third state of consciousness, which
+I have _after_ having the two sensations of colour, or whether (like the
+feeling of their succession) it is involved in the sensations
+themselves, may be a matter of discussion. But in either case, these
+feelings of resemblance, and of its opposite dissimilarity, are parts of
+our nature; and parts so far from being capable of analysis, that they
+are presupposed in every attempt to analyse any of our other feelings.
+Likeness and unlikeness, therefore, as well as antecedence, sequence,
+and simultaneousness, must stand apart among relations, as things _sui
+generis_. They are attributes grounded on facts, that is, on states of
+consciousness, but on states which are peculiar, unresolvable, and
+inexplicable.
+
+But, though likeness or unlikeness cannot be resolved into anything
+else, complex cases of likeness or unlikeness can be resolved into
+simpler ones. When we say of two things which consist of parts, that
+they are like one another, the likeness of the wholes does admit of
+analysis; it is compounded of likenesses between the various parts
+respectively, and of likeness in their arrangement. Of how vast a
+variety of resemblances of parts must that resemblance be composed,
+which induces us to say that a portrait, or a landscape, is like its
+original. If one person mimics another with any success, of how many
+simple likenesses must the general or complex likeness be compounded:
+likeness in a succession of bodily postures; likeness in voice, or in
+the accents and intonations of the voice; likeness in the choice of
+words, and in the thoughts or sentiments expressed, whether by word,
+countenance, or gesture.
+
+All likeness and unlikeness of which we have any cognizance, resolve
+themselves into likeness and unlikeness between states of our own, or
+some other, mind. When we say that one body is like another, (since we
+know nothing of bodies but the sensations which they excite,) we mean
+really that there is a resemblance between the sensations excited by the
+two bodies, or between some portions at least of those sensations. If we
+say that two attributes are like one another, (since we know nothing of
+attributes except the sensations or states of feeling on which they are
+grounded,) we mean really that those sensations, or states of feeling,
+resemble each other. We may also say that two relations are alike. The
+fact of resemblance between relations is sometimes called _analogy_,
+forming one of the numerous meanings of that word. The relation in which
+Priam stood to Hector, namely, that of father and son, resembles the
+relation in which Philip stood to Alexander; resembles it so closely
+that they are called the same relation. The relation in which Cromwell
+stood to England resembles the relation in which Napoleon stood to
+France, though not so closely as to be called the same relation. The
+meaning in both these instances must be, that a resemblance existed
+between the facts which constituted the _fundamentum relationis_.
+
+This resemblance may exist in all conceivable gradations, from perfect
+undistinguishableness to something extremely slight. When we say, that a
+thought suggested to the mind of a person of genius is like a seed cast
+into the ground, because the former produces a multitude of other
+thoughts, and the latter a multitude of other seeds, this is saying that
+between the relation of an inventive mind to a thought contained in it,
+and the relation of a fertile soil to a seed contained in it, there
+exists a resemblance: the real resemblance being in the two _fundamenta
+relationis_, in each of which there occurs a germ, producing by its
+development a multitude of other things similar to itself. And as,
+whenever two objects are jointly concerned in a phenomenon, this
+constitutes a relation between those objects, so, if we suppose a second
+pair of objects concerned in a second phenomenon, the slightest
+resemblance between the two phenomena is sufficient to admit of its
+being said that the two relations resemble; provided, of course, the
+points of resemblance are found in those portions of the two phenomena
+respectively which are connoted by the relative names.
+
+While speaking of resemblance, it is necessary to take notice of an
+ambiguity of language, against which scarcely any one is sufficiently on
+his guard. Resemblance, when it exists in the highest degree of all,
+amounting to undistinguishableness, is often called identity, and the
+two similar things are said to be the same. I say often, not always; for
+we do not say that two visible objects, two persons for instance, are
+the same, because they are so much alike that one might be mistaken for
+the other: but we constantly use this mode of expression when speaking
+of feelings; as when I say that the sight of any object gives me the
+_same_ sensation or emotion to-day that it did yesterday, or the _same_
+which it gives to some other person. This is evidently an incorrect
+application of the word _same_; for the feeling which I had yesterday is
+gone, never to return; what I have to-day is another feeling, exactly
+like the former perhaps, but distinct from it; and it is evident that
+two different persons cannot be experiencing the same feeling, in the
+sense in which we say that they are both sitting at the same table. By a
+similar ambiguity we say, that two persons are ill of the _same_
+disease; that two persons hold the _same_ office; not in the sense in
+which we say that they are engaged in the same adventure, or sailing in
+the same ship, but in the sense that they fill offices exactly similar,
+though, perhaps, in distant places. Great confusion of ideas is often
+produced, and many fallacies engendered, in otherwise enlightened
+understandings, by not being sufficiently alive to the fact (in itself
+not always to be avoided), that they use the same name to express ideas
+so different as those of identity and undistinguishable resemblance.
+Among modern writers, Archbishop Whately stands almost alone in having
+drawn attention to this distinction, and to the ambiguity connected with
+it.
+
+Several relations, generally called by other names, are really cases of
+resemblance. As, for example, equality; which is but another word for
+the exact resemblance commonly called identity, considered as subsisting
+between things in respect of their _quantity_. And this example forms a
+suitable transition to the third and last of the three heads under
+which, as already remarked, Attributes are commonly arranged.
+
+
+V. QUANTITY.
+
+Sec. 12. Let us imagine two things, between which there is no difference
+(that is, no dissimilarity), except in quantity alone: for instance, a
+gallon of water, and more than a gallon of water. A gallon of water,
+like any other external object, makes its presence known to us by a set
+of sensations which it excites. Ten gallons of water are also an
+external object, making its presence known to us in a similar manner;
+and as we do not mistake ten gallons of water for a gallon of water, it
+is plain that the set of sensations is more or less different in the two
+cases. In like manner, a gallon of water, and a gallon of wine, are two
+external objects, making their presence known by two sets of sensations,
+which sensations are different from each other. In the first case,
+however, we say that the difference is in quantity; in the last there is
+a difference in quality, while the quantity of the water and of the wine
+is the same. What is the real distinction between the two cases? It is
+not the province of Logic to analyse it; nor to decide whether it is
+susceptible of analysis or not. For us the following considerations are
+sufficient. It is evident that the sensations I receive from the gallon
+of water, and those I receive from the gallon of wine, are not the same,
+that is, not precisely alike; neither are they altogether unlike: they
+are partly similar, partly dissimilar; and that in which they resemble
+is precisely that in which alone the gallon of water and the ten gallons
+do not resemble. That in which the gallon of water and the gallon of
+wine are like each other, and in which the gallon and the ten gallons of
+water are unlike each other, is called their quantity. This likeness
+and unlikeness I do not pretend to explain, no more than any other kind
+of likeness or unlikeness. But my object is to show, that when we say of
+two things that they differ in quantity, just as when we say that they
+differ in quality, the assertion is always grounded on a difference in
+the sensations which they excite. Nobody, I presume, will say, that to
+see, or to lift, or to drink, ten gallons of water, does not include in
+itself a different set of sensations from those of seeing, lifting, or
+drinking one gallon; or that to see or handle a foot-rule, and to see or
+handle a yard-measure made exactly like it, are the same sensations. I
+do not undertake to say what the difference in the sensations is.
+Everybody knows, and nobody can tell; no more than any one could tell
+what white is to a person who had never had the sensation. But the
+difference, so far as cognizable by our faculties, lies in the
+sensations. Whatever difference we say there is in the things
+themselves, is, in this as in all other cases, grounded, and grounded
+exclusively, on a difference in the sensations excited by them.
+
+
+VI. ATTRIBUTES CONCLUDED.
+
+Sec. 13. Thus, then, all the attributes of bodies which are classed under
+Quality or Quantity, are grounded on the sensations which we receive
+from those bodies, and may be defined, the powers which the bodies have
+of exciting those sensations. And the same general explanation has been
+found to apply to most of the attributes usually classed under the head
+of Relation. They, too, are grounded on some fact or phenomenon into
+which the related objects enter as parts; that fact or phenomenon having
+no meaning and no existence to us, except the series of sensations or
+other states of consciousness by which it makes itself known; and the
+relation being simply the power or capacity which the object possesses
+of taking part along with the correlated object in the production of
+that series of sensations or states of consciousness. We have been
+obliged, indeed, to recognise a somewhat different character in certain
+peculiar relations, those of succession and simultaneity, of likeness
+and unlikeness. These, not being grounded on any fact or phenomenon
+distinct from the related objects themselves, do not admit of the same
+kind of analysis. But these relations, though not, like other relations,
+grounded on states of consciousness, are themselves states of
+consciousness: resemblance is nothing but our feeling of resemblance;
+succession is nothing but our feeling of succession. Or, if this be
+disputed (and we cannot, without transgressing the bounds of our
+science, discuss it here), at least our knowledge of these relations,
+and even our possibility of knowledge, is confined to those which
+subsist between sensations, or other states of consciousness; for,
+though we ascribe resemblance, or succession, or simultaneity, to
+objects and to attributes, it is always in virtue of resemblance or
+succession or simultaneity in the sensations or states of consciousness
+which those objects excite, and on which those attributes are grounded.
+
+
+Sec. 14. In the preceding investigation we have, for the sake of
+simplicity, considered bodies only, and omitted minds. But what we have
+said, is applicable, _mutatis mutandis_, to the latter. The attributes
+of minds, as well as those of bodies, are grounded on states of feeling
+or consciousness. But in the case of a mind, we have to consider its own
+states, as well as those which it produces in other minds. Every
+attribute of a mind consists either in being itself affected in a
+certain way, or affecting other minds in a certain way. Considered in
+itself, we can predicate nothing of it but the series of its own
+feelings. When we say of any mind, that it is devout, or superstitious,
+or meditative, or cheerful, we mean that the ideas, emotions, or
+volitions implied in those words, form a frequently recurring part of
+the series of feelings, or states of consciousness, which fill up the
+sentient existence of that mind.
+
+In addition, however, to those attributes of a mind which are grounded
+on its own states of feeling, attributes may also be ascribed to it, in
+the same manner as to a body, grounded on the feelings which it excites
+in other minds. A mind does not, indeed, like a body, excite
+sensations, but it may excite thoughts or emotions. The most important
+example of attributes ascribed on this ground, is the employment of
+terms expressive of approbation or blame. When, for example, we say of
+any character, or (in other words) of any mind, that it is admirable, we
+mean that the contemplation of it excites the sentiment of admiration;
+and indeed somewhat more, for the word implies that we not only feel
+admiration, but approve that sentiment in ourselves. In some cases,
+under the semblance of a single attribute, two are really predicated:
+one of them, a state of the mind itself; the other, a state with which
+other minds are affected by thinking of it. As when we say of any one
+that he is generous. The word generosity expresses a certain state of
+mind, but being a term of praise, it also expresses that this state of
+mind excites in us another mental state, called approbation. The
+assertion made, therefore, is twofold, and of the following purport:
+Certain feelings form habitually a part of this person's sentient
+existence; and the idea of those feelings of his, excites the sentiment
+of approbation in ourselves or others.
+
+As we thus ascribe attributes to minds on the ground of ideas and
+emotions, so may we to bodies on similar grounds, and not solely on the
+ground of sensations: as in speaking of the beauty of a statue; since
+this attribute is grounded on the peculiar feeling of pleasure which the
+statue produces in our minds; which is not a sensation, but an emotion.
+
+
+VII. GENERAL RESULTS.
+
+Sec. 15. Our survey of the varieties of Things which have been, or which
+are capable of being, named--which have been, or are capable of being,
+either predicated of other Things, or themselves made the subject of
+predications--is now concluded.
+
+Our enumeration commenced with Feelings. These we scrupulously
+distinguished from the objects which excite them, and from the organs by
+which they are, or may be supposed to be, conveyed. Feelings are of
+four sorts: Sensations, Thoughts, Emotions, and Volitions. What are
+called Perceptions are merely a particular case of Belief, and belief is
+a kind of thought. Actions are merely volitions followed by an effect.
+If there be any other kind of mental state not included under these
+subdivisions, we did not think it necessary or proper in this place to
+discuss its existence, or the rank which ought to be assigned to it.
+
+After Feelings we proceeded to Substances. These are either Bodies or
+Minds. Without entering into the grounds of the metaphysical doubts
+which have been raised concerning the existence of Matter and Mind as
+objective realities, we stated as sufficient for us the conclusion in
+which the best thinkers are now for the most part agreed, that all we
+can know of Matter is the sensations which it gives us, and the order of
+occurrence of those sensations; and that while the substance Body is the
+unknown cause of our sensations, the substance Mind is the unknown
+recipient.
+
+The only remaining class of Nameable Things is Attributes; and these are
+of three kinds, Quality, Relation, and Quantity. Qualities, like
+substances, are known to us no otherwise than by the sensations or other
+states of consciousness which they excite: and while, in compliance with
+common usage, we have continued to speak of them as a distinct class of
+Things, we showed that in predicating them no one means to predicate
+anything but those sensations or states of consciousness, on which they
+may be said to be grounded, and by which alone they can be defined or
+described. Relations, except the simple cases of likeness and
+unlikeness, succession and simultaneity, are similarly grounded on some
+fact or phenomenon, that is, on some series of sensations or states of
+consciousness, more or less complicated. The third species of Attribute,
+Quantity, is also manifestly grounded on something in our sensations or
+states of feeling, since there is an indubitable difference in the
+sensations excited by a larger and a smaller bulk, or by a greater or a
+less degree of intensity, in any object of sense or of consciousness.
+All attributes, therefore, are to us nothing but either our sensations
+and other states of feeling, or something inextricably involved
+therein; and to this even the peculiar and simple relations just
+adverted to are not exceptions. Those peculiar relations, however, are
+so important, and, even if they might in strictness be classed among
+states of consciousness, are so fundamentally distinct from any other of
+those states, that it would be a vain subtlety to bring them under that
+common description, and it is necessary that they should be classed
+apart.
+
+As the result, therefore, of our analysis, we obtain the following as an
+enumeration and classification of all Nameable Things:--
+
+1st. Feelings, or States of Consciousness.
+
+2nd. The Minds which experience those feelings.
+
+3rd. The Bodies, or external objects, which excite certain of those
+feelings, together with the powers or properties whereby they excite
+them; these last being included rather in compliance with common
+opinion, and because their existence is taken for granted in the common
+language from which I cannot prudently deviate, than because the
+recognition of such powers or properties as real existences appears to
+be warranted by a sound philosophy.
+
+4th, and last. The Successions and Co-existences, the Likenesses and
+Unlikenesses, between feelings or states of consciousness. Those
+relations, when considered as subsisting between other things, exist in
+reality only between the states of consciousness which those things, if
+bodies, excite, if minds, either excite or experience.
+
+This, until a better can be suggested, may serve as a substitute for the
+abortive Classification of Existences, termed the Categories of
+Aristotle. The practical application of it will appear when we commence
+the inquiry into the Import of Propositions; in other words, when we
+inquire what it is which the mind actually believes, when it gives what
+is called its assent to a proposition.
+
+These four classes comprising, if the classification be correct, all
+Nameable Things, these or some of them must of course compose the
+signification of all names; and of these, or some of them, is made up
+whatever we call a fact.
+
+For distinction's sake, every fact which is solely composed of feelings
+or states of consciousness considered as such, is often called a
+Psychological or Subjective fact; while every fact which is composed,
+either wholly or in part, of something different from these, that is, of
+substances and attributes, is called an Objective fact. We may say,
+then, that every objective fact is grounded on a corresponding
+subjective one; and has no meaning to us, (apart from the subjective
+fact which corresponds to it,) except as a name for the unknown and
+inscrutable process by which that subjective or psychological fact is
+brought to pass.
+
+
+
+
+CHAPTER IV.
+
+OF PROPOSITIONS.
+
+
+Sec. 1. In treating of Propositions, as already in treating of Names, some
+considerations of a comparatively elementary nature respecting their
+form and varieties must be premised, before entering upon that analysis
+of the import conveyed by them, which is the real subject and purpose of
+this preliminary book.
+
+A proposition, we have before said, is a portion of discourse in which a
+predicate is affirmed or denied of a subject. A predicate and a subject
+are all that is necessarily required to make up a proposition: but as we
+cannot conclude from merely seeing two names put together, that they are
+a predicate and a subject, that is, that one of them is intended to be
+affirmed or denied of the other, it is necessary that there should be
+some mode or form of indicating that such is the intention; some sign to
+distinguish a predication from any other kind of discourse. This is
+sometimes done by a slight alteration of one of the words, called an
+_inflection_; as when we say, Fire burns; the change of the second word
+from _burn_ to _burns_ showing that we mean to affirm the predicate burn
+of the subject fire. But this function is more commonly fulfilled by the
+word _is_, when an affirmation is intended, _is not_, when a negation;
+or by some other part of the verb _to be_. The word which thus serves
+the purpose of a sign of predication is called, as we formerly observed,
+the _copula_. It is important that there should be no indistinctness in
+our conception of the nature and office of the copula; for confused
+notions respecting it are among the causes which have spread mysticism
+over the field of logic, and perverted its speculations into
+logomachies.
+
+It is apt to be supposed that the copula is something more than a mere
+sign of predication; that it also signifies existence. In the
+proposition, Socrates is just, it may seem to be implied not only that
+the quality _just_ can be affirmed of Socrates, but moreover that
+Socrates _is_, that is to say, exists. This, however, only shows that
+there is an ambiguity in the word _is_; a word which not only performs
+the function of the copula in affirmations, but has also a meaning of
+its own, in virtue of which it may itself be made the predicate of a
+proposition. That the employment of it as a copula does not necessarily
+include the affirmation of existence, appears from such a proposition as
+this, A centaur is a fiction of the poets; where it cannot possibly be
+implied that a centaur exists, since the proposition itself expressly
+asserts that the thing has no real existence.
+
+Many volumes might be filled with the frivolous speculations concerning
+the nature of Being, ([Greek: to on, ousia], Ens, Entitas, Essentia, and
+the like) which have arisen from overlooking this double meaning of the
+word _to be_; from supposing that when it signifies _to exist_, and when
+it signifies to _be_ some specified thing, as to _be_ a man, to _be_
+Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a
+nonentity, it must still, at bottom, answer to the same idea; and that a
+meaning must be found for it which shall suit all these cases. The fog
+which rose from this narrow spot diffused itself at an early period over
+the whole surface of metaphysics. Yet it becomes us not to triumph over
+the great intellects of Plato and Aristotle because we are now able to
+preserve ourselves from many errors into which they, perhaps inevitably,
+fell. The fire-teazer of a modern steam-engine produces by his exertions
+far greater effects than Milo of Crotona could, but he is not therefore
+a stronger man. The Greeks seldom knew any language but their own. This
+rendered it far more difficult for them than it is for us, to acquire a
+readiness in detecting ambiguities. One of the advantages of having
+accurately studied a plurality of languages, especially of those
+languages which eminent thinkers have used as the vehicle of their
+thoughts, is the practical lesson we learn respecting the ambiguities of
+words, by finding that the same word in one language corresponds, on
+different occasions, to different words in another. When not thus
+exercised, even the strongest understandings find it difficult to
+believe that things which have a common name, have not in some respect
+or other a common nature; and often expend much labour very unprofitably
+(as was frequently done by the two philosophers just mentioned) in vain
+attempts to discover in what this common nature consists. But, the habit
+once formed, intellects much inferior are capable of detecting even
+ambiguities which are common to many languages: and it is surprising
+that the one now under consideration, though it exists in the modern
+languages as well as in the ancient, should have been overlooked by
+almost all authors. The quantity of futile speculation which had been
+caused by a misapprehension of the nature of the copula, was hinted at
+by Hobbes; but Mr. James Mill[15] was, I believe, the first who
+distinctly characterized the ambiguity, and pointed out how many errors
+in the received systems of philosophy it has had to answer for. It has
+indeed misled the moderns scarcely less than the ancients, though their
+mistakes, because our understandings are not yet so completely
+emancipated from their influence, do not appear equally irrational.
+
+We shall now briefly review the principal distinctions which exist among
+propositions, and the technical terms most commonly in use to express
+those distinctions.
+
+
+Sec. 2. A proposition being a portion of discourse in which something is
+affirmed or denied of something, the first division of propositions is
+into affirmative and negative. An affirmative proposition is that in
+which the predicate is _affirmed_ of the subject; as, Caesar is dead. A
+negative proposition is that in which the predicate is _denied_ of the
+subject; as, Caesar is not dead. The copula, in this last species of
+proposition, consists of the words _is not_, which are the sign of
+negation; _is_ being the sign of affirmation.
+
+Some logicians, among whom may be mentioned Hobbes, state this
+distinction differently; they recognise only one form of copula, _is_,
+and attach the negative sign to the predicate. "Caesar is dead," and
+"Caesar is not dead," according to these writers, are propositions
+agreeing not in the subject and predicate, but in the subject only. They
+do not consider "dead," but "not dead," to be the predicate of the
+second proposition, and they accordingly define a negative proposition
+to be one in which the predicate is a negative name. The point, though
+not of much practical moment, deserves notice as an example (not
+unfrequent in logic) where by means of an apparent simplification, but
+which is merely verbal, matters are made more complex than before. The
+notion of these writers was, that they could get rid of the distinction
+between affirming and denying, by treating every case of denying as the
+affirming of a negative name. But what is meant by a negative name? A
+name expressive of the _absence_ of an attribute. So that when we affirm
+a negative name, what we are really predicating is absence and not
+presence; we are asserting not that anything is, but that something is
+not; to express which operation no word seems so proper as the word
+denying. The fundamental distinction is between a fact and the
+non-existence of that fact; between seeing something and not seeing it,
+between Caesar's being dead and his not being dead; and if this were a
+merely verbal distinction, the generalization which brings both within
+the same form of assertion would be a real simplification: the
+distinction, however, being real, and in the facts, it is the
+generalization confounding the distinction that is merely verbal; and
+tends to obscure the subject, by treating the difference between two
+kinds of truths as if it were only a difference between two kinds of
+words. To put things together, and to put them or keep them asunder,
+will remain different operations, whatever tricks we may play with
+language.
+
+A remark of a similar nature may be applied to most of those
+distinctions among propositions which are said to have reference to
+their _modality_; as, difference of tense or time; the sun _did_ rise,
+the sun _is_ rising, the sun _will_ rise. These differences, like that
+between affirmation and negation, might be glossed over by considering
+the incident of time as a mere modification of the predicate: thus, The
+sun is _an object having risen_, The sun is _an object now rising_, The
+sun is _an object to rise hereafter_. But the simplification would be
+merely verbal. Past, present, and future, do not constitute so many
+different kinds of rising; they are designations belonging to the event
+asserted, to the _sun's_ rising to-day. They affect, not the predicate,
+but the applicability of the predicate to the particular subject. That
+which we affirm to be past, present, or future, is not what the subject
+signifies, nor what the predicate signifies, but specifically and
+expressly what the predication signifies; what is expressed only by the
+proposition as such, and not by either or both of the terms. Therefore
+the circumstance of time is properly considered as attaching to the
+copula, which is the sign of predication, and not to the predicate. If
+the same cannot be said of such modifications as these, Caesar _may_ be
+dead; Caesar is _perhaps_ dead; it is _possible_ that Caesar is dead; it
+is only because these fall altogether under another head, being properly
+assertions not of anything relating to the fact itself, but of the state
+of our own mind in regard to it; namely, our absence of disbelief of it.
+Thus "Caesar may be dead" means "I am not sure that Caesar is alive."
+
+
+Sec. 3. The next division of propositions is into Simple and Complex. A
+simple proposition is that in which one predicate is affirmed or denied
+of one subject. A complex proposition is that in which there is more
+than one predicate, or more than one subject, or both.
+
+At first sight this division has the air of an absurdity; a solemn
+distinction of things into one and more than one; as if we were to
+divide horses into single horses and teams of horses. And it is true
+that what is called a complex proposition is often not a proposition at
+all, but several propositions, held together by a conjunction. Such, for
+example, is this: Caesar is dead, and Brutus is alive: or even this,
+Caesar is dead, _but_ Brutus is alive. There are here two distinct
+assertions; and we might as well call a street a complex house, as
+these two propositions a complex proposition. It is true that the
+syncategorematic words _and_ and _but_ have a meaning; but that meaning
+is so far from making the two propositions one, that it adds a third
+proposition to them. All particles are abbreviations, and generally
+abbreviations of propositions; a kind of short-hand, whereby something
+which, to be expressed fully, would have required a proposition or a
+series of propositions, is suggested to the mind at once. Thus the
+words, Caesar is dead and Brutus is alive, are equivalent to these: Caesar
+is dead; Brutus is alive; it is desired that the two preceding
+propositions should be thought of together. If the words were, Caesar is
+dead _but_ Brutus is alive, the sense would be equivalent to the same
+three propositions together with a fourth; "between the two preceding
+propositions there exists a contrast:" viz. either between the two facts
+themselves, or between the feelings with which it is desired that they
+should be regarded.
+
+In the instances cited the two propositions are kept visibly distinct,
+each subject having its separate predicate, and each predicate its
+separate subject. For brevity, however, and to avoid repetition, the
+propositions are often blended together: as in this, "Peter and James
+preached at Jerusalem and in Galilee," which contains four propositions:
+Peter preached at Jerusalem, Peter preached in Galilee, James preached
+at Jerusalem, James preached in Galilee.
+
+We have seen that when the two or more propositions comprised in what is
+called a complex proposition are stated absolutely, and not under any
+condition or proviso, it is not a proposition at all, but a plurality of
+propositions; since what it expresses is not a single assertion, but
+several assertions, which, if true when joined, are true also when
+separated. But there is a kind of proposition which, though it contains
+a plurality of subjects and of predicates, and may be said in one sense
+of the word to consist of several propositions, contains but one
+assertion; and its truth does not at all imply that of the simple
+propositions which compose it. An example of this is, when the simple
+propositions are connected by the particle _or_; as, Either A is B or C
+is D; or by the particle _if_; as, A is B if C is D. In the former case,
+the proposition is called _disjunctive_, in the latter, _conditional_:
+the name _hypothetical_ was originally common to both. As has been well
+remarked by Archbishop Whately and others, the disjunctive form is
+resolvable into the conditional; every disjunctive proposition being
+equivalent to two or more conditional ones. "Either A is B or C is D,"
+means, "if A is not B, C is D; and if C is not D, A is B." All
+hypothetical propositions, therefore, though disjunctive in form, are
+conditional in meaning; and the words hypothetical and conditional may
+be, as indeed they generally are, used synonymously. Propositions in
+which the assertion is not dependent on a condition, are said, in the
+language of logicians, to be _categorical_.
+
+An hypothetical proposition is not, like the pretended complex
+propositions which we previously considered, a mere aggregation of
+simple propositions. The simple propositions which form part of the
+words in which it is couched, form no part of the assertion which it
+conveys. When we say, If the Koran comes from God, Mahomet is the
+prophet of God, we do not intend to affirm either that the Koran does
+come from God, or that Mahomet is really his prophet. Neither of these
+simple propositions may be true, and yet the truth of the hypothetical
+proposition may be indisputable. What is asserted is not the truth of
+either of the propositions, but the inferribility of the one from the
+other. What, then, is the subject, and what the predicate of the
+hypothetical proposition? "The Koran" is not the subject of it, nor is
+"Mahomet:" for nothing is affirmed or denied either of the Koran or of
+Mahomet. The real subject of the predication is the entire proposition,
+"Mahomet is the prophet of God;" and the affirmation is, that this is a
+legitimate inference from the proposition, "The Koran comes from God."
+The subject and predicate, therefore, of an hypothetical proposition are
+names of propositions. The subject is some one proposition. The
+predicate is a general relative name applicable to propositions; of this
+form--"an inference from so and so." A fresh instance is here afforded
+of the remark, that particles are abbreviations; since "_If_ A is B, C
+is D," is found to be an abbreviation of the following: "The proposition
+C is D, is a legitimate inference from the proposition A is B."
+
+The distinction, therefore, between hypothetical and categorical
+propositions, is not so great as it at first appears. In the
+conditional, as well as in the categorical form, one predicate is
+affirmed of one subject, and no more: but a conditional proposition is a
+proposition concerning a proposition; the subject of the assertion is
+itself an assertion. Nor is this a property peculiar to hypothetical
+propositions. There are other classes of assertions concerning
+propositions. Like other things, a proposition has attributes which may
+be predicated of it. The attribute predicated of it in an hypothetical
+proposition, is that of being an inference from a certain other
+proposition. But this is only one of many attributes that might be
+predicated. We may say, That the whole is greater than its part, is an
+axiom in mathematics: That the Holy Ghost proceeds from the Father
+alone, is a tenet of the Greek Church: The doctrine of the divine right
+of kings was renounced by Parliament at the Revolution: The
+infallibility of the Pope has no countenance from Scripture. In all
+these cases the subject of the predication is an entire proposition.
+That which these different predicates are affirmed of, is _the
+proposition_, "the whole is greater than its part;" _the proposition_,
+"the Holy Ghost proceeds from the Father alone;" _the proposition_,
+"kings have a divine right;" _the proposition_, "the Pope is
+infallible."
+
+Seeing, then, that there is much less difference between hypothetical
+propositions and any others, than one might be led to imagine from their
+form, we should be at a loss to account for the conspicuous position
+which they have been selected to fill in treatises on logic, if we did
+not remember that what they predicate of a proposition, namely, its
+being an inference from something else, is precisely that one of its
+attributes with which most of all a logician is concerned.
+
+
+Sec. 4. The next of the common divisions of Propositions is into
+Universal, Particular, Indefinite, and Singular: a distinction founded
+on the degree of generality in which the name, which is the subject of
+the proposition, is to be understood. The following are examples:
+
+  _All men_ are mortal--       Universal.
+  _Some men_ are mortal--      Particular.
+  _Man_ is mortal--            Indefinite.
+  _Julius Caesar_ is mortal--   Singular.
+
+The proposition is Singular, when the subject is an individual name. The
+individual name needs not be a proper name. "The Founder of Christianity
+was crucified," is as much a singular proposition as "Christ was
+crucified."
+
+When the name which is the subject of the proposition is a general name,
+we may intend to affirm or deny the predicate, either of all the things
+that the subject denotes, or only of some. When the predicate is
+affirmed or denied of all and each of the things denoted by the subject,
+the proposition is universal; when of some undefined portion of them
+only, it is particular. Thus, All men are mortal; Every man is mortal;
+are universal propositions. No man is immortal, is also an universal
+proposition, since the predicate, immortal, is denied of each and every
+individual denoted by the term man; the negative proposition being
+exactly equivalent to the following, Every man is not-immortal. But
+"some men are wise," "some men are not wise," are particular
+propositions; the predicate _wise_ being in the one case affirmed and in
+the other denied not of each and every individual denoted by the term
+man, but only of each and every one of some portion of those
+individuals, without specifying what portion; for if this were
+specified, the proposition would be changed either into a singular
+proposition, or into an universal proposition with a different subject;
+as, for instance, "all _properly instructed_ men are wise." There are
+other forms of particular propositions; as, "_Most_ men are imperfectly
+educated:" it being immaterial how large a portion of the subject the
+predicate is asserted of, as long as it is left uncertain how that
+portion is to be distinguished from the rest.
+
+When the form of the expression does not clearly show whether the
+general name which is the subject of the proposition is meant to stand
+for all the individuals denoted by it, or only for some of them, the
+proposition is, by some logicians, called Indefinite; but this, as
+Archbishop Whately observes, is a solecism, of the same nature as that
+committed by some grammarians when in their list of genders they
+enumerate the _doubtful_ gender. The speaker must mean to assert the
+proposition either as an universal or as a particular proposition,
+though he has failed to declare which: and it often happens that though
+the words do not show which of the two he intends, the context, or the
+custom of speech, supplies the deficiency. Thus, when it is affirmed
+that "Man is mortal," nobody doubts that the assertion is intended of
+all human beings; and the word indicative of universality is commonly
+omitted, only because the meaning is evident without it. In the
+proposition, "Wine is good," it is understood with equal readiness,
+though for somewhat different reasons, that the assertion is not
+intended to be universal, but particular.[16]
+
+When a general name stands for each and every individual which it is a
+name of, or in other words, which it denotes, it is said by logicians to
+be _distributed_, or taken distributively. Thus, in the proposition, All
+men are mortal, the subject, Man, is distributed, because mortality is
+affirmed of each and every man. The predicate, Mortal, is not
+distributed, because the only mortals who are spoken of in the
+proposition are those who happen to be men; while the word may, for
+aught that appears, and in fact does, comprehend within it an indefinite
+number of objects besides men. In the proposition, Some men are mortal,
+both the predicate and the subject are undistributed. In the following,
+No men have wings, both the predicate and the subject are distributed.
+Not only is the attribute of having wings denied of the entire class
+Man, but that class is severed and cast out from the whole of the class
+Winged, and not merely from some part of that class.
+
+This phraseology, which is of great service in stating and
+demonstrating the rules of the syllogism, enables us to express very
+concisely the definitions of an universal and a particular proposition.
+An universal proposition is that of which the subject is distributed; a
+particular proposition is that of which the subject is undistributed.
+
+There are many more distinctions among propositions than those we have
+here stated, some of them of considerable importance. But, for
+explaining and illustrating these, more suitable opportunities will
+occur in the sequel.
+
+
+
+
+CHAPTER V.
+
+OF THE IMPORT OF PROPOSITIONS.
+
+
+Sec. 1. An inquiry into the nature of propositions must have one of two
+objects: to analyse the state of mind called Belief, or to analyse what
+is believed. All language recognises a difference between a doctrine or
+opinion, and the fact of entertaining the opinion; between assent, and
+what is assented to.
+
+Logic, according to the conception here formed of it, has no concern
+with the nature of the act of judging or believing; the consideration of
+that act, as a phenomenon of the mind, belongs to another science.
+Philosophers, however, from Descartes downwards, and especially from the
+era of Leibnitz and Locke, have by no means observed this distinction;
+and would have treated with great disrespect any attempt to analyse the
+import of Propositions, unless founded on an analysis of the act of
+Judgment. A proposition, they would have said, is but the expression in
+words of a Judgment. The thing expressed, not the mere verbal
+expression, is the important matter. When the mind assents to a
+proposition, it judges. Let us find out what the mind does when it
+judges, and we shall know what propositions mean, and not otherwise.
+
+Conformably to these views, almost all the writers on Logic in the last
+two centuries, whether English, German, or French, have made their
+theory of Propositions, from one end to the other, a theory of
+Judgments. They considered a Proposition, or a Judgment, for they used
+the two words indiscriminately, to consist in affirming or denying one
+_idea_ of another. To judge, was to put two ideas together, or to bring
+one idea under another, or to compare two ideas, or to perceive the
+agreement or disagreement between two ideas: and the whole doctrine of
+Propositions, together with the theory of Reasoning, (always necessarily
+founded on the theory of Propositions,) was stated as if Ideas, or
+Conceptions, or whatever other term the writer preferred as a name for
+mental representations generally, constituted essentially the subject
+matter and substance of those operations.
+
+It is, of course, true, that in any case of judgment, as for instance
+when we judge that gold is yellow, a process takes place in our minds,
+of which some one or other of these theories is a partially correct
+account. We must have the idea of gold and the idea of yellow, and these
+two ideas must be brought together in our mind. But in the first place,
+it is evident that this is only a part of what takes place; for we may
+put two ideas together without any act of belief; as when we merely
+imagine something, such as a golden mountain; or when we actually
+disbelieve: for in order even to disbelieve that Mahomet was an apostle
+of God, we must put the idea of Mahomet and that of an apostle of God
+together. To determine what it is that happens in the case of assent or
+dissent besides putting two ideas together, is one of the most intricate
+of metaphysical problems. But whatever the solution may be, we may
+venture to assert that it can have nothing whatever to do with the
+import of propositions; for this reason, that propositions (except
+sometimes when the mind itself is the subject treated of) are not
+assertions respecting our ideas of things, but assertions respecting the
+things themselves. In order to believe that gold is yellow, I must,
+indeed, have the idea of gold, and the idea of yellow, and something
+having reference to those ideas must take place in my mind; but my
+belief has not reference to the ideas, it has reference to the things.
+What I believe, is a fact relating to the outward thing, gold, and to
+the impression made by that outward thing upon the human organs; not a
+fact relating to my conception of gold, which would be a fact in my
+mental history, not a fact of external nature. It is true, that in order
+to believe this fact in external nature, another fact must take place in
+my mind, a process must be performed upon my ideas; but so it must in
+everything else that I do. I cannot dig the ground unless I have the
+idea of the ground, and of a spade, and of all the other things I am
+operating upon, and unless I put those ideas together.[17] But it would
+be a very ridiculous description of digging the ground to say that it is
+putting one idea into another. Digging is an operation which is
+performed upon the things themselves, though it cannot be performed
+unless I have in my mind the ideas of them. And in like manner,
+believing is an act which has for its subject the facts themselves,
+though a previous mental conception of the facts is an indispensable
+condition. When I say that fire causes heat, do I mean that my idea of
+fire causes my idea of heat? No: I mean that the natural phenomenon,
+fire, causes the natural phenomenon, heat. When I mean to assert
+anything respecting the ideas, I give them their proper name, I call
+them ideas: as when I say, that a child's idea of a battle is unlike the
+reality, or that the ideas entertained of the Deity have a great effect
+on the characters of mankind.
+
+The notion that what is of primary importance to the logician in a
+proposition, is the relation between the two _ideas_ corresponding to
+the subject and predicate, (instead of the relation between the two
+_phenomena_ which they respectively express,) seems to me one of the
+most fatal errors ever introduced into the philosophy of Logic; and the
+principal cause why the theory of the science has made such
+inconsiderable progress during the last two centuries. The treatises on
+Logic, and on the branches of Mental Philosophy connected with Logic,
+which have been produced since the intrusion of this cardinal error,
+though sometimes written by men of extraordinary abilities and
+attainments, almost always tacitly imply a theory that the investigation
+of truth consists in contemplating and handling our ideas, or
+conceptions of things, instead of the things themselves: a doctrine
+tantamount to the assertion, that the only mode of acquiring knowledge
+of nature is to study it at second hand, as represented in our own
+minds. Meanwhile, inquiries into every kind of natural phenomena were
+incessantly establishing great and fruitful truths on most important
+subjects, by processes upon which these views of the nature of Judgment
+and Reasoning threw no light, and in which they afforded no assistance
+whatever. No wonder that those who knew by practical experience how
+truths are arrived at, should deem a science futile, which consisted
+chiefly of such speculations. What has been done for the advancement of
+Logic since these doctrines came into vogue, has been done not by
+professed logicians, but by discoverers in the other sciences; in whose
+methods of investigation many principles of logic, not previously
+thought of, have successively come forth into light, but who have
+generally committed the error of supposing that nothing whatever was
+known of the art of philosophizing by the old logicians, because their
+modern interpreters have written to so little purpose respecting it.
+
+We have to inquire, then, on the present occasion, not into Judgment,
+but judgments; not into the act of believing, but into the thing
+believed. What is the immediate object of belief in a Proposition? What
+is the matter of fact signified by it? What is it to which, when I
+assert the proposition, I give my assent, and call upon others to give
+theirs? What is that which is expressed by the form of discourse called
+a Proposition, and the conformity of which to fact constitutes the truth
+of the proposition?
+
+
+Sec. 2. One of the clearest and most consecutive thinkers whom this country
+or the world has produced, I mean Hobbes, has given the following answer
+to this question. In every proposition (says he) what is signified is,
+the belief of the speaker that the predicate is a name of the same thing
+of which the subject is a name; and if it really is so, the proposition
+is true. Thus the proposition, All men are living beings (he would say)
+is true, because _living being_ is a name of everything of which _man_
+is a name. All men are six feet high, is not true, because _six feet
+high_ is not a name of everything (though it is of some things) of which
+_man_ is a name.
+
+What is stated in this theory as the definition of a true proposition,
+must be allowed to be a property which all true propositions possess.
+The subject and predicate being both of them names of things, if they
+were names of quite different things the one name could not,
+consistently with its signification, be predicated of the other. If it
+be true that some men are copper-coloured, it must be true--and the
+proposition does really assert--that among the individuals denoted by
+the name man, there are some who are also among those denoted by the
+name copper-coloured. If it be true that all oxen ruminate, it must be
+true that all the individuals denoted by the name ox are also among
+those denoted by the name ruminating; and whoever asserts that all oxen
+ruminate, undoubtedly does assert that this relation subsists between
+the two names.
+
+The assertion, therefore, which, according to Hobbes, is the only one
+made in any proposition, really is made in every proposition: and his
+analysis has consequently one of the requisites for being the true one.
+We may go a step farther; it is the only analysis that is rigorously
+true of all propositions without exception. What he gives as the meaning
+of propositions, is part of the meaning of all propositions, and the
+whole meaning of some. This, however, only shows what an extremely
+minute fragment of meaning it is quite possible to include within the
+logical formula of a proposition. It does not show that no proposition
+means more. To warrant us in putting together two words with a copula
+between them, it is really enough that the thing or things denoted by
+one of the names should be capable, without violation of usage, of being
+called by the other name also. If, then, this be all the meaning
+necessarily implied in the form of discourse called a Proposition, why
+do I object to it as the scientific definition of what a proposition
+means? Because, though the mere collocation which makes the proposition
+a proposition, conveys no more than this scanty amount of meaning, that
+same collocation combined with other circumstances, that _form_
+combined with other _matter_, does convey more, and much more.
+
+The only propositions of which Hobbes' principle is a sufficient
+account, are that limited and unimportant class in which both the
+predicate and the subject are proper names. For, as has already been
+remarked, proper names have strictly no meaning; they are mere marks for
+individual objects: and when a proper name is predicated of another
+proper name, all the signification conveyed is, that both the names are
+marks for the same object. But this is precisely what Hobbes produces as
+a theory of predication in general. His doctrine is a full explanation
+of such predications as these: Hyde was Clarendon, or, Tully is Cicero.
+It exhausts the meaning of those propositions. But it is a sadly
+inadequate theory of any others. That it should ever have been thought
+of as such, can be accounted for only by the fact, that Hobbes, in
+common with the other Nominalists, bestowed little or no attention upon
+the _connotation_ of words; and sought for their meaning exclusively in
+what they _denote_: as if all names had been (what none but proper names
+really are) marks put upon individuals; and as if there were no
+difference between a proper and a general name, except that the first
+denotes only one individual, and the last a greater number.
+
+It has been seen, however, that the meaning of all names, except proper
+names and that portion of the class of abstract names which are not
+connotative, resides in the connotation. When, therefore, we are
+analysing the meaning of any proposition in which the predicate and the
+subject, or either of them, are connotative names, it is to the
+connotation of those terms that we must exclusively look, and not to
+what they _denote_, or in the language of Hobbes (language so far
+correct) are names of.
+
+In asserting that the truth of a proposition depends on the conformity
+of import between its terms, as, for instance, that the proposition,
+Socrates is wise, is a true proposition, because Socrates and wise are
+names applicable to, or, as he expresses it, names of, the same person;
+it is very remarkable that so powerful a thinker should not have asked
+himself the question, But how came they to be names of the same person?
+Surely not because such was the intention of those who invented the
+words. When mankind fixed the meaning of the word wise, they were not
+thinking of Socrates, nor, when his parents gave him the name of
+Socrates, were they thinking of wisdom. The names _happen_ to fit the
+same person because of a certain _fact_, which fact was not known, nor
+in being, when the names were invented. If we want to know what the fact
+is, we shall find the clue to it in the _connotation_ of the names.
+
+A bird or a stone, a man, or a wise man, means simply, an object having
+such and such attributes. The real meaning of the word man, is those
+attributes, and not Smith, Brown, and the remainder of the individuals.
+The word _mortal_, in like manner connotes a certain attribute or
+attributes; and when we say, All men are mortal, the meaning of the
+proposition is, that all beings which possess the one set of attributes,
+possess also the other. If, in our experience, the attributes connoted
+by _man_ are always accompanied by the attribute connoted by _mortal_,
+it will follow as a consequence, that the class _man_ will be wholly
+included in the class _mortal_, and that _mortal_ will be a name of all
+things of which _man_ is a name: but why? Those objects are brought
+under the name, by possessing the attributes connoted by it: but their
+possession of the attributes is the real condition on which the truth of
+the proposition depends; not their being called by the name. Connotative
+names do not precede, but follow, the attributes which they connote. If
+one attribute happens to be always found in conjunction with another
+attribute, the concrete names which answer to those attributes will of
+course be predicable of the same subjects, and may be said, in Hobbes'
+language, (in the propriety of which on this occasion I fully concur,)
+to be two names for the same things. But the possibility of a concurrent
+application of the two names, is a mere consequence of the conjunction
+between the two attributes, and was, in most cases, never thought of
+when the names were introduced and their signification fixed. That the
+diamond is combustible, was a proposition certainly not dreamt of when
+the words Diamond and Combustible first received their meaning; and
+could not have been discovered by the most ingenious and refined
+analysis of the signification of those words. It was found out by a very
+different process, namely, by exerting the senses, and learning from
+them, that the attribute of combustibility existed in the diamonds upon
+which the experiment was tried; the number or character of the
+experiments being such, that what was true of those individuals might be
+concluded to be true of all substances "called by the name," that is, of
+all substances possessing the attributes which the name connotes. The
+assertion, therefore, when analysed, is, that wherever we find certain
+attributes, there will be found a certain other attribute: which is not
+a question of the signification of names, but of laws of nature; the
+order existing among phenomena.
+
+
+Sec. 3. Although Hobbes' theory of Predication has not, in the terms in
+which he stated it, met with a very favourable reception from subsequent
+thinkers, a theory virtually identical with it, and not by any means so
+perspicuously expressed, may almost be said to have taken the rank of an
+established opinion. The most generally received notion of Predication
+decidedly is that it consists in referring something to a class, _i.e._,
+either placing an individual under a class, or placing one class under
+another class. Thus, the proposition, Man is mortal, asserts, according
+to this view of it, that the class man is included in the class mortal.
+"Plato is a philosopher," asserts that the individual Plato is one of
+those who compose the class philosopher. If the proposition is negative,
+then instead of placing something in a class, it is said to exclude
+something from a class. Thus, if the following be the proposition, The
+elephant is not carnivorous; what is asserted (according to this theory)
+is, that the elephant is excluded, from the class carnivorous, or is not
+numbered among the things comprising that class. There is no real
+difference, except in language, between this theory of Predication and
+the theory of Hobbes. For a class _is_ absolutely nothing but an
+indefinite number of individuals denoted by a general name. The name
+given to them in common, is what makes them a class. To refer anything
+to a class, therefore, is to look upon it as one of the things which are
+to be called by that common name. To exclude it from a class, is to say
+that the common name is not applicable to it.
+
+How widely these views of predication have prevailed, is evident from
+this, that they are the basis of the celebrated _dictum de omni et
+nullo_. When the syllogism is resolved, by all who treat of it, into an
+inference that what is true of a class is true of all things whatever
+that belong to the class; and when this is laid down by almost all
+professed logicians as the ultimate principle to which all reasoning
+owes its validity; it is clear that in the general estimation of
+logicians, the propositions of which reasonings are composed can be the
+expression of nothing but the process of dividing things into classes,
+and referring everything to its proper class.
+
+This theory appears to me a signal example of a logical error very often
+committed in logic, that of [Greek: hysteron proteron], or explaining a
+thing by something which presupposes it. When I say that snow is white,
+I may and ought to be thinking of snow as a class, because I am
+asserting a proposition as true of all snow: but I am certainly not
+thinking of white objects as a class; I am thinking of no white object
+whatever except snow, but only of that, and of the sensation of white
+which it gives me. When, indeed, I have judged, or assented to the
+propositions, that snow is white, and that several other things are also
+white, I gradually begin to think of white objects as a class, including
+snow and those other things. But this is a conception which followed,
+not preceded, those judgments, and therefore cannot be given as an
+explanation of them. Instead of explaining the effect by the cause, this
+doctrine explains the cause by the effect, and is, I conceive, founded
+on a latent misconception of the nature of classification.
+
+There is a sort of language very generally prevalent in these
+discussions, which seems to suppose that classification is an
+arrangement and grouping of definite and known individuals: that when
+names were imposed, mankind took into consideration all the individual
+objects in the universe, distributed them into parcels or lists, and
+gave to the objects of each list a common name, repeating this operation
+_toties quoties_ until they had invented all the general names of which
+language consists; which having been once done, if a question
+subsequently arises whether a certain general name can be truly
+predicated of a certain particular object, we have only (as it were) to
+read the roll of the objects upon which that name was conferred, and see
+whether the object about which the question arises is to be found among
+them. The framers of language (it would seem to be supposed) have
+predetermined all the objects that are to compose each class, and we
+have only to refer to the record of an antecedent decision.
+
+So absurd a doctrine will be owned by nobody when thus nakedly stated;
+but if the commonly received explanations of classification and naming
+do not imply this theory, it requires to be shown how they admit of
+being reconciled with any other.
+
+General names are not marks put upon definite objects; classes are not
+made by drawing a line round a given number of assignable individuals.
+The objects which compose any given class are perpetually fluctuating.
+We may frame a class without knowing the individuals, or even any of the
+individuals, of which it may be composed; we may do so while believing
+that no such individuals exist. If by the _meaning_ of a general name
+are to be understood the things which it is the name of, no general
+name, except by accident, has a fixed meaning at all, or ever long
+retains the same meaning. The only mode in which any general name has a
+definite meaning, is by being a name of an indefinite variety of things;
+namely, of all things, known or unknown, past, present, or future, which
+possess certain definite attributes. When, by studying not the meaning
+of words, but the phenomena of nature, we discover that these attributes
+are possessed by some object not previously known to possess them, (as
+when chemists found that the diamond was combustible), we include this
+new object in the class; but it did not already belong to the class. We
+place the individual in the class because the proposition is true; the
+proposition is not true because the object is placed in the class.
+
+It will appear hereafter, in treating of reasoning, how much the theory
+of that intellectual process has been vitiated by the influence of these
+erroneous notions, and by the habit which they exemplify of assimilating
+all the operations of the human understanding which have truth for their
+object, to processes of mere classification and naming. Unfortunately,
+the minds which have been entangled in this net are precisely those
+which have escaped the other cardinal error commented upon in the
+beginning of the present chapter. Since the revolution which dislodged
+Aristotle from the schools, logicians may almost be divided into those
+who have looked upon reasoning as essentially an affair of Ideas, and
+those who have looked upon it as essentially an affair of Names.
+
+Although, however, Hobbes' theory of Predication, according to the
+well-known remark of Leibnitz, and the avowal of Hobbes himself,[18]
+renders truth and falsity completely arbitrary, with no standard but the
+will of men, it must not be concluded that either Hobbes, or any of the
+other thinkers who have in the main agreed with him, did in fact
+consider the distinction between truth and error as less real, or
+attached less importance to it, than other people. To suppose that they
+did so would argue total unacquaintance with their other speculations.
+But this shows how little hold their doctrine possessed over their own
+minds. No person, at bottom, ever imagined that there was nothing more
+in truth than propriety of expression; than using language in conformity
+to a previous convention. When the inquiry was brought down from
+generals to a particular case, it has always been acknowledged that
+there is a distinction between verbal and real questions; that some
+false propositions are uttered from ignorance of the meaning of words,
+but that in others the source of the error is a misapprehension of
+things; that a person who has not the use of language at all may form
+propositions mentally, and that they may be untrue, that is, he may
+believe as matters of fact what are not really so. This last admission
+cannot be made in stronger terms than it is by Hobbes himself;[19]
+though he will not allow such erroneous belief to be called falsity, but
+only error. And he has himself laid down, in other places, doctrines in
+which the true theory of predication is by implication contained. He
+distinctly says that general names are given to things on account of
+their attributes, and that abstract names are the names of those
+attributes. "Abstract is that which in any subject denotes the cause of
+the concrete name.... And these causes of names are the same with the
+causes of our conceptions, namely, some power of action, or affection,
+of the thing conceived, which some call the manner by which anything
+works upon our senses, but by most men they are called _accidents_."[20]
+It is strange that having gone so far, he should not have gone one step
+farther, and seen that what he calls the cause of the concrete name, is
+in reality the meaning of it; and that when we predicate of any subject
+a name which is given _because_ of an attribute (or, as he calls it, an
+accident), our object is not to affirm the name, but, by means of the
+name, to affirm the attribute.
+
+
+Sec. 4. Let the predicate be, as we have said, a connotative term; and to
+take the simplest case first, let the subject be a proper name: "The
+summit of Chimborazo is white." The word white connotes an attribute
+which is possessed by the individual object designated by the words
+"summit of Chimborazo;" which attribute consists in the physical fact,
+of its exciting in human beings the sensation which we call a sensation
+of white. It will be admitted that, by asserting the proposition, we
+wish to communicate information of that physical fact, and are not
+thinking of the names, except as the necessary means of making that
+communication. The meaning of the proposition, therefore, is, that the
+individual thing denoted by the subject, has the attributes connoted by
+the predicate.
+
+If we now suppose the subject also to be a connotative name, the meaning
+expressed by the proposition has advanced a step farther in
+complication. Let us first suppose the proposition to be universal, as
+well as affirmative: "All men are mortal." In this case, as in the last,
+what the proposition asserts (or expresses a belief of) is, of course,
+that the objects denoted by the subject (man) possess the attributes
+connoted by the predicate (mortal). But the characteristic of this case
+is, that the objects are no longer _individually_ designated. They are
+pointed out only by some of their attributes: they are the objects
+called men, that is, possessing the attributes connoted by the name man;
+and the only thing known of them may be those attributes: indeed, as the
+proposition is general, and the objects denoted by the subject are
+therefore indefinite in number, most of them are not known individually
+at all. The assertion, therefore, is not, as before, that the attributes
+which the predicate connotes are possessed by any given individual, or
+by any number of individuals previously known as John, Thomas, &c., but
+that those attributes are possessed by each and every individual
+possessing certain other attributes; that whatever has the attributes
+connoted by the subject, has also those connoted by the predicate; that
+the latter set of attributes _constantly accompany_ the former set.
+Whatever has the attributes of man has the attribute of mortality;
+mortality constantly accompanies the attributes of man.[21]
+
+If it be remembered that every attribute is _grounded_ on some fact or
+phenomenon, either of outward sense or of inward consciousness, and that
+to _possess_ an attribute is another phrase for being the cause of, or
+forming part of, the fact or phenomenon upon which the attribute is
+grounded; we may add one more step to complete the analysis. The
+proposition which asserts that one attribute always accompanies another
+attribute, really asserts thereby no other thing than this, that one
+phenomenon always accompanies another phenomenon; insomuch that where we
+find the one, we have assurance of the existence of the other. Thus, in
+the proposition, All men are mortal, the word man connotes the
+attributes which we ascribe to a certain kind of living creatures, on
+the ground of certain phenomena which they exhibit, and which are partly
+physical phenomena, namely the impressions made on our senses by their
+bodily form and structure, and partly mental phenomena, namely the
+sentient and intellectual life which they have of their own. All this is
+understood when we utter the word man, by any one to whom the meaning of
+the word is known. Now, when we say, Man is mortal, we mean that
+wherever these various physical and mental phenomena are all found,
+there we have assurance that the other physical and mental phenomenon,
+called death, will not fail to take place. The proposition does not
+affirm _when_; for the connotation of the word _mortal_ goes no farther
+than to the occurrence of the phenomenon at some time or other, leaving
+the precise time undecided.
+
+
+Sec. 5. We have already proceeded far enough, not only to demonstrate the
+error of Hobbes, but to ascertain the real import of by far the most
+numerous class of propositions. The object of belief in a proposition,
+when it asserts anything more than the meaning of words, is generally,
+as in the cases which we have examined, either the co-existence or the
+sequence of two phenomena. At the very commencement of our inquiry, we
+found that every act of belief implied two Things: we have now
+ascertained what, in the most frequent case, these two things are,
+namely two Phenomena, in other words, two states of consciousness; and
+what it is which the proposition affirms (or denies) to subsist between
+them, namely either succession or co-existence. And this case includes
+innumerable instances which no one, previous to reflection, would think
+of referring to it. Take the following example: A generous person is
+worthy of honour. Who would expect to recognise here a case of
+co-existence between phenomena? But so it is. The attribute which causes
+a person to be termed generous, is ascribed to him on the ground of
+states of his mind, and particulars of his conduct: both are phenomena:
+the former are facts of internal consciousness; the latter, so far as
+distinct from the former, are physical facts, or perceptions of the
+senses. Worthy of honour admits of a similar analysis. Honour, as here
+used, means a state of approving and admiring emotion, followed on
+occasion by corresponding outward acts. "Worthy of honour" connotes all
+this, together with our approval of the act of showing honour. All these
+are phenomena; states of internal consciousness, accompanied or followed
+by physical facts. When we say, A generous person is worthy of honour,
+we affirm co-existence between the two complicated phenomena connoted by
+the two terms respectively. We affirm, that wherever and whenever the
+inward feelings and outward facts implied in the word generosity have
+place, then and there the existence and manifestation of an inward
+feeling, honour, would be followed in our minds by another inward
+feeling, approval.
+
+After the analysis, in a former chapter, of the import of names, many
+examples are not needed to illustrate the import of propositions. When
+there is any obscurity, or difficulty, it does not lie in the meaning of
+the proposition, but in the meaning of the names which compose it; in
+the extremely complicated connotation of many words; the immense
+multitude and prolonged series of facts which often constitute the
+phenomenon connoted by a name. But where it is seen what the phenomenon
+is, there is seldom any difficulty in seeing that the assertion conveyed
+by the proposition is, the co-existence of one such phenomenon with
+another; or the succession of one such phenomenon to another: their
+_conjunction_, in short, so that where the one is found, we may
+calculate on finding both.
+
+This, however, though the most common, is not the only meaning which
+propositions are ever intended to convey. In the first place, sequences
+and co-existences are not only asserted respecting Phenomena; we make
+propositions also respecting those hidden causes of phenomena, which are
+named substances and attributes. A substance, however, being to us
+nothing but either that which causes, or that which is conscious of,
+phenomena; and the same being true, _mutatis mutandis_, of attributes;
+no assertion can be made, at least with a meaning, concerning these
+unknown and unknowable entities, except in virtue of the Phenomena by
+which alone they manifest themselves to our faculties. When we say,
+Socrates was cotemporary with the Peloponnesian war, the foundation of
+this assertion, as of all assertions concerning substances, is an
+assertion concerning the phenomena which they exhibit,--namely, that the
+series of facts by which Socrates manifested himself to mankind, and the
+series of mental states which constituted his sentient existence, went
+on simultaneously with the series of facts known by the name of the
+Peloponnesian war. Still, the proposition does not assert that alone; it
+asserts that the Thing in itself, the _noumenon_ Socrates, was existing,
+and doing or experiencing those various facts during the same time.
+Co-existence and sequence, therefore, may be affirmed or denied not only
+between phenomena, but between noumena, or between a noumenon and
+phenomena. And both of noumena and of phenomena we may affirm simple
+existence. But what is a noumenon? An unknown cause. In affirming,
+therefore, the existence of a noumenon, we affirm causation. Here,
+therefore, are two additional kinds of fact, capable of being asserted
+in a proposition. Besides the propositions which assert Sequence or
+Coexistence, there are some which assert simple Existence; and others
+assert Causation, which, subject to the explanations which will follow
+in the Third Book, must be considered provisionally as a distinct and
+peculiar kind of assertion.
+
+
+Sec. 6. To these four kinds of matter-of-fact or assertion, must be added a
+fifth, Resemblance. This was a species of attribute which we found it
+impossible to analyse; for which no _fundamentum_, distinct from the
+objects themselves, could be assigned. Besides propositions which assert
+a sequence or co-existence between two phenomena, there are therefore
+also propositions which assert resemblance between them: as, This colour
+is like that colour;--The heat of to-day is _equal_ to the heat of
+yesterday. It is true that such an assertion might with some
+plausibility be brought within the description of an affirmation of
+sequence, by considering it as an assertion that the simultaneous
+contemplation of the two colours is _followed_ by a specific feeling
+termed the feeling of resemblance. But there would be nothing gained by
+encumbering ourselves, especially in this place, with a generalization
+which may be looked upon as strained. Logic does not undertake to
+analyse mental facts into their ultimate elements. Resemblance between
+two phenomena is more intelligible in itself than any explanation could
+make it, and under any classification must remain specifically distinct
+from the ordinary cases of sequence and co-existence.
+
+It is sometimes said, that all propositions whatever, of which the
+predicate is a general name, do, in point of fact, affirm or deny
+resemblance. All such propositions affirm that a thing belongs to a
+class; but things being classed together according to their resemblance,
+everything is of course classed with the things which it is supposed to
+resemble most; and thence, it may be said, when we affirm that Gold is a
+metal, or that Socrates is a man, the affirmation intended is, that
+gold resembles other metals, and Socrates other men, more nearly than
+they resemble the objects contained in any other of the classes
+co-ordinate with these.
+
+There is some slight degree of foundation for this remark, but no more
+than a slight degree. The arrangement of things into classes, such as
+the class _metal_, or the class _man_, is grounded indeed on a
+resemblance among the things which are placed in the same class, but not
+on a mere general resemblance: the resemblance it is grounded on
+consists in the possession by all those things, of certain common
+peculiarities; and those peculiarities it is which the terms connote,
+and which the propositions consequently assert; not the resemblance: for
+though when I say, Gold is a metal, I say by implication that if there
+be any other metals it must resemble them, yet if there were no other
+metals I might still assert the proposition with the same meaning as at
+present, namely, that gold has the various properties implied in the
+word metal; just as it might be said, Christians are men, even if there
+were no men who were not Christians. Propositions, therefore, in which
+objects are referred to a class because they possess the attributes
+constituting the class, are so far from asserting nothing but
+resemblance, that they do not, properly speaking, assert resemblance at
+all.
+
+But we remarked some time ago (and the reasons of the remark will be
+more fully entered into in a subsequent Book[22]) that there is
+sometimes a convenience in extending the boundaries of a class so as to
+include things which possess in a very inferior degree, if in any, some
+of the characteristic properties of the class,--provided they resemble
+that class more than any other, insomuch that the general propositions
+which are true of the class, will be nearer to being true of those
+things than any other equally general propositions. For instance, there
+are substances called metals which have very few of the properties by
+which metals are commonly recognised; and almost every great family of
+plants or animals has a few anomalous genera or species on its borders,
+which are admitted into it by a sort of courtesy, and concerning which
+it has been matter of discussion to what family they properly belonged.
+Now when the class-name is predicated of any object of this description,
+we do, by so predicating it, affirm resemblance and nothing more. And in
+order to be scrupulously correct it ought to be said, that in every case
+in which we predicate a general name, we affirm, not absolutely that the
+object possesses the properties designated by the name, but that it
+_either_ possesses those properties, or if it does not, at any rate
+resembles the things which do so, more than it resembles any other
+things. In most cases, however, it is unnecessary to suppose any such
+alternative, the latter of the two grounds being very seldom that on
+which the assertion is made: and when it is, there is generally some
+slight difference in the form of the expression, as, This species (or
+genus) is _considered_, or _may be ranked_, as belonging to such and
+such a family: we should hardly say positively that it does belong to
+it, unless it possessed unequivocally the properties of which the
+class-name is scientifically significant.
+
+There is still another exceptional case, in which, though the predicate
+is the name of a class, yet in predicating it we affirm nothing but
+resemblance, the class being founded not on resemblance in any given
+particular, but on general unanalysable resemblance. The classes in
+question are those into which our simple sensations, or other simple
+feelings, are divided. Sensations of white, for instance, are classed
+together, not because we can take them to pieces, and say they are alike
+in this, and not alike in that, but because we feel them to be alike
+altogether, though in different degrees. When, therefore, I say, The
+colour I saw yesterday was a white colour, or, The sensation I feel is
+one of tightness, in both cases the attribute I affirm of the colour or
+of the other sensation is mere resemblance--simple _likeness_ to
+sensations which I have had before, and which have had those names
+bestowed upon them. The names of feelings, like other concrete general
+names, are connotative; but they connote a mere resemblance. When
+predicated of any individual feeling, the information they convey is
+that of its likeness to the other feelings which we have been accustomed
+to call by the same name. Thus much may suffice in illustration of the
+kind of propositions in which the matter-of-fact asserted (or denied) is
+simple Resemblance.
+
+Existence, Coexistence, Sequence, Causation, Resemblance: one or other
+of these is asserted (or denied) in every proposition which is not
+merely verbal. This five-fold division is an exhaustive classification
+of matters-of-fact; of all things that can be believed, or tendered for
+belief; of all questions that can be propounded, and all answers that
+can be returned to them. Instead of Coexistence and Sequence, we shall
+sometimes say, for greater particularity, Order in Place, and Order in
+Time: Order in Place being the specific mode of coexistence, not
+necessary to be more particularly analysed here; while the mere fact of
+coexistence, or simultaneousness, may be classed, together with
+Sequence, under the head of Order in Time.
+
+
+Sec. 7. In the foregoing inquiry into the import of Propositions, we have
+thought it necessary to analyse directly those alone, in which the terms
+of the proposition (or the predicate at least) are concrete terms. But,
+in doing so, we have indirectly analysed those in which the terms are
+abstract. The distinction between an abstract term and its corresponding
+concrete, does not turn upon any difference in what they are appointed
+to signify; for the real signification of a concrete general name is, as
+we have so often said, its connotation; and what the concrete term
+connotes, forms the entire meaning of the abstract name. Since there is
+nothing in the import of an abstract name which is not in the import of
+the corresponding concrete, it is natural to suppose that neither can
+there be anything in the import of a proposition of which the terms are
+abstract, but what there is in some proposition which can be framed of
+concrete terms.
+
+And this presumption a closer examination will confirm. An abstract name
+is the name of an attribute, or combination of attributes. The
+corresponding concrete is a name given to things, because of, and in
+order to express, their possessing that attribute, or that combination
+of attributes. When, therefore, we predicate of anything a concrete
+name, the attribute is what we in reality predicate of it. But it has
+now been shown that in all propositions of which the predicate is a
+concrete name, what is really predicated is one of five things:
+Existence, Coexistence, Causation, Sequence, or Resemblance. An
+attribute, therefore, is necessarily either an existence, a coexistence,
+a causation, a sequence, or a resemblance. When a proposition consists
+of a subject and predicate which are abstract terms, it consists of
+terms which must necessarily signify one or other of these things. When
+we predicate of anything an abstract name, we affirm of the thing that
+it is one or other of these five things; that it is a case of Existence,
+or of Coexistence, or of Causation, or of Sequence, or of Resemblance.
+
+It is impossible to imagine any proposition expressed in abstract terms,
+which cannot be transformed into a precisely equivalent proposition in
+which the terms are concrete; namely, either the concrete names which
+connote the attributes themselves, or the names of the _fundamenta_ of
+those attributes; the facts or phenomena on which they are grounded. To
+illustrate the latter case, let us take this proposition, of which the
+subject only is an abstract name, "Thoughtlessness is dangerous."
+Thoughtlessness is an attribute, grounded on the facts which we call
+thoughtless actions; and the proposition is equivalent to this,
+Thoughtless actions are dangerous. In the next example the predicate as
+well as the subject are abstract names: "Whiteness is a colour;" or "The
+colour of snow is a whiteness." These attributes being grounded on
+sensations, the equivalent propositions in the concrete would be, The
+sensation of white is one of the sensations called those of colour,--The
+sensation of sight, caused by looking at snow, is one of the sensations
+called sensations of white. In these propositions, as we have before
+seen, the matter-of-fact asserted is a Resemblance. In the following
+examples, the concrete terms are those which directly correspond to the
+abstract names; connoting the attribute which these denote. "Prudence
+is a virtue:" this may be rendered, "All prudent persons, _in so far as_
+prudent, are virtuous:" "Courage is deserving of honour," thus, "All
+courageous persons are deserving of honour _in so far_ as they are
+courageous:" which is equivalent to this--"All courageous persons
+deserve an addition to the honour, or a diminution of the disgrace,
+which would attach to them on other grounds."
+
+In order to throw still further light upon the import of propositions of
+which the terms are abstract, we will subject one of the examples given
+above to a minuter analysis. The proposition we shall select is the
+following:--"Prudence is a virtue." Let us substitute for the word
+virtue an equivalent but more definite expression, such as "a mental
+quality beneficial to society," or "a mental quality pleasing to God,"
+or whatever else we adopt as the definition of virtue. What the
+proposition asserts is a sequence, accompanied with causation; namely,
+that benefit to society, or that the approval of God, is consequent on,
+and caused by, prudence. Here is a sequence; but between what? We
+understand the consequent of the sequence, but we have yet to analyse
+the antecedent. Prudence is an attribute; and, in connexion with it, two
+things besides itself are to be considered; prudent persons, who are the
+_subjects_ of the attribute, and prudential conduct, which may be called
+the _foundation_ of it. Now is either of these the antecedent? and,
+first, is it meant, that the approval of God, or benefit to society, is
+attendant upon all prudent _persons_? No; except _in so far_ as they are
+prudent; for prudent persons who are scoundrels can seldom on the whole
+be beneficial to society, nor can they be acceptable to a good being. Is
+it upon prudential _conduct_, then, that divine approbation and benefit
+to mankind are supposed to be invariably consequent? Neither is this the
+assertion meant, when it is said that prudence is a virtue; except with
+the same reservation as before, and for the same reason, namely, that
+prudential conduct, although in _so far as_ it is prudential it is
+beneficial to society, may yet, by reason of some other of its
+qualities, be productive of an injury outweighing the benefit, and
+deserve a displeasure exceeding the approbation which would be due to
+the prudence. Neither the substance, therefore, (viz. the person,) nor
+the phenomenon, (the conduct,) is an antecedent on which the other term
+of the sequence is universally consequent. But the proposition,
+"Prudence is a virtue," is an universal proposition. What is it, then,
+upon which the proposition affirms the effects in question to be
+universally consequent? Upon that in the person, and in the conduct,
+which causes them to be called prudent, and which is equally in them
+when the action, though prudent, is wicked; namely, a correct foresight
+of consequences, a just estimation of their importance to the object in
+view, and repression of any unreflecting impulse at variance with the
+deliberate purpose. These, which are states of the person's mind, are
+the real antecedent in the sequence, the real cause in the causation,
+asserted by the proposition. But these are also the real ground, or
+foundation, of the attribute Prudence; since wherever these states of
+mind exist we may predicate prudence, even before we know whether any
+conduct has followed. And in this manner every assertion respecting an
+attribute, may be transformed into an assertion exactly equivalent
+respecting the fact or phenomenon which is the ground of the attribute.
+And no case can be assigned, where that which is predicated of the fact
+or phenomenon, does not belong to one or other of the five species
+formerly enumerated: it is either simple Existence, or it is some
+Sequence, Coexistence, Causation, or Resemblance.
+
+And as these five are the only things which can be affirmed, so are they
+the only things which can be denied. "No horses are web-footed" denies
+that the attributes of a horse ever coexist with web-feet. It is
+scarcely necessary to apply the same analysis to Particular affirmations
+and negations. "Some birds are web-footed," affirms that, with the
+attributes connoted by _bird_, the phenomenon web-feet is sometimes
+co-existent: "Some birds are not web-footed," asserts that there are
+other instances in which this coexistence does not have place. Any
+further explanation of a thing which, if the previous exposition has
+been assented to, is so obvious, may here be spared.
+
+
+
+
+CHAPTER VI.
+
+OF PROPOSITIONS MERELY VERBAL.
+
+
+Sec. 1. As a preparation for the inquiry which is the proper object of
+Logic, namely, in what manner propositions are to be proved, we have
+found it necessary to inquire what they contain which requires, or is
+susceptible of, proof; or (which is the same thing) what they assert. In
+the course of this preliminary investigation into the import of
+Propositions, we examined the opinion of the Conceptualists, that a
+proposition is the expression of a relation between two ideas; and the
+doctrine of the Nominalists, that it is the expression of an agreement
+or disagreement between the meanings of two names. We decided that, as
+general theories, both of these are erroneous; and that, though
+propositions may be made both respecting names and respecting ideas,
+neither the one nor the other are the subject-matter of Propositions
+considered generally. We then examined the different kinds of
+Propositions, and found that, with the exception of those which are
+merely verbal, they assert five different kinds of matters of fact,
+namely, Existence, Order in Place, Order in Time, Causation, and
+Resemblance; that in every proposition one of these five is either
+affirmed, or denied, of some fact or phenomenon, or of some object the
+unknown source of a fact or phenomenon.
+
+In distinguishing, however, the different kinds of matters of fact
+asserted in propositions, we reserved one class of propositions, which
+do not relate to any matter of fact, in the proper sense of the term, at
+all, but to the meaning of names. Since names and their signification
+are entirely arbitrary, such propositions are not, strictly speaking,
+susceptible of truth or falsity, but only of conformity or disconformity
+to usage or convention; and all the proof they are capable of, is proof
+of usage; proof that the words have been employed by others in the
+acceptation in which the speaker or writer desires to use them. These
+propositions occupy, however, a conspicuous place in philosophy; and
+their nature and characteristics are of as much importance in logic, as
+those of any of the other classes of propositions previously adverted
+to.
+
+If all propositions respecting the signification of words were as simple
+and unimportant as those which served us for examples when examining
+Hobbes' theory of predication, viz. those of which the subject and
+predicate are proper names, and which assert only that those names have,
+or that they have not, been conventionally assigned to the same
+individual, there would be little to attract to such propositions the
+attention of philosophers. But the class of merely verbal propositions
+embraces not only much more than these, but much more than any
+propositions which at first sight present themselves as verbal;
+comprehending a kind of assertions which have been regarded not only as
+relating to things, but as having actually a more intimate relation with
+them than any other propositions whatever. The student in philosophy
+will perceive that I allude to the distinction on which so much stress
+was laid by the schoolmen, and which has been retained either under the
+same or under other names by most metaphysicians to the present day,
+viz. between what were called _essential_, and what were called
+_accidental_, propositions, and between essential and accidental
+properties or attributes.
+
+
+Sec. 2. Almost all metaphysicians prior to Locke, as well as many since his
+time, have made a great mystery of Essential Predication, and of
+predicates which are said to be of the _essence_ of the subject. The
+essence of a thing, they said, was that without which the thing could
+neither be, nor be conceived to be. Thus, rationality was of the essence
+of man, because without rationality, man could not be conceived to
+exist. The different attributes which made up the essence of the thing
+were called its essential properties; and a proposition in which any of
+these were predicated of it was called an Essential Proposition, and was
+considered to go deeper into the nature of the thing, and to convey more
+important information respecting it, than any other proposition could
+do. All properties, not of the essence of the thing, were called its
+accidents; were supposed to have nothing at all, or nothing
+comparatively, to do with its inmost nature; and the propositions in
+which any of these were predicated of it were called Accidental
+Propositions. A connexion may be traced between this distinction, which
+originated with the schoolmen, and the well-known dogmas of _substantiae
+secundae_ or general substances, and _substantial forms_, doctrines which
+under varieties of language pervaded alike the Aristotelian and the
+Platonic schools, and of which more of the spirit has come down to
+modern times than might be conjectured from the disuse of the
+phraseology. The false views of the nature of classification and
+generalization which prevailed among the schoolmen, and of which these
+dogmas were the technical expression, afford the only explanation which
+can be given of their having misunderstood the real nature of those
+Essences which held so conspicuous a place in their philosophy. They
+said, truly, that _man_ cannot be conceived without rationality. But
+though _man_ cannot, a being may be conceived exactly like a man in all
+points except that one quality, and those others which are the
+conditions or consequences of it. All therefore which is really true in
+the assertion that man cannot be conceived without rationality, is only,
+that if he had not rationality, he would not be reputed a man. There is
+no impossibility in conceiving the _thing_, nor, for aught we know, in
+its existing: the impossibility is in the conventions of language, which
+will not allow the thing, even if it exist, to be called by the name
+which is reserved for rational beings. Rationality, in short, is
+involved in the meaning of the word man: is one of the attributes
+connoted by the name. The essence of man, simply means the whole of the
+attributes connoted by the word; and any one of those attributes taken
+singly, is an essential property of man.
+
+But these reflections, so easy to us, would have been difficult to
+persons who thought, as most of the later Aristotelians did, that
+objects were made what they were called, that gold (for instance) was
+made gold, not by the possession of certain properties to which mankind
+have chosen to attach that name, but by participation in the nature of
+a certain general substance, called gold in general, which substance,
+together with all the properties that belonged to it, _inhered_ in every
+individual piece of gold.[23] As they did not consider these universal
+substances to be attached to all general names, but only to some, they
+thought that an object borrowed only a part of its properties from an
+universal substance, and that the rest belonged to it individually: the
+former they called its essence, and the latter its accidents. The
+scholastic doctrine of essences long survived the theory on which it
+rested, that of the existence of real entities corresponding to general
+terms; and it was reserved for Locke at the end of the seventeenth
+century, to convince philosophers that the supposed essences of classes
+were merely the signification of their names; nor, among the signal
+services which his writings rendered to philosophy, was there one more
+needful or more valuable.
+
+Now, as the most familiar of the general names by which an object is
+designated usually connotes not one only, but several attributes of the
+object, each of which attributes separately forms also the bond of union
+of some class, and the meaning of some general name; we may predicate of
+a name which connotes a variety of attributes, another name which
+connotes only one of these attributes, or some smaller number of them
+than all. In such cases, the universal affirmative proposition will be
+true; since whatever possesses the whole of any set of attributes, must
+possess any part of that same set. A proposition of this sort, however,
+conveys no information to any one who previously understood the whole
+meaning of the terms. The propositions, Every man is a corporeal being,
+Every man is a living creature, Every man is rational, convey no
+knowledge to any one who was already aware of the entire meaning of the
+word _man_, for the meaning of the word includes all this: and that
+every _man_ has the attributes connoted by all these predicates, is
+already asserted when he is called a man. Now, of this nature are all
+the propositions which have been called essential. They are, in fact,
+identical propositions.
+
+It is true that a proposition which predicates any attribute, even
+though it be one implied in the name, is in most cases understood to
+involve a tacit assertion that there _exists_ a thing corresponding to
+the name, and possessing the attributes connoted by it; and this implied
+assertion may convey information, even to those who understood the
+meaning of the name. But all information of this sort, conveyed by all
+the essential propositions of which man can be made the subject, is
+included in the assertion, Men exist. And this assumption of real
+existence is, after all, the result of an imperfection of language. It
+arises from the ambiguity of the copula, which, in addition to its
+proper office of a mark to show that an assertion is made, is also, as
+formerly remarked, a concrete word connoting existence. The actual
+existence of the subject of the proposition is therefore only
+apparently, not really, implied in the predication, if an essential one:
+we may say, A ghost is a disembodied spirit, without believing in
+ghosts. But an accidental, or non-essential, affirmation, does imply the
+real existence of the subject, because in the case of a non-existent
+subject there is nothing for the proposition to assert. Such a
+proposition as, The ghost of a murdered person haunts the couch of the
+murderer, can only have a meaning if understood as implying a belief in
+ghosts; for since the signification of the word ghost implies nothing of
+the kind, the speaker either means nothing, or means to assert a thing
+which he wishes to be believed to have really taken place.
+
+It will be hereafter seen that when any important consequences seem to
+follow, as in mathematics, from an essential proposition, or, in other
+words, from a proposition involved in the meaning of a name, what they
+really flow from is the tacit assumption of the real existence of the
+objects so named. Apart from this assumption of real existence, the
+class of propositions in which the predicate is of the essence of the
+subject (that is, in which the predicate connotes the whole or part of
+what the subject connotes, but nothing besides) answer no purpose but
+that of unfolding the whole or some part of the meaning of the name, to
+those who did not previously know it. Accordingly, the most useful, and
+in strictness the only useful kind of essential propositions, are
+Definitions: which, to be complete, should unfold the whole of what is
+involved in the meaning of the word defined; that is, (when it is a
+connotative word,) the whole of what it connotes. In defining a name,
+however, it is not usual to specify its entire connotation, but so much
+only as is sufficient to mark out the objects usually denoted by it from
+all other known objects. And sometimes a merely accidental property, not
+involved in the meaning of the name, answers this purpose equally well.
+The various kinds of definition which these distinctions give rise to,
+and the purposes to which they are respectively subservient, will be
+minutely considered in the proper place.
+
+
+Sec. 3. According to the above view of essential propositions, no
+proposition can be reckoned such which relates to an individual by name,
+that is, in which the subject is a proper name. Individuals have no
+essences. When the schoolmen talked of the essence of an individual,
+they did not mean the properties implied in its name, for the names of
+individuals imply no properties. They regarded as of the essence of an
+individual, whatever was of the essence of the species in which they
+were accustomed to place that individual; _i.e._ of the class to which
+it was most familiarly referred, and to which, therefore, they conceived
+that it by nature belonged. Thus, because the proposition Man is a
+rational being, was an essential proposition, they affirmed the same
+thing of the proposition, Julius Caesar is a rational being. This
+followed very naturally if genera and species were to be considered as
+entities, distinct from, but _inhering_ in, the individuals composing
+them. If _man_ was a substance inhering in each individual man, the
+_essence_ of man (whatever that might mean) was naturally supposed to
+accompany it; to inhere in John Thompson, and to form the _common
+essence_ of Thompson and Julius Caesar. It might then be fairly said,
+that rationality, being of the essence of Man, was of the essence also
+of Thompson. But if Man altogether be only the individual men and a name
+bestowed upon them in consequence of certain common properties, what
+becomes of John Thompson's essence?
+
+A fundamental error is seldom expelled from philosophy by a single
+victory. It retreats slowly, defends every inch of ground, and often,
+after it has been driven from the open country, retains a footing in
+some remote fastness. The essences of individuals were an unmeaning
+figment arising from a misapprehension of the essences of classes, yet
+even Locke, when he extirpated the parent error, could not shake himself
+free from that which was its fruit. He distinguished two sorts of
+essences, Real and Nominal. His nominal essences were the essences of
+classes, explained nearly as we have now explained them. Nor is anything
+wanting to render the third book of Locke's Essay a nearly
+unexceptionable treatise on the connotation of names, except to free its
+language from the assumption of what are called Abstract Ideas, which
+unfortunately is involved in the phraseology, though not necessarily
+connected with the thoughts contained in that immortal Third Book.[24]
+But, besides nominal essences, he admitted real essences, or essences of
+individual objects, which he supposed to be the causes of the sensible
+properties of those objects. We know not (said he) what these are; (and
+this acknowledgment rendered the fiction comparatively innocuous;) but
+if we did, we could, from them alone, demonstrate the sensible
+properties of the object, as the properties of the triangle are
+demonstrated from the definition of the triangle. I shall have occasion
+to revert to this theory in treating of Demonstration, and of the
+conditions under which one property of a thing admits of being
+demonstrated from another property. It is enough here to remark that,
+according to this definition, the real essence of an object has, in the
+progress of physics, come to be conceived as nearly equivalent, in the
+case of bodies, to their corpuscular structure: what it is now supposed
+to mean in the case of any other entities, I would not take upon myself
+to define.
+
+
+Sec. 4. An essential proposition, then, is one which is purely verbal;
+which asserts of a thing under a particular name, only what is asserted
+of it in the fact of calling it by that name; and which therefore either
+gives no information, or gives it respecting the name, not the thing.
+Non-essential, or accidental propositions, on the contrary, may be
+called Real Propositions, in opposition to Verbal. They predicate of a
+thing some fact not involved in the signification of the name by which
+the proposition speaks of it; some attribute not connoted by that name.
+Such are all propositions concerning things individually designated, and
+all general or particular propositions in which the predicate connotes
+any attribute not connoted by the subject. All these, if true, add to
+our knowledge: they convey information, not already involved in the
+names employed. When I am told that all, or even that some objects,
+which have certain qualities, or which stand in certain relations, have
+also certain other qualities, or stand in certain other relations, I
+learn from this proposition a new fact; a fact not included in my
+knowledge of the meaning of the words, nor even of the existence of
+Things answering to the signification of those words. It is this class
+of propositions only which are in themselves instructive, or from which
+any instructive propositions can be inferred.[25]
+
+Nothing has probably contributed more to the opinion so long prevalent
+of the futility of the school logic, than the circumstance that almost
+all the examples used in the common school books to illustrate the
+doctrine of predication and that of the syllogism, consist of essential
+propositions. They were usually taken either from the branches or from
+the main trunk of the Predicamental Tree, which included nothing but
+what was of the _essence_ of the species: _Omne corpus est substantia_,
+_Omne animal est corpus_, _Omnis homo est corpus_, _Omnis homo est
+animal_, _Omnis homo est rationalis_, and so forth. It is far from
+wonderful that the syllogistic art should have been thought to be of no
+use in assisting correct reasoning, when almost the only propositions
+which, in the hands of its professed teachers, it was employed to prove,
+were such as every one assented to without proof the moment he
+comprehended the meaning of the words; and stood exactly on a level, in
+point of evidence, with the premises from which they were drawn. I have,
+therefore, throughout this work, avoided the employment of essential
+propositions as examples, except where the nature of the principle to be
+illustrated specifically required them.
+
+
+Sec. 5. With respect to propositions which do convey information--which
+assert something of a Thing, under a name that does not already
+presuppose what is about to be asserted; there are two different aspects
+in which these, or rather such of them as are general propositions, may
+be considered: we may either look at them as portions of speculative
+truth, or as memoranda for practical use. According as we consider
+propositions in one or the other of these lights, their import may be
+conveniently expressed in one or in the other of two formulas.
+
+According to the formula which we have hitherto employed, and which is
+best adapted to express the import of the proposition as a portion of
+our theoretical knowledge, All men are mortal, means that the attributes
+of man are always accompanied by the attribute mortality: No men are
+gods, means that the attributes of man are never accompanied by the
+attributes, or at least never by all the attributes, signified by the
+word god. But when the proposition is considered as a memorandum for
+practical use, we shall find a different mode of expressing the same
+meaning better adapted to indicate the office which the proposition
+performs. The practical use of a proposition is, to apprise or remind us
+what we have to expect, in any individual case which comes within the
+assertion contained in the proposition. In reference to this purpose,
+the proposition, All men are mortal, means that the attributes of man
+are _evidence of_, are a _mark_ of, mortality; an indication by which
+the presence of that attribute is made manifest. No men are gods, means
+that the attributes of man are a mark or evidence that some or all of
+the attributes understood to belong to a god are not there; that where
+the former are, we need not expect to find the latter.
+
+These two forms of expression are at bottom equivalent; but the one
+points the attention more directly to what a proposition means, the
+latter to the manner in which it is to be used.
+
+Now it is to be observed that Reasoning (the subject to which we are
+next to proceed) is a process into which propositions enter not as
+ultimate results, but as means to the establishment of other
+propositions. We may expect, therefore, that the mode of exhibiting the
+import of a general proposition which shows it in its application to
+practical use, will best express the function which propositions perform
+in Reasoning. And accordingly, in the theory of Reasoning, the mode of
+viewing the subject which considers a Proposition as asserting that one
+fact or phenomenon is a _mark_ or _evidence_ of another fact or
+phenomenon, will be found almost indispensable. For the purposes of that
+Theory, the best mode of defining the import of a proposition is not the
+mode which shows most clearly what it is in itself, but that which most
+distinctly suggests the manner in which it may be made available for
+advancing from it to other propositions.
+
+
+
+
+CHAPTER VII.
+
+OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
+
+
+Sec. 1. In examining into the nature of general propositions, we have
+adverted much less than is usual with logicians to the ideas of a Class,
+and Classification; ideas which, since the Realist doctrine of General
+Substances went out of vogue, have formed the basis of almost every
+attempt at a philosophical theory of general terms and general
+propositions. We have considered general names as having a meaning,
+quite independently of their being the names of classes. That
+circumstance is in truth accidental, it being wholly immaterial to the
+signification of the name whether there are many objects, or only one,
+to which it happens to be applicable, or whether there be any at all.
+God is as much a general term to the Christian or Jew as to the
+Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much
+so as if real objects existed, corresponding to those names. Every name
+the signification of which is constituted by attributes, is potentially
+a name of an indefinite number of objects; but it needs not be actually
+the name of any; and if of any, it may be the name of only one. As soon
+as we employ a name to connote attributes, the things, be they more or
+fewer, which happen to possess those attributes, are constituted _ipso
+facto_ a class. But in predicating the name we predicate only the
+attributes; and the fact of belonging to a class does not, in many
+cases, come into view at all.
+
+Although, however, Predication does not presuppose Classification, and
+though the theory of Names and of Propositions is not cleared up, but
+only encumbered, by intruding the idea of classification into it, there
+is nevertheless a close connexion between Classification and the
+employment of General Names. By every general name which we introduce,
+we create a class, if there be any things, real or imaginary, to compose
+it; that is, any Things corresponding to the signification of the name.
+Classes, therefore, mostly owe their existence to general language. But
+general language, also, though that is not the most common case,
+sometimes owes its existence to classes. A general, which is as much as
+to say a significant, name, is indeed mostly introduced because we have
+a signification to express by it; because we need a word by means of
+which to predicate the attributes which it connotes. But it is also true
+that a name is sometimes introduced because we have found it convenient
+to create a class; because we have thought it useful for the regulation
+of our mental operations, that a certain group of objects should be
+thought of together. A naturalist, for purposes connected with his
+particular science, sees reason to distribute the animal or vegetable
+creation into certain groups rather than into any others, and he
+requires a name to bind, as it were, each of his groups together. It
+must not however be supposed that such names, when introduced, differ in
+any respect, as to their mode of signification, from other connotative
+names. The classes which they denote are, as much as any other classes,
+constituted by certain common attributes, and their names are
+significant of those attributes, and of nothing else. The names of
+Cuvier's classes and orders, _Plantigrades_, _Digitigrades_, &c., are as
+much the expression of attributes as if those names had preceded,
+instead of grown out of, his classification of animals. The only
+peculiarity of the case is, that the convenience of classification was
+here the primary motive for introducing the names; while in other cases
+the name is introduced as a means of predication, and the formation of a
+class denoted by it is only an indirect consequence.
+
+The principles which ought to regulate Classification as a logical
+process subservient to the investigation of truth, cannot be discussed
+to any purpose until a much later stage of our inquiry. But, of
+Classification as resulting from, and implied in, the fact of employing
+general language, we cannot forbear to treat here, without leaving the
+theory of general names and of their employment in predication,
+mutilated and formless.
+
+
+Sec. 2. This portion of the theory of general language is the subject of
+what is termed the doctrine of the Predicables; a set of distinctions
+handed down from Aristotle, and his follower Porphyry, many of which
+have taken a firm root in scientific, and some of them even in popular,
+phraseology. The predicables are a five-fold division of General Names,
+not grounded as usual on a difference in their meaning, that is, in the
+attribute which they connote, but on a difference in the kind of class
+which they denote. We may predicate of a thing five different varieties
+of class-name:--
+
+  A _genus_ of the thing  ([Greek: genos]).
+  A _species_             ([Greek: eidos]).
+  A _differentia_         ([Greek: diaphora]).
+  A _proprium_            ([Greek: idion]).
+  An _accidens_           ([Greek: symbebekos]).
+
+It is to be remarked of these distinctions, that they express, not what
+the predicate is in its own meaning, but what relation it bears to the
+subject of which it happens on the particular occasion to be predicated.
+There are not some names which are exclusively genera, and others which
+are exclusively species, or differentiae; but the same name is referred
+to one or another predicable, according to the subject of which it is
+predicated on the particular occasion. _Animal_, for instance, is a
+genus with respect to man, or John; a species with respect to Substance,
+or Being. _Rectangular_ is one of the Differentiae of a geometrical
+square; it is merely one of the Accidentia of the table at which I am
+writing. The words genus, species, &c. are therefore relative terms;
+they are names applied to certain predicates, to express the relation
+between them and some given subject: a relation grounded, as we shall
+see, not on what the predicate connotes, but on the class which it
+denotes, and on the place which, in some given classification, that
+class occupies relatively to the particular subject.
+
+
+Sec. 3. Of these five names, two, Genus and Species, are not only used by
+naturalists in a technical acceptation not precisely agreeing with their
+philosophical meaning, but have also acquired a popular acceptation,
+much more general than either. In this popular sense any two classes,
+one of which includes the whole of the other and more, may be called a
+Genus and a Species. Such, for instance, are Animal and Man; Man and
+Mathematician. Animal is a Genus; Man and Brute are its two species; or
+we may divide it into a greater number of species, as man, horse, dog,
+&c. _Biped_, or _two-footed animal_, may also be considered a genus, of
+which man and bird are two species. _Taste_ is a genus, of which sweet
+taste, sour taste, salt taste, &c. are species. _Virtue_ is a genus;
+justice, prudence, courage, fortitude, generosity, &c. are its species.
+
+The same class which is a genus with reference to the sub-classes or
+species included in it, may be itself a species with reference to a more
+comprehensive, or, as it is often called, a superior genus. Man is a
+species with reference to animal, but a genus with reference to the
+species Mathematician. Animal is a genus, divided into two species, man
+and brute; but animal is also a species, which, with another species,
+vegetable, makes up the genus, organized being. Biped is a genus with
+reference to man and bird, but a species with respect to the superior
+genus, animal. Taste is a genus divided into species, but also a species
+of the genus sensation. Virtue, a genus with reference to justice,
+temperance, &c., is one of the species of the genus, mental quality.
+
+In this popular sense the words Genus and Species have passed into
+common discourse. And it should be observed that in ordinary parlance,
+not the name of the class, but the class itself, is said to be the genus
+or species; not, of course, the class in the sense of each individual of
+the class, but the individuals collectively, considered as an aggregate
+whole; the name by which the class is designated being then called not
+the genus or species, but the generic or specific name. And this is an
+admissible form of expression; nor is it of any importance which of the
+two modes of speaking we adopt, provided the rest of our language is
+consistent with it; but, if we call the class itself the genus, we must
+not talk of predicating the genus. We predicate of man the _name_
+mortal; and by predicating the name, we may be said, in an intelligible
+sense, to predicate what the name expresses, the _attribute_ mortality;
+but in no allowable sense of the word predication do we predicate of man
+the _class_ mortal. We predicate of him the fact of belonging to the
+class.
+
+By the Aristotelian logicians, the terms genus and species were used in
+a more restricted sense. They did not admit every class which could be
+divided into other classes to be a genus, or every class which could be
+included in a larger class to be a species. Animal was by them
+considered a genus; man and brute co-ordinate species under that genus:
+_biped_, however, would not have been admitted to be a genus with
+reference to man, but a _proprium_ or _accidens_ only. It was requisite,
+according to their theory, that genus and species should be of the
+_essence_ of the subject. Animal was of the essence of man; biped was
+not. And in every classification they considered some one class as the
+lowest or _infima_ species. Man, for instance, was a lowest species. Any
+further divisions into which the class might be capable of being broken
+down, as man into white, black, and red man, or into priest and layman,
+they did not admit to be species.
+
+It has been seen, however, in the preceding chapter, that the
+distinction between the essence of a class, and the attributes or
+properties which are not of its essence--a distinction which has given
+occasion to so much abstruse speculation, and to which so mysterious a
+character was formerly, and by many writers is still, attached,--amounts
+to nothing more than the difference between those attributes of the
+class which are, and those which are not, involved in the signification
+of the class-name. As applied to individuals, the word Essence, we
+found, has no meaning, except in connexion with the exploded tenets of
+the Realists; and what the schoolmen chose to call the essence of an
+individual, was simply the essence of the class to which that individual
+was most familiarly referred.
+
+Is there no difference, then, save this merely verbal one, between the
+classes which the schoolmen admitted to be genera or species, and those
+to which they refused the title? Is it an error to regard some of the
+differences which exist among objects as differences _in kind_ (_genere_
+or _specie_), and others only as differences in the accidents? Were the
+schoolmen right or wrong in giving to some of the classes into which
+things may be divided, the name of _kinds_, and considering others as
+secondary divisions, grounded on differences of a comparatively
+superficial nature? Examination will show that the Aristotelians did
+mean something by this distinction, and something important; but which,
+being but indistinctly conceived, was inadequately expressed by the
+phraseology of essences, and the various other modes of speech to which
+they had recourse.
+
+
+Sec. 4. It is a fundamental principle in logic, that the power of framing
+classes is unlimited, as long as there is any (even the smallest)
+difference to found a distinction upon. Take any attribute whatever, and
+if some things have it, and others have not, we may ground on the
+attribute a division of all things into two classes; and we actually do
+so, the moment we create a name which connotes the attribute. The number
+of possible classes, therefore, is boundless; and there are as many
+actual classes (either of real or of imaginary things) as there are
+general names, positive and negative together.
+
+But if we contemplate any one of the classes so formed, such as the
+class animal or plant, or the class sulphur or phosphorus, or the class
+white or red, and consider in what particulars the individuals included
+in the class differ from those which do not come within it, we find a
+very remarkable diversity in this respect between some classes and
+others. There are some classes, the things contained in which differ
+from other things only in certain particulars which may be numbered,
+while others differ in more than can be numbered, more even than we need
+ever expect to know. Some classes have little or nothing in common to
+characterize them by, except precisely what is connoted by the name:
+white things, for example, are not distinguished by any common
+properties, except whiteness; or if they are, it is only by such as are
+in some way dependent on, or connected with, whiteness. But a hundred
+generations have not exhausted the common properties of animals or of
+plants, of sulphur or of phosphorus; nor do we suppose them to be
+exhaustible, but proceed to new observations and experiments, in the
+full confidence of discovering new properties which were by no means
+implied in those we previously knew. While, if any one were to propose
+for investigation the common properties of all things which are of the
+same colour, the same shape, or the same specific gravity, the absurdity
+would be palpable. We have no ground to believe that any such common
+properties exist, except such as may be shown to be involved in the
+supposition itself, or to be derivable from it by some law of causation.
+It appears, therefore, that the properties, on which we ground our
+classes, sometimes exhaust all that the class has in common, or contain
+it all by some mode of implication; but in other instances we make a
+selection of a few properties from among not only a greater number, but
+a number inexhaustible by us, and to which as we know no bounds, they
+may, so far as we are concerned, be regarded as infinite.
+
+There is no impropriety in saying that, of these two classifications,
+the one answers to a much more radical distinction in the things
+themselves, than the other does. And if any one even chooses to say that
+the one classification is made by nature, the other by us for our
+convenience, he will be right; provided he means no more than this:
+Where a certain apparent difference between things (though perhaps in
+itself of little moment) answers to we know not what number of other
+differences, pervading not only their known properties, but properties
+yet undiscovered, it is not optional but imperative to recognise this
+difference as the foundation of a specific distinction; while, on the
+contrary, differences that are merely finite and determinate, like those
+designated by the words white, black, or red, may be disregarded if the
+purpose for which the classification is made does not require attention
+to those particular properties. The differences, however, are made by
+nature, in both cases; while the recognition of those differences as
+grounds of classification and of naming, is, equally in both cases, the
+act of man: only in the one case, the ends of language and of
+classification would be subverted if no notice were taken of the
+difference, while in the other case, the necessity of taking notice of
+it depends on the importance or unimportance of the particular qualities
+in which the difference happens to consist.
+
+Now, these classes, distinguished by unknown multitudes of properties,
+and not solely by a few determinate ones--which are parted off from one
+another by an unfathomable chasm, instead of a mere ordinary ditch with
+a visible bottom--are the only classes which, by the Aristotelian
+logicians, were considered as genera or species. Differences which
+extended only to a certain property or properties, and there terminated,
+they considered as differences only in the _accidents_ of things; but
+where any class differed from other things by an infinite series of
+differences, known and unknown, they considered the distinction as one
+of _kind_, and spoke of it as being an _essential_ difference, which is
+also one of the current meanings of that vague expression at the present
+day.
+
+Conceiving the schoolmen to have been justified in drawing a broad line
+of separation between these two kinds of classes and of
+class-distinctions, I shall not only retain the division itself, but
+continue to express it in their language. According to that language,
+the proximate (or lowest) Kind to which any individual is referrible, is
+called its species. Conformably to this, Sir Isaac Newton would be said
+to be of the species man. There are indeed numerous sub-classes included
+in the class man, to which Newton also belongs; for example, Christian,
+and Englishman, and Mathematician. But these, though distinct classes,
+are not, in our sense of the term, distinct Kinds of men. A Christian,
+for example, differs from other human beings; but he differs only in the
+attribute which the word expresses, namely, belief in Christianity, and
+whatever else that implies, either as involved in the fact itself, or
+connected with it through some law of cause and effect. We should never
+think of inquiring what properties, unconnected with Christianity either
+as cause or effect, are common to all Christians and peculiar to them;
+while in regard to all Men, physiologists are perpetually carrying on
+such an inquiry; nor is the answer ever likely to be completed. Man,
+therefore, we may call a species; Christian, or Mathematician, we
+cannot.
+
+Note here, that it is by no means intended to imply that there may not
+be different Kinds, or logical species, of man. The various races and
+temperaments, the two sexes, and even the various ages, may be
+differences of kind, within our meaning of the term. I do not say that
+they are so. For in the progress of physiology it may almost be said to
+be made out, that the differences which really exist between different
+races, sexes, &c., follow as consequences, under laws of nature, from a
+small number of primary differences which can be precisely determined,
+and which, as the phrase is, _account for_ all the rest. If this be so,
+these are not distinctions in kind; no more than Christian, Jew,
+Mussulman, and Pagan, a difference which also carries many consequences
+along with it. And in this way classes are often mistaken for real
+Kinds, which are afterwards proved not to be so. But if it turned out
+that the differences were not capable of being thus accounted for, then
+Caucasian, Mongolian, Negro, &c. would be really different Kinds of
+human beings, and entitled to be ranked as species by the logician;
+though not by the naturalist. For (as already noticed) the word species
+is used in a different signification in logic and in natural history. By
+the naturalist, organized beings are not usually said to be of different
+species, if it is supposed that they could possibly have descended from
+the same stock. That, however, is a sense artificially given to the
+word, for the technical purposes of a particular science. To the
+logician, if a negro and a white man differ in the same manner (however
+less in degree) as a horse and a camel do, that is, if their differences
+are inexhaustible, and not referrible to any common cause, they are
+different species, whether they are descended from common ancestors or
+not. But if their differences can all be traced to climate and habits,
+or to some one or a few special differences in structure, they are not,
+in the logician's view, specially distinct.
+
+When the _infima species_, or proximate Kind, to which an individual
+belongs, has been ascertained, the properties common to that Kind
+include necessarily the whole of the common properties of every other
+real Kind to which the individual can be referrible. Let the individual,
+for example, be Socrates, and the proximate Kind, man. Animal, or living
+creature, is also a real Kind, and includes Socrates; but, since it
+likewise includes man, or in other words, since all men are animals, the
+properties common to animals form a portion of the common properties of
+the sub-class, man. And if there be any class which includes Socrates
+without including man, that class is not a real Kind. Let the class for
+example, be _flat-nosed_; that being a class which includes Socrates,
+without including all men. To determine whether it is a real Kind, we
+must ask ourselves this question: Have all flat-nosed animals, in
+addition to whatever is implied in their flat noses, any common
+properties, other than those which are common to all animals whatever?
+If they had; if a flat nose were a mark or index to an indefinite number
+of other peculiarities, not deducible from the former by an
+ascertainable law, then out of the class man we might cut another class,
+flat-nosed man, which according to our definition, would be a Kind. But
+if we could do this, man would not be, as it was assumed to be, the
+proximate Kind. Therefore, the properties of the proximate Kind do
+comprehend those (whether known or unknown) of all other Kinds to which
+the individual belongs; which was the point we undertook to prove. And
+hence, every other Kind which is predicable of the individual, will be
+to the proximate Kind in the relation of a genus, according to even the
+popular acceptation of the terms genus and species; that is, it will be
+a larger class, including it and more.
+
+We are now able to fix the logical meaning of these terms. Every class
+which is a real Kind, that is, which is distinguished from all other
+classes by an indeterminate multitude of properties not derivable from
+one another, is either a genus or a species. A Kind which is not
+divisible into other Kinds, cannot be a genus, because it has no
+species under it; but it is itself a species, both with reference to the
+individuals below and to the genera above (Species Praedicabilis and
+Species Subjicibilis.) But every Kind which admits of division into real
+Kinds (as animal into mammal, bird, fish, &c., or bird into various
+species of birds) is a genus to all below it, a species to all genera in
+which it is itself included. And here we may close this part of the
+discussion, and pass to the three remaining predicables, Differentia,
+Proprium, and Accidens.
+
+
+Sec. 5. To begin with Differentia. This word is correlative with the words
+genus and species, and as all admit, it signifies the attribute which
+distinguishes a given species from every other species of the same
+genus. This is so far clear: but we may still ask, which of the
+distinguishing attributes it signifies. For we have seen that every Kind
+(and a species must be a Kind) is distinguished from other Kinds not by
+any one attribute, but by an indefinite number. Man, for instance, is a
+species of the genus animal: Rational (or rationality, for it is of no
+consequence here whether we use the concrete or the abstract form) is
+generally assigned by logicians as the Differentia; and doubtless this
+attribute serves the purpose of distinction: but it has also been
+remarked of man, that he is a cooking animal; the only animal that
+dresses its food. This, therefore, is another of the attributes by which
+the species man is distinguished from other species of the same genus:
+would this attribute serve equally well for a differentia? The
+Aristotelians say No; having laid it down that the differentia must,
+like the genus and species, be of the _essence_ of the subject.
+
+And here we lose even that vestige of a meaning grounded in the nature
+of the things themselves, which may be supposed to be attached to the
+word essence when it is said that genus and species must be of the
+essence of the thing. There can be no doubt that when the schoolmen
+talked of the essences of things as opposed to their accidents, they had
+confusedly in view the distinction between differences of kind, and the
+differences which are not of kind; they meant to intimate that genera
+and species must be Kinds. Their notion of the essence of a thing was a
+vague notion of a something which makes it what it is, _i. e._ which
+makes it the Kind of thing that it is--which causes it to have all that
+variety of properties which distinguish its Kind. But when the matter
+came to be looked at more closely, nobody could discover what caused the
+thing to have all those properties, nor even that there was anything
+which caused it to have them. Logicians, however, not liking to admit
+this, and being unable to detect what made the thing to be what it was,
+satisfied themselves with what made it to be what it was called. Of the
+innumerable properties, known and unknown, that are common to the class
+man, a portion only, and of course a very small portion, are connoted by
+its name; these few, however, will naturally have been thus
+distinguished from the rest either for their greater obviousness, or for
+greater supposed importance. These properties, then, which were connoted
+by the name, logicians seized upon, and called them the essence of the
+species; and not stopping there, they affirmed them, in the case of the
+_infima species_, to be the essence of the individual too; for it was
+their maxim, that the species contained the "whole essence" of the
+thing. Metaphysics, that fertile field of delusion propagated by
+language, does not afford a more signal instance of such delusion. On
+this account it was that rationality, being connoted by the name man,
+was allowed to be a differentia of the class; but the peculiarity of
+cooking their food, not being connoted, was relegated to the class of
+accidental properties.
+
+The distinction, therefore, between Differentia, Proprium, and Accidens,
+is not grounded in the nature of things, but in the connotation of
+names; and we must seek it there, if we wish to find what it is.
+
+From the fact that the genus includes the species, in other words
+_de_notes more than the species, or is predicable of a greater number of
+individuals, it follows that the species must connote more than the
+genus. It must connote all the attributes which the genus connotes, or
+there would be nothing to prevent it from denoting individuals not
+included in the genus. And it must connote something besides, otherwise
+it would include the whole genus. Animal denotes all the individuals
+denoted by man, and many more. Man, therefore, must connote all that
+animal connotes, otherwise there might be men who are not animals; and
+it must connote something more than animal connotes, otherwise all
+animals would be men. This surplus of connotation--this which the
+species connotes over and above the connotation of the genus--is the
+Differentia, or specific difference; or, to state the same proposition
+in other words, the Differentia is that which must be added to the
+connotation of the genus, to complete the connotation of the species.
+
+The word man, for instance, exclusively of what it connotes in common
+with animal, also connotes rationality, and at least some approximation
+to that external form which we all know, but which as we have no name
+for it considered in itself, we are content to call the human. The
+Differentia, or specific difference, therefore, of man, as referred to
+the genus animal, is that outward form and the possession of reason. The
+Aristotelians said, the possession of reason, without the outward form.
+But if they adhered to this, they would have been obliged to call the
+Houyhnhnms men. The question never arose, and they were never called
+upon to decide how such a case would have affected their notion of
+essentiality. However this may be, they were satisfied with taking such
+a portion of the differentia as sufficed to distinguish the species from
+all other _existing_ things, though by so doing they might not exhaust
+the connotation of the name.
+
+
+Sec. 6. And here, to prevent the notion of differentia from being
+restricted within too narrow limits, it is necessary to remark, that a
+species, even as referred to the same genus, will not always have the
+same differentia, but a different one, according to the principle and
+purpose which preside over the particular classification. For example, a
+naturalist surveys the various kinds of animals, and looks out for the
+classification of them most in accordance with the order in which, for
+zoological purposes, he considers it desirable that we should think of
+them. With this view he finds it advisable that one of his fundamental
+divisions should be into warm-blooded and cold-blooded animals; or into
+animals which breathe with lungs and those which breathe with gills; or
+into carnivorous, and frugivorous or graminivorous; or into those which
+walk on the flat part and those which walk on the extremity of the foot,
+a distinction on which two of Cuvier's families are founded. In doing
+this, the naturalist creates as many new classes; which are by no means
+those to which the individual animal is familiarly and spontaneously
+referred; nor should we ever think of assigning to them so prominent a
+position in our arrangement of the animal kingdom, unless for a
+preconceived purpose of scientific convenience. And to the liberty of
+doing this there is no limit. In the examples we have given, most of the
+classes are real Kinds, since each of the peculiarities is an index to a
+multitude of properties belonging to the class which it characterizes:
+but even if the case were otherwise--if the other properties of those
+classes could all be derived, by any process known to us, from the one
+peculiarity on which the class is founded--even then, if these
+derivative properties were of primary importance for the purposes of the
+naturalist, he would be warranted in founding his primary divisions on
+them.
+
+If, however, practical convenience is a sufficient warrant for making
+the main demarcations in our arrangement of objects run in lines not
+coinciding with any distinction of Kind, and so creating genera and
+species in the popular sense which are not genera or species in the
+rigorous sense at all, _a fortiori_ must we be warranted, when our
+genera and species _are_ real genera and species, in marking the
+distinction between them by those of their properties which
+considerations of practical convenience most strongly recommend. If we
+cut a species out of a given genus--the species man, for instance, out
+of the genus animal--with an intention on our part that the peculiarity
+by which we are to be guided in the application of the name man should
+be rationality, then rationality is the differentia of the species man.
+Suppose, however, that being naturalists, we, for the purposes of our
+particular study, cut out of the genus animal the same species man, but
+with an intention that the distinction between man and all other species
+of animal should be, not rationality, but the possession of "four
+incisors in each jaw, tusks solitary, and erect posture." It is evident
+that the word man, when used by us as naturalists, no longer connotes
+rationality, but connotes the three other properties specified; for that
+which we have expressly in view when we impose a name, assuredly forms
+part of the meaning of that name. We may, therefore, lay it down as a
+maxim, that wherever there is a Genus, and a Species marked out from
+that genus by an assignable differentia, the name of the species must be
+connotative, and must connote the differentia; but the connotation may
+be special--not involved in the signification of the term as ordinarily
+used, but given to it when employed as a term of art or science. The
+word Man in common use, connotes rationality and a certain form, but
+does not connote the number or character of the teeth; in the Linnaean
+system it connotes the number of incisor and canine teeth, but does not
+connote rationality nor any particular form. The word _man_ has,
+therefore, two different meanings; though not commonly considered as
+ambiguous, because it happens in both cases to _de_note the same
+individual objects. But a case is conceivable in which the ambiguity
+would become evident: we have only to imagine that some new kind of
+animal were discovered, having Linnaeus's three characteristics of
+humanity, but not rational, or not of the human form. In ordinary
+parlance, these animals would not be called men; but in natural history
+they must still be called so by those, if any there be, who adhere to
+the Linnaean classification; and the question would arise, whether the
+word should continue to be used in two senses, or the classification be
+given up, and the technical sense of the term be abandoned along with
+it.
+
+Words not otherwise connotative may, in the mode just adverted to,
+acquire a special or technical connotation. Thus the word whiteness, as
+we have so often remarked, connotes nothing; it merely denotes the
+attribute corresponding to a certain sensation: but if we are making a
+classification of colours, and desire to justify, or even merely to
+point out, the particular place assigned to whiteness in our
+arrangement, we may define it "the colour produced by the mixture of all
+the simple rays;" and this fact, though by no means implied in the
+meaning of the word whiteness as ordinarily used, but only known by
+subsequent scientific investigation, is part of its meaning in the
+particular essay or treatise, and becomes the differentia of the
+species.[26]
+
+The differentia, therefore, of a species may be defined to be, that part
+of the connotation of the specific name, whether ordinary or special and
+technical, which distinguishes the species in question from all other
+species of the genus to which on the particular occasion we are
+referring it.
+
+
+Sec. 7. Having disposed of Genus, Species, and Differentia, we shall not
+find much difficulty in attaining a clear conception of the distinction
+between the other two predicables, as well as between them and the first
+three.
+
+In the Aristotelian phraseology, Genus and Differentia are of the
+_essence_ of the subject; by which, as we have seen, is really meant
+that the properties signified by the genus and those signified by the
+differentia, form part of the connotation of the name denoting the
+species. Proprium and Accidens, on the other hand, form no part of the
+essence, but are predicated of the species only _accidentally_. Both are
+Accidents, in the wider sense in which the accidents of a thing are
+opposed to its essence; though, in the doctrine of the Predicables,
+Accidens is used for one sort of accident only, Proprium being another
+sort. Proprium, continue the schoolmen, is predicated _accidentally_,
+indeed, but _necessarily_; or, as they further explain it, signifies an
+attribute which is not indeed part of the essence, but which flows from,
+or is a consequence of, the essence, and is, therefore, inseparably
+attached to the species; _e. g._ the various properties of a triangle,
+which, though no part of its definition, must necessarily be possessed
+by whatever comes under that definition. Accidens, on the contrary, has
+no connexion whatever with the essence, but may come and go, and the
+species still remain what it was before. If a species could exist
+without its Propria, it must be capable of existing without that on
+which its Propria are necessarily consequent, and therefore without its
+essence, without that which constitutes it a species. But an Accidens,
+whether separable or inseparable from the species in actual experience,
+may be supposed separated, without the necessity of supposing any other
+alteration; or at least, without supposing any of the essential
+properties of the species to be altered, since with them an Accidens has
+no connexion.
+
+A Proprium, therefore, of the species, may be defined, any attribute
+which belongs to all the individuals included in the species, and which,
+though not connoted by the specific name, (either ordinarily if the
+classification we are considering be for ordinary purposes, or specially
+if it be for a special purpose,) yet follows from some attribute which
+the name either ordinarily or specially connotes.
+
+One attribute may follow from another in two ways; and there are
+consequently two kinds of Proprium. It may follow as a conclusion
+follows premises, or it may follow as an effect follows a cause. Thus,
+the attribute of having the opposite sides equal, which is not one of
+those connoted by the word Parallelogram, nevertheless follows from
+those connoted by it, namely, from having the opposite sides straight
+lines and parallel, and the number of sides four. The attribute,
+therefore, of having the opposite sides equal, is a Proprium of the
+class parallelogram; and a Proprium of the first kind, which follows
+from the connoted attributes by way of _demonstration_. The attribute of
+being capable of understanding language, is a Proprium of the species
+man, since without being connoted by the word, it follows from an
+attribute which the word does connote, viz. from the attribute of
+rationality. But this is a Proprium of the second kind, which follows by
+way of _causation_. How it is that one property of a thing follows, or
+can be inferred, from another; under what conditions this is possible,
+and what is the exact meaning of the phrase; are among the questions
+which will occupy us in the two succeeding Books. At present it needs
+only be said, that whether a Proprium follows by demonstration or by
+causation, it follows _necessarily_; that is to say, its not following
+would be inconsistent with some law which we regard as a part of the
+constitution either of our thinking faculty or of the universe.
+
+
+Sec. 8. Under the remaining predicable, Accidens, are included all
+attributes of a thing which are neither involved in the signification of
+the name (whether ordinarily or as a term of art), nor have, so far as
+we know, any necessary connexion with attributes which are so involved.
+They are commonly divided into Separable and Inseparable Accidents.
+Inseparable accidents are those which--although we know of no connexion
+between them and the attributes constitutive of the species, and
+although, therefore, so far as we are aware, they might be absent
+without making the name inapplicable and the species a different
+species--are yet never in fact known to be absent. A concise mode of
+expressing the same meaning is, that inseparable accidents are
+properties which are universal to the species, but not necessary to it.
+Thus, blackness is an attribute of a crow, and, as far as we know, an
+universal one. But if we were to discover a race of white birds, in
+other respects resembling crows, we should not say, These are not crows;
+we should say, These are white crows. Crow, therefore, does not connote
+blackness; nor, from any of the attributes which it does connote,
+whether as a word in popular use or as a term of art, could blackness be
+inferred. Not only, therefore, can we conceive a white crow, but we know
+of no reason why such an animal should not exist. Since, however, none
+but black crows are known to exist, blackness, in the present state of
+our knowledge, ranks as an accident, but an inseparable accident, of
+the species crow.
+
+Separable Accidents are those which are found, in point of fact, to be
+sometimes absent from the species; which are not only not necessary, but
+not even universal. They are such as do not belong to every individual
+of the species, but only to some individuals; or if to all, not at all
+times. Thus the colour of an European is one of the separable accidents
+of the species man, because it is not an attribute of all human
+creatures. Being born, is also (speaking in the logical sense) a
+separable accident of the species man, because, though an attribute of
+all human beings, it is so only at one particular time. _A fortiori_
+those attributes which are not constant even in the same individual, as,
+to be in one or in another place, to be hot or cold, sitting or walking,
+must be ranked as separable accidents.
+
+
+
+
+CHAPTER VIII.
+
+OF DEFINITION.
+
+
+Sec. 1. One necessary part of the theory of Names and of Propositions
+remains to be treated of in this place: the theory of Definitions. As
+being the most important of the class of propositions which we have
+characterized as purely verbal, they have already received some notice
+in the chapter preceding the last. But their fuller treatment was at
+that time postponed, because definition is so closely connected with
+classification, that, until the nature of the latter process is in some
+measure understood, the former cannot be discussed to much purpose.
+
+The simplest and most correct notion of a Definition is, a proposition
+declaratory of the meaning of a word; namely, either the meaning which
+it bears in common acceptation, or that which the speaker or writer, for
+the particular purposes of his discourse, intends to annex to it.
+
+The definition of a word being the proposition which enunciates its
+meaning, words which have no meaning are unsusceptible of definition.
+Proper names, therefore, cannot be defined. A proper name being a mere
+mark put upon an individual, and of which it is the characteristic
+property to be destitute of meaning, its meaning cannot of course be
+declared; though we may indicate by language, as we might indicate still
+more conveniently by pointing with the finger, upon what individual that
+particular mark has been, or is intended to be, put. It is no definition
+of "John Thomson" to say he is "the son of General Thomson;" for the
+name John Thomson does not express this. Neither is it any definition of
+"John Thomson" to say he is "the man now crossing the street." These
+propositions may serve to make known who is the particular man to whom
+the name belongs, but that may be done still more unambiguously by
+pointing to him, which, however, has not been esteemed one of the modes
+of definition.
+
+In the case of connotative names, the meaning, as has been so often
+observed, is the connotation; and the definition of a connotative name,
+is the proposition which declares its connotation. This might be done
+either directly or indirectly. The direct mode would be by a proposition
+in this form: "Man" (or whatsoever the word may be) "is a name connoting
+such and such attributes," or "is a name which, when predicated of
+anything, signifies the possession of such and such attributes by that
+thing." Or thus: Man is everything which possesses such and such
+attributes: Man is everything which possesses corporeity, organization,
+life, rationality, and certain peculiarities of external form.
+
+This form of definition is the most precise and least equivocal of any;
+but it is not brief enough, and is besides too technical for common
+discourse. The more usual mode of declaring the connotation of a name,
+is to predicate of it another name or names of known signification,
+which connote the same aggregation of attributes. This may be done
+either by predicating of the name intended to be defined, another
+connotative name exactly synonymous, as, "Man is a human being," which
+is not commonly accounted a definition at all; or by predicating two or
+more connotative names, which make up among them the whole connotation
+of the name to be defined. In this last case, again, we may either
+compose our definition of as many connotative names as there are
+attributes, each attribute being connoted by one, as, Man is a
+corporeal, organized, animated, rational being, shaped so and so; or we
+may employ names which connote several of the attributes at once, as,
+Man is a rational _animal_, shaped so and so.
+
+The definition of a name, according to this view of it, is the sum total
+of all the _essential_ propositions which can be framed with that name
+for their subject. All propositions the truth of which is implied in the
+name, all those which we are made aware of by merely hearing the name,
+are included in the definition, if complete, and may be evolved from it
+without the aid of any other premises; whether the definition expresses
+them in two or three words, or in a larger number. It is, therefore, not
+without reason that Condillac and other writers have affirmed a
+definition to be an _analysis_. To resolve any complex whole into the
+elements of which it is compounded, is the meaning of analysis: and this
+we do when we replace one word which connotes a set of attributes
+collectively, by two or more which connote the same attributes singly,
+or in smaller groups.
+
+
+Sec. 2. From this, however, the question naturally arises, in what manner
+are we to define a name which connotes only a single attribute: for
+instance, "white," which connotes nothing but whiteness; "rational,"
+which connotes nothing but the possession of reason. It might seem that
+the meaning of such names could only be declared in two ways; by a
+synonymous term, if any such can be found; or in the direct way already
+alluded to: "White is a name connoting the attribute whiteness." Let us
+see, however, whether the analysis of the meaning of the name, that is,
+the breaking down of that meaning into several parts, admits of being
+carried farther. Without at present deciding this question as to the
+word _white_, it is obvious that in the case of _rational_ some further
+explanation may be given of its meaning than is contained in the
+proposition, "Rational is that which possesses the attribute of reason;"
+since the attribute reason itself admits of being defined. And here we
+must turn our attention to the definitions of attributes, or rather of
+the names of attributes, that is, of abstract names.
+
+In regard to such names of attributes as are connotative, and express
+attributes of those attributes, there is no difficulty: like other
+connotative names they are defined by declaring their connotation. Thus,
+the word _fault_ may be defined, "a quality productive of evil or
+inconvenience." Sometimes, again, the attribute to be defined is not one
+attribute, but an union of several: we have only, therefore, to put
+together the names of all the attributes taken separately, and we obtain
+the definition of the name which belongs to them all taken together; a
+definition which will correspond exactly to that of the corresponding
+concrete name. For, as we define a concrete name by enumerating the
+attributes which it connotes, and as the attributes connoted by a
+concrete name form the entire signification of the corresponding
+abstract name, the same enumeration will serve for the definition of
+both. Thus, if the definition of _a human being_ be this, "a being,
+corporeal, animated, rational, shaped so and so," the definition of
+_humanity_ will be corporeity and animal life, combined with
+rationality, and with such and such a shape.
+
+When, on the other hand, the abstract name does not express a
+complication of attributes, but a single attribute, we must remember
+that every attribute is grounded on some fact or phenomenon, from which,
+and which alone, it derives its meaning. To that fact or phenomenon,
+called in a former chapter the foundation of the attribute, we must,
+therefore, have recourse for its definition. Now, the foundation of the
+attribute may be a phenomenon of any degree of complexity, consisting of
+many different parts, either coexistent or in succession. To obtain a
+definition of the attribute, we must analyse the phenomenon into these
+parts. Eloquence, for example, is the name of one attribute only; but
+this attribute is grounded on external effects of a complicated nature,
+flowing from acts of the person to whom we ascribed the attribute; and
+by resolving this phenomenon of causation into its two parts, the cause
+and the effect, we obtain a definition of eloquence, viz. the power of
+influencing the feelings by speech or writing.
+
+A name, therefore, whether concrete or abstract, admits of definition,
+provided we are able to analyse, that is, to distinguish into parts, the
+attribute or set of attributes which constitute the meaning both of the
+concrete name and of the corresponding abstract: if a set of attributes,
+by enumerating them; if a single attribute, by dissecting the fact or
+phenomenon (whether of perception or of internal consciousness) which is
+the foundation of the attribute. But, further, even when the fact is one
+of our simple feelings or states of consciousness, and therefore
+unsusceptible of analysis, the names both of the object and of the
+attribute still admit of definition: or rather, would do so if all our
+simple feelings had names. Whiteness may be defined, the property or
+power of exciting the sensation of white. A white object may be defined,
+an object which excites the sensation of white. The only names which are
+unsusceptible of definition, because their meaning is unsusceptible of
+analysis, are the names of the simple feelings themselves. These are in
+the same condition as proper names. They are not indeed, like proper
+names, unmeaning; for the words _sensation of white_ signify, that the
+sensation which I so denominate resembles other sensations which I
+remember to have had before, and to have called by that name. But as we
+have no words by which to recal those former sensations, except the very
+word which we seek to define, or some other which, being exactly
+synonymous with it, requires definition as much, words cannot unfold the
+signification of this class of names; and we are obliged to make a
+direct appeal to the personal experience of the individual whom we
+address.
+
+
+Sec. 3. Having stated what seems to be the true idea of a Definition, we
+proceed to examine some opinions of philosophers, and some popular
+conceptions on the subject, which conflict more or less with that idea.
+
+The only adequate definition of a name is, as already remarked, one
+which declares the facts, and the whole of the facts, which the name
+involves in its signification. But with most persons the object of a
+definition does not embrace so much; they look for nothing more, in a
+definition, than a guide to the correct use of the term--a protection
+against applying it in a manner inconsistent with custom and convention.
+Anything, therefore, is to them a sufficient definition of a term, which
+will serve as a correct index to what the term denotes; though not
+embracing the whole, and sometimes, perhaps, not even any part, of what
+it connotes. This gives rise to two sorts of imperfect, or unscientific
+definition; Essential but incomplete Definitions, and Accidental
+Definitions, or Descriptions. In the former, a connotative name is
+defined by a part only of its connotation; in the latter, by something
+which forms no part of the connotation at all.
+
+An example of the first kind of imperfect definitions is the
+following:--Man is a rational animal. It is impossible to consider this
+as a complete definition of the word Man, since (as before remarked) if
+we adhered to it we should be obliged to call the Houyhnhnms men; but as
+there happen to be no Houyhnhnms, this imperfect definition is
+sufficient to mark out and distinguish from all other things, the
+objects at present denoted by "man;" all the beings actually known to
+exist, of whom the name is predicable. Though the word is defined by
+some only among the attributes which it connotes, not by all, it happens
+that all known objects which possess the enumerated attributes, possess
+also those which are omitted; so that the field of predication which the
+word covers, and the employment of it which is conformable to usage, are
+as well indicated by the inadequate definition as by an adequate one.
+Such definitions, however, are always liable to be overthrown by the
+discovery of new objects in nature.
+
+Definitions of this kind are what logicians have had in view, when they
+laid down the rule, that the definition of a species should be _per
+genus et differentiam_. Differentia being seldom taken to mean the whole
+of the peculiarities constitutive of the species, but some one of those
+peculiarities only, a complete definition would be _per genus et
+differentias_, rather than _differentiam_. It would include, with the
+name of the superior genus, not merely _some_ attribute which
+distinguishes the species intended to be defined from all other species
+of the same genus, but _all_ the attributes implied in the name of the
+species, which the name of the superior genus has not already implied.
+The assertion, however, that a definition must of necessity consist of a
+genus and differentiae, is not tenable. It was early remarked by
+logicians, that the _summum genus_ in any classification, having no
+genus superior to itself, could not be defined in this manner. Yet we
+have seen that all names, except those of our elementary feelings, are
+susceptible of definition in the strictest sense; by setting forth in
+words the constituent parts of the fact or phenomenon, of which the
+connotation of every word is ultimately composed.
+
+
+Sec. 4. Although the first kind of imperfect definition, (which defines a
+connotative term by a part only of what it connotes, but a part
+sufficient to mark out correctly the boundaries of its denotation,) has
+been considered by the ancients, and by logicians in general, as a
+complete definition; it has always been deemed necessary that the
+attributes employed should really form part of the connotation; for the
+rule was that the definition must be drawn from the _essence_ of the
+class; and this would not have been the case if it had been in any
+degree made up of attributes not connoted by the name. The second kind
+of imperfect definition, therefore, in which the name of a class is
+defined by any of its accidents,--that is, by attributes which are not
+included in its connotation,--has been rejected from the rank of genuine
+Definition by all logicians, and has been termed Description.
+
+This kind of imperfect definition, however, takes its rise from the same
+cause as the other, namely, the willingness to accept as a definition
+anything which, whether it expounds the meaning of the name or not,
+enables us to discriminate the things denoted by the name from all other
+things, and consequently to employ the term in predication without
+deviating from established usage. This purpose is duly answered by
+stating any (no matter what) of the attributes which are common to the
+whole of the class, and peculiar to it; or any combination of attributes
+which happens to be peculiar to it, though separately each of those
+attributes may be common to it with some other things. It is only
+necessary that the definition (or description) thus formed, should be
+_convertible_ with the name which it professes to define; that is,
+should be exactly co-extensive with it, being predicable of everything
+of which it is predicable, and of nothing of which it is not predicable;
+though the attributes specified may have no connexion with those which
+mankind had in view when they formed or recognised the class, and gave
+it a name. The following are correct definitions of Man, according to
+this test: Man is a mammiferous animal, having (by nature) two hands
+(for the human species answers to this description, and no other animal
+does): Man is an animal who cooks his food: Man is a featherless biped.
+
+What would otherwise be a mere description, may be raised to the rank of
+a real definition by the peculiar purpose which the speaker or writer
+has in view. As was seen in the preceding chapter, it may, for the ends
+of a particular art or science, or for the more convenient statement of
+an author's particular doctrines, be advisable to give to some general
+name, without altering its denotation, a special connotation, different
+from its ordinary one. When this is done, a definition of the name by
+means of the attributes which make up the special connotation, though in
+general a mere accidental definition or description, becomes on the
+particular occasion and for the particular purpose a complete and
+genuine definition. This actually occurs with respect to one of the
+preceding examples, "Man is a mammiferous animal having two hands,"
+which is the scientific definition of man, considered as one of the
+species in Cuvier's distribution of the animal kingdom.
+
+In cases of this sort, though the definition is still a declaration of
+the meaning which in the particular instance the name is appointed to
+convey, it cannot be said that to state the meaning of the word is the
+purpose of the definition. The purpose is not to expound a name, but a
+classification. The special meaning which Cuvier assigned to the word
+Man, (quite foreign to its ordinary meaning, though involving no change
+in the denotation of the word,) was incidental to a plan of arranging
+animals into classes on a certain principle, that is, according to a
+certain set of distinctions. And since the definition of Man according
+to the ordinary connotation of the word, though it would have answered
+every other purpose of a definition, would not have pointed out the
+place which the species ought to occupy in that particular
+classification; he gave the word a special connotation, that he might be
+able to define it by the kind of attributes on which, for reasons of
+scientific convenience, he had resolved to found his division of
+animated nature.
+
+Scientific definitions, whether they are definitions of scientific
+terms, or of common terms used in a scientific sense, are almost always
+of the kind last spoken of: their main purpose is to serve as the
+landmarks of scientific classification. And since the classifications in
+any science are continually modified as scientific knowledge advances,
+the definitions in the sciences are also constantly varying. A striking
+instance is afforded by the words Acid and Alkali, especially the
+former. As experimental discovery advanced, the substances classed with
+acids have been constantly multiplying, and by a natural consequence the
+attributes connoted by the word have receded and become fewer. At first
+it connoted the attributes, of combining with an alkali to form a
+neutral substance (called a salt); being compounded of a base and
+oxygen; causticity to the taste and touch; fluidity, &c. The true
+analysis of muriatic acid, into chlorine and hydrogen, caused the second
+property, composition from a base and oxygen, to be excluded from the
+connotation. The same discovery fixed the attention of chemists upon
+hydrogen as an important element in acids; and more recent discoveries
+having led to the recognition of its presence in sulphuric, nitric, and
+many other acids, where its existence was not previously suspected,
+there is now a tendency to include the presence of this element in the
+connotation of the word. But carbonic acid, silica, sulphurous acid,
+have no hydrogen in their composition; that property cannot therefore be
+connoted by the term, unless those substances are no longer to be
+considered acids. Causticity and fluidity have long since been excluded
+from the characteristics of the class, by the inclusion of silica and
+many other substances in it; and the formation of neutral bodies by
+combination with alkalis, together with such electro-chemical
+peculiarities as this is supposed to imply, are now the only
+_differentiae_ which form the fixed connotation of the word Acid, as a
+term of chemical science.
+
+What is true of the definition of any term of science, is of course true
+of the definition of a science itself: and accordingly, (as observed in
+the Introductory Chapter of this work,) the definition of a science must
+necessarily be progressive and provisional. Any extension of knowledge
+or alteration in the current opinions respecting the subject matter, may
+lead to a change more or less extensive in the particulars included in
+the science; and its composition being thus altered, it may easily
+happen that a different set of characteristics will be found better
+adapted as differentiae for defining its name.
+
+In the same manner in which a special or technical definition has for
+its object to expound the artificial classification out of which it
+grows; the Aristotelian logicians seem to have imagined that it was also
+the business of ordinary definition to expound the ordinary, and what
+they deemed the natural, classification of things, namely, the division
+of them into Kinds; and to show the place which each Kind occupies, as
+superior, collateral, or subordinate, among other Kinds. This notion
+would account for the rule that all definition must necessarily be _per
+genus et differentiam_, and would also explain why a single differentia
+was deemed sufficient. But to expound, or express in words, a
+distinction of Kind, has already been shown to be an impossibility: the
+very meaning of a Kind is, that the properties which distinguish it do
+not grow out of one another, and cannot therefore be set forth in words,
+even by implication, otherwise than by enumerating them all: and all are
+not known, nor are ever likely to be so. It is idle, therefore, to look
+to this as one of the purposes of a definition: while, if it be only
+required that the definition of a Kind should indicate what Kinds
+include it or are included by it, any definitions which expound the
+connotation of the names will do this: for the name of each class must
+necessarily connote enough of its properties to fix the boundaries of
+the class. If the definition, therefore, be a full statement of the
+connotation, it is all that a definition can be required to be.
+
+
+Sec. 5. Of the two incomplete and popular modes of definition, and in what
+they differ from the complete or philosophical mode, enough has now been
+said. We shall next examine an ancient doctrine, once generally
+prevalent and still by no means exploded, which I regard as the source
+of a great part of the obscurity hanging over some of the most important
+processes of the understanding in the pursuit of truth. According to
+this, the definitions of which we have now treated are only one of two
+sorts into which definitions may be divided, viz. definitions of names,
+and definitions of things. The former are intended to explain the
+meaning of a term; the latter, the nature of a thing; the last being
+incomparably the most important.
+
+This opinion was held by the ancient philosophers, and by their
+followers, with the exception of the Nominalists; but as the spirit of
+modern metaphysics, until a recent period, has been on the whole a
+Nominalist spirit, the notion of definitions of things has been to a
+certain extent in abeyance, still continuing, however, to breed
+confusion in logic, by its consequences indeed rather than by itself.
+Yet the doctrine in its own proper form now and then breaks out, and has
+appeared (among other places) where it was scarcely to be expected, in a
+justly admired work, Archbishop Whately's _Logic_.[27] In a review of
+that work published by me in the _Westminster Review_ for January 1828,
+and containing some opinions which I no longer entertain, I find the
+following observations on the question now before us; observations with
+which my present view of that question is still sufficiently in
+accordance.
+
+"The distinction between nominal and real definitions, between
+definitions of words and what are called definitions of things, though
+conformable to the ideas of most of the Aristotelian logicians, cannot,
+as it appears to us, be maintained. We apprehend that no definition is
+ever intended to 'explain and unfold the nature of a thing.' It is some
+confirmation of our opinion, that none of those writers who have thought
+that there were definitions of things, have ever succeeded in
+discovering any criterion by which the definition of a thing can be
+distinguished from any other proposition relating to the thing. The
+definition, they say, unfolds the nature of the thing: but no definition
+can unfold its whole nature; and every proposition in which any quality
+whatever is predicated of the thing, unfolds some part of its nature.
+The true state of the case we take to be this. All definitions are of
+names, and of names only; but, in some definitions, it is clearly
+apparent, that nothing is intended except to explain the meaning of the
+word; while in others, besides explaining the meaning of the word, it is
+intended to be implied that there exists a thing, corresponding to the
+word. Whether this be or be not implied in any given case, cannot be
+collected from the mere form of the expression. 'A centaur is an animal
+with the upper parts of a man and the lower parts of a horse,' and 'A
+triangle is a rectilineal figure with three sides,' are, in form,
+expressions precisely similar; although in the former it is not implied
+that any _thing_, conformable to the term, really exists, while in the
+latter it is; as may be seen by substituting, in both definitions, the
+word _means_ for _is_. In the first expression, 'A centaur means an
+animal,' &c., the sense would remain unchanged: in the second, 'A
+triangle means,' &c., the meaning would be altered, since it would be
+obviously impossible to deduce any of the truths of geometry from a
+proposition expressive only of the manner in which we intend to employ a
+particular sign.
+
+"There are, therefore, expressions, commonly passing for definitions,
+which include in themselves more than the mere explanation of the
+meaning of a term. But it is not correct to call an expression of this
+sort a peculiar kind of definition. Its difference from the other kind
+consists in this, that it is not a definition, but a definition and
+something more. The definition above given of a triangle, obviously
+comprises not one, but two propositions, perfectly distinguishable. The
+one is, 'There may exist a figure, bounded by three straight lines;' the
+other, 'And this figure may be termed a triangle.' The former of these
+propositions is not a definition at all: the latter is a mere nominal
+definition, or explanation of the use and application of a term. The
+first is susceptible of truth or falsehood, and may therefore be made
+the foundation of a train of reasoning. The latter can neither be true
+nor false; the only character it is susceptible of is that of conformity
+or disconformity to the ordinary usage of language."
+
+There is a real distinction, then, between definitions of names, and
+what are erroneously called definitions of things; but it is, that the
+latter, along with the meaning of a name, covertly asserts a matter of
+fact. This covert assertion is not a definition, but a postulate. The
+definition is a mere identical proposition, which gives information only
+about the use of language, and from which no conclusions affecting
+matters of fact can possibly be drawn. The accompanying postulate, on
+the other hand, affirms a fact, which may lead to consequences of every
+degree of importance. It affirms the actual or possible existence of
+Things possessing the combination of attributes set forth in the
+definition; and this, if true, may be foundation sufficient on which to
+build a whole fabric of scientific truth.
+
+We have already made, and shall often have to repeat, the remark, that
+the philosophers who overthrew Realism by no means got rid of the
+consequences of Realism, but retained long afterwards, in their own
+philosophy, numerous propositions which could only have a rational
+meaning as part of a Realistic system. It had been handed down from
+Aristotle, and probably from earlier times, as an obvious truth, that
+the science of Geometry is deduced from definitions. This, so long as a
+definition was considered to be a proposition "unfolding the nature of
+the thing," did well enough. But Hobbes followed, and rejected utterly
+the notion that a definition declares the nature of the thing, or does
+anything but state the meaning of a name; yet he continued to affirm as
+broadly as any of his predecessors, that the [Greek: archai],
+_principia_, or original premises of mathematics, and even of all
+science, are definitions; producing the singular paradox, that systems
+of scientific truth, nay, all truths whatever at which we arrive by
+reasoning, are deduced from the arbitrary conventions of mankind
+concerning the signification of words.
+
+To save the credit of the doctrine that definitions are the premises of
+scientific knowledge, the proviso is sometimes added, that they are so
+only under a certain condition, namely, that they be framed conformably
+to the phenomena of nature; that is, that they ascribe such meanings to
+terms as shall suit objects actually existing. But this is only an
+instance of the attempt so often made, to escape from the necessity of
+abandoning old language after the ideas which it expresses have been
+exchanged for contrary ones. From the meaning of a name (we are told) it
+is possible to infer physical facts, provided the name has corresponding
+to it an existing thing. But if this proviso be necessary, from which of
+the two is the inference really drawn? From the existence of a thing
+having the properties, or from the existence of a name meaning them?
+
+Take, for instance, any of the definitions laid down as premises in
+Euclid's Elements; the definition, let us say, of a circle. This, being
+analysed, consists of two propositions; the one an assumption with
+respect to a matter of fact, the other a genuine definition. "A figure
+may exist, having all the points in the line which bounds it equally
+distant from a single point within it:" "Any figure possessing this
+property is called a circle." Let us look at one of the demonstrations
+which are said to depend on this definition, and observe to which of the
+two propositions contained in it the demonstration really appeals.
+"About the centre A, describe the circle B C D." Here is an assumption
+that a figure, such as the definition expresses, _may_ be described;
+which is no other than the postulate, or covert assumption, involved in
+the so-called definition. But whether that figure be called a circle or
+not is quite immaterial. The purpose would be as well answered, in all
+respects except brevity, were we to say, "Through the point B, draw a
+line returning into itself, of which every point shall be at an equal
+distance from the point A." By this the definition of a circle would be
+got rid of, and rendered needless; but not the postulate implied in it;
+without that the demonstration could not stand. The circle being now
+described, let us proceed to the consequence. "Since B C D is a circle,
+the radius B A is equal to the radius C A." B A is equal to C A, not
+because B C D is a circle, but because B C D is a figure with the radii
+equal. Our warrant for assuming that such a figure about the centre A,
+with the radius B A, may be made to exist, is the postulate. Whether the
+admissibility of these postulates rests on intuition, or on proof, may
+be a matter of dispute; but in either case they are the premises on
+which the theorems depend; and while these are retained it would make no
+difference in the certainty of geometrical truths, though every
+definition in Euclid, and every technical term therein defined, were
+laid aside.
+
+It is, perhaps, superfluous to dwell at so much length on what is so
+nearly self-evident; but when a distinction, obvious as it may appear,
+has been confounded, and by powerful intellects, it is better to say too
+much than too little for the purpose of rendering such mistakes
+impossible in future. I will, therefore, detain the reader while I point
+out one of the absurd consequences flowing from the supposition that
+definitions, as such, are the premises in any of our reasonings, except
+such as relate to words only. If this supposition were true, we might
+argue correctly from true premises, and arrive at a false conclusion. We
+should only have to assume as a premise the definition of a nonentity;
+or rather of a name which has no entity corresponding to it. Let this,
+for instance, be our definition:
+
+  A dragon is a serpent breathing flame.
+
+This proposition, considered only as a definition, is indisputably
+correct. A dragon _is_ a serpent breathing flame: the word _means_ that.
+The tacit assumption, indeed, (if there were any such understood
+assertion), of the existence of an object with properties corresponding
+to the definition, would, in the present instance, be false. Out of this
+definition we may carve the premises of the following syllogism:
+
+  A dragon is a thing which breathes flame:
+  A dragon is a serpent:
+
+From which the conclusion is,
+
+  Therefore some serpent or serpents breathe flame:--
+
+an unexceptionable syllogism in the first mode of the third figure, in
+which both premises are true and yet the conclusion false; which every
+logician knows to be an absurdity. The conclusion being false and the
+syllogism correct, the premises cannot be true. But the premises,
+considered as parts of a definition, are true. Therefore, the premises
+considered as parts of a definition cannot be the real ones. The real
+premises must be--
+
+  A dragon is a _really existing_ thing which breathes flame:
+  A dragon is a _really existing_ serpent:
+
+which implied premises being false, the falsity of the conclusion
+presents no absurdity.
+
+If we would determine what conclusion follows from the same ostensible
+premises when the tacit assumption of real existence is left out, let
+us, according to the recommendation in a previous page, substitute
+_means_ for _is_. We then have--
+
+  Dragon is _a word meaning_ a thing which breathes flame:
+  Dragon is _a word meaning_ a serpent:
+
+From which the conclusion is,
+
+  Some _word or words which mean_ a serpent, also mean a thing which
+  breathes flame:
+
+where the conclusion (as well as the premises) is true, and is the only
+kind of conclusion which can ever follow from a definition, namely, a
+proposition relating to the meaning of words.
+
+There is still another shape into which we may transform this syllogism.
+We may suppose the middle term to be the designation neither of a thing
+nor of a name, but of an idea. We then have--
+
+  The _idea of_ a dragon is _an idea of_ a thing which breathes
+    flame:
+  The _idea of_ a dragon is _an idea of_ a serpent:
+  Therefore, there is _an idea of_ a serpent, which is _an idea of_
+    a thing breathing flame.
+
+Here the conclusion is true, and also the premises; but the premises are
+not definitions. They are propositions affirming that an idea existing
+in the mind, includes certain ideal elements. The truth of the
+conclusion follows from the existence of the psychological phenomenon
+called the idea of a dragon; and therefore still from the tacit
+assumption of a matter of fact.[28]
+
+When, as in this last syllogism, the conclusion is a proposition
+respecting an idea, the assumption on which it depends may be merely
+that of the existence of an idea. But when the conclusion is a
+proposition concerning a Thing, the postulate involved in the definition
+which stands as the apparent premise, is the existence of a thing
+conformable to the definition, and not merely of an idea conformable to
+it. This assumption of real existence will always convey the impression
+that we intend to make, when we profess to define any name which is
+already known to be a name of really existing objects. On this account
+it is, that the assumption was not necessarily implied in the definition
+of a dragon, while there was no doubt of its being included in the
+definition of a circle.
+
+
+Sec. 6. One of the circumstances which have contributed to keep up the
+notion, that demonstrative truths follow from definitions rather than
+from the postulates implied in those definitions, is, that the
+postulates, even in those sciences which are considered to surpass all
+others in demonstrative certainty, are not always exactly true. It is
+not true that a circle exists, or can be described, which has all its
+radii _exactly_ equal. Such accuracy is ideal only; it is not found in
+nature, still less can it be realized by art. People had a difficulty,
+therefore, in conceiving that the most certain of all conclusions could
+rest on premises which, instead of being certainly true, are certainly
+not true to the full extent asserted. This apparent paradox will be
+examined when we come to treat of Demonstration; where we shall be able
+to show that as much of the postulate is true, as is required to support
+as much as is true of the conclusion. Philosophers, however, to whom
+this view had not occurred, or whom it did not satisfy, have thought it
+indispensable that there should be found in definitions something _more_
+certain, or at least more accurately true, than the implied postulate of
+the real existence of a corresponding object. And this something they
+flattered themselves they had found, when they laid it down that a
+definition is a statement and analysis not of the mere meaning of a
+word, nor yet of the nature of a thing, but of an idea. Thus, the
+proposition, "A circle is a plane figure bounded by a line all the
+points of which are at an equal distance from a given point within it,"
+was considered by them, not as an assertion that any real circle has
+that property, (which would not be exactly true,) but that we _conceive_
+a circle as having it; that our abstract idea of a circle is an idea of
+a figure with its radii exactly equal.
+
+Conformably to this it is said, that the subject-matter of mathematics,
+and of every other demonstrative science, is not things as they really
+exist, but abstractions of the mind. A geometrical line is a line
+without breadth; but no such line exists in nature; it is a notion
+merely suggested to the mind by its experience of nature. The definition
+(it is said) is a definition of this mental line, not of any actual
+line: and it is only of the mental line, not of any line existing in
+nature, that the theorems of geometry are accurately true.
+
+Allowing this doctrine respecting the nature of demonstrative truth to
+be correct (which, in a subsequent place, I shall endeavour to prove
+that it is not;) even on that supposition, the conclusions which seem to
+follow from a definition, do not follow from the definition as such, but
+from an implied postulate. Even if it be true that there is no object in
+nature answering to the definition of a line, and that the geometrical
+properties of lines are not true of any lines in nature, but only of the
+idea of a line; the definition, at all events, postulates the real
+existence of such an idea: it assumes that the mind can frame, or rather
+has framed, the notion of length without breadth, and without any other
+sensible property whatever. To me, indeed, it appears that the mind
+cannot form any such notion; it cannot conceive length without breadth;
+it can only, in contemplating objects, attend to their length,
+exclusively of their other sensible qualities, and so determine what
+properties may be predicated of them in virtue of their length alone. If
+this be true, the postulate involved in the geometrical definition of a
+line, is the real existence, not of length without breadth, but merely
+of length, that is, of long objects. This is quite enough to support all
+the truths of geometry, since every property of a geometrical line is
+really a property of all physical objects in so far as possessing
+length. But even what I hold to be the false doctrine on the subject,
+leaves the conclusion that our reasonings are grounded on the matters of
+fact postulated in definitions, and not on the definitions themselves,
+entirely unaffected; and accordingly this conclusion is one which I have
+in common with Dr. Whewell, in his _Philosophy of the Inductive
+Sciences_: though, on the nature of demonstrative truth, Dr. Whewell's
+opinions are greatly at variance with mine. And here, as in many other
+instances, I gladly acknowledge that his writings are eminently
+serviceable in clearing from confusion the initial steps in the analysis
+of the mental processes, even where his views respecting the ultimate
+analysis are such as (though with unfeigned respect) I cannot but regard
+as fundamentally erroneous.
+
+
+Sec. 7. Although, according to the opinion here presented, Definitions are
+properly of names only, and not of things, it does not follow from this
+that definitions are arbitrary. How to define a name, may not only be an
+inquiry of considerable difficulty and intricacy, but may involve
+considerations going deep into the nature of the things which are
+denoted by the name. Such, for instance, are the inquiries which form
+the subjects of the most important of Plato's Dialogues; as, "What is
+rhetoric?" the topic of the Gorgias, or "What is justice?" that of the
+Republic. Such, also, is the question scornfully asked by Pilate, "What
+is truth?" and the fundamental question with speculative moralists in
+all ages, "What is virtue?"
+
+It would be a mistake to represent these difficult and noble inquiries
+as having nothing in view beyond ascertaining the conventional meaning
+of a name. They are inquiries not so much to determine what is, as what
+should be, the meaning of a name; which, like other practical questions
+of terminology, requires for its solution that we should enter, and
+sometimes enter very deeply, into the properties not merely of names but
+of the things named.
+
+Although the meaning of every concrete general name resides in the
+attributes which it connotes, the objects were named before the
+attributes; as appears from the fact that in all languages, abstract
+names are mostly compounds or other derivatives of the concrete names
+which correspond to them. Connotative names, therefore, were, after
+proper names, the first which were used: and in the simpler cases, no
+doubt, a distinct connotation was present to the minds of those who
+first used the name, and was distinctly intended by them to be conveyed
+by it. The first person who used the word white, as applied to snow or
+to any other object, knew, no doubt, very well what quality he intended
+to predicate, and had a perfectly distinct conception in his mind of the
+attribute signified by the name.
+
+But where the resemblances and differences on which our classifications
+are founded are not of this palpable and easily determinable kind;
+especially where they consist not in any one quality but in a number of
+qualities, the effects of which being blended together are not very
+easily discriminated, and referred each to its true source; it often
+happens that names are applied to nameable objects, with no distinct
+connotation present to the minds of those who apply them. They are only
+influenced by a general resemblance between the new object and all or
+some of the old familiar objects which they have been accustomed to call
+by that name. This, as we have seen, is the law which even the mind of
+the philosopher must follow, in giving names to the simple elementary
+feelings of our nature: but, where the things to be named are complex
+wholes, a philosopher is not content with noticing a general
+resemblance; he examines what the resemblance consists in: and he only
+gives the same name to things which resemble one another in the same
+definite particulars. The philosopher, therefore, habitually employs his
+general names with a definite connotation. But language was not made,
+and can only in some small degree be mended, by philosophers. In the
+minds of the real arbiters of language, general names, especially where
+the classes they denote cannot be brought before the tribunal of the
+outward senses to be identified and discriminated, connote little more
+than a vague gross resemblance to the things which they were earliest,
+or have been most, accustomed to call by those names. When, for
+instance, ordinary persons predicate the words _just_ or _unjust_ of any
+action, _noble_ or _mean_ of any sentiment, expression, or demeanour,
+_statesman_ or _charlatan_ of any personage figuring in politics, do
+they mean to affirm of those various subjects any determinate
+attributes, of whatever kind? No: they merely recognise, as they think,
+some likeness, more or less vague and loose, between these and some
+other things which they have been accustomed to denominate or to hear
+denominated by those appellations.
+
+Language, as Sir James Mackintosh used to say of governments, "is not
+made, but grows." A name is not imposed at once and by previous purpose
+upon a _class_ of objects, but is first applied to one thing, and then
+extended by a series of transitions to another and another. By this
+process (as has been remarked by several writers, and illustrated with
+great force and clearness by Dugald Stewart in his Philosophical Essays)
+a name not unfrequently passes by successive links of resemblance from
+one object to another, until it becomes applied to things having nothing
+in common with the first things to which the name was given; which,
+however, do not, for that reason, drop the name; so that it at last
+denotes a confused huddle of objects, having nothing whatever in common;
+and connotes nothing, not even a vague and general resemblance. When a
+name has fallen into this state, in which by predicating it of any
+object we assert literally nothing about the object, it has become unfit
+for the purposes either of thought or of the communication of thought;
+and can only be made serviceable by stripping it of some part of its
+multifarious denotation, and confining it to objects possessed of some
+attributes in common, which it may be made to connote. Such are the
+inconveniences of a language which "is not made, but grows." Like the
+governments which are in a similar case, it may be compared to a road
+which is not made but has made itself: it requires continual mending in
+order to be passable.
+
+From this it is already evident, why the question respecting the
+definition of an abstract name is often one of so much difficulty. The
+question, What is justice? is, in other words, What is the attribute
+which mankind mean to predicate when they call an action just? To which
+the first answer is, that having come to no precise agreement on the
+point, they do not mean to predicate distinctly any attribute at all.
+Nevertheless, all believe that there is some common attribute belonging
+to all the actions which they are in the habit of calling just. The
+question then must be, whether there is any such common attribute? and,
+in the first place, whether mankind agree sufficiently with one another
+as to the particular actions which they do or do not call just, to
+render the inquiry, what quality those actions have in common, a
+possible one: if so, whether the actions really have any quality in
+common; and if they have, what it is. Of these three, the first alone is
+an inquiry into usage and convention; the other two are inquiries into
+matters of fact. And if the second question (whether the actions form a
+class at all) has been answered negatively, there remains a fourth,
+often more arduous than all the rest, namely, how best to form a class
+artificially, which the name may denote.
+
+And here it is fitting to remark, that the study of the spontaneous
+growth of languages is of the utmost importance to those who would
+logically remodel them. The classifications rudely made by established
+language, when retouched, as they almost all require to be, by the hands
+of the logician, are often in themselves excellently suited to his
+purposes. As compared with the classifications of a philosopher, they
+are like the customary law of a country, which has grown up as it were
+spontaneously, compared with laws methodized and digested into a code:
+the former are a far less perfect instrument than the latter; but being
+the result of a long, though unscientific, course of experience, they
+contain a mass of materials which may be made very usefully available in
+the formation of the systematic body of written law. In like manner, the
+established grouping of objects under a common name, even when founded
+only on a gross and general resemblance, is evidence, in the first
+place, that the resemblance is obvious, and therefore considerable;
+and, in the next place, that it is a resemblance which has struck great
+numbers of persons during a series of years and ages. Even when a name,
+by successive extensions, has come to be applied to things among which
+there does not exist this gross resemblance common to them all, still at
+every step in its progress we shall find such a resemblance. And these
+transitions of the meaning of words are often an index to real
+connexions between the things denoted by them, which might otherwise
+escape the notice of thinkers; of those at least who, from using a
+different language, or from any difference in their habitual
+associations, have fixed their attention in preference on some other
+aspect of the things. The history of philosophy abounds in examples of
+such oversights, committed for want of perceiving the hidden link that
+connected together the seemingly disparate meanings of some ambiguous
+word.[29]
+
+Whenever the inquiry into the definition of the name of any real object
+consists of anything else than a mere comparison of authorities, we
+tacitly assume that a meaning must be found for the name, compatible
+with its continuing to denote, if possible all, but at any rate the
+greater or the more important part, of the things of which it is
+commonly predicated. The inquiry, therefore, into the definition, is an
+inquiry into the resemblances and differences among those things:
+whether there be any resemblance running through them all; if not,
+through what portion of them such a general resemblance can be traced:
+and finally, what are the common attributes, the possession of which
+gives to them all, or to that portion of them, the character of
+resemblance which has led to their being classed together. When these
+common attributes have been ascertained and specified, the name which
+belongs in common to the resembling objects acquires a distinct instead
+of a vague connotation; and by possessing this distinct connotation,
+becomes susceptible of definition.
+
+In giving a distinct connotation to the general name, the philosopher
+will endeavour to fix upon such attributes as, while they are common to
+all the things usually denoted by the name, are also of greatest
+importance in themselves; either directly, or from the number, the
+conspicuousness, or the interesting character, of the consequences to
+which they lead. He will select, as far as possible, such _differentiae_
+as lead to the greatest number of interesting _propria_. For these,
+rather than the more obscure and recondite qualities on which they often
+depend, give that general character and aspect to a set of objects,
+which determine the groups into which they naturally fall. But to
+penetrate to the more hidden agreement on which these obvious and
+superficial agreements depend, is often one of the most difficult of
+scientific problems. As it is among the most difficult, so it seldom
+fails to be among the most important. And since upon the result of this
+inquiry respecting the causes of the properties of a class of things,
+there incidentally depends the question what shall be the meaning of a
+word; some of the most profound and most valuable investigations which
+philosophy presents to us, have been introduced by, and have offered
+themselves under the guise of, inquiries into the definition of a name.
+
+FOOTNOTES:
+
+[1] _Computation or Logic_, chap. ii.
+
+[2] In the original "had, _or had not_." These last words, as involving
+a subtlety foreign to our present purpose, I have forborne to quote.
+
+[3] Vide infra, note at the end of Sec. 3, book ii. ch. ii.
+
+[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one
+thing _with_ or _in addition to_ another.
+
+[5] Archbishop Whately, who, in the later editions of his _Elements of
+Logic_, aided in reviving the important distinction treated of in the
+text, proposes the term "Attributive" as a substitute for "Connotative"
+(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it
+has not the advantage of being connected with any verb, of so markedly
+distinctive a character as "to connote," it is not, I think, fitted to
+supply the place of the word Connotative in scientific use.
+
+[6] A writer who entitles his book _Philosophy; or, the Science of
+Truth_, charges me in his very first page (referring at the foot of it
+to this passage) with asserting that _general_ names have properly no
+signification. And he repeats this statement many times in the course of
+his volume, with comments, not at all flattering, thereon. It is well to
+be now and then reminded to how great a length perverse misquotation
+(for, strange as it appears, I do not believe that the writer is
+dishonest) can sometimes go. It is a warning to readers, when they see
+an author accused, with volume and page referred to, and the apparent
+guarantee of inverted commas, of maintaining something more than
+commonly absurd, not to give implicit credence to the assertion without
+verifying the reference.
+
+[7] Before quitting the subject of connotative names, it is proper to
+observe, that the first writer who, in our times, has adopted from the
+schoolmen the word _to connote_, Mr. James Mill, in his _Analysis of the
+Phenomena of the Human Mind_, employs it in a signification different
+from that in which it is here used. He uses the word in a sense
+coextensive with its etymology, applying it to every case in which a
+name, while pointing directly to one thing, (which is consequently
+termed its signification,) includes also a tacit reference to some other
+thing. In the case considered in the text, that of concrete general
+names, his language and mine are the converse of one another.
+Considering (very justly) the signification of the name to lie in the
+attribute, he speaks of the word as _noting_ the attribute, and
+_connoting_ the things possessing the attribute. And he describes
+abstract names as being properly concrete names with their connotation
+dropped: whereas, in my view, it is the _de_notation which would be said
+to be dropped, what was previously connoted becoming the whole
+signification.
+
+In adopting a phraseology at variance with that which so high an
+authority, and one which I am less likely than any other person to
+undervalue, has deliberately sanctioned, I have been influenced by the
+urgent necessity for a term exclusively appropriated to express the
+manner in which a concrete general name serves to mark the attributes
+which are involved in its signification. This necessity can scarcely be
+felt in its full force by any one who has not found by experience how
+vain is the attempt to communicate clear ideas on the philosophy of
+language without such a word. It is hardly an exaggeration to say, that
+some of the most prevalent of the errors with which logic has been
+infected, and a large part of the cloudiness and confusion of ideas
+which have enveloped it, would, in all probability, have been avoided,
+if a term had been in common use to express exactly what I have
+signified by the term to connote. And the schoolmen, to whom we are
+indebted for the greater part of our logical language, gave us this
+also, and in this very sense. For though some of their general
+expressions countenance the use of the word in the more extensive and
+vague acceptation in which it is taken by Mr. Mill, yet when they had to
+define it specifically as a technical term, and to fix its meaning as
+such, with that admirable precision which always characterizes their
+definitions, they clearly explained that nothing was said to be connoted
+except _forms_, which word may generally, in their writings, be
+understood as synonymous with _attributes_.
+
+Now, if the word _to connote_, so well suited to the purpose to which
+they applied it, be diverted from that purpose by being taken to fulfil
+another, for which it does not seem to me to be at all required; I am
+unable to find any expression to replace it, but such as are commonly
+employed in a sense so much more general, that it would be useless
+attempting to associate them peculiarly with this precise idea. Such are
+the words, to involve, to imply, &c. By employing these, I should fail
+of attaining the object for which alone the name is needed, namely, to
+distinguish this particular kind of involving and implying from all
+other kinds, and to assure to it the degree of habitual attention which
+its importance demands.
+
+[8] Or rather, all objects except itself and the percipient mind; for,
+as we shall see hereafter, to ascribe any attribute to an object,
+necessarily implies a mind to perceive it.
+
+The simple and clear explanation given in the text, of relation and
+relative names, a subject so long the opprobrium of metaphysics, was
+given (as far as I know) for the first time, by Mr. James Mill, in his
+Analysis of the Phenomena of the Human Mind.
+
+[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.
+
+[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.
+
+[11] It is to be regretted that Sir William Hamilton, though he often
+strenuously insists on this doctrine, and though, in the passage quoted,
+he states it with a comprehensiveness and force which leave nothing to
+be desired, did not consistently adhere to his own doctrine, but
+maintained along with it opinions with which it is utterly
+irreconcileable. See the third and other chapters of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous
+ne pouvons expliquer nos perceptions sans les rattacher a des causes
+distinctes de nous-memes; nous savons de plus que ces causes, dont nous
+ne connaissons pas d'ailleurs l'essence, produisent les effets les plus
+variables, les plus divers, et meme les plus contraires, selon qu'elles
+rencontrent telle nature ou telle disposition du sujet. Mais savons-nous
+quelque chose de plus? et meme, vu le caractere indetermine des causes
+que nous concevons dans les corps, y a-t-il quelque chose de plus a
+savoir? Y a-t-il lieu de nous enquerir si nous percevons les choses
+telles qu'elles sont? Non evidemment.... Je ne dis pas que le probleme
+est insoluble, _je dis qu'il est absurde et enferme une contradiction_.
+Nous _ne savons pas ce que ces causes sont en elles-memes_, et la raison
+nous defend de chercher a le connaitre: mais il est bien evident _a
+priori_, qu'_elles ne sont pas en elles-memes ce qu'elles sont par
+rapport a nous_, puisque la presence du sujet modifie necessairement
+leur action. Supprimez tout sujet sentant, il est certain que ces causes
+agiraient encore puisqu'elles continueraient d'exister; mais elles
+agiraient autrement; elles seraient encore des qualites et des
+proprietes, mais qui ne ressembleraient a rien de ce que nous
+connaissons. Le feu ne manifesterait plus aucune des proprietes que nous
+lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.
+_C'est d'ailleurs peut-etre un probleme qui ne repugne pas seulement a
+la nature de notre esprit, mais a l'essence meme des choses._ Quand meme
+en effet on supprimerait par la pensee tous les sujets sentants, il
+faudrait encore admettre que nul corps ne manifesterait ses proprietes
+autrement qu'en relation avec un sujet quelconque, et dans ce cas _ses
+proprietes ne seraient encore que relatives_: en sorte qu'il me parait
+fort raisonnable d'admettre que les proprietes determinees des corps
+n'existent pas independamment d'un sujet quelconque, et que quand on
+demande si les proprietes de la matiere sont telles que nous les
+percevons, il faudrait voir auparavant si elles sont en tant que
+determinees, et dans quel sens il est vrai de dire qu'elles
+sont."--_Cours d'Histoire de la Philosophie Morale au 18me siecle_, 8me
+lecon.
+
+[13] An attempt, indeed, has been made by Reid and others, to establish
+that although some of the properties we ascribe to objects exist only in
+our sensations, others exist in the things themselves, being such as
+cannot possibly be copies of any impression upon the senses; and they
+ask, from what sensations our notions of extension and figure have been
+derived? The gauntlet thrown down by Reid was taken up by Brown, who,
+applying greater powers of analysis than had previously been applied to
+the notions of extension and figure, pointed out that the sensations
+from which those notions are derived, are sensations of touch, combined
+with sensations of a class previously too little adverted to by
+metaphysicians, those which have their seat in our muscular frame. His
+analysis, which was adopted and followed up by James Mill, has been
+further and greatly improved upon in Professor Bain's profound work,
+_The Senses and the Intellect_, and in the chapters on "Perception" of a
+work of eminent analytic power, Mr. Herbert Spencer's _Principles of
+Psychology_.
+
+On this point M. Cousin may again be cited in favour of the better
+doctrine. M. Cousin recognises, in opposition to Reid, the essential
+subjectivity of our conceptions of what are called the primary qualities
+of matter, as extension, solidity, &c., equally with those of colour,
+heat, and the remainder of the so-called secondary qualities.--_Cours_,
+ut supra, 9me lecon.
+
+[14] This doctrine, which is the most complete form of the philosophical
+theory known as the Relativity of Human Knowledge, has, since the recent
+revival in this country of an active interest in metaphysical
+speculation, been the subject of a greatly increased amount of
+discussion and controversy; and dissentients have manifested themselves
+in considerably greater number than I had any knowledge of when the
+passage in the text was written. The doctrine has been attacked from two
+sides. Some thinkers, among whom are the late Professor Ferrier, in his
+_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio
+Philosophica_, appear to deny altogether the reality of Noumena, or
+Things in themselves--of an unknowable substratum or support for the
+sensations which we experience, and which, according to the theory,
+constitute all our knowledge of an external world. It seems to me,
+however, that in Professor Grote's case at least, the denial of Noumena
+is only apparent, and that he does not essentially differ from the other
+class of objectors, including Mr. Bailey in his valuable _Letters on the
+Philosophy of the Human Mind_, and (in spite of the striking passage
+quoted in the text) also Sir William Hamilton, who contend for a direct
+knowledge by the human mind of more than the sensations--of certain
+attributes or properties as they exist not in us, but in the Things
+themselves.
+
+With the first of these opinions, that which denies Noumena, I have, as
+a metaphysician, no quarrel; but, whether it be true or false, it is
+irrelevant to Logic. And since all the forms of language are in
+contradiction to it, nothing but confusion could result from its
+unnecessary introduction into a treatise, every essential doctrine of
+which could stand equally well with the opposite and accredited opinion.
+The other and rival doctrine, that of a direct perception or intuitive
+knowledge of the outward object as it is in itself, considered as
+distinct from the sensations we receive from it, is of far greater
+practical moment. But even this question, depending on the nature and
+laws of Intuitive Knowledge, is not within the province of Logic. For
+the grounds of my own opinion concerning it, I must content myself with
+referring to a work already mentioned--_An Examination of Sir William
+Hamilton's Philosophy_; several chapters of which are devoted to a full
+discussion of the questions and theories relating to the supposed direct
+perception of external objects.
+
+[15] _Analysis of the Human Mind_, i. 126 et seq.
+
+[16] It may, however, be considered as equivalent to an universal
+proposition with a different predicate, viz. "All wine is good _qua_
+wine," or "is good in respect of the qualities which constitute it
+wine."
+
+[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
+statement, and asks, "Are we to say that a mole cannot dig the ground,
+except he has an idea of the ground, and of the snout and paws with
+which he digs it?" I do not know what passes in a mole's mind, nor what
+amount of mental apprehension may or may not accompany his instinctive
+actions. But a human being does not use a spade by instinct; and he
+certainly could not use it unless he had knowledge of a spade, and of
+the earth which he uses it upon.
+
+[18] "From hence also this may be deduced, that the first truths were
+arbitrarily made by those that first of all imposed names upon things,
+or received them from the imposition of others. For it is true (for
+example) that _man is a living creature_, but it is for this reason,
+that it pleased men to impose both these names on the same
+thing."--_Computation or Logic_, ch. iii. sect. 8.
+
+[19] "Men are subject to err not only in affirming and denying, but also
+in perception, and in silent cogitation.... Tacit errors, or the errors
+of sense and cogitation, are made by passing from one imagination to the
+imagination of another different thing; or by feigning that to be past,
+or future, which never was, nor ever shall be; as when by seeing the
+image of the sun in water, we imagine the sun itself to be there; or by
+seeing swords, that there has been, or shall be, fighting, because it
+uses to be so for the most part; or when from promises we feign the mind
+of the promiser to be such and such; or, lastly, when from any sign we
+vainly imagine something to be signified which is not. And errors of
+this sort are common to all things that have sense."--_Computation or
+Logic_, ch. v. sect. 1.
+
+[20] Ch. iii. sect. 3.
+
+[21] To the preceding statement it has been objected, that "we naturally
+construe the subject of a proposition in its extension, and the
+predicate (which therefore may be an adjective) in its intension,
+(connotation): and that consequently coexistence of attributes does not,
+any more than the opposite theory of equation of groups, correspond with
+the living processes of thought and language." I acknowledge the
+distinction here drawn, which, indeed, I had myself laid down and
+exemplified a few pages back (p. 104). But though it is true that we
+naturally "construe the subject of a proposition in its extension," this
+extension, or in other words, the extent of the class denoted by the
+name, is not apprehended or indicated directly. It is both apprehended
+and indicated solely through the attributes. In the "living processes of
+thought and language" the extension, though in this case really thought
+of (which in the case of the predicate it is not), is thought of only
+through the medium of what my acute and courteous critic terms the
+"intension."
+
+For further illustrations of this subject, see _Examination of Sir
+William Hamilton's Philosophy_, ch. xxii.
+
+[22] Book iv. ch. vii.
+
+[23] The doctrines which prevented the real meaning of Essences from
+being understood, had not assumed so settled a shape in the time of
+Aristotle and his immediate followers, as was afterwards given to them
+by the Realists of the middle ages. Aristotle himself (in his Treatise
+on the Categories) expressly denies that the [Greek: deuterai ousiai],
+or Substantiae Secundae, inhere in a subject. They are only, he says,
+predicated of it.
+
+[24] The always acute and often profound author of _An Outline of
+Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more
+intelligible if, in the majority of places, we substitute 'the knowledge
+of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms
+on Locke's use of the word Idea, this is the one which, as it appears to
+me, most nearly hits the mark; and I quote it for the additional reason
+that it precisely expresses the point of difference respecting the
+import of Propositions, between my view and what I have spoken of as the
+Conceptualist view of them. Where a Conceptualist says that a name or a
+proposition expresses our Idea of a thing, I should generally say
+(instead of our Idea) our Knowledge, or Belief, concerning the thing
+itself.
+
+[25] This distinction corresponds to that which is drawn by Kant and
+other metaphysicians between what they term _analytic_, and _synthetic_,
+judgments; the former being those which can be evolved from the meaning
+of the terms used.
+
+[26] If we allow a differentia to what is not really a species. For the
+distinction of Kinds, in the sense explained by us, not being in any way
+applicable to attributes, it of course follows that although attributes
+may be put into classes, those classes can be admitted to be genera or
+species only by courtesy.
+
+[27] In the fuller discussion which Archbishop Whately has given to this
+subject in his later editions, he almost ceases to regard the
+definitions of names and those of things as, in any important sense,
+distinct. He seems (9th ed. p. 145) to limit the notion of a Real
+Definition to one which "explains anything _more_ of the nature of the
+thing than is implied in the name;" (including under the word "implied,"
+not only what the name connotes, but everything which can be deduced by
+reasoning from the attributes connoted). Even this, as he adds, is
+usually called, not a Definition, but a Description; and (as it seems to
+me) rightly so called. A Description, I conceive, can only be ranked
+among Definitions, when taken (as in the case of the zoological
+definition of man) to fulfil the true office of a Definition, by
+declaring the connotation given to a word in some special use, as a term
+of science or art: which special connotation of course would not be
+expressed by the proper definition of the word in its ordinary
+employment.
+
+Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
+understands by a Real Definition one which contains _less_ than the
+Nominal Definition, provided only that what it contains is sufficient
+for distinction. "By _real_ definition I mean such an explanation of the
+word, be it the whole of the meaning or only part, as will be sufficient
+to separate the things contained under that word from all others. Thus
+the following, I believe, is a complete definition of an elephant: An
+animal which naturally drinks by drawing the water into its nose, and
+then spurting it into its mouth."--_Formal Logic_, p. 36. Mr. De
+Morgan's general proposition and his example are at variance; for the
+peculiar mode of drinking of the elephant certainly forms no part of the
+meaning of the word elephant. It could not be said, because a person
+happened to be ignorant of this property, that he did not know what an
+elephant means.
+
+[28] In the only attempt which, so far as I know, has been made to
+refute the preceding argumentation, it is maintained that in the first
+form of the syllogism,
+
+  A dragon is a thing which breathes flame,
+  A dragon is a serpent,
+  Therefore some serpent or serpents breathe flame,
+
+"there is just as much truth in the conclusion as there is in the
+premises, or rather, no more in the latter than in the former. If the
+general name serpent includes both real and imaginary serpents, there is
+no falsity in the conclusion; if not, there is falsity in the minor
+premise."
+
+Let us, then, try to set out the syllogism on the hypothesis that the
+name serpent includes imaginary serpents. We shall find that it is now
+necessary to alter the predicates; for it cannot be asserted that an
+imaginary creature breathes flame: in predicating of it such a fact, we
+assert by the most positive implication that it is real and not
+imaginary. The conclusion must run thus, "Some serpent or serpents
+either do or are _imagined_ to breathe flame." And to prove this
+conclusion by the instance of dragons, the premises must be, A dragon is
+_imagined_ as breathing flame, A dragon is a (real or imaginary)
+serpent: from which it undoubtedly follows, that there are serpents
+which are imagined to breathe flame; but the major premise is not a
+definition, nor part of a definition; which is all that I am concerned
+to prove.
+
+Let us now examine the other assertion--that if the word serpent stands
+for none but real serpents, the minor premise (a dragon is a serpent) is
+false. This is exactly what I have myself said of the premise,
+considered as a statement of fact: but it is not false as part of the
+definition of a dragon; and since the premises, or one of them, must be
+false, (the conclusion being so,) the real premise cannot be the
+definition, which is true, but the statement of fact, which is false.
+
+[29] "Few people" (I have said in another place) "have reflected how
+great a knowledge of Things is required to enable a man to affirm that
+any given argument turns wholly upon words. There is, perhaps, not one
+of the leading terms of philosophy which is not used in almost
+innumerable shades of meaning, to express ideas more or less widely
+different from one another. Between two of these ideas a sagacious and
+penetrating mind will discern, as it were intuitively, an unobvious link
+of connexion, upon which, though perhaps unable to give a logical
+account of it, he will found a perfectly valid argument, which his
+critic, not having so keen an insight into the Things, will mistake for
+a fallacy turning on the double meaning of a term. And the greater the
+genius of him who thus safely leaps over the chasm, the greater will
+probably be the crowing and vain-glory of the mere logician, who,
+hobbling after him, evinces his own superior wisdom by pausing on its
+brink, and giving up as desperate his proper business of bridging it
+over."
+
+
+
+
+BOOK II.
+
+OF REASONING.
+
+
+[Greek: Diorismenon de touton legomen ede, dia tinon, kai pote, kai pos
+ginetai pas syllogismos hysteron de lekteon peri apodeixeos. Proteron
+gar peri syllogismou lekteon, e peri apodeixeos, dia to katholou mallon
+einai ton syllogismon. He men gar apodeixis, syllogismos tis; ho
+syllogismos de ou pas, apodeixis.]
+
+                    ARIST. _Analyt. Prior._ l. i. cap. 4.
+
+
+
+
+CHAPTER I.
+
+OF INFERENCE, OR REASONING, IN GENERAL.
+
+
+Sec. 1. In the preceding Book, we have been occupied not with the nature of
+Proof, but with the nature of Assertion: the import conveyed by a
+Proposition, whether that Proposition be true or false; not the means by
+which to discriminate true from false Propositions. The proper subject,
+however, of Logic is Proof. Before we could understand what Proof is, it
+was necessary to understand what that is to which proof is applicable;
+what that is which can be a subject of belief or disbelief, of
+affirmation or denial; what, in short, the different kinds of
+Propositions assert.
+
+This preliminary inquiry we have prosecuted to a definite result.
+Assertion, in the first place, relates either to the meaning of words,
+or to some property of the things which words signify. Assertions
+respecting the meaning of words, among which definitions are the most
+important, hold a place, and an indispensable one, in philosophy; but as
+the meaning of words is essentially arbitrary, this class of assertions
+are not susceptible of truth or falsity, nor therefore of proof or
+disproof. Assertions respecting Things, or what may be called Real
+Propositions, in contradistinction to verbal ones, are of various sorts.
+We have analysed the import of each sort, and have ascertained the
+nature of the things they relate to, and the nature of what they
+severally assert respecting those things. We found that whatever be the
+form of the proposition, and whatever its nominal subject or predicate,
+the real subject of every proposition is some one or more facts or
+phenomena of consciousness, or some one or more of the hidden causes or
+powers to which we ascribe those facts; and that what is predicated or
+asserted, either in the affirmative or negative, of those phenomena or
+those powers, is always either Existence, Order in Place, Order in Time,
+Causation, or Resemblance. This, then, is the theory of the Import of
+Propositions, reduced to its ultimate elements: but there is another and
+a less abstruse expression for it, which, though stopping short in an
+earlier stage of the analysis, is sufficiently scientific for many of
+the purposes for which such a general expression is required. This
+expression recognises the commonly received distinction between Subject
+and Attribute, and gives the following as the analysis of the meaning of
+propositions:--Every Proposition asserts, that some given subject does
+or does not possess some attribute; or that some attribute is or is not
+(either in all or in some portion of the subjects in which it is met
+with) conjoined with some other attribute.
+
+We shall now for the present take our leave of this portion of our
+inquiry, and proceed to the peculiar problem of the Science of Logic,
+namely, how the assertions, of which we have analysed the import, are
+proved or disproved; such of them, at least, as, not being amenable to
+direct consciousness or intuition, are appropriate subjects of proof.
+
+We say of a fact or statement, that it is proved, when we believe its
+truth by reason of some other fact or statement from which it is said to
+_follow_. Most of the propositions, whether affirmative or negative,
+universal, particular, or singular, which we believe, are not believed
+on their own evidence, but on the ground of something previously
+assented to, from which they are said to be _inferred_. To infer a
+proposition from a previous proposition or propositions; to give
+credence to it, or claim credence for it, as a conclusion from something
+else; is to _reason_, in the most extensive sense of the term. There is
+a narrower sense, in which the name reasoning is confined to the form of
+inference which is termed ratiocination, and of which the syllogism is
+the general type. The reasons for not conforming to this restricted use
+of the term were stated in an earlier stage of our inquiry, and
+additional motives will be suggested by the considerations on which we
+are now about to enter.
+
+
+Sec. 2. In proceeding to take into consideration the cases in which
+inferences can legitimately be drawn, we shall first mention some cases
+in which the inference is apparent, not real; and which require notice
+chiefly that they may not be confounded with cases of inference properly
+so called. This occurs when the proposition ostensibly inferred from
+another, appears on analysis to be merely a repetition of the same, or
+part of the same, assertion, which was contained in the first. All the
+cases mentioned in books of Logic as examples of aequipollency or
+equivalence of propositions, are of this nature. Thus, if we were to
+argue, No man is incapable of reason, for every man is rational; or, All
+men are mortal, for no man is exempt from death; it would be plain that
+we were not proving the proposition, but only appealing to another mode
+of wording it, which may or may not be more readily comprehensible by
+the hearer, or better adapted to suggest the real proof, but which
+contains in itself no shadow of proof.
+
+Another case is where, from an universal proposition, we affect to infer
+another which differs from it only in being particular: as All A is B,
+therefore Some A is B: No A is B, therefore Some A is not B. This, too,
+is not to conclude one proposition from another, but to repeat a second
+time something which had been asserted at first; with the difference,
+that we do not here repeat the whole of the previous assertion, but only
+an indefinite part of it.
+
+A third case is where, the antecedent having affirmed a predicate of a
+given subject, the consequent affirms of the same subject something
+already connoted by the former predicate: as, Socrates is a man,
+therefore Socrates is a living creature; where all that is connoted by
+living creature was affirmed of Socrates when he was asserted to be a
+man. If the propositions are negative, we must invert their order, thus:
+Socrates is not a living creature, therefore he is not a man; for if we
+deny the less, the greater, which includes it, is already denied by
+implication. These, therefore, are not really cases of inference; and
+yet the trivial examples by which, in manuals of Logic, the rules of the
+syllogism are illustrated, are often of this ill-chosen kind; formal
+demonstrations of conclusions to which whoever understands the terms
+used in the statement of the data, has already, and consciously,
+assented.
+
+The most complex case of this sort of apparent inference is what is
+called the Conversion of propositions; which consists in turning the
+predicate into a subject, and the subject into a predicate, and framing
+out of the same terms thus reversed, another proposition, which must be
+true if the former is true. Thus, from the particular affirmative
+proposition, Some A is B, we may infer that Some B is A. From the
+universal negative, No A is B, we may conclude that No B is A. From the
+universal affirmative proposition, All A is B, it cannot be inferred
+that all B is A; though all water is liquid, it is not implied that all
+liquid is water; but it is implied that some liquid is so; and hence the
+proposition, All A is B, is legitimately convertible into Some B is A.
+This process, which converts an universal proposition into a particular,
+is termed conversion _per accidens_. From the proposition, Some A is not
+B, we cannot even infer that some B is not A; though some men are not
+Englishmen, it does not follow that some Englishmen are not men. The
+only mode usually recognised of converting a particular negative
+proposition, is in the form, Some A is not B, therefore, something which
+is not B is A; and this is termed conversion by contraposition. In this
+case, however, the predicate and subject are not merely reversed, but
+one of them is changed. Instead of [A] and [B], the terms of the new
+proposition are [a thing which is not B], and [A]. The original
+proposition, Some A _is not_ B, is first changed into a proposition
+aequipollent with it, Some A _is_ "a thing which is not B;" and the
+proposition, being now no longer a particular negative, but a particular
+affirmative, _admits_ of conversion in the first mode, or as it is
+called, _simple_ conversion.[1]
+
+In all these cases there is not really any inference; there is in the
+conclusion no new truth, nothing but what was already asserted in the
+premises, and obvious to whoever apprehends them. The fact asserted in
+the conclusion is either the very same fact, or part of the fact
+asserted in the original proposition. This follows from our previous
+analysis of the Import of Propositions. When we say, for example, that
+some lawful sovereigns are tyrants, what is the meaning of the
+assertion? That the attributes connoted by the term "lawful sovereign,"
+and the attributes connoted by the term "tyrant," sometimes coexist in
+the same individual. Now this is also precisely what we mean, when we
+say that some tyrants are lawful sovereigns; which, therefore, is not a
+second proposition inferred from the first, any more than the English
+translation of Euclid's Elements is a collection of theorems different
+from, and consequences of, those contained in the Greek original. Again,
+if we assert that no great general is a rash man, we mean that the
+attributes connoted by "great general," and those connoted by "rash,"
+never coexist in the same subject; which is also the exact meaning which
+would be expressed by saying, that no rash man is a great general. When
+we say that all quadrupeds are warm-blooded, we assert, not only that
+the attributes connoted by "quadruped" and those connoted by
+"warm-blooded" sometimes coexist, but that the former never exist
+without the latter: now the proposition, Some warm-blooded creatures are
+quadrupeds, expresses the first half of this meaning, dropping the
+latter half; and therefore has been already affirmed in the antecedent
+proposition, All quadrupeds are warm-blooded. But that _all_
+warm-blooded creatures are quadrupeds, or, in other words, that the
+attributes connoted by "warm-blooded" never exist without those connoted
+by "quadruped," has not been asserted, and cannot be inferred. In order
+to reassert, in an inverted form, the whole of what was affirmed in the
+proposition, All quadrupeds are warm-blooded, we must convert it by
+contraposition, thus, Nothing which is not warm-blooded is a quadruped.
+This proposition, and the one from which it is derived, are exactly
+equivalent, and either of them may be substituted for the other; for,
+to say that when the attributes of a quadruped are present, those of a
+warm-blooded creature are present, is to say that when the latter are
+absent the former are absent.
+
+In a manual for young students, it would be proper to dwell at greater
+length on the conversion and aequipollency of propositions. For, though
+that cannot be called reasoning or inference which is a mere reassertion
+in different words of what had been asserted before, there is no more
+important intellectual habit, nor any the cultivation of which falls
+more strictly within the province of the art of logic, than that of
+discerning rapidly and surely the identity of an assertion when
+disguised under diversity of language. That important chapter in logical
+treatises which relates to the Opposition of Propositions, and the
+excellent technical language which logic provides for distinguishing the
+different kinds or modes of opposition, are of use chiefly for this
+purpose. Such considerations as these, that contrary propositions may
+both be false, but cannot both be true; that subcontrary propositions
+may both be true, but cannot both be false; that of two contradictory
+propositions one must be true and the other false; that of two
+subalternate propositions the truth of the universal proves the truth of
+the particular, and the falsity of the particular proves the falsity of
+the universal, but not _vice versa_;[2] are apt to appear, at first
+sight, very technical and mysterious, but when explained, seem almost
+too obvious to require so formal a statement, since the same amount of
+explanation which is necessary to make the principles intelligible,
+would enable the truths which they convey to be apprehended in any
+particular case which can occur. In this respect, however, these axioms
+of logic are on a level with those of mathematics. That things which are
+equal to the same thing are equal to one another, is as obvious in any
+particular case as it is in the general statement: and if no such
+general maxim had ever been laid down, the demonstrations in Euclid
+would never have halted for any difficulty in stepping across the gap
+which this axiom at present serves to bridge over. Yet no one has ever
+censured writers on geometry, for placing a list of these elementary
+generalizations at the head of their treatises, as a first exercise to
+the learner of the faculty which will be required in him at every step,
+that of apprehending a _general_ truth. And the student of logic, in the
+discussion even of such truths as we have cited above, acquires habits
+of circumspect interpretation of words, and of exactly measuring the
+length and breadth of his assertions, which are among the most
+indispensable conditions of any considerable mental attainment, and
+which it is one of the primary objects of logical discipline to
+cultivate.
+
+
+Sec. 3. Having noticed, in order to exclude from the province of Reasoning
+or Inference properly so called, the cases in which the progression from
+one truth to another is only apparent, the logical consequent being a
+mere repetition of the logical antecedent; we now pass to those which
+are cases of inference in the proper acceptation of the term, those in
+which we set out from known truths, to arrive at others really distinct
+from them.
+
+Reasoning, in the extended sense in which I use the term, and in which
+it is synonymous with Inference, is popularly said to be of two kinds:
+reasoning from particulars to generals, and reasoning from generals to
+particulars; the former being called Induction, the latter Ratiocination
+or Syllogism. It will presently be shown that there is a third species
+of reasoning, which falls under neither of these descriptions, and
+which, nevertheless, is not only valid, but is the foundation of both
+the others.
+
+It is necessary to observe, that the expressions, reasoning from
+particulars to generals, and reasoning from generals to particulars, are
+recommended by brevity rather than by precision, and do not adequately
+mark, without the aid of a commentary, the distinction between Induction
+(in the sense now adverted to) and Ratiocination. The meaning intended
+by these expressions is, that Induction is inferring a proposition from
+propositions _less general_ than itself, and Ratiocination is inferring
+a proposition from propositions _equally_ or _more_ general. When, from
+the observation of a number of individual instances, we ascend to a
+general proposition, or when, by combining a number of general
+propositions, we conclude from them another proposition still more
+general, the process, which is substantially the same in both instances,
+is called Induction. When from a general proposition, not alone (for
+from a single proposition nothing can be concluded which is not involved
+in the terms), but by combining it with other propositions, we infer a
+proposition of the same degree of generality with itself, or a less
+general proposition, or a proposition merely individual, the process is
+Ratiocination. When, in short, the conclusion is more general than the
+largest of the premises, the argument is commonly called Induction; when
+less general, or equally general, it is Ratiocination.
+
+As all experience begins with individual cases, and proceeds from them
+to generals, it might seem most conformable to the natural order of
+thought that Induction should be treated of before we touch upon
+Ratiocination. It will, however, be advantageous, in a science which
+aims at tracing our acquired knowledge to its sources, that the inquirer
+should commence with the latter rather than with the earlier stages of
+the process of constructing our knowledge; and should trace derivative
+truths backward to the truths from which they are deduced, and on which
+they depend for their evidence, before attempting to point out the
+original spring from which both ultimately take their rise. The
+advantages of this order of proceeding in the present instance will
+manifest themselves as we advance, in a manner superseding the necessity
+of any further justification or explanation.
+
+Of Induction, therefore, we shall say no more at present, than that it
+at least is, without doubt, a process of real inference. The conclusion
+in an induction embraces more than is contained in the premises. The
+principle or law collected from particular instances, the general
+proposition in which we embody the result of our experience, covers a
+much larger extent of ground than the individual experiments which form
+its basis. A principle ascertained by experience, is more than a mere
+summing up of what has been specifically observed in the individual
+cases which have been examined; it is a generalization grounded on those
+cases, and expressive of our belief, that what we there found true is
+true in an indefinite number of cases which we have not examined, and
+are never likely to examine. The nature and grounds of this inference,
+and the conditions necessary to make it legitimate, will be the subject
+of discussion in the Third Book: but that such inference really takes
+place is not susceptible of question. In every induction we proceed from
+truths which we knew, to truths which we did not know; from facts
+certified by observation, to facts which we have not observed, and even
+to facts not capable of being now observed; future facts, for example;
+but which we do not hesitate to believe on the sole evidence of the
+induction itself.
+
+Induction, then, is a real process of Reasoning or Inference. Whether,
+and in what sense, as much can be said of the Syllogism, remains to be
+determined by the examination into which we are about to enter.
+
+
+
+
+CHAPTER II.
+
+OF RATIOCINATION, OR SYLLOGISM.
+
+
+Sec. 1. The analysis of the Syllogism has been so accurately and fully
+performed in the common manuals of Logic, that in the present work,
+which is not designed as a manual, it is sufficient to recapitulate,
+_memoriae causa_, the leading results of that analysis, as a foundation
+for the remarks to be afterwards made on the functions of the syllogism,
+and the place which it holds in science.
+
+To a legitimate syllogism it is essential that there should be three,
+and no more than three, propositions, namely, the conclusion, or
+proposition to be proved, and two other propositions which together
+prove it, and which are called the premises. It is essential that there
+should be three, and no more than three, terms, namely, the subject and
+predicate of the conclusion, and another called the middleterm, which
+must be found in both premises, since it is by means of it that the
+other two terms are to be connected together. The predicate of the
+conclusion is called the major term of the syllogism; the subject of the
+conclusion is called the minor term. As there can be but three terms,
+the major and minor terms must each be found in one, and only one, of
+the premises, together with the middleterm which is in them both. The
+premise which contains the middleterm and the major term is called the
+major premise; that which contains the middleterm and the minor term is
+called the minor premise.
+
+Syllogisms are divided by some logicians into three _figures_, by others
+into four, according to the position of the middleterm, which may either
+be the subject in both premises, the predicate in both, or the subject
+in one and the predicate in the other. The most common case is that in
+which the middleterm is the subject of the major premise and the
+predicate of the minor. This is reckoned as the first figure. When the
+middleterm is the predicate in both premises, the syllogism belongs to
+the second figure; when it is the subject in both, to the third. In the
+fourth figure the middleterm is the subject of the minor premise and the
+predicate of the major. Those writers who reckon no more than three
+figures, include this case in the first.
+
+Each figure is divided into _moods_, according to what are called the
+_quantity_ and _quality_ of the propositions, that is, according as they
+are universal or particular, affirmative or negative. The following are
+examples of all the legitimate moods, that is, all those in which the
+conclusion correctly follows from the premises. A is the minor term, C
+the major, B the middleterm.
+
+FIRST FIGURE.
+
+  All B is C    No B is C     All B is C     No B is C
+  All A is B    All A is B    Some A is B    Some A is B
+    therefore     therefore     therefore      therefore
+  All A is C    No A is C     Some A is C    Some A is not C
+
+SECOND FIGURE.
+
+  No C is B     All C is B    No C is B         All C is B
+  All A is B    No A is B     Some A is B       Some A is not B
+    therefore     therefore     therefore         therefore
+  No A is C     No A is C     Some A is not C   Some A is not C
+
+THIRD FIGURE.
+
+  All B is C   No B is C    Some B is C  All B is C   Some B      No B is C
+                                                        is not C
+  All B is A   All B is A   All B is A   Some B is A  All B is A  Some B is A
+    therefore    therefore    therefore    therefore    therefore   therefore
+  Some A is C  Some A       Some A is C  Some A is C  Some A      Some A
+                 is not C                               is not C    is not C
+
+FOURTH FIGURE.
+
+  All C is B   All C is B       Some C is B  No C is B        No C is B
+  All B is A   No B is A        All B is A   All B is A       Some B is A
+    therefore    therefore        therefore    therefore        therefore
+  Some A is C  Some A is not C  Some A is C  Some A is not C  Some A is not C
+
+In these exemplars, or blank forms for making syllogisms, no place is
+assigned to _singular_ propositions; not, of course, because such
+propositions are not used in ratiocination, but because, their predicate
+being affirmed or denied of the whole of the subject, they are ranked,
+for the purposes of the syllogism, with universal propositions. Thus,
+these two syllogisms--
+
+  All men are mortal,      All men are mortal,
+  All kings are men,       Socrates is a man,
+    therefore                therefore
+  All kings are mortal,    Socrates is mortal,
+
+are arguments precisely similar, and are both ranked in the first mood
+of the first figure.
+
+The reasons why syllogisms in any of the above forms are legitimate,
+that is, why, if the premises are true, the conclusion must inevitably
+be so, and why this is not the case in any other possible mood, (that
+is, in any other combination of universal and particular, affirmative
+and negative propositions,) any person taking interest in these
+inquiries may be presumed to have either learned from the common school
+books of the syllogistic logic, or to be capable of discovering for
+himself. The reader may, however, be referred, for every needful
+explanation, to Archbishop Whately's _Elements of Logic_, where he will
+find stated with philosophical precision, and explained with remarkable
+perspicuity, the whole of the common doctrine of the syllogism.
+
+All valid ratiocination; all reasoning by which, from general
+propositions previously admitted, other propositions equally or less
+general are inferred; may be exhibited in some of the above forms. The
+whole of Euclid, for example, might be thrown without difficulty into a
+series of syllogisms, regular in mood and figure.
+
+Though a syllogism framed according to any of these formulae is a valid
+argument, all correct ratiocination admits of being stated in syllogisms
+of the first figure alone. The rules for throwing an argument in any of
+the other figures into the first figure, are called rules for the
+_reduction_ of syllogisms. It is done by the _conversion_ of one or
+other, or both, of the premises. Thus an argument in the first mood of
+the second figure, as--
+
+  No C is B
+  All A is B
+    therefore
+  No A is C,
+
+may be reduced as follows. The proposition, No C is B, being an
+universal negative, admits of simple conversion, and may be changed into
+No B is C, which, as we showed, is the very same assertion in other
+words--the same fact differently expressed. This transformation having
+been effected, the argument assumes the following form:--
+
+  No B is C
+  All A is B
+    therefore
+  No A is C,
+
+which is a good syllogism in the second mood of the first figure. Again,
+an argument in the first mood of the third figure must resemble the
+following:--
+
+  All B is C
+  All B is A
+    therefore
+  Some A is C,
+
+where the minor premise, All B is A, conformably to what was laid down
+in the last chapter respecting universal affirmatives, does not admit of
+simple conversion, but may be converted _per accidens_, thus, Some A is
+B; which, though it does not express the whole of what is asserted in
+the proposition All B is A, expresses, as was formerly shown, part of
+it, and must therefore be true if the whole is true. We have, then, as
+the result of the reduction, the following syllogism in the third mood
+of the first figure:--
+
+  All B is C
+  Some A is B,
+
+from which it obviously follows, that
+
+  Some A is C.
+
+In the same manner, or in a manner on which after these examples it is
+not necessary to enlarge, every mood of the second, third, and fourth
+figures may be reduced to some one of the four moods of the first. In
+other words, every conclusion which can be proved in any of the last
+three figures, may be proved in the first figure from the same premises,
+with a slight alteration in the mere manner of expressing them. Every
+valid ratiocination, therefore, may be stated in the first figure, that
+is, in one of the following forms:--
+
+  Every B is C            No B is C
+  All A   }  is B,        All A   } is B,
+  Some A  }               Some A  }
+      therefore               therefore
+  All A   }  is C.        No A is        }  C.
+  Some A  }               Some A is not  }
+
+Or if more significant symbols are preferred:--
+
+To prove an affirmative, the argument must admit of being stated in this
+form:--
+
+  All animals are mortal;
+  All men   }
+  Some men  }  are animals;
+  Socrates  }
+        therefore
+  All men   }
+  Some men  }  are mortal.
+  Socrates  }
+
+To prove a negative, the argument must be capable of being expressed in
+this form:--
+
+  No one who is capable of self-control is necessarily vicious;
+  All negroes   }
+  Some negroes  }  are capable of self-control;
+  Mr. A's negro }
+        therefore
+  No negroes are        }
+  Some negroes are not  }  necessarily vicious.
+  Mr. A's negro is not  }
+
+Though all ratiocination admits of being thrown into one or the other of
+these forms, and sometimes gains considerably by the transformation,
+both in clearness and in the obviousness of its consequence; there are,
+no doubt, cases in which the argument falls more naturally into one of
+the other three figures, and in which its conclusiveness is more
+apparent at the first glance in those figures, than when reduced to the
+first. Thus, if the proposition were that pagans may be virtuous, and
+the evidence to prove it were the example of Aristides; a syllogism in
+the third figure,
+
+  Aristides was virtuous,
+  Aristides was a pagan,
+       therefore
+  Some pagan was virtuous,
+
+would be a more natural mode of stating the argument, and would carry
+conviction more instantly home, than the same ratiocination strained
+into the first figure, thus--
+
+  Aristides was virtuous,
+  Some pagan was Aristides,
+       therefore
+  Some pagan was virtuous.
+
+A German philosopher, Lambert, whose _Neues Organon_ (published in the
+year 1764) contains among other things one of the most elaborate and
+complete expositions which had ever been made of the syllogistic
+doctrine, has expressly examined what sort of arguments fall most
+naturally and suitably into each of the four figures; and his
+investigation is characterized by great ingenuity and clearness of
+thought.[3] The argument, however, is one and the same, in whichever
+figure it is expressed; since, as we have already seen, the premises of
+a syllogism in the second, third, or fourth figure, and those of the
+syllogism in the first figure to which it may be reduced, are the same
+premises in everything except language, or, at least, as much of them as
+contributes to the proof of the conclusion is the same. We are
+therefore at liberty, in conformity with the general opinion of
+logicians, to consider the two elementary forms of the first figure as
+the universal types of all correct ratiocination; the one, when the
+conclusion to be proved is affirmative, the other, when it is negative;
+even though certain arguments may have a tendency to clothe themselves
+in the forms of the second, third, and fourth figures; which, however,
+cannot possibly happen with the only class of arguments which are of
+first-rate scientific importance, those in which the conclusion is an
+universal affirmative, such conclusions being susceptible of proof in
+the first figure alone.[4]
+
+
+Sec. 2. On examining, then, these two general formulae, we find that in
+both of them, one premise, the major, is an universal proposition; and
+according as this is affirmative or negative, the conclusion is so too.
+All ratiocination, therefore, starts from a _general_ proposition,
+principle, or assumption: a proposition in which a predicate is
+affirmed or denied of an entire class; that is, in which some attribute,
+or the negation of some attribute, is asserted of an indefinite number
+of objects distinguished by a common characteristic, and designated in
+consequence, by a common name.
+
+The other premise is always affirmative, and asserts that something
+(which may be either an individual, a class, or part of a class)
+belongs to, or is included in, the class respecting which something was
+affirmed or denied in the major premise. It follows that the attribute
+affirmed or denied of the entire class may (if that affirmation or
+denial was correct) be affirmed or denied of the object or objects
+alleged to be included in the class: and this is precisely the assertion
+made in the conclusion.
+
+Whether or not the foregoing is an adequate account of the constituent
+parts of the syllogism, will be presently considered; but as far as it
+goes it is a true account. It has accordingly been generalized, and
+erected into a logical maxim, on which all ratiocination is said to be
+founded, insomuch that to reason, and to apply the maxim, are supposed
+to be one and the same thing. The maxim is, That whatever can be
+affirmed (or denied) of a class, may be affirmed (or denied) of
+everything included in the class. This axiom, supposed to be the basis
+of the syllogistic theory, is termed by logicians the _dictum de omni et
+nullo_.
+
+This maxim, however, when considered as a principle of reasoning,
+appears suited to a system of metaphysics once indeed generally
+received, but which for the last two centuries has been considered as
+finally abandoned, though there have not been wanting in our own day
+attempts at its revival. So long as what are termed Universals were
+regarded as a peculiar kind of substances, having an objective existence
+distinct from the individual objects classed under them, the _dictum de
+omni_ conveyed an important meaning; because it expressed the
+intercommunity of nature, which it was necessary on that theory that we
+should suppose to exist between those general substances and the
+particular substances which were subordinated to them. That everything
+predicable of the universal was predicable of the various individuals
+contained under it, was then no identical proposition, but a statement
+of what was conceived as a fundamental law of the universe. The
+assertion that the entire nature and properties of the _substantia
+secunda_ formed part of the nature and properties of each of the
+individual substances called by the same name; that the properties of
+Man, for example, were properties of all men; was a proposition of real
+significance when man did not _mean_ all men, but something inherent in
+men, and vastly superior to them in dignity. Now, however, when it is
+known that a class, an universal, a genus or species, is not an entity
+_per se_, but neither more nor less than the individual substances
+themselves which are placed in the class, and that there is nothing real
+in the matter except those objects, a common name given to them, and
+common attributes indicated by the name; what, I should be glad to know,
+do we learn by being told, that whatever can be affirmed of a class, may
+be affirmed of every object contained in the class? The class is nothing
+but the objects contained in it: and the _dictum de omni_ merely amounts
+to the identical proposition, that whatever is true of certain objects,
+is true of each of those objects. If all ratiocination were no more than
+the application of this maxim to particular cases, the syllogism would
+indeed be, what it has so often been declared to be, solemn trifling.
+The _dictum de omni_ is on a par with another truth, which in its time
+was also reckoned of great importance, "Whatever is, is." To give any
+real meaning to the _dictum de omni_, we must consider it not as an
+axiom, but as a definition; we must look upon it as intended to explain,
+in a circuitous and paraphrastic manner, the meaning of the word,
+_class_.
+
+An error which seemed finally refuted and dislodged from thought, often
+needs only put on a new suit of phrases, to be welcomed back to its old
+quarters, and allowed to repose unquestioned for another cycle of ages.
+Modern philosophers have not been sparing in their contempt for the
+scholastic dogma that genera and species are a peculiar kind of
+substances, which general substances being the only permanent things,
+while the individual substances comprehended under them are in a
+perpetual flux, knowledge, which necessarily imports stability, can only
+have relation to those general substances or universals, and not to the
+facts or particulars included under them. Yet, though nominally
+rejected, this very doctrine, whether disguised under the Abstract Ideas
+of Locke (whose speculations, however, it has less vitiated than those
+of perhaps any other writer who has been infected with it), under the
+ultra-nominalism of Hobbes and Condillac, or the ontology of the later
+Kantians, has never ceased to poison philosophy. Once accustomed to
+consider scientific investigation as essentially consisting in the study
+of universals, men did not drop this habit of thought when they ceased
+to regard universals as possessing an independent existence: and even
+those who went the length of considering them as mere names, could not
+free themselves from the notion that the investigation of truth
+consisted entirely or partly in some kind of conjuration or juggle with
+those names. When a philosopher adopted fully the Nominalist view of the
+signification of general language, retaining along with it the _dictum
+de omni_ as the foundation of all reasoning, two such premises fairly
+put together were likely, if he was a consistent thinker, to land him in
+rather startling conclusions. Accordingly it has been seriously held, by
+writers of deserved celebrity, that the process of arriving at new
+truths by reasoning consists in the mere substitution of one set of
+arbitrary signs for another; a doctrine which they suppose to derive
+irresistible confirmation from the example of algebra. If there were any
+process in sorcery or necromancy more preternatural than this, I should
+be much surprised. The culminating point of this philosophy is the noted
+aphorism of Condillac, that a science is nothing, or scarcely anything,
+but _une langue bien faite_; in other words, that the one sufficient
+rule for discovering the nature and properties of objects is to name
+them properly: as if the reverse were not the truth, that it is
+impossible to name them properly except in proportion as we are already
+acquainted with their nature and properties. Can it be necessary to say,
+that none, not even the most trivial knowledge with respect to Things,
+ever was or could be originally got at by any conceivable manipulation
+of mere names, as such; and that what can be learned from names, is only
+what somebody who used the names knew before? Philosophical analysis
+confirms the indication of common sense, that the function of names is
+but that of enabling us to _remember_ and to _communicate_ our thoughts.
+That they also strengthen, even to an incalculable extent, the power of
+thought itself, is most true: but they do this by no intrinsic and
+peculiar virtue; they do it by the power inherent in an artificial
+memory, an instrument of which few have adequately considered the
+immense potency. As an artificial memory, language truly is, what it has
+so often been called, an instrument of thought; but it is one thing to
+be the instrument, and another to be the exclusive subject upon which
+the instrument is exercised. We think, indeed, to a considerable extent,
+by means of names, but what we think of, are the things called by those
+names; and there cannot be a greater error than to imagine that thought
+can be carried on with nothing in our mind but names, or that we can
+make the names think for us.
+
+
+Sec. 3. Those who considered the _dictum de omni_ as the foundation of the
+syllogism, looked upon arguments in a manner corresponding to the
+erroneous view which Hobbes took of propositions. Because there are some
+propositions which are merely verbal, Hobbes, in order apparently that
+his definition might be rigorously universal, defined a proposition as
+if no propositions declared anything except the meaning of words. If
+Hobbes was right; if no further account than this could be given of the
+import of propositions; no theory could be given but the commonly
+received one, of the combination of propositions in a syllogism. If the
+minor premise asserted nothing more than that something belongs to a
+class, and if the major premise asserted nothing of that class except
+that it is included in another class, the conclusion would only be that
+what was included in the lower class is included in the higher, and the
+result, therefore, nothing except that the classification is consistent
+with itself. But we have seen that it is no sufficient account of the
+meaning of a proposition, to say that it refers something to, or
+excludes something from, a class. Every proposition which conveys real
+information asserts a matter of fact, dependent on the laws of nature,
+and not on classification. It asserts that a given object does or does
+not possess a given attribute; or it asserts that two attributes, or
+sets of attributes, do or do not (constantly or occasionally) coexist.
+Since such is the purport of all propositions which convey any real
+knowledge, and since ratiocination is a mode of acquiring real
+knowledge, any theory of ratiocination which does not recognise this
+import of propositions, cannot, we may be sure, be the true one.
+
+Applying this view of propositions to the two premises of a syllogism,
+we obtain the following results. The major premise, which, as already
+remarked, is always universal, asserts, that all things which have a
+certain attribute (or attributes) have or have not along with it, a
+certain other attribute (or attributes). The minor premise asserts that
+the thing or set of things which are the subject of that premise, have
+the first-mentioned attribute; and the conclusion is, that they have (or
+that they have not) the second. Thus in our former example,
+
+  All men are mortal,
+  Socrates is a man,
+        therefore
+  Socrates is mortal,
+
+the subject and predicate of the major premise are connotative terms,
+denoting objects and connoting attributes. The assertion in the major
+premise is, that along with one of the two sets of attributes, we always
+find the other: that the attributes connoted by "man" never exist unless
+conjoined with the attribute called mortality. The assertion in the
+minor premise is that the individual named Socrates possesses the former
+attributes; and it is concluded that he possesses also the attribute
+mortality. Or if both the premises are general propositions, as
+
+  All men are mortal,
+  All kings are men,
+        therefore
+  All kings are mortal,
+
+the minor premise asserts that the attributes denoted by kingship only
+exist in conjunction with those signified by the word man. The major
+asserts as before, that the last-mentioned attributes are never found
+without the attribute of mortality. The conclusion is, that wherever the
+attributes of kingship are found, that of mortality is found also.
+
+If the major premise were negative, as, No men are omnipotent, it would
+assert, not that the attributes connoted by "man" never exist without,
+but that they never exist with, those connoted by "omnipotent:" from
+which, together with the minor premise, it is concluded, that the same
+incompatibility exists between the attribute omnipotence and those
+constituting a king. In a similar manner we might analyse any other
+example of the syllogism.
+
+If we generalize this process, and look out for the principle or law
+involved in every such inference, and presupposed in every syllogism,
+the propositions of which are anything more than merely verbal; we find,
+not the unmeaning _dictum de omni et nullo_, but a fundamental
+principle, or rather two principles, strikingly resembling the axioms of
+mathematics. The first, which is the principle of affirmative
+syllogisms, is, that things which coexist with the same thing, coexist
+with one another. The second is the principle of negative syllogisms,
+and is to this effect: that a thing which coexists with another thing,
+with which other a third thing does not coexist, is not coexistent with
+that third thing. These axioms manifestly relate to facts, and not to
+conventions; and one or other of them is the ground of the legitimacy of
+every argument in which facts and not conventions are the matter treated
+of.[5]
+
+
+Sec. 4. It remains to translate this exposition of the syllogism from the
+one into the other of the two languages in which we formerly
+remarked[6] that all propositions, and of course therefore all
+combinations of propositions, might be expressed. We observed that a
+proposition might be considered in two different lights; as a portion of
+our knowledge of nature, or as a memorandum for our guidance. Under the
+former, or speculative aspect, an affirmative general proposition is an
+assertion of a speculative truth, viz. that whatever has a certain
+attribute has a certain other attribute. Under the other aspect, it is
+to be regarded not as a part of our knowledge, but as an aid for our
+practical exigencies, by enabling us, when we see or learn that an
+object possesses one of the two attributes, to infer that it possesses
+the other; thus employing the first attribute as a mark or evidence of
+the second. Thus regarded, every syllogism comes within the following
+general formula:--
+
+  Attribute A is a mark of attribute B,
+  The given object has the mark A,
+              therefore
+  The given object has the attribute B.
+
+Referred to this type, the arguments which we have lately cited as
+specimens of the syllogism, will express themselves in the following
+manner:--
+
+  The attributes of man are a mark of the attribute mortality,
+  Socrates has the attributes of man,
+              therefore
+  Socrates has the attribute mortality.
+
+And again,
+
+  The attributes of man are a mark of the attribute mortality,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the attribute mortality.
+
+And, lastly,
+
+  The attributes of man are a mark of the absence of
+    the attribute omnipotence,
+  The attributes of a king are a mark of the attributes of man,
+                            therefore
+  The attributes of a king are a mark of the absence of
+    the attribute signified by the word omnipotent
+    (or, are evidence of the absence of that attribute).
+
+To correspond with this alteration in the form of the syllogisms, the
+axioms on which the syllogistic process is founded must undergo a
+corresponding transformation. In this altered phraseology, both those
+axioms may be brought under one general expression; namely, that
+whatever has any mark, has that which it is a mark of. Or, when the
+minor premise as well as the major is universal, we may state it thus:
+Whatever is a mark of any mark, is a mark of that which this last is a
+mark of. To trace the identity of these axioms with those previously
+laid down, may be left to the intelligent reader. We shall find, as we
+proceed, the great convenience of the phraseology into which we have
+last thrown them, and which is better adapted than any I am acquainted
+with, to express with precision and force what is aimed at, and actually
+accomplished, in every case of the ascertainment of a truth by
+ratiocination.
+
+
+
+
+CHAPTER III.
+
+OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.
+
+
+Sec. 1. We have shown what is the real nature of the truths with which the
+Syllogism is conversant, in contradistinction to the more superficial
+manner in which their import is conceived in the common theory; and what
+are the fundamental axioms on which its probative force or
+conclusiveness depends. We have now to inquire, whether the syllogistic
+process, that of reasoning from generals to particulars, is, or is not,
+a process of inference; a progress from the known to the unknown: a
+means of coming to a knowledge of something which we did not know
+before.
+
+Logicians have been remarkably unanimous in their mode of answering this
+question. It is universally allowed that a syllogism is vicious if there
+be anything more in the conclusion than was assumed in the premises. But
+this is, in fact, to say, that nothing ever was, or can be, proved by
+syllogism, which was not known, or assumed to be known, before. Is
+ratiocination, then, not a process of inference? And is the syllogism,
+to which the word reasoning has so often been represented to be
+exclusively appropriate, not really entitled to be called reasoning at
+all? This seems an inevitable consequence of the doctrine, admitted by
+all writers on the subject, that a syllogism can prove no more than is
+involved in the premises. Yet the acknowledgment so explicitly made, has
+not prevented one set of writers from continuing to represent the
+syllogism as the correct analysis of what the mind actually performs in
+discovering and proving the larger half of the truths, whether of
+science or of daily life, which we believe; while those who have avoided
+this inconsistency, and followed out the general theorem respecting the
+logical value of the syllogism to its legitimate corollary, have been
+led to impute uselessness and frivolity to the syllogistic theory
+itself, on the ground of the _petitio principii_ which they allege to be
+inherent in every syllogism. As I believe both these opinions to be
+fundamentally erroneous, I must request the attention of the reader to
+certain considerations, without which any just appreciation of the true
+character of the syllogism, and the functions it performs in philosophy,
+appears to me impossible; but which seem to have been either overlooked,
+or insufficiently adverted to, both by the defenders of the syllogistic
+theory and by its assailants.
+
+
+Sec. 2. It must be granted that in every syllogism, considered as an
+argument to prove the conclusion, there is a _petitio principii_. When
+we say,
+
+  All men are mortal,
+  Socrates is a man,
+      therefore
+  Socrates is mortal;
+
+it is unanswerably urged by the adversaries of the syllogistic theory,
+that the proposition, Socrates is mortal, is presupposed in the more
+general assumption, All men are mortal: that we cannot be assured of the
+mortality of all men, unless we are already certain of the mortality of
+every individual man: that if it be still doubtful whether Socrates, or
+any other individual we choose to name, be mortal or not, the same
+degree of uncertainty must hang over the assertion, All men are mortal:
+that the general principle, instead of being given as evidence of the
+particular case, cannot itself be taken for true without exception,
+until every shadow of doubt which could affect any case comprised with
+it, is dispelled by evidence _aliunde_; and then what remains for the
+syllogism to prove? That, in short, no reasoning from generals to
+particulars can, as such, prove anything: since from a general principle
+we cannot infer any particulars, but those which the principle itself
+assumes as known.
+
+This doctrine appears to me irrefragable; and if logicians, though
+unable to dispute it, have usually exhibited a strong disposition to
+explain it away, this was not because they could discover any flaw in
+the argument itself, but because the contrary opinion seemed to rest on
+arguments equally indisputable. In the syllogism last referred to, for
+example, or in any of those which we previously constructed, is it not
+evident that the conclusion may, to the person to whom the syllogism is
+presented, be actually and _bona fide_ a new truth? Is it not matter of
+daily experience that truths previously unthought of, facts which have
+not been, and cannot be, directly observed, are arrived at by way of
+general reasoning? We believe that the Duke of Wellington is mortal. We
+do not know this by direct observation, so long as he is not yet dead.
+If we were asked how, this being the case, we know the duke to be
+mortal, we should probably answer, Because all men are so. Here,
+therefore, we arrive at the knowledge of a truth not (as yet)
+susceptible of observation, by a reasoning which admits of being
+exhibited in the following syllogism:--
+
+  All men are mortal,
+  The Duke of Wellington is a man,
+              therefore
+  The Duke of Wellington is mortal.
+
+And since a large portion of our knowledge is thus acquired, logicians
+have persisted in representing the syllogism as a process of inference
+or proof; though none of them has cleared up the difficulty which arises
+from the inconsistency between that assertion, and the principle, that
+if there be anything in the conclusion which was not already asserted in
+the premises, the argument is vicious. For it is impossible to attach
+any serious scientific value to such a mere salvo, as the distinction
+drawn between being involved _by implication_ in the premises, and being
+directly asserted in them. When Archbishop Whately says[7] that the
+object of reasoning is "merely to expand and unfold the assertions wrapt
+up, as it were, and implied in those with which we set out, and to bring
+a person to perceive and acknowledge the full force of that which he
+has admitted," he does not, I think, meet the real difficulty requiring
+to be explained, namely, how it happens that a science, like geometry,
+_can_ be all "wrapt up" in a few definitions and axioms. Nor does this
+defence of the syllogism differ much from what its assailants urge
+against it as an accusation, when they charge it with being of no use
+except to those who seek to press the consequences of an admission into
+which a person has been entrapped without having considered and
+understood its full force. When you admitted the major premise, you
+asserted the conclusion; but, says Archbishop Whately, you asserted it
+by implication merely: this, however, can here only mean that you
+asserted it unconsciously; that you did not know you were asserting it;
+but, if so, the difficulty revives in this shape--Ought you not to have
+known? Were you warranted in asserting the general proposition without
+having satisfied yourself of the truth of everything which it fairly
+includes? And if not, is not the syllogistic art _prima facie_ what its
+assailants affirm it to be, a contrivance for catching you in a trap,
+and holding you fast in it?[8]
+
+
+Sec. 3. From this difficulty there appears to be but one issue. The
+proposition that the Duke of Wellington is mortal, is evidently an
+inference; it is got at as a conclusion from something else; but do we,
+in reality, conclude it from the proposition, All men are mortal? I
+answer, no.
+
+The error committed is, I conceive, that of overlooking the distinction
+between two parts of the process of philosophizing, the inferring part,
+and the registering part; and ascribing to the latter the functions of
+the former. The mistake is that of referring a person to his own notes
+for the origin of his knowledge. If a person is asked a question, and is
+at the moment unable to answer it, he may refresh his memory by turning
+to a memorandum which he carries about with him. But if he were asked,
+how the fact came to his knowledge, he would scarcely answer, because it
+was set down in his note-book: unless the book was written, like the
+Koran, with a quill from the wing of the angel Gabriel.
+
+Assuming that the proposition, The Duke of Wellington is mortal, is
+immediately an inference from the proposition, All men are mortal;
+whence do we derive our knowledge of that general truth? Of course from
+observation. Now, all which man can observe are individual cases. From
+these all general truths must be drawn, and into these they may be again
+resolved; for a general truth is but an aggregate of particular truths;
+a comprehensive expression, by which an indefinite number of individual
+facts are affirmed or denied at once. But a general proposition is not
+merely a compendious form for recording and preserving in the memory a
+number of particular facts, all of which have been observed.
+Generalization is not a process of mere naming, it is also a process of
+inference. From instances which we have observed, we feel warranted in
+concluding, that what we found true in those instances, holds in all
+similar ones, past, present, and future, however numerous they may be.
+We then, by that valuable contrivance of language which enables us to
+speak of many as if they were one, record all that we have observed,
+together with all that we infer from our observations, in one concise
+expression; and have thus only one proposition, instead of an endless
+number, to remember or to communicate. The results of many observations
+and inferences, and instructions for making innumerable inferences in
+unforeseen cases, are compressed into one short sentence.
+
+When, therefore, we conclude from the death of John and Thomas, and
+every other person we ever heard of in whose case the experiment had
+been fairly tried, that the Duke of Wellington is mortal like the rest;
+we may, indeed, pass through the generalization, All men are mortal, as
+an intermediate stage; but it is not in the latter half of the process,
+the descent from all men to the Duke of Wellington, that the _inference_
+resides. The inference is finished when we have asserted that all men
+are mortal. What remains to be performed afterwards is merely
+decyphering our own notes.
+
+Archbishop Whately has contended that syllogizing, or reasoning from
+generals to particulars, is not, agreeably to the vulgar idea, a
+peculiar _mode_ of reasoning, but the philosophical analysis of _the_
+mode in which all men reason, and must do so if they reason at all. With
+the deference due to so high an authority, I cannot help thinking that
+the vulgar notion is, in this case, the more correct. If, from our
+experience of John, Thomas, &c., who once were living, but are now dead,
+we are entitled to conclude that all human beings are mortal, we might
+surely without any logical inconsequence have concluded at once from
+those instances, that the Duke of Wellington is mortal. The mortality of
+John, Thomas, and company is, after all, the whole evidence we have for
+the mortality of the Duke of Wellington. Not one iota is added to the
+proof by interpolating a general proposition. Since the individual cases
+are all the evidence we can possess, evidence which no logical form into
+which we choose to throw it can make greater than it is; and since that
+evidence is either sufficient in itself, or, if insufficient for the one
+purpose, cannot be sufficient for the other; I am unable to see why we
+should be forbidden to take the shortest cut from these sufficient
+premises to the conclusion, and constrained to travel the "high priori
+road," by the arbitrary fiat of logicians. I cannot perceive why it
+should be impossible to journey from one place to another unless we
+"march up a hill, and then march down again." It may be the safest road,
+and there may be a resting-place at the top of the hill, affording a
+commanding view of the surrounding country; but for the mere purpose of
+arriving at our journey's end, our taking that road is perfectly
+optional; it is a question of time, trouble, and danger.
+
+Not only _may_ we reason from particulars to particulars without passing
+through generals, but we perpetually do so reason. All our earliest
+inferences are of this nature. From the first dawn of intelligence we
+draw inferences, but years elapse before we learn the use of general
+language. The child, who, having burnt his fingers, avoids to thrust
+them again into the fire, has reasoned or inferred, though he has never
+thought of the general maxim, Fire burns. He knows from memory that he
+has been burnt, and on this evidence believes, when he sees a candle,
+that if he puts his finger into the flame of it, he will be burnt again.
+He believes this in every case which happens to arise; but without
+looking, in each instance, beyond the present case. He is not
+generalizing; he is inferring a particular from particulars. In the same
+way, also, brutes reason. There is no ground for attributing to any of
+the lower animals the use of signs, of such a nature as to render
+general propositions possible. But those animals profit by experience,
+and avoid what they have found to cause them pain, in the same manner,
+though not always with the same skill, as a human creature. Not only the
+burnt child, but the burnt dog, dreads the fire.
+
+I believe that, in point of fact, when drawing inferences from our
+personal experience, and not from maxims handed down to us by books or
+tradition, we much oftener conclude from particulars to particulars
+directly, than through the intermediate agency of any general
+proposition. We are constantly reasoning from ourselves to other people,
+or from one person to another, without giving ourselves the trouble to
+erect our observations into general maxims of human or external nature.
+When we conclude that some person will, on some given occasion, feel or
+act so and so, we sometimes judge from an enlarged consideration of the
+manner in which human beings in general, or persons of some particular
+character, are accustomed to feel and act: but much oftener from merely
+recollecting the feelings and conduct of the same person in some
+previous instance, or from considering how we should feel or act
+ourselves. It is not only the village matron, who, when called to a
+consultation upon the case of a neighbour's child, pronounces on the
+evil and its remedy simply on the recollection and authority of what she
+accounts the similar case of her Lucy. We all, where we have no definite
+maxims to steer by, guide ourselves in the same way: and if we have an
+extensive experience, and retain its impressions strongly, we may
+acquire in this manner a very considerable power of accurate judgment,
+which we may be utterly incapable of justifying or of communicating to
+others. Among the higher order of practical intellects there have been
+many of whom it was remarked how admirably they suited their means to
+their ends, without being able to give any sufficient reasons for what
+they did; and applied, or seemed to apply, recondite principles which
+they were wholly unable to state. This is a natural consequence of
+having a mind stored with appropriate particulars, and having been long
+accustomed to reason at once from these to fresh particulars, without
+practising the habit of stating to oneself or to others the
+corresponding general propositions. An old warrior, on a rapid glance at
+the outlines of the ground, is able at once to give the necessary orders
+for a skilful arrangement of his troops; though if he has received
+little theoretical instruction, and has seldom been called upon to
+answer to other people for his conduct, he may never have had in his
+mind a single general theorem respecting the relation between ground and
+array. But his experience of encampments, in circumstances more or less
+similar, has left a number of vivid, unexpressed, ungeneralized
+analogies in his mind, the most appropriate of which, instantly
+suggesting itself, determines him to a judicious arrangement.
+
+The skill of an uneducated person in the use of weapons, or of tools,
+is of a precisely similar nature. The savage who executes unerringly the
+exact throw which brings down his game, or his enemy, in the manner most
+suited to his purpose, under the operation of all the conditions
+necessarily involved, the weight and form of the weapon, the direction
+and distance of the object, the action of the wind, &c., owes this power
+to a long series of previous experiments, the results of which he
+certainly never framed into any verbal theorems or rules. The same thing
+may generally be said of any other extraordinary manual dexterity. Not
+long ago a Scotch manufacturer procured from England, at a high rate of
+wages, a working dyer, famous for producing very fine colours, with the
+view of teaching to his other workmen the same skill. The workman came;
+but his mode of proportioning the ingredients, in which lay the secret
+of the effects he produced, was by taking them up in handfuls, while the
+common method was to weigh them. The manufacturer sought to make him
+turn his handling system into an equivalent weighing system, that the
+general principle of his peculiar mode of proceeding might be
+ascertained. This, however, the man found himself quite unable to do,
+and therefore could impart his skill to nobody. He had, from the
+individual cases of his own experience, established a connexion in his
+mind between fine effects of colour, and tactual perceptions in handling
+his dyeing materials; and from these perceptions he could, in any
+particular case, infer the means to be employed, and the effects which
+would be produced, but could not put others in possession of the grounds
+on which he proceeded, from having never generalized them in his own
+mind, or expressed them in language.
+
+Almost every one knows Lord Mansfield's advice to a man of practical
+good sense, who, being appointed governor of a colony, had to preside in
+its court of justice, without previous judicial practice or legal
+education. The advice was to give his decision boldly, for it would
+probably be right; but never to venture on assigning reasons, for they
+would almost infallibly be wrong. In cases like this, which are of no
+uncommon occurrence, it would be absurd to suppose that the bad reason
+was the source of the good decision. Lord Mansfield knew that if any
+reason were assigned it would be necessarily an afterthought, the judge
+being _in fact_ guided by impressions from past experience, without the
+circuitous process of framing general principles from them, and that if
+he attempted to frame any such he would assuredly fail. Lord Mansfield,
+however, would not have doubted that a man of equal experience who had
+also a mind stored with general propositions derived by legitimate
+induction from that experience, would have been greatly preferable as a
+judge, to one, however sagacious, who could not be trusted with the
+explanation and justification of his own judgments. The cases of men of
+talent performing wonderful things they know not how, are examples of
+the rudest and most spontaneous form of the operations of superior
+minds. It is a defect in them, and often a source of errors, not to have
+generalized as they went on; but generalization, though a help, the most
+important indeed of all helps, is not an essential.
+
+Even the scientifically instructed, who possess, in the form of general
+propositions, a systematic record of the results of the experience of
+mankind, need not always revert to those general propositions in order
+to apply that experience to a new case. It is justly remarked by Dugald
+Stewart, that though the reasonings in mathematics depend entirely on
+the axioms, it is by no means necessary to our seeing the conclusiveness
+of the proof, that the axioms should be expressly adverted to. When it
+is inferred that AB is equal to CD because each of them is equal to EF,
+the most uncultivated understanding, as soon as the propositions were
+understood, would assent to the inference, without having ever heard of
+the general truth that "things which are equal to the same thing are
+equal to one another." This remark of Stewart, consistently followed
+out, goes to the root, as I conceive, of the philosophy of
+ratiocination; and it is to be regretted that he himself stopt short at
+a much more limited application of it. He saw that the general
+propositions on which a reasoning is said to depend, may, in certain
+cases, be altogether omitted, without impairing its probative force.
+But he imagined this to be a peculiarity belonging to axioms; and argued
+from it, that axioms are not the foundations or first principles of
+geometry, from which all the other truths of the science are
+synthetically deduced (as the laws of motion and of the composition of
+forces in dynamics, the equal mobility of fluids in hydrostatics, the
+laws of reflection and refraction in optics, are the first principles of
+those sciences); but are merely necessary assumptions, self-evident
+indeed, and the denial of which would annihilate all demonstration, but
+from which, as premises, nothing can be demonstrated. In the present, as
+in many other instances, this thoughtful and elegant writer has
+perceived an important truth, but only by halves. Finding, in the case
+of geometrical axioms, that general names have not any talismanic virtue
+for conjuring new truths out of the well where they lie hid, and not
+seeing that this is equally true in every other case of generalization,
+he contended that axioms are in their nature barren of consequences, and
+that the really fruitful truths, the real first principles of geometry,
+are the definitions; that the definition, for example, of the circle is
+to the properties of the circle, what the laws of equilibrium and of the
+pressure of the atmosphere are to the rise of the mercury in the
+Torricellian tube. Yet all that he had asserted respecting the function
+to which the axioms are confined in the demonstrations of geometry,
+holds equally true of the definitions. Every demonstration in Euclid
+might be carried on without them. This is apparent from the ordinary
+process of proving a proposition of geometry by means of a diagram. What
+assumption, in fact, do we set out from, to demonstrate by a diagram any
+of the properties of the circle? Not that in all circles the radii are
+equal, but only that they are so in the circle ABC. As our warrant for
+assuming this, we appeal, it is true, to the definition of a circle in
+general; but it is only necessary that the assumption be granted in the
+case of the particular circle supposed. From this, which is not a
+general but a singular proposition, combined with other propositions of
+a similar kind, some of which _when generalized_ are called definitions,
+and others axioms, we prove that a certain conclusion is true, not of
+all circles, but of the particular circle ABC; or at least would be so,
+if the facts precisely accorded with our assumptions. The enunciation,
+as it is called, that is, the general theorem which stands at the head
+of the demonstration, is not the proposition actually demonstrated. One
+instance only is demonstrated: but the process by which this is done, is
+a process which, when we consider its nature, we perceive might be
+exactly copied in an indefinite number of other instances; in every
+instance which conforms to certain conditions. The contrivance of
+general language furnishing us with terms which connote these
+conditions, we are able to assert this indefinite multitude of truths in
+a single expression, and this expression is the general theorem. By
+dropping the use of diagrams, and substituting, in the demonstrations,
+general phrases for the letters of the alphabet, we might prove the
+general theorem directly, that is, we might demonstrate all the cases at
+once; and to do this we must, of course, employ as our premises, the
+axioms and definitions in their general form. But this only means, that
+if we can prove an individual conclusion by assuming an individual fact,
+then in whatever case we are warranted in making an exactly similar
+assumption, we may draw an exactly similar conclusion. The definition is
+a sort of notice to ourselves and others, what assumptions we think
+ourselves entitled to make. And so in all cases, the general
+propositions, whether called definitions, axioms, or laws of nature,
+which we lay down at the beginning of our reasonings, are merely
+abridged statements, in a kind of short-hand, of the particular facts,
+which, as occasion arises, we either think we may proceed on as proved,
+or intend to assume. In any one demonstration it is enough if we assume
+for a particular case suitably selected, what by the statement of the
+definition or principle we announce that we intend to assume in all
+cases which may arise. The definition of the circle, therefore, is to
+one of Euclid's demonstrations, exactly what, according to Stewart, the
+axioms are; that is, the demonstration does not depend on it, but yet if
+we deny it the demonstration fails. The proof does not rest on the
+general assumption, but on a similar assumption confined to the
+particular case: that case, however, being chosen as a specimen or
+paradigm of the whole class of cases included in the theorem, there can
+be no ground for making the assumption in that case which does not exist
+in every other; and to deny the assumption as a general truth, is to
+deny the right of making it in the particular instance.
+
+There are, undoubtedly, the most ample reasons for stating both the
+principles and the theorems in their general form, and these will be
+explained presently, so far as explanation is requisite. But, that
+unpractised learners, even in making use of one theorem to demonstrate
+another, reason rather from particular to particular than from the
+general proposition, is manifest from the difficulty they find in
+applying a theorem to a case in which the configuration of the diagram
+is extremely unlike that of the diagram by which the original theorem
+was demonstrated. A difficulty which, except in cases of unusual mental
+power, long practice can alone remove, and removes chiefly by rendering
+us familiar with all the configurations consistent with the general
+conditions of the theorem.
+
+
+Sec. 4. From the considerations now adduced, the following conclusions seem
+to be established. All inference is from particulars to particulars:
+General propositions are merely registers of such inferences already
+made, and short formulae for making more: The major premise of a
+syllogism, consequently, is a formula of this description: and the
+conclusion is not an inference drawn _from_ the formula, but an
+inference drawn _according_ to the formula: the real logical antecedent,
+or premise, being the particular facts from which the general
+proposition was collected by induction. Those facts, and the individual
+instances which supplied them, may have been forgotten: but a record
+remains, not indeed descriptive of the facts themselves, but showing how
+those cases may be distinguished, respecting which the facts, when
+known, were considered to warrant a given inference. According to the
+indications of this record we draw our conclusion; which is, to all
+intents and purposes, a conclusion from the forgotten facts. For this
+it is essential that we should read the record correctly: and the rules
+of the syllogism are a set of precautions to ensure our doing so.
+
+This view of the functions of the syllogism is confirmed by the
+consideration of precisely those cases which might be expected to be
+least favourable to it, namely, those in which ratiocination is
+independent of any previous induction. We have already observed that the
+syllogism, in the ordinary course of our reasoning, is only the latter
+half of the process of travelling from premises to a conclusion. There
+are, however, some peculiar cases in which it is the whole process.
+Particulars alone are capable of being subjected to observation; and all
+knowledge which is derived from observation, begins, therefore, of
+necessity, in particulars; but our knowledge may, in cases of certain
+descriptions, be conceived as coming to us from other sources than
+observation. It may present itself as coming from testimony, which, on
+the occasion and for the purpose in hand, is accepted as of an
+authoritative character: and the information thus communicated, may be
+conceived to comprise not only particular facts but general
+propositions, as when a scientific doctrine is accepted without
+examination on the authority of writers, or a theological doctrine on
+that of Scripture. Or the generalization may not be, in the ordinary
+sense, an assertion at all, but a command; a law, not in the
+philosophical, but in the moral and political sense of the term: an
+expression of the desire of a superior, that we, or any number of other
+persons, shall conform our conduct to certain general instructions. So
+far as this asserts a fact, namely, a volition of the legislator, that
+fact is an individual fact, and the proposition, therefore, is not a
+general proposition. But the description therein contained of the
+conduct which it is the will of the legislator that his subjects should
+observe, is general. The proposition asserts, not that all men _are_
+anything, but that all men _shall_ do something.
+
+In both these cases the generalities are the original data, and the
+particulars are elicited from them by a process which correctly resolves
+itself into a series of syllogisms. The real nature, however, of the
+supposed deductive process, is evident enough. The only point to be
+determined is, whether the authority which declared the general
+proposition, intended to include this case in it; and whether the
+legislator intended his command to apply to the present case among
+others, or not. This is ascertained by examining whether the case
+possesses the marks by which, as those authorities have signified, the
+cases which they meant to certify or to influence may be known. The
+object of the inquiry is to make out the witness's or the legislator's
+intention, through the indication given by their words. This is a
+question, as the Germans express it, of hermeneutics. The operation is
+not a process of inference, but a process of interpretation.
+
+In this last phrase we have obtained an expression which appears to me
+to characterize, more aptly than any other, the functions of the
+syllogism in all cases. When the premises are given by authority, the
+function of Reasoning is to ascertain the testimony of a witness, or the
+will of a legislator, by interpreting the signs in which the one has
+intimated his assertion and the other his command. In like manner, when
+the premises are derived from observation, the function of Reasoning is
+to ascertain what we (or our predecessors) formerly thought might be
+inferred from the observed facts, and to do this by interpreting a
+memorandum of ours, or of theirs. The memorandum reminds us, that from
+evidence, more or less carefully weighed, it formerly appeared that a
+certain attribute might be inferred wherever we perceive a certain mark.
+The proposition, All men are mortal (for instance) shows that we have
+had experience from which we thought it followed that the attributes
+connoted by the term man, are a mark of mortality. But when we conclude
+that the Duke of Wellington is mortal, we do not infer this from the
+memorandum, but from the former experience. All that we infer from the
+memorandum is our own previous belief, (or that of those who transmitted
+to us the proposition), concerning the inferences which that former
+experience would warrant.
+
+This view of the nature of the syllogism renders consistent and
+intelligible what otherwise remains obscure and confused in the theory
+of Archbishop Whately and other enlightened defenders of the syllogistic
+doctrine, respecting the limits to which its functions are confined.
+They affirm in as explicit terms as can be used, that the sole office of
+general reasoning is to prevent inconsistency in our opinions; to
+prevent us from assenting to anything, the truth of which would
+contradict something to which we had previously on good grounds given
+our assent. And they tell us, that the sole ground which a syllogism
+affords for assenting to the conclusion, is that the supposition of its
+being false, combined with the supposition that the premises are true,
+would lead to a contradiction in terms. Now this would be but a lame
+account of the real grounds which we have for believing the facts which
+we learn from reasoning, in contradistinction to observation. The true
+reason why we believe that the Duke of Wellington will die, is that his
+fathers, and our fathers, and all other persons who were cotemporary
+with them, have died. Those facts are the real premises of the
+reasoning. But we are not led to infer the conclusion from those
+premises, by the necessity of avoiding any verbal inconsistency. There
+is no contradiction in supposing that all those persons have died, and
+that the Duke of Wellington may, notwithstanding, live for ever. But
+there would be a contradiction if we first, on the ground of those same
+premises, made a general assertion including and covering the case of
+the Duke of Wellington, and then refused to stand to it in the
+individual case. There is an inconsistency to be avoided between the
+memorandum we make of the inferences which may be justly drawn in future
+cases, and the inferences we actually draw in those cases when they
+arise. With this view we interpret our own formula, precisely as a judge
+interprets a law: in order that we may avoid drawing any inferences not
+conformable to our former intention, as a judge avoids giving any
+decision not conformable to the legislator's intention. The rules for
+this interpretation are the rules of the syllogism: and its sole purpose
+is to maintain consistency between the conclusions we draw in every
+particular case, and the previous general directions for drawing them;
+whether those general directions were framed by ourselves as the result
+of induction, or were received by us from an authority competent to give
+them.
+
+
+Sec. 5. In the above observations it has, I think, been shown, that, though
+there is always a process of reasoning or inference where a syllogism is
+used, the syllogism is not a correct analysis of that process of
+reasoning or inference; which is, on the contrary, (when not a mere
+inference from testimony) an inference from particulars to particulars;
+authorized by a previous inference from particulars to generals, and
+substantially the same with it; of the nature, therefore, of Induction.
+But while these conclusions appear to me undeniable, I must yet enter a
+protest, as strong as that of Archbishop Whately himself, against the
+doctrine that the syllogistic art is useless for the purposes of
+reasoning. The reasoning lies in the act of generalization, not in
+interpreting the record of that act; but the syllogistic form is an
+indispensable collateral security for the correctness of the
+generalization itself.
+
+It has already been seen, that if we have a collection of particulars
+sufficient for grounding an induction, we need not frame a general
+proposition; we may reason at once from those particulars to other
+particulars. But it is to be remarked withal, that whenever, from a set
+of particular cases, we can legitimately draw any inference, we may
+legitimately make our inference a general one. If, from observation and
+experiment, we can conclude to one new case, so may we to an indefinite
+number. If that which has held true in our past experience will
+therefore hold in time to come, it will hold not merely in some
+individual case, but in all cases of some given description. Every
+induction, therefore, which suffices to prove one fact, proves an
+indefinite multitude of facts: the experience which justifies a single
+prediction must be such as will suffice to bear out a general theorem.
+This theorem it is extremely important to ascertain and declare, in its
+broadest form of generality; and thus to place before our minds, in its
+full extent, the whole of what our evidence must prove if it proves
+anything.
+
+This throwing of the whole body of possible inferences from a given set
+of particulars, into one general expression, operates as a security for
+their being just inferences, in more ways than one. First, the general
+principle presents a larger object to the imagination than any of the
+singular propositions which it contains. A process of thought which
+leads to a comprehensive generality, is felt as of greater importance
+than one which terminates in an insulated fact; and the mind is, even
+unconsciously, led to bestow greater attention upon the process, and to
+weigh more carefully the sufficiency of the experience appealed to, for
+supporting the inference grounded upon it. There is another, and a more
+important, advantage. In reasoning from a course of individual
+observations to some new and unobserved case, which we are but
+imperfectly acquainted with (or we should not be inquiring into it), and
+in which, since we are inquiring into it, we probably feel a peculiar
+interest; there is very little to prevent us from giving way to
+negligence, or to any bias which may affect our wishes or our
+imagination, and, under that influence, accepting insufficient evidence
+as sufficient. But if, instead of concluding straight to the particular
+case, we place before ourselves an entire class of facts--the whole
+contents of a general proposition, every tittle of which is legitimately
+inferrible from our premises, if that one particular conclusion is so;
+there is then a considerable likelihood that if the premises are
+insufficient, and the general inference, therefore, groundless, it will
+comprise within it some fact or facts the reverse of which we already
+know to be true; and we shall thus discover the error in our
+generalization by a _reductio ad impossibile_.
+
+Thus if, during the reign of Marcus Aurelius, a subject of the Roman
+empire, under the bias naturally given to the imagination and
+expectations by the lives and characters of the Antonines, had been
+disposed to expect that Commodus would be a just ruler; supposing him to
+stop there, he might only have been undeceived by sad experience. But if
+he reflected that this expectation could not be justifiable unless from
+the same evidence he was warranted in concluding some general
+proposition, as, for instance, that all Roman emperors are just rulers;
+he would immediately have thought of Nero, Domitian, and other
+instances, which, showing the falsity of the general conclusion, and
+therefore the insufficiency of the premises, would have warned him that
+those premises could not prove in the instance of Commodus, what they
+were inadequate to prove in any collection of cases in which his was
+included.
+
+The advantage, in judging whether any controverted inference is
+legitimate, of referring to a parallel case, is universally
+acknowledged. But by ascending to the general proposition, we bring
+under our view not one parallel case only, but all possible parallel
+cases at once; all cases to which the same set of evidentiary
+considerations are applicable.
+
+When, therefore, we argue from a number of known cases to another case
+supposed to be analogous, it is always possible, and generally
+advantageous, to divert our argument into the circuitous channel of an
+induction from those known cases to a general proposition, and a
+subsequent application of that general proposition to the unknown case.
+This second part of the operation, which, as before observed, is
+essentially a process of interpretation, will be resolvable into a
+syllogism or a series of syllogisms, the majors of which will be general
+propositions embracing whole classes of cases; every one of which
+propositions must be true in all its extent, if the argument is
+maintainable. If, therefore, any fact fairly coming within the range of
+one of these general propositions, and consequently asserted by it, is
+known or suspected to be other than the proposition asserts it to be,
+this mode of stating the argument causes us to know or to suspect that
+the original observations, which are the real grounds of our conclusion,
+are not sufficient to support it. And in proportion to the greater
+chance of our detecting the inconclusiveness of our evidence, will be
+the increased reliance we are entitled to place in it if no such
+evidence of defect shall appear.
+
+The value, therefore, of the syllogistic form, and of the rules for
+using it correctly, does not consist in their being the form and the
+rules according to which our reasonings are necessarily, or even
+usually, made; but in their furnishing us with a mode in which those
+reasonings may always be represented, and which is admirably calculated,
+if they are inconclusive, to bring their inconclusiveness to light. An
+induction from particulars to generals, followed by a syllogistic
+process from those generals to other particulars, is a form in which we
+may always state our reasonings if we please. It is not a form in which
+we _must_ reason, but it is a form in which we _may_ reason, and into
+which it is indispensable to throw our reasoning, when there is any
+doubt of its validity: though when the case is familiar and little
+complicated, and there is no suspicion of error, we may, and do, reason
+at once from the known particular cases to unknown ones.[9]
+
+These are the uses of syllogism, as a mode of verifying any given
+argument. Its ulterior uses, as respects the general course of our
+intellectual operations, hardly require illustration, being in fact the
+acknowledged uses of general language. They amount substantially to
+this, that the inductions may be made once for all: a single careful
+interrogation of experience may suffice, and the result may be
+registered in the form of a general proposition, which is committed to
+memory or to writing, and from which afterwards we have only to
+syllogize. The particulars of our experiments may then be dismissed from
+the memory, in which it would be impossible to retain so great a
+multitude of details; while the knowledge which those details afforded
+for future use, and which would otherwise be lost as soon as the
+observations were forgotten, or as their record became too bulky for
+reference, is retained in a commodious and immediately available shape
+by means of general language.
+
+Against this advantage is to be set the countervailing inconvenience,
+that inferences originally made on insufficient evidence, become
+consecrated, and, as it were, hardened into general maxims; and the mind
+cleaves to them from habit, after it has outgrown any liability to be
+misled by similar fallacious appearances if they were now for the first
+time presented; but having forgotten the particulars, it does not think
+of revising its own former decision. An inevitable drawback, which,
+however considerable in itself, forms evidently but a small set-off
+against the immense benefits of general language.
+
+The use of the syllogism is in truth no other than the use of general
+propositions in reasoning. We _can_ reason without them; in simple and
+obvious cases we habitually do so; minds of great sagacity can do it in
+cases not simple and obvious, provided their experience supplies them
+with instances essentially similar to every combination of circumstances
+likely to arise. But other minds, and the same minds where they have not
+the same pre-eminent advantages of personal experience, are quite
+helpless without the aid of general propositions, wherever the case
+presents the smallest complication; and if we made no general
+propositions, few persons would get much beyond those simple inferences
+which are drawn by the more intelligent of the brutes. Though not
+necessary to reasoning, general propositions are necessary to any
+considerable progress in reasoning. It is, therefore, natural and
+indispensable to separate the process of investigation into two parts;
+and obtain general formulae for determining what inferences may be drawn,
+before the occasion arises for drawing the inferences. The work of
+drawing them is then that of applying the formulae; and the rules of
+syllogism are a system of securities for the correctness of the
+application.
+
+
+Sec. 6. To complete the series of considerations connected with the
+philosophical character of the syllogism, it is requisite to consider,
+since the syllogism is not the universal type of the reasoning process,
+what is the real type. This resolves itself into the question, what is
+the nature of the minor premise, and in what manner it contributes to
+establish the conclusion: for as to the major, we now fully understand,
+that the place which it nominally occupies in our reasonings, properly
+belongs to the individual facts or observations of which it expresses
+the general result; the major itself being no real part of the argument,
+but an intermediate halting-place for the mind, interposed by an
+artifice of language between the real premises and the conclusion, by
+way of a security, which it is in a most material degree, for the
+correctness of the process. The minor, however, being an indispensable
+part of the syllogistic expression of an argument, without doubt either
+is, or corresponds to, an equally indispensable part of the argument
+itself, and we have only to inquire what part.
+
+It is perhaps worth while to notice here a speculation of a philosopher
+to whom mental science is much indebted, but who, though a very
+penetrating, was a very hasty thinker, and whose want of due
+circumspection rendered him fully as remarkable for what he did not see,
+as for what he saw. I allude to Dr. Thomas Brown, whose theory of
+ratiocination is peculiar. He saw the _petitio principii_ which is
+inherent in every syllogism, if we consider the major to be itself the
+evidence by which the conclusion is proved, instead of being, what in
+fact it is, an assertion of the existence of evidence sufficient to
+prove any conclusion of a given description. Seeing this, Dr. Brown not
+only failed to see the immense advantage, in point of security for
+correctness, which is gained by interposing this step between the real
+evidence and the conclusion; but he thought it incumbent on him to
+strike out the major altogether from the reasoning process, without
+substituting anything else, and maintained that our reasonings consist
+only of the minor premise and the conclusion, Socrates is a man,
+therefore Socrates is mortal: thus actually suppressing, as an
+unnecessary step in the argument, the appeal to former experience. The
+absurdity of this was disguised from him by the opinion he adopted, that
+reasoning is merely analysing our own general notions, or abstract
+ideas; and that the proposition, Socrates is mortal, is evolved from the
+proposition, Socrates is a man, simply by recognising the notion of
+mortality as already contained in the notion we form of a man.
+
+After the explanations so fully entered into on the subject of
+propositions, much further discussion cannot be necessary to make the
+radical error of this view of ratiocination apparent. If the word man
+connoted mortality; if the meaning of "mortal" were involved in the
+meaning of "man;" we might, undoubtedly, evolve the conclusion from the
+minor alone, because the minor would have already asserted it. But if,
+as is in fact the case, the word man does not connote mortality, how
+does it appear that in the mind of every person who admits Socrates to
+be a man, the idea of man must include the idea of mortality? Dr. Brown
+could not help seeing this difficulty, and in order to avoid it, was
+led, contrary to his intention, to re-establish, under another name,
+that step in the argument which corresponds to the major, by affirming
+the necessity of _previously perceiving_ the relation between the idea
+of man and the idea of mortal. If the reasoner has not previously
+perceived this relation, he will not, says Dr. Brown, infer because
+Socrates is a man, that Socrates is mortal. But even this admission,
+though amounting to a surrender of the doctrine that an argument
+consists of the minor and the conclusion alone, will not save the
+remainder of Dr. Brown's theory. The failure of assent to the argument
+does not take place merely because the reasoner, for want of due
+analysis, does not perceive that his idea of man includes the idea of
+mortality; it takes place, much more commonly, because in his mind that
+relation between the two ideas has never existed. And in truth it never
+does exist, except as the result of experience. Consenting, for the sake
+of the argument, to discuss the question on a supposition of which we
+have recognised the radical incorrectness, namely, that the meaning of a
+proposition relates to the ideas of the things spoken of, and not to
+the things themselves; I must yet observe, that the idea of man, as an
+universal idea, the common property of all rational creatures, cannot
+involve anything but what is strictly implied in the name. If any one
+includes in his own private idea of man, as no doubt is always the case,
+some other attributes, such for instance as mortality, he does so only
+as the consequence of experience, after having satisfied himself that
+all men possess that attribute: so that whatever the idea contains, in
+any person's mind, beyond what is included in the conventional
+signification of the word, has been added to it as the result of assent
+to a proposition; while Dr. Brown's theory requires us to suppose, on
+the contrary, that assent to the proposition is produced by evolving,
+through an analytic process, this very element out of the idea. This
+theory, therefore, may be considered as sufficiently refuted; and the
+minor premise must be regarded as totally insufficient to prove the
+conclusion, except with the assistance of the major, or of that which
+the major represents, namely, the various singular propositions
+expressive of the series of observations, of which the generalization
+called the major premise is the result.
+
+In the argument, then, which proves that Socrates is mortal, one
+indispensable part of the premises will be as follows: "My father, and
+my father's father, A, B, C, and an indefinite number of other persons,
+were mortal;" which is only an expression in different words of the
+observed fact that they have died. This is the major premise divested of
+the _petitio principii_, and cut down to as much as is really known by
+direct evidence.
+
+In order to connect this proposition with the conclusion Socrates is
+mortal, the additional link necessary is such a proposition as the
+following: "Socrates resembles my father, and my father's father, and
+the other individuals specified." This proposition we assert when we say
+that Socrates is a man. By saying so we likewise assert in what respect
+he resembles them, namely, in the attributes connoted by the word man.
+And we conclude that he further resembles them in the attribute
+mortality.
+
+
+Sec. 7. We have thus obtained what we were seeking, an universal type of
+the reasoning process. We find it resolvable in all cases into the
+following elements: Certain individuals have a given attribute; an
+individual or individuals resemble the former in certain other
+attributes; therefore they resemble them also in the given attribute.
+This type of ratiocination does not claim, like the syllogism, to be
+conclusive, from the mere form of the expression; nor can it possibly be
+so. That one proposition does or does not assert the very fact which was
+already asserted in another, may appear from the form of the expression,
+that is, from a comparison of the language; but when the two
+propositions assert facts which are _bona fide_ different, whether the
+one fact proves the other or not can never appear from the language, but
+must depend on other considerations. Whether, from the attributes in
+which Socrates resembles those men who have heretofore died, it is
+allowable to infer that he resembles them also in being mortal, is a
+question of Induction; and is to be decided by the principles or canons
+which we shall hereafter recognise as tests of the correct performance
+of that great mental operation.
+
+Meanwhile, however, it is certain, as before remarked, that if this
+inference can be drawn as to Socrates, it can be drawn as to all others
+who resemble the observed individuals in the same attributes in which he
+resembles them; that is (to express the thing concisely) of all mankind.
+If, therefore, the argument be admissible in the case of Socrates, we
+are at liberty, once for all, to treat the possession of the attributes
+of man as a mark, or satisfactory evidence, of the attribute of
+mortality. This we do by laying down the universal proposition, All men
+are mortal, and interpreting this, as occasion arises, in its
+application to Socrates and others. By this means we establish a very
+convenient division of the entire logical operation into two steps;
+first, that of ascertaining what attributes are marks of mortality; and,
+secondly, whether any given individuals possess those marks. And it will
+generally be advisable, in our speculations on the reasoning process, to
+consider this double operation as in fact taking place, and all
+reasoning as carried on in the form into which it must necessarily be
+thrown to enable us to apply to it any test of its correct performance.
+
+Although, therefore, all processes of thought in which the ultimate
+premises are particulars, whether we conclude from particulars to a
+general formula, or from particulars to other particulars according to
+that formula, are equally Induction: we shall yet, conformably to usage,
+consider the name Induction as more peculiarly belonging to the process
+of establishing the general proposition, and the remaining operation,
+which is substantially that of interpreting the general proposition, we
+shall call by its usual name, Deduction. And we shall consider every
+process by which anything is inferred respecting an unobserved case, as
+consisting of an Induction followed by a Deduction; because, although
+the process needs not necessarily be carried on in this form, it is
+always susceptible of the form, and must be thrown into it when
+assurance of scientific accuracy is needed and desired.
+
+
+Sec. 8. The theory of the syllogism, laid down in the preceding pages, has
+obtained, among other important adhesions, three of peculiar value;
+those of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir
+John Herschel considering the doctrine, though not strictly "a
+discovery,"[13] to be "one of the greatest steps which have yet been
+made in the philosophy of Logic." "When we consider" (to quote the
+further words of the same authority) "the inveteracy of the habits and
+prejudices which it has cast to the winds," there is no cause for
+misgiving in the fact that other thinkers, no less entitled to
+consideration, have formed a very different estimate of it. Their
+principal objection cannot be better or more succinctly stated than by
+borrowing a sentence from Archbishop Whately.[14] "In every case where
+an inference is drawn from Induction (unless that name is to be given to
+a mere random guess without any grounds at all) we must form a judgment
+that the instance or instances adduced are _sufficient_ to authorize the
+conclusion; that it is _allowable_ to take these instances as a sample
+warranting an inference respecting the whole class;" and the expression
+of this judgment in words (it has been said by several of my critics)
+_is_ the major premise.
+
+I quite admit that the major is an affirmation of the sufficiency of the
+evidence on which the conclusion rests. That it is so, is the very
+essence of my own theory. And whoever admits that the major premise is
+_only_ this, adopts the theory in its essentials.
+
+But I cannot concede that this recognition of the sufficiency of the
+evidence--that is, of the correctness of the induction--is a part of the
+induction itself; unless we ought to say that it is a part of everything
+we do, to satisfy ourselves that it has been done rightly. We conclude
+from known instances to unknown by the impulse of the generalizing
+propensity; and (until after a considerable amount of practice and
+mental discipline) the question of the sufficiency of the evidence is
+only raised by a retrospective act, turning back upon our own footsteps,
+and examining whether we were warranted in doing what we have already
+done. To speak of this reflex operation as part of the original one,
+requiring to be expressed in words in order that the verbal formula may
+correctly represent the psychological process, appears to me false
+psychology.[15] We review our syllogistic as well as our inductive
+processes, and recognise that they have been correctly performed; but
+logicians do not add a third premise to the syllogism, to express this
+act of recognition. A careful copyist verifies his transcript by
+collating it with the original; and if no error appears, he recognises
+that the transcript has been correctly made. But we do not call the
+examination of the copy a part of the act of copying.
+
+The conclusion in an induction is inferred from the evidence itself, and
+not from a recognition of the sufficiency of the evidence; as I infer
+that my friend is walking towards me because I see him, and not because
+I recognise that my eyes are open, and that eyesight is a means of
+knowledge. In all operations which require care, it is good to assure
+ourselves that the process has been performed accurately; but the
+testing of the process is not the process itself; and, besides, may have
+been omitted altogether, and yet the process be correct. It is precisely
+because that operation is omitted in ordinary unscientific reasoning,
+that there is anything gained in certainty by throwing reasoning into
+the syllogistic form. To make sure, as far as possible, that it shall
+not be omitted, we make the testing operation a part of the reasoning
+process itself. We insist that the inference from particulars to
+particulars shall pass through a general proposition. But this is a
+security for good reasoning, not a condition of all reasoning; and in
+some cases not even a security. Our most familiar inferences are all
+made before we learn the use of general propositions; and a person of
+untutored sagacity will skilfully apply his acquired experience to
+adjacent cases, though he would bungle grievously in fixing the limits
+of the appropriate general theorem. But though he may conclude rightly,
+he never, properly speaking, knows whether he has done so or not; he has
+not tested his reasoning. Now, this is precisely what forms of reasoning
+do for us. We do not need them to enable us to reason, but to enable us
+to know whether we reason correctly.
+
+In still further answer to the objection, it may be added that, even
+when the test has been applied, and the sufficiency of the evidence
+recognised,--if it is sufficient to support the general proposition, it
+is sufficient also to support an inference from particulars to
+particulars without passing through the general proposition. The
+inquirer who has logically satisfied himself that the conditions of
+legitimate induction were realized in the cases A, B, C, would be as
+much justified in concluding directly to the Duke of Wellington as in
+concluding to all men. The general conclusion is never legitimate,
+unless the particular one would be so too; and in no sense, intelligible
+to me, can the particular conclusion be said to be drawn from the
+general one. Whenever there is ground for drawing any conclusion at all
+from particular instances, there is ground for a general conclusion; but
+that this general conclusion should be actually drawn, however useful,
+cannot be an indispensable condition of the validity of the inference in
+the particular case. A man gives away sixpence by the same power by
+which he disposes of his whole fortune; but it is not necessary to the
+legality of the smaller act, that he should make a formal assertion of
+his right to the greater one.
+
+Some additional remarks, in reply to minor objections, are appended.[16]
+
+
+Sec. 9. The preceding considerations enable us to understand the true
+nature of what is termed, by recent writers, Formal Logic, and the
+relation between it and Logic in the widest sense. Logic, as I conceive
+it, is the entire theory of the ascertainment of reasoned or inferred
+truth. Formal Logic, therefore, which Sir William Hamilton from his own
+point of view, and Archbishop Whately from his, have represented as the
+whole of Logic properly so called, is really a very subordinate part of
+it, not being directly concerned with the process of Reasoning or
+Inference in the sense in which that process is a part of the
+Investigation of Truth. What, then, is Formal Logic? The name seems to
+be properly applied to all that portion of doctrine which relates to the
+equivalence of different modes of expression; the rules for determining
+when assertions in a given form imply or suppose the truth or falsity of
+other assertions. This includes the theory of the Import of
+Propositions, and of their Conversion, AEquipollence, and Opposition; of
+those falsely called Inductions (to be hereafter spoken of[17]), in
+which the apparent generalization is a mere abridged statement of cases
+known individually; and finally, of the syllogism: while the theory of
+Naming, and of (what is inseparably connected with it) Definition,
+though belonging still more to the other and larger kind of logic than
+to this, is a necessary preliminary to this. The end aimed at by Formal
+Logic, and attained by the observance of its precepts, is not truth, but
+consistency. It has been seen that this is the only direct purpose of
+the rules of the syllogism; the intention and effect of which is simply
+to keep our inferences or conclusions in complete consistency with our
+general formulae or directions for drawing them. The Logic of Consistency
+is a necessary auxiliary to the logic of truth, not only because what is
+inconsistent with itself or with other truths cannot be true, but also
+because truth can only be successfully pursued by drawing inferences
+from experience, which, if warrantable at all, admit of being
+generalized, and, to test their warrantableness, require to be exhibited
+in a generalized form; after which the correctness of their application
+to particular cases is a question which specially concerns the Logic of
+Consistency. This Logic, not requiring any preliminary knowledge of the
+processes or conclusions of the various sciences, may be studied with
+benefit in a much earlier stage of education than the Logic of Truth:
+and the practice which has empirically obtained of teaching it apart,
+through elementary treatises which do not attempt to include anything
+else, though the reasons assigned for the practice are in general very
+far from philosophical, admits of a philosophical justification.
+
+
+
+
+CHAPTER IV.
+
+OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
+
+
+Sec. 1. In our analysis of the syllogism, it appeared that the minor
+premise always affirms a resemblance between a new case and some cases
+previously known; while the major premise asserts something which,
+having been found true of those known cases, we consider ourselves
+warranted in holding true of any other case resembling the former in
+certain given particulars.
+
+If all ratiocinations resembled, as to the minor premise, the examples
+which were exclusively employed in the preceding chapter; if the
+resemblance, which that premise asserts, were obvious to the senses, as
+in the proposition "Socrates is a man," or were at once ascertainable by
+direct observation; there would be no necessity for trains of reasoning,
+and Deductive or Ratiocinative Sciences would not exist. Trains of
+reasoning exist only for the sake of extending an induction founded, as
+all inductions must be, on observed cases, to other cases in which we
+not only cannot directly observe what is to be proved, but cannot
+directly observe even the mark which is to prove it.
+
+
+Sec. 2. Suppose the syllogism to be, All cows ruminate, the animal which is
+before me is a cow, therefore it ruminates. The minor, if true at all,
+is obviously so: the only premise the establishment of which requires
+any anterior process of inquiry, is the major; and provided the
+induction of which that premise is the expression was correctly
+performed, the conclusion respecting the animal now present will be
+instantly drawn; because, as soon as she is compared with the formula,
+she will be identified as being included in it. But suppose the
+syllogism to be the following:--All arsenic is poisonous, the substance
+which is before me is arsenic, therefore it is poisonous. The truth of
+the minor may not here be obvious at first sight; it may not be
+intuitively evident, but may itself be known only by inference. It may
+be the conclusion of another argument, which, thrown into the
+syllogistic form, would stand thus:--Whatever when lighted produces a
+dark spot on a piece of white porcelain held in the flame, which spot is
+soluble in hypochlorite of calcium, is arsenic; the substance before me
+conforms to this condition; therefore it is arsenic. To establish,
+therefore, the ultimate conclusion, The substance before me is
+poisonous, requires a process, which, in order to be syllogistically
+expressed, stands in need of two syllogisms; and we have a Train of
+Reasoning.
+
+When, however, we thus add syllogism to syllogism, we are really adding
+induction to induction. Two separate inductions must have taken place to
+render this chain of inference possible; inductions founded, probably,
+on different sets of individual instances, but which converge in their
+results, so that the instance which is the subject of inquiry comes
+within the range of them both. The record of these inductions is
+contained in the majors of the two syllogisms. First, we, or others for
+us, have examined various objects which yielded under the given
+circumstances a dark spot with the given property, and found that they
+possessed the properties connoted by the word arsenic; they were
+metallic, volatile, their vapour had a smell of garlic, and so forth.
+Next, we, or others for us, have examined various specimens which
+possessed this metallic and volatile character, whose vapour had this
+smell, &c., and have invariably found that they were poisonous. The
+first observation we judge that we may extend to all substances whatever
+which yield that particular kind of dark spot; the second, to all
+metallic and volatile substances resembling those we examined; and
+consequently, not to those only which are seen to be such, but to those
+which are concluded to be such by the prior induction. The substance
+before us is only seen to come within one of these inductions; but by
+means of this one, it is brought within the other. We are still, as
+before, concluding from particulars to particulars; but we are now
+concluding from particulars observed, to other particulars which are
+not, as in the simple case, _seen_ to resemble them in the material
+points, but _inferred_ to do so, because resembling them in something
+else, which we have been led by quite a different set of instances to
+consider as a mark of the former resemblance.
+
+This first example of a train of reasoning is still extremely simple,
+the series consisting of only two syllogisms. The following is somewhat
+more complicated:--No government, which earnestly seeks the good of its
+subjects, is likely to be overthrown; some particular government
+earnestly seeks the good of its subjects, therefore it is not likely to
+be overthrown. The major premise in this argument we shall suppose not
+to be derived from considerations _a priori_, but to be a generalization
+from history, which, whether correct or erroneous, must have been
+founded on observation of governments concerning whose desire of the
+good of their subjects there was no doubt. It has been found, or thought
+to be found, that these were not easily overthrown, and it has been
+deemed that those instances warranted an extension of the same predicate
+to any and every government which resembles them in the attribute of
+desiring earnestly the good of its subjects. But _does_ the government
+in question thus resemble them? This may be debated _pro_ and _con_ by
+many arguments, and must, in any case, be proved by another induction;
+for we cannot directly observe the sentiments and desires of the persons
+who carry on the government. To prove the minor, therefore, we require
+an argument in this form: Every government which acts in a certain
+manner, desires the good of its subjects; the supposed government acts
+in that particular manner, therefore it desires the good of its
+subjects. But is it true that the government acts in the manner
+supposed? This minor also may require proof; still another induction, as
+thus:--What is asserted by intelligent and disinterested witnesses, may
+be believed to be true; that the government acts in this manner, is
+asserted by such witnesses, therefore it may be believed to be true. The
+argument hence consists of three steps. Having the evidence of our
+senses that the case of the government under consideration resembles a
+number of former cases, in the circumstance of having something asserted
+respecting it by intelligent and disinterested witnesses, we infer,
+first, that, as in those former instances, so in this instance, the
+assertion is true. Secondly, what was asserted of the government being
+that it acts in a particular manner, and other governments or persons
+having been observed to act in the same manner, the government in
+question is brought into known resemblance with those other governments
+or persons; and since they were known to desire the good of the people,
+it is thereupon, by a second induction, inferred that the particular
+government spoken of, desires the good of the people. This brings that
+government into known resemblance with the other governments which were
+thought likely to escape revolution, and thence, by a third induction,
+it is concluded that this particular government is also likely to
+escape. This is still reasoning from particulars to particulars, but we
+now reason to the new instance from three distinct sets of former
+instances: to one only of those sets of instances do we directly
+perceive the new one to be similar; but from that similarity we
+inductively infer that it has the attribute by which it is assimilated
+to the next set, and brought within the corresponding induction; after
+which by a repetition of the same operation we infer it to be similar to
+the third set, and hence a third induction conducts us to the ultimate
+conclusion.
+
+
+Sec. 3. Notwithstanding the superior complication of these examples,
+compared with those by which in the preceding chapter we illustrated the
+general theory of reasoning, every doctrine which we then laid down
+holds equally true in these more intricate cases. The successive general
+propositions are not steps in the reasoning, are not intermediate links
+in the chain of inference, between the particulars observed and those to
+which we apply the observation. If we had sufficiently capacious
+memories, and a sufficient power of maintaining order among a huge mass
+of details, the reasoning could go on without any general propositions;
+they are mere formulae for inferring particulars from particulars. The
+principle of general reasoning is (as before explained), that if from
+observation of certain known particulars, what was seen to be true of
+them can be inferred to be true of any others, it may be inferred of all
+others which are of a certain description. And in order that we may
+never fail to draw this conclusion in a new case when it can be drawn
+correctly, and may avoid drawing it when it cannot, we determine once
+for all what are the distinguishing marks by which such cases may be
+recognised. The subsequent process is merely that of identifying an
+object, and ascertaining it to have those marks; whether we identify it
+by the very marks themselves, or by others which we have ascertained
+(through another and a similar process) to be marks of those marks. The
+real inference is always from particulars to particulars, from the
+observed instances to an unobserved one: but in drawing this inference,
+we conform to a formula which we have adopted for our guidance in such
+operations, and which is a record of the criteria by which we thought we
+had ascertained that we might distinguish when the inference could, and
+when it could not, be drawn. The real premises are the individual
+observations, even though they may have been forgotten, or, being the
+observations of others and not of ourselves, may, to us, never have been
+known: but we have before us proof that we or others once thought them
+sufficient for an induction, and we have marks to show whether any new
+case is one of those to which, if then known, the induction would have
+been deemed to extend. These marks we either recognise at once, or by
+the aid of other marks, which by another previous induction we collected
+to be marks of the first. Even these marks of marks may only be
+recognised through a third set of marks; and we may have a train of
+reasoning, of any length, to bring a new case within the scope of an
+induction grounded on particulars its similarity to which is only
+ascertained in this indirect manner.
+
+Thus, in the preceding example, the ultimate inductive inference was,
+that a certain government was not likely to be overthrown; this
+inference was drawn according to a formula in which desire of the public
+good was set down as a mark of not being likely to be overthrown; a mark
+of this mark was, acting in a particular manner; and a mark of acting in
+that manner was, being asserted to do so by intelligent and
+disinterested witnesses: this mark, the government under discussion was
+recognised by the senses as possessing. Hence that government fell
+within the last induction, and by it was brought within all the others.
+The perceived resemblance of the case to one set of observed particular
+cases, brought it into known resemblance with another set, and that with
+a third.
+
+In the more complex branches of knowledge, the deductions seldom
+consist, as in the examples hitherto exhibited, of a single chain, _a_ a
+mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They
+consist (to carry on the same metaphor) of several chains united at the
+extremity, as thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_
+of _n_, therefore _a b c_ a mark of _n_. Suppose, for example, the
+following combination of circumstances; 1st, rays of light impinging on
+a reflecting surface; 2nd, that surface parabolic; 3rd, those rays
+parallel to each other and to the axis of the surface. It is to be
+proved that the concourse of these three circumstances is a mark that
+the reflected rays will pass through the focus of the parabolic surface.
+Now, each of the three circumstances is singly a mark of something
+material to the case. Rays of light impinging on a reflecting surface,
+are a mark that those rays will be reflected at an angle equal to the
+angle of incidence. The parabolic form of the surface is a mark that,
+from any point of it, a line drawn to the focus and a line parallel to
+the axis will make equal angles with the surface. And finally, the
+parallelism of the rays to the axis is a mark that their angle of
+incidence coincides with one of these equal angles. The three marks
+taken together are therefore a mark of all these three things united.
+But the three united are evidently a mark that the angle of reflection
+must coincide with the other of the two equal angles, that formed by a
+line drawn to the focus; and this again, by the fundamental axiom
+concerning straight lines, is a mark that the reflected rays pass
+through the focus. Most chains of physical deduction are of this more
+complicated type; and even in mathematics such are abundant, as in all
+propositions where the hypothesis includes numerous conditions: "_If_ a
+circle be taken, and _if_ within that circle a point be taken, not the
+centre, and _if_ straight lines be drawn from that point to the
+circumference, then," &c.
+
+
+Sec. 4. The considerations now stated remove a serious difficulty from the
+view we have taken of reasoning; which view might otherwise have seemed
+not easily reconcileable with the fact that there are Deductive or
+Ratiocinative Sciences. It might seem to follow, if all reasoning be
+induction, that the difficulties of philosophical investigation must lie
+in the inductions exclusively, and that when these were easy, and
+susceptible of no doubt or hesitation, there could be no science, or, at
+least, no difficulties in science. The existence, for example, of an
+extensive Science of Mathematics, requiring the highest scientific
+genius in those who contributed to its creation, and calling for a most
+continued and vigorous exertion of intellect in order to appropriate it
+when created, may seem hard to be accounted for on the foregoing theory.
+But the considerations more recently adduced remove the mystery, by
+showing, that even when the inductions themselves are obvious, there may
+be much difficulty in finding whether the particular case which is the
+subject of inquiry comes within them; and ample room for scientific
+ingenuity in so combining various inductions, as, by means of one within
+which the case evidently falls, to bring it within others in which it
+cannot be directly seen to be included.
+
+When the more obvious of the inductions which can be made in any science
+from direct observations, have been made, and general formulas have been
+framed, determining the limits within which these inductions are
+applicable; as often as a new case can be at once seen to come within
+one of the formulas, the induction is applied to the new case, and the
+business is ended. But new cases are continually arising, which do not
+obviously come within any formula whereby the question we want solved in
+respect of them could be answered. Let us take an instance from
+geometry: and as it is taken only for illustration, let the reader
+concede to us for the present, what we shall endeavour to prove in the
+next chapter, that the first principles of geometry are results of
+induction. Our example shall be the fifth proposition of the first book
+of Euclid. The inquiry is, Are the angles at the base of an isosceles
+triangle equal or unequal? The first thing to be considered is, what
+inductions we have, from which we can infer equality or inequality. For
+inferring equality we have the following formulae:--Things which being
+applied to each other coincide, are equals. Things which are equal to
+the same thing are equals. A whole and the sum of its parts are equals.
+The sums of equal things are equals. The differences of equal things are
+equals. There are no other original formulae to prove equality. For
+inferring inequality we have the following:--A whole and its parts are
+unequals. The sums of equal things and unequal things are unequals. The
+differences of equal things and unequal things are unequals. In all,
+eight formulae. The angles at the base of an isosceles triangle do not
+obviously come within any of these. The formulae specify certain marks of
+equality and of inequality, but the angles cannot be perceived
+intuitively to have any of those marks. On examination it appears that
+they have; and we ultimately succeed in bringing them within the
+formula, "The differences of equal things are equal." Whence comes the
+difficulty of recognising these angles as the differences of equal
+things? Because each of them is the difference not of one pair only, but
+of innumerable pairs of angles; and out of these we had to imagine and
+select two, which could either be intuitively perceived to be equals, or
+possessed some of the marks of equality set down in the various formulae.
+By an exercise of ingenuity, which, on the part of the first inventor,
+deserves to be regarded as considerable, two pairs of angles were hit
+upon, which united these requisites. First, it could be perceived
+intuitively that their differences were the angles at the base; and,
+secondly, they possessed one of the marks of equality, namely,
+coincidence when applied to one another. This coincidence, however, was
+not perceived intuitively, but inferred, in conformity to another
+formula.
+
+For greater clearness, I subjoin an analysis of the demonstration.
+Euclid, it will be remembered, demonstrates his fifth proposition by
+means of the fourth. This it is not allowable for us to do, because we
+are undertaking to trace deductive truths not to prior deductions, but
+to their original inductive foundation. We must therefore use the
+premises of the fourth proposition instead of its conclusion, and prove
+the fifth directly from first principles. To do so requires six
+formulas. (We must begin, as in Euclid, by prolonging the equal sides
+AB, AC, to equal distances, and joining the extremities BE, DC.)
+
+[Illustration]
+
+FIRST FORMULA. _The sums of equals are equal._
+
+AD and AE are sums of equals by the supposition. Having that mark of
+equality, they are concluded by this formula to be equal.
+
+SECOND FORMULA. _Equal straight lines being applied to one another
+coincide._
+
+AC, AB, are within this formula by supposition; AD, AE, have been
+brought within it by the preceding step. Both these pairs of straight
+lines have the property of equality; which, according to the second
+formula, is a mark that, if applied to each other, they will coincide.
+Coinciding altogether means coinciding in every part, and of course at
+their extremities, D, E, and B, C.
+
+THIRD FORMULA. _Straight lines, having their extremities coincident,
+coincide._
+
+BE and CD have been brought within this formula by the preceding
+induction; they will, therefore, coincide.
+
+FOURTH FORMULA. _Angles, having their sides coincident, coincide._
+
+The third induction having shown that BE and CD coincide, and the second
+that AB, AC, coincide, the angles ABE and ACD are thereby brought within
+the fourth formula, and accordingly coincide.
+
+FIFTH FORMULA. _Things which coincide are equal._
+
+The angles ABE and ACD are brought within this formula by the induction
+immediately preceding. This train of reasoning being also applicable,
+_mutatis mutandis_, to the angles EBC, DCB, these also are brought
+within the fifth formula. And, finally,
+
+SIXTH FORMULA. _The differences of equals are equal._
+
+The angle ABC being the difference of ABE, CBE, and the angle ACB being
+the difference of ACD, DCB; which have been proved to be equals; ABC and
+ACB are brought within the last formula by the whole of the previous
+process.
+
+The difficulty here encountered is chiefly that of figuring to ourselves
+the two angles at the base of the triangle ABC as remainders made by
+cutting one pair of angles out of another, while each pair shall be
+corresponding angles of triangles which have two sides and the
+intervening angle equal. It is by this happy contrivance that so many
+different inductions are brought to bear upon the same particular case.
+And this not being at all an obvious thought, it may be seen from an
+example so near the threshold of mathematics, how much scope there may
+well be for scientific dexterity in the higher branches of that and
+other sciences, in order so to combine a few simple inductions, as to
+bring within each of them innumerable cases which are not obviously
+included in it; and how long, and numerous, and complicated may be the
+processes necessary for bringing the inductions together, even when each
+induction may itself be very easy and simple. All the inductions
+involved in all geometry are comprised in those simple ones, the formulae
+of which are the Axioms, and a few of the so-called Definitions. The
+remainder of the science is made up of the processes employed for
+bringing unforeseen cases within these inductions; or (in syllogistic
+language) for proving the minors necessary to complete the syllogisms;
+the majors being the definitions and axioms. In those definitions and
+axioms are laid down the whole of the marks, by an artful combination of
+which it has been found possible to discover and prove all that is
+proved in geometry. The marks being so few, and the inductions which
+furnish them being so obvious and familiar; the connecting of several of
+them together, which constitutes Deductions, or Trains of Reasoning,
+forms the whole difficulty of the science, and with a trifling
+exception, its whole bulk; and hence Geometry is a Deductive Science.
+
+
+Sec. 5. It will be seen hereafter[18] that there are weighty scientific
+reasons for giving to every science as much of the character of a
+Deductive Science as possible; for endeavouring to construct the science
+from the fewest and the simplest possible inductions, and to make these,
+by any combinations however complicated, suffice for proving even such
+truths, relating to complex cases, as could be proved, if we chose, by
+inductions from specific experience. Every branch of natural philosophy
+was originally experimental; each generalization rested on a special
+induction, and was derived from its own distinct set of observations and
+experiments. From being sciences of pure experiment, as the phrase is,
+or, to speak more correctly, sciences in which the reasonings mostly
+consist of no more than one step, and are expressed by single
+syllogisms, all these sciences have become to some extent, and some of
+them in nearly the whole of their extent, sciences of pure reasoning;
+whereby multitudes of truths, already known by induction from as many
+different sets of experiments, have come to be exhibited as deductions
+or corollaries from inductive propositions of a simpler and more
+universal character. Thus mechanics, hydrostatics, optics, acoustics,
+thermology, have successively been rendered mathematical; and astronomy
+was brought by Newton within the laws of general mechanics. Why it is
+that the substitution of this circuitous mode of proceeding for a
+process apparently much easier and more natural, is held, and justly, to
+be the greatest triumph of the investigation of nature, we are not, in
+this stage of our inquiry, prepared to examine. But it is necessary to
+remark, that although, by this progressive transformation, all sciences
+tend to become more and more Deductive, they are not, therefore, the
+less Inductive; every step in the Deduction is still an Induction. The
+opposition is not between the terms Deductive and Inductive, but between
+Deductive and Experimental. A science is experimental, in proportion as
+every new case, which presents any peculiar features, stands in need of
+a new set of observations and experiments--a fresh induction. It is
+deductive, in proportion as it can draw conclusions, respecting cases of
+a new kind, by processes which bring those cases under old inductions;
+by ascertaining that cases which cannot be observed to have the
+requisite marks, have, however, marks of those marks.
+
+We can now, therefore, perceive what is the generic distinction between
+sciences which can be made Deductive, and those which must as yet remain
+Experimental. The difference consists in our having been able, or not
+yet able, to discover marks of marks. If by our various inductions we
+have been able to proceed no further than to such propositions as these,
+_a_ a mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of
+_d_, or _c_ and _d_ marks of one another, without anything to connect
+_a_ or _b_ with _c_ or _d_; we have a science of detached and mutually
+independent generalizations, such as these, that acids redden vegetable
+blues, and that alkalies colour them green; from neither of which
+propositions could we, directly or indirectly, infer the other: and a
+science, so far as it is composed of such propositions, is purely
+experimental. Chemistry, in the present state of our knowledge, has not
+yet thrown off this character. There are other sciences, however, of
+which the propositions are of this kind: _a_ a mark of _b_, _b_ a mark
+of _c_, _c_ of _d_, _d_ of _e_, &c. In these sciences we can mount the
+ladder from _a_ to _e_ by a process of ratiocination; we can conclude
+that _a_ is a mark of _e_, and that every object which has the mark _a_
+has the property _e_, although, perhaps, we never were able to observe
+_a_ and _e_ together, and although even _d_, our only direct mark of
+_e_, may not be perceptible in those objects, but only inferrible. Or,
+varying the first metaphor, we may be said to get from _a_ to _e_
+underground: the marks _b_, _c_, _d_, which indicate the route, must all
+be possessed somewhere by the objects concerning which we are inquiring;
+but they are below the surface: _a_ is the only mark that is visible,
+and by it we are able to trace in succession all the rest.
+
+
+Sec. 6. We can now understand how an experimental may transform itself into
+a deductive science by the mere progress of experiment. In an
+experimental science, the inductions, as we have said, lie detached, as,
+_a_ a mark of _b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now,
+a new set of instances, and a consequent new induction, may at any time
+bridge over the interval between two of these unconnected arches; _b_,
+for example, may be ascertained to be a mark of _c_, which enables us
+thenceforth to prove deductively that _a_ is a mark of _c_. Or, as
+sometimes happens, some comprehensive induction may raise an arch high
+in the air, which bridges over hosts of them at once: _b_, _d_, _f_, and
+all the rest, turning out to be marks of some one thing, or of things
+between which a connexion has already been traced. As when Newton
+discovered that the motions, whether regular or apparently anomalous, of
+all the bodies of the solar system, (each of which motions had been
+inferred by a separate logical operation, from separate marks,) were all
+marks of moving round a common centre, with a centripetal force varying
+directly as the mass, and inversely as the square of the distance from
+that centre. This is the greatest example which has yet occurred of the
+transformation, at one stroke, of a science which was still to a great
+degree merely experimental, into a deductive science.
+
+Transformations of the same nature, but on a smaller scale, continually
+take place in the less advanced branches of physical knowledge, without
+enabling them to throw off the character of experimental sciences. Thus
+with regard to the two unconnected propositions before cited, namely,
+Acids redden vegetable blues, Alkalies make them green; it is remarked
+by Liebig, that all blue colouring matters which are reddened by acids
+(as well as, reciprocally, all red colouring matters which are rendered
+blue by alkalies) contain nitrogen: and it is quite possible that this
+circumstance may one day furnish a bond of connexion between the two
+propositions in question, by showing that the antagonistic action of
+acids and alkalies in producing or destroying the colour blue, is the
+result of some one, more general, law. Although this connecting of
+detached generalizations is so much gain, it tends but little to give a
+deductive character to any science as a whole; because the new courses
+of observation and experiment, which thus enable us to connect together
+a few general truths, usually make known to us a still greater number of
+unconnected new ones. Hence chemistry, though similar extensions and
+simplifications of its generalizations are continually taking place, is
+still in the main an experimental science; and is likely so to continue
+unless some comprehensive induction should be hereafter arrived at,
+which, like Newton's, shall connect a vast number of the smaller known
+inductions together, and change the whole method of the science at once.
+Chemistry has already one great generalization, which, though relating
+to one of the subordinate aspects of chemical phenomena, possesses
+within its limited sphere this comprehensive character; the principle of
+Dalton, called the atomic theory, or the doctrine of chemical
+equivalents: which by enabling us to a certain extent to foresee the
+proportions in which two substances will combine, before the experiment
+has been tried, constitutes undoubtedly a source of new chemical truths
+obtainable by deduction, as well as a connecting principle for all
+truths of the same description previously obtained by experiment.
+
+
+Sec. 7. The discoveries which change the method of a science from
+experimental to deductive, mostly consist in establishing, either by
+deduction or by direct experiment, that the varieties of a particular
+phenomenon uniformly accompany the varieties of some other phenomenon
+better known. Thus the science of sound, which previously stood in the
+lowest rank of merely experimental science, became deductive when it was
+proved by experiment that every variety of sound was consequent on, and
+therefore a mark of, a distinct and definable variety of oscillatory
+motion among the particles of the transmitting medium. When this was
+ascertained, it followed that every relation of succession or
+coexistence which obtained between phenomena of the more known class,
+obtained also between the phenomena which corresponded to them in the
+other class. Every sound, being a mark of a particular oscillatory
+motion, became a mark of everything which, by the laws of dynamics, was
+known to be inferrible from that motion; and everything which by those
+same laws was a mark of any oscillatory motion among the particles of an
+elastic medium, became a mark of the corresponding sound. And thus many
+truths, not before suspected, concerning sound, become deducible from
+the known laws of the propagation of motion through an elastic medium;
+while facts already empirically known respecting sound, become an
+indication of corresponding properties of vibrating bodies, previously
+undiscovered.
+
+But the grand agent for transforming experimental into deductive
+sciences, is the science of number. The properties of numbers, alone
+among all known phenomena, are, in the most rigorous sense, properties
+of all things whatever. All things are not coloured, or ponderable, or
+even extended; but all things are numerable. And if we consider this
+science in its whole extent, from common arithmetic up to the calculus
+of variations, the truths already ascertained seem all but infinite, and
+admit of indefinite extension.
+
+These truths, though affirmable of all things whatever, of course apply
+to them only in respect of their quantity. But if it comes to be
+discovered that variations of quality in any class of phenomena,
+correspond regularly to variations of quantity either in those same or
+in some other phenomena; every formula of mathematics applicable to
+quantities which vary in that particular manner, becomes a mark of a
+corresponding general truth respecting the variations in quality which
+accompany them: and the science of quantity being (as far as any science
+can be) altogether deductive, the theory of that particular kind of
+qualities becomes, to this extent, deductive likewise.
+
+The most striking instance in point which history affords (though not an
+example of an experimental science rendered deductive, but of an
+unparalleled extension given to the deductive process in a science which
+was deductive already), is the revolution in geometry which originated
+with Descartes, and was completed by Clairaut. These great
+mathematicians pointed out the importance of the fact, that to every
+variety of position in points, direction in lines, or form in curves or
+surfaces (all of which are Qualities), there corresponds a peculiar
+relation of quantity between either two or three rectilineal
+co-ordinates; insomuch that if the law were known according to which
+those co-ordinates vary relatively to one another, every other
+geometrical property of the line or surface in question, whether
+relating to quantity or quality, would be capable of being inferred.
+Hence it followed that every geometrical question could be solved, if
+the corresponding algebraical one could; and geometry received an
+accession (actual or potential) of new truths, corresponding to every
+property of numbers which the progress of the calculus had brought, or
+might in future bring, to light. In the same general manner, mechanics,
+astronomy, and in a less degree, every branch of natural philosophy
+commonly so called, have been made algebraical. The varieties of
+physical phenomena with which those sciences are conversant, have been
+found to answer to determinable varieties in the quantity of some
+circumstance or other; or at least to varieties of form or position, for
+which corresponding equations of quantity had already been, or were
+susceptible of being, discovered by geometers.
+
+In these various transformations, the propositions of the science of
+number do but fulfil the function proper to all propositions forming a
+train of reasoning, viz. that of enabling us to arrive in an indirect
+method, by marks of marks, at such of the properties of objects as we
+cannot directly ascertain (or not so conveniently) by experiment. We
+travel from a given visible or tangible fact, through the truths of
+numbers, to the facts sought. The given fact is a mark that a certain
+relation subsists between the quantities of some of the elements
+concerned; while the fact sought presupposes a certain relation between
+the quantities of some other elements: now, if these last quantities are
+dependent in some known manner upon the former, or _vice versa_, we can
+argue from the numerical relation between the one set of quantities, to
+determine that which subsists between the other set; the theorems of the
+calculus affording the intermediate links. And thus one of the two
+physical facts becomes a mark of the other, by being a mark of a mark of
+a mark of it.
+
+
+
+
+CHAPTER V.
+
+OF DEMONSTRATION, AND NECESSARY TRUTHS.
+
+
+Sec. 1. If, as laid down in the two preceding chapters, the foundation of
+all sciences, even deductive or demonstrative sciences, is Induction; if
+every step in the ratiocinations even of geometry is an act of
+induction; and if a train of reasoning is but bringing many inductions
+to bear upon the same subject of inquiry, and drawing a case within one
+induction by means of another; wherein lies the peculiar certainty
+always ascribed to the sciences which are entirely, or almost entirely,
+deductive? Why are they called the Exact Sciences? Why are mathematical
+certainty, and the evidence of demonstration, common phrases to express
+the very highest degree of assurance attainable by reason? Why are
+mathematics by almost all philosophers, and (by some) even those
+branches of natural philosophy which, through the medium of mathematics,
+have been converted into deductive sciences, considered to be
+independent of the evidence of experience and observation, and
+characterized as systems of Necessary Truth?
+
+The answer I conceive to be, that this character of necessity, ascribed
+to the truths of mathematics, and even (with some reservations to be
+hereafter made) the peculiar certainty attributed to them, is an
+illusion; in order to sustain which, it is necessary to suppose that
+those truths relate to, and express the properties of, purely imaginary
+objects. It is acknowledged that the conclusions of geometry are
+deduced, partly at least, from the so-called Definitions, and that those
+definitions are assumed to be correct representations, as far as they
+go, of the objects with which geometry is conversant. Now we have
+pointed out that, from a definition as such, no proposition, unless it
+be one concerning the meaning of a word, can ever follow; and that what
+apparently follows from a definition, follows in reality from an
+implied assumption that there exists a real thing conformable thereto.
+This assumption, in the case of the definitions of geometry, is false:
+there exist no real things exactly conformable to the definitions. There
+exist no points without magnitude; no lines without breadth, nor
+perfectly straight; no circles with all their radii exactly equal, nor
+squares with all their angles perfectly right. It will perhaps be said
+that the assumption does not extend to the actual, but only to the
+possible, existence of such things. I answer that, according to any test
+we have of possibility, they are not even possible. Their existence, so
+far as we can form any judgment, would seem to be inconsistent with the
+physical constitution of our planet at least, if not of the universe. To
+get rid of this difficulty, and at the same time to save the credit of
+the supposed system of necessary truth, it is customary to say that the
+points, lines, circles, and squares which are the subject of geometry,
+exist in our conceptions merely, and are part of our minds; which minds,
+by working on their own materials, construct an _a priori_ science, the
+evidence of which is purely mental, and has nothing whatever to do with
+outward experience. By howsoever high authorities this doctrine may have
+been sanctioned, it appears to me psychologically incorrect. The points,
+lines, circles, and squares, which any one has in his mind, are (I
+apprehend) simply copies of the points, lines, circles, and squares
+which he has known in his experience. Our idea of a point, I apprehend
+to be simply our idea of the _minimum visibile_, the smallest portion of
+surface which we can see. A line, as defined by geometers, is wholly
+inconceivable. We can reason about a line as if it had no breadth;
+because we have a power, which is the foundation of all the control we
+can exercise over the operations of our minds; the power, when a
+perception is present to our senses, or a conception to our intellects,
+of _attending_ to a part only of that perception or conception, instead
+of the whole. But we cannot _conceive_ a line without breadth; we can
+form no mental picture of such a line: all the lines which we have in
+our minds are lines possessing breadth. If any one doubts this, we may
+refer him to his own experience. I much question if any one who fancies
+that he can conceive what is called a mathematical line, thinks so from
+the evidence of his consciousness: I suspect it is rather because he
+supposes that unless such a conception were possible, mathematics could
+not exist as a science: a supposition which there will be no difficulty
+in showing to be entirely groundless.
+
+Since, then, neither in nature, nor in the human mind, do there exist
+any objects exactly corresponding to the definitions of geometry, while
+yet that science cannot be supposed to be conversant about non-entities;
+nothing remains but to consider geometry as conversant with such lines,
+angles, and figures, as really exist; and the definitions, as they are
+called, must be regarded as some of our first and most obvious
+generalizations concerning those natural objects. The correctness of
+those generalizations, as generalizations, is without a flaw: the
+equality of all the radii of a circle is true of all circles, so far as
+it is true of any one: but it is not exactly true of any circle; it is
+only nearly true; so nearly that no error of any importance in practice
+will be incurred by feigning it to be exactly true. When we have
+occasion to extend these inductions, or their consequences, to cases in
+which the error would be appreciable--to lines of perceptible breadth or
+thickness, parallels which deviate sensibly from equidistance, and the
+like--we correct our conclusions, by combining with them a fresh set of
+propositions relating to the aberration; just as we also take in
+propositions relating to the physical or chemical properties of the
+material, if those properties happen to introduce any modification into
+the result; which they easily may, even with respect to figure and
+magnitude, as in the case, for instance, of expansion by heat. So long,
+however, as there exists no practical necessity for attending to any of
+the properties of the object except its geometrical properties, or to
+any of the natural irregularities in those, it is convenient to neglect
+the consideration of the other properties and of the irregularities, and
+to reason as if these did not exist: accordingly, we formally announce
+in the definitions, that we intend to proceed on this plan. But it is
+an error to suppose, because we resolve to confine our attention to a
+certain number of the properties of an object, that we therefore
+conceive, or have an idea of, the object, denuded of its other
+properties. We are thinking, all the time, of precisely such objects as
+we have seen and touched, and with all the properties which naturally
+belong to them; but, for scientific convenience, we feign them to be
+divested of all properties, except those which are material to our
+purpose, and in regard to which we design to consider them.
+
+The peculiar accuracy, supposed to be characteristic of the first
+principles of geometry, thus appears to be fictitious. The assertions on
+which the reasonings of the science are founded, do not, any more than
+in other sciences, exactly correspond with the fact; but we suppose that
+they do so, for the sake of tracing the consequences which follow from
+the supposition. The opinion of Dugald Stewart respecting the
+foundations of geometry, is, I conceive, substantially correct; that it
+is built on hypotheses; that it owes to this alone the peculiar
+certainty supposed to distinguish it; and that in any science whatever,
+by reasoning from a set of hypotheses, we may obtain a body of
+conclusions as certain as those of geometry, that is, as strictly in
+accordance with the hypotheses, and as irresistibly compelling assent,
+_on condition_ that those hypotheses are true.
+
+When, therefore, it is affirmed that the conclusions of geometry are
+necessary truths, the necessity consists in reality only in this, that
+they correctly follow from the suppositions from which they are deduced.
+Those suppositions are so far from being necessary, that they are not
+even true; they purposely depart, more or less widely, from the truth.
+The only sense in which necessity can be ascribed to the conclusions of
+any scientific investigation, is that of legitimately following from
+some assumption, which, by the conditions of the inquiry, is not to be
+questioned. In this relation, of course, the derivative truths of every
+deductive science must stand to the inductions, or assumptions, on which
+the science is founded, and which, whether true or untrue, certain or
+doubtful in themselves, are always supposed certain for the purposes of
+the particular science. And therefore the conclusions of all deductive
+sciences were said by the ancients to be necessary propositions. We have
+observed already that to be predicated necessarily was characteristic of
+the predicable Proprium, and that a proprium was any property of a thing
+which could be deduced from its essence, that is, from the properties
+included in its definition.
+
+
+Sec. 2. The important doctrine of Dugald Stewart, which I have endeavoured
+to enforce, has been contested by Dr. Whewell, both in the dissertation
+appended to his excellent _Mechanical Euclid_, and in his elaborate work
+on the _Philosophy of the Inductive Sciences_; in which last he also
+replies to an article in the Edinburgh Review, (ascribed to a writer of
+great scientific eminence), in which Stewart's opinion was defended
+against his former strictures. The supposed refutation of Stewart
+consists in proving against him (as has also been done in this work)
+that the premises of geometry are not definitions, but assumptions of
+the real existence of things corresponding to those definitions. This,
+however, is doing little for Dr. Whewell's purpose; for it is these very
+assumptions which are asserted to be hypotheses, and which he, if he
+denies that geometry is founded on hypotheses, must show to be absolute
+truths. All he does, however, is to observe, that they at any rate, are
+not _arbitrary_ hypotheses; that we should not be at liberty to
+substitute other hypotheses for them; that not only "a definition, to be
+admissible, must necessarily refer to and agree with some conception
+which we can distinctly frame in our thoughts," but that the straight
+lines, for instance, which we define, must be "those by which angles are
+contained, those by which triangles are bounded, those of which
+parallelism may be predicated, and the like."[19] And this is true; but
+this has never been contradicted. Those who say that the premises of
+geometry are hypotheses, are not bound to maintain them to be hypotheses
+which have no relation whatever to fact. Since an hypothesis framed for
+the purpose of scientific inquiry must relate to something which has
+real existence, (for there can be no science respecting non-entities,)
+it follows that any hypothesis we make respecting an object, to
+facilitate our study of it, must not involve anything which is
+distinctly false, and repugnant to its real nature: we must not ascribe
+to the thing any property which it has not; our liberty extends only to
+slightly exaggerating some of those which it has, (by assuming it to be
+completely what it really is very nearly,) and suppressing others, under
+the indispensable obligation of restoring them whenever, and in as far
+as, their presence or absence would make any material difference in the
+truth of our conclusions. Of this nature, accordingly, are the first
+principles involved in the definitions of geometry. That the hypotheses
+should be of this particular character, is however no further necessary,
+than inasmuch as no others could enable us to deduce conclusions which,
+with due corrections, would be true of real objects: and in fact, when
+our aim is only to illustrate truths, and not to investigate them, we
+are not under any such restriction. We might suppose an imaginary
+animal, and work out by deduction, from the known laws of physiology,
+its natural history; or an imaginary commonwealth, and from the elements
+composing it, might argue what would be its fate. And the conclusions
+which we might thus draw from purely arbitrary hypotheses, might form a
+highly useful intellectual exercise: but as they could only teach us
+what _would_ be the properties of objects which do not really exist,
+they would not constitute any addition to our knowledge of nature: while
+on the contrary, if the hypothesis merely divests a real object of some
+portion of its properties, without clothing it in false ones, the
+conclusions will always express, under known liability to correction,
+actual truth.
+
+
+Sec. 3. But though Dr. Whewell has not shaken Stewart's doctrine as to the
+hypothetical character of that portion of the first principles of
+geometry which are involved in the so-called definitions, he has, I
+conceive, greatly the advantage of Stewart on another important point in
+the theory of geometrical reasoning; the necessity of admitting, among
+those first principles, axioms as well as definitions. Some of the
+axioms of Euclid might, no doubt, be exhibited in the form of
+definitions, or might be deduced, by reasoning, from propositions
+similar to what are so called. Thus, if instead of the axiom, Magnitudes
+which can be made to coincide are equal, we introduce a definition,
+"Equal magnitudes are those which may be so applied to one another as to
+coincide;" the three axioms which follow (Magnitudes which are equal to
+the same are equal to one another--If equals are added to equals the
+sums are equal--If equals are taken from equals the remainders are
+equal,) may be proved by an imaginary superposition, resembling that by
+which the fourth proposition of the first book of Euclid is
+demonstrated. But though these and several others may be struck out of
+the list of first principles, because, though not requiring
+demonstration, they are susceptible of it; there will be found in the
+list of axioms two or three fundamental truths, not capable of being
+demonstrated: among which must be reckoned the proposition that two
+straight lines cannot inclose a space, (or its equivalent, Straight
+lines which coincide in two points coincide altogether,) and some
+property of parallel lines, other than that which constitutes their
+definition: one of the most suitable for the purpose being that selected
+by Professor Playfair: "Two straight lines which intersect each other
+cannot both of them be parallel to a third straight line."[20]
+
+The axioms, as well those which are indemonstrable as those which admit
+of being demonstrated, differ from that other class of fundamental
+principles which are involved in the definitions, in this, that they
+are true without any mixture of hypothesis. That things which are equal
+to the same thing are equal to one another, is as true of the lines and
+figures in nature, as it would be of the imaginary ones assumed in the
+definitions. In this respect, however, mathematics are only on a par
+with most other sciences. In almost all sciences there are some general
+propositions which are exactly true, while the greater part are only
+more or less distant approximations to the truth. Thus in mechanics, the
+first law of motion (the continuance of a movement once impressed, until
+stopped or slackened by some resisting force) is true without
+qualification or error. The rotation of the earth in twenty-four hours,
+of the same length as in our time, has gone on since the first accurate
+observations, without the increase or diminution of one second in all
+that period. These are inductions which require no fiction to make them
+be received as accurately true: but along with them there are others, as
+for instance the propositions respecting the figure of the earth, which
+are but approximations to the truth; and in order to use them for the
+further advancement of our knowledge, we must feign that they are
+exactly true, though they really want something of being so.
+
+
+Sec. 4. It remains to inquire, what is the ground of our belief in
+axioms--what is the evidence on which they rest? I answer, they are
+experimental truths; generalizations from observation. The proposition,
+Two straight lines cannot inclose a space--or in other words, Two
+straight lines which have once met, do not meet again, but continue to
+diverge--is an induction from the evidence of our senses.
+
+This opinion runs counter to a scientific prejudice of long standing and
+great strength, and there is probably no proposition enunciated in this
+work for which a more unfavourable reception is to be expected. It is,
+however, no new opinion; and even if it were so, would be entitled to be
+judged, not by its novelty, but by the strength of the arguments by
+which it can be supported. I consider it very fortunate that so eminent
+a champion of the contrary opinion as Dr. Whewell, has found occasion
+for a most elaborate treatment of the whole theory of axioms, in
+attempting to construct the philosophy of the mathematical and physical
+sciences on the basis of the doctrine against which I now contend.
+Whoever is anxious that a discussion should go to the bottom of the
+subject, must rejoice to see the opposite side of the question worthily
+represented. If what is said by Dr. Whewell, in support of an opinion
+which he has made the foundation of a systematic work, can be shown not
+to be conclusive, enough will have been done, without going further in
+quest of stronger arguments and a more powerful adversary.
+
+It is not necessary to show that the truths which we call axioms are
+originally _suggested_ by observation, and that we should never have
+known that two straight lines cannot inclose a space if we had never
+seen a straight line: thus much being admitted by Dr. Whewell, and by
+all, in recent times, who have taken his view of the subject. But they
+contend, that it is not experience which _proves_ the axiom; but that
+its truth is perceived _a priori_, by the constitution of the mind
+itself, from the first moment when the meaning of the proposition is
+apprehended; and without any necessity for verifying it by repeated
+trials, as is requisite in the case of truths really ascertained by
+observation.
+
+They cannot, however, but allow that the truth of the axiom, Two
+straight lines cannot inclose a space, even if evident independently of
+experience, is also evident from experience. Whether the axiom needs
+confirmation or not, it receives confirmation in almost every instant of
+our lives; since we cannot look at any two straight lines which
+intersect one another, without seeing that from that point they continue
+to diverge more and more. Experimental proof crowds in upon us in such
+endless profusion, and without one instance in which there can be even a
+suspicion of an exception to the rule, that we should soon have stronger
+ground for believing the axiom, even as an experimental truth, than we
+have for almost any of the general truths which we confessedly learn
+from the evidence of our senses. Independently of _a priori_ evidence,
+we should certainly believe it with an intensity of conviction far
+greater than we accord to any ordinary physical truth: and this too at a
+time of life much earlier than that from which we date almost any part
+of our acquired knowledge, and much too early to admit of our retaining
+any recollection of the history of our intellectual operations at that
+period. Where then is the necessity for assuming that our recognition of
+these truths has a different origin from the rest of our knowledge, when
+its existence is perfectly accounted for by supposing its origin to be
+the same? when the causes which produce belief in all other instances,
+exist in this instance, and in a degree of strength as much superior to
+what exists in other cases, as the intensity of the belief itself is
+superior? The burden of proof lies on the advocates of the contrary
+opinion: it is for them to point out some fact, inconsistent with the
+supposition that this part of our knowledge of nature is derived from
+the same sources as every other part.[21]
+
+This, for instance, they would be able to do, if they could prove
+chronologically that we had the conviction (at least practically) so
+early in infancy as to be anterior to those impressions on the senses,
+upon which, on the other theory, the conviction is founded. This,
+however, cannot be proved: the point being too far back to be within the
+reach of memory, and too obscure for external observation. The advocates
+of the _a priori_ theory are obliged to have recourse to other
+arguments. These are reducible to two, which I shall endeavour to state
+as clearly and as forcibly as possible.
+
+
+Sec. 5. In the first place it is said that if our assent to the proposition
+that two straight lines cannot inclose a space, were derived from the
+senses, we could only be convinced of its truth by actual trial, that
+is, by seeing or feeling the straight lines; whereas in fact it is seen
+to be true by merely thinking of them. That a stone thrown into water
+goes to the bottom, may be perceived by our senses, but mere thinking of
+a stone thrown into the water would never have led us to that
+conclusion: not so, however, with the axioms relating to straight lines:
+if I could be made to conceive what a straight line is, without having
+seen one, I should at once recognise that two such lines cannot inclose
+a space. Intuition is "imaginary looking;"[22] but experience must be
+real looking: if we see a property of straight lines to be true by
+merely fancying ourselves to be looking at them, the ground of our
+belief cannot be the senses, or experience; it must be something mental.
+
+To this argument it might be added in the case of this particular axiom,
+(for the assertion would not be true of all axioms,) that the evidence
+of it from actual ocular inspection is not only unnecessary, but
+unattainable. What says the axiom? That two straight lines _cannot_
+inclose a space; that after having once intersected, if they are
+prolonged to infinity they do not meet, but continue to diverge from one
+another. How can this, in any single case, be proved by actual
+observation? We may follow the lines to any distance we please; but we
+cannot follow them to infinity: for aught our senses can testify, they
+may, immediately beyond the farthest point to which we have traced them,
+begin to approach, and at last meet. Unless, therefore, we had some
+other proof of the impossibility than observation affords us, we should
+have no ground for believing the axiom at all.
+
+To these arguments, which I trust I cannot be accused of understating, a
+satisfactory answer will, I conceive, be found, if we advert to one of
+the characteristic properties of geometrical forms--their capacity of
+being painted in the imagination with a distinctness equal to reality:
+in other words, the exact resemblance of our ideas of form to the
+sensations which suggest them. This, in the first place, enables us to
+make (at least with a little practice) mental pictures of all possible
+combinations of lines and angles, which resemble the realities quite as
+well as any which we could make on paper; and in the next place, make
+those pictures just as fit subjects of geometrical experimentation as
+the realities themselves; inasmuch as pictures, if sufficiently
+accurate, exhibit of course all the properties which would be manifested
+by the realities at one given instant, and on simple inspection: and in
+geometry we are concerned only with such properties, and not with that
+which pictures could not exhibit, the mutual action of bodies one upon
+another. The foundations of geometry would therefore be laid in direct
+experience, even if the experiments (which in this case consist merely
+in attentive contemplation) were practised solely upon what we call our
+ideas, that is, upon the diagrams in our minds, and not upon outward
+objects. For in all systems of experimentation we take some objects to
+serve as representatives of all which resemble them; and in the present
+case the conditions which qualify a real object to be the representative
+of its class, are completely fulfilled by an object existing only in our
+fancy. Without denying, therefore, the possibility of satisfying
+ourselves that two straight lines cannot inclose a space, by merely
+thinking of straight lines without actually looking at them; I contend,
+that we do not believe this truth on the ground of the imaginary
+intuition simply, but because we know that the imaginary lines exactly
+resemble real ones, and that we may conclude from them to real ones with
+quite as much certainty as we could conclude from one real line to
+another. The conclusion, therefore, is still an induction from
+observation. And we should not be authorized to substitute observation
+of the image in our mind, for observation of the reality, if we had not
+learnt by long-continued experience that the properties of the reality
+are faithfully represented in the image; just as we should be
+scientifically warranted in describing an animal which we have never
+seen, from a picture made of it with a daguerreotype; but not until we
+had learnt by ample experience, that observation of such a picture is
+precisely equivalent to observation of the original.
+
+These considerations also remove the objection arising from the
+impossibility of ocularly following the lines in their prolongation to
+infinity. For though, in order actually to see that two given lines
+never meet, it would be necessary to follow them to infinity; yet
+without doing so we may know that if they ever do meet, or if, after
+diverging from one another, they begin again to approach, this must take
+place not at an infinite, but at a finite distance. Supposing,
+therefore, such to be the case, we can transport ourselves thither in
+imagination, and can frame a mental image of the appearance which one or
+both of the lines must present at that point, which we may rely on as
+being precisely similar to the reality. Now, whether we fix our
+contemplation upon this imaginary picture, or call to mind the
+generalizations we have had occasion to make from former ocular
+observation, we learn by the evidence of experience, that a line which,
+after diverging from another straight line, begins to approach to it,
+produces the impression on our senses which we describe by the
+expression, "a bent line," not by the expression, "a straight line."[23]
+
+
+Sec. 6. The first of the two arguments in support of the theory that
+axioms are _a priori_ truths, having, I think, been sufficiently
+answered; I proceed to the second, which is usually the most relied on.
+Axioms (it is asserted) are conceived by us not only as true, but as
+universally and necessarily true. Now, experience cannot possibly give
+to any proposition this character. I may have seen snow a hundred
+times, and may have seen that it was white, but this cannot give me
+entire assurance even that all snow is white; much less that snow _must_
+be white. "However many instances we may have observed of the truth of a
+proposition, there is nothing to assure us that the next case shall not
+be an exception to the rule. If it be strictly true that every ruminant
+animal yet known has cloven hoofs, we still cannot be sure that some
+creature will not hereafter be discovered which has the first of these
+attributes, without having the other.... Experience must always consist
+of a limited number of observations; and, however numerous these may be,
+they can show nothing with regard to the infinite number of cases in
+which the experiment has not been made." Besides, Axioms are not only
+universal, they are also necessary. Now "experience cannot offer the
+smallest ground for the necessity of a proposition. She can observe and
+record what has happened; but she cannot find, in any case, or in any
+accumulation of cases, any reason for what _must_ happen. She may see
+objects side by side; but she cannot see a reason why they must ever be
+side by side. She finds certain events to occur in succession; but the
+succession supplies, in its occurrence, no reason for its recurrence.
+She contemplates external objects; but she cannot detect any internal
+bond, which indissolubly connects the future with the past, the possible
+with the real. To learn a proposition by experience, and to see it to be
+necessarily true, are two altogether different processes of
+thought."[24] And Dr. Whewell adds, "If any one does not clearly
+comprehend this distinction of necessary and contingent truths, he will
+not be able to go along with us in our researches into the foundations
+of human knowledge; nor, indeed, to pursue with success any speculation
+on the subject."[25]
+
+In the following passage, we are told what the distinction is, the
+non-recognition of which incurs this denunciation. "Necessary truths are
+those in which we not only learn that the proposition is true, but see
+that it _must_ be true; in which the negation of the truth is not only
+false, but impossible; in which we cannot, even by an effort of
+imagination, or in a supposition, conceive the reverse of that which is
+asserted. That there are such truths cannot be doubted. We may take, for
+example, all relations of number. Three and Two added together make
+Five. We cannot conceive it to be otherwise. We cannot, by any freak of
+thought, imagine Three and Two to make Seven."[26]
+
+Although Dr. Whewell has naturally and properly employed a variety of
+phrases to bring his meaning more forcibly home, he would, I presume,
+allow that they are all equivalent; and that what he means by a
+necessary truth, would be sufficiently defined, a proposition the
+negation of which is not only false but inconceivable. I am unable to
+find in any of his expressions, turn them what way you will, a meaning
+beyond this, and I do not believe he would contend that they mean
+anything more.
+
+This, therefore, is the principle asserted: that propositions, the
+negation of which is inconceivable, or in other words, which we cannot
+figure to ourselves as being false, must rest on evidence of a higher
+and more cogent description than any which experience can afford.
+
+Now I cannot but wonder that so much stress should be laid on the
+circumstance of inconceivableness, when there is such ample experience
+to show, that our capacity or incapacity of conceiving a thing has very
+little to do with the possibility of the thing in itself; but is in
+truth very much an affair of accident, and depends on the past history
+and habits of our own minds. There is no more generally acknowledged
+fact in human nature, than the extreme difficulty at first felt in
+conceiving anything as possible, which is in contradiction to long
+established and familiar experience; or even to old familiar habits of
+thought. And this difficulty is a necessary result of the fundamental
+laws of the human mind. When we have often seen and thought of two
+things together, and have never in any one instance either seen or
+thought of them separately, there is by the primary law of association
+an increasing difficulty, which may in the end become insuperable, of
+conceiving the two things apart. This is most of all conspicuous in
+uneducated persons, who are in general utterly unable to separate any
+two ideas which have once become firmly associated in their minds; and
+if persons of cultivated intellect have any advantage on the point, it
+is only because, having seen and heard and read more, and being more
+accustomed to exercise their imagination, they have experienced their
+sensations and thoughts in more varied combinations, and have been
+prevented from forming many of these inseparable associations. But this
+advantage has necessarily its limits. The most practised intellect is
+not exempt from the universal laws of our conceptive faculty. If daily
+habit presents to any one for a long period two facts in combination,
+and if he is not led during that period either by accident or by his
+voluntary mental operations to think of them apart, he will probably in
+time become incapable of doing so even by the strongest effort; and the
+supposition that the two facts can be separated in nature, will at last
+present itself to his mind with all the characters of an inconceivable
+phenomenon.[27] There are remarkable instances of this in the history of
+science: instances in which the most instructed men rejected as
+impossible, because inconceivable, things which their posterity, by
+earlier practice and longer perseverance in the attempt, found it quite
+easy to conceive, and which everybody now knows to be true. There was a
+time when men of the most cultivated intellects, and the most
+emancipated from the dominion of early prejudice, could not credit the
+existence of antipodes; were unable to conceive, in opposition to old
+association, the force of gravity acting upwards instead of downwards.
+The Cartesians long rejected the Newtonian doctrine of the
+gravitation of all bodies towards one another, on the faith of
+a general proposition, the reverse of which seemed to them to be
+inconceivable--the proposition that a body cannot act where it is not.
+All the cumbrous machinery of imaginary vortices, assumed without the
+smallest particle of evidence, appeared to these philosophers a more
+rational mode of explaining the heavenly motions, than one which
+involved what seemed to them so great an absurdity.[28] And they no
+doubt found it as impossible to conceive that a body should act upon the
+earth at the distance of the sun or moon, as we find it to conceive an
+end to space or time, or two straight lines inclosing a space. Newton
+himself had not been able to realize the conception, or we should not
+have had his hypothesis of a subtle ether, the occult cause of
+gravitation; and his writings prove, that though he deemed the
+particular nature of the intermediate agency a matter of conjecture, the
+necessity of _some_ such agency appeared to him indubitable. It would
+seem that even now the majority of scientific men have not completely
+got over this very difficulty; for though they have at last learnt to
+conceive the sun _attracting_ the earth without any intervening fluid,
+they cannot yet conceive the sun _illuminating_ the earth without some
+such medium.
+
+If, then, it be so natural to the human mind, even in a high state of
+culture, to be incapable of conceiving, and on that ground to believe
+impossible, what is afterwards not only found to be conceivable but
+proved to be true; what wonder if in cases where the association is
+still older, more confirmed, and more familiar, and in which nothing
+ever occurs to shake our conviction, or even suggest to us any
+conception at variance with the association, the acquired incapacity
+should continue, and be mistaken for a natural incapacity? It is true,
+our experience of the varieties in nature enables us, within certain
+limits, to conceive other varieties analogous to them. We can conceive
+the sun or moon falling; for though we never saw them fall, nor ever
+perhaps imagined them falling, we have seen so many other things fall,
+that we have innumerable familiar analogies to assist the conception;
+which, after all, we should probably have some difficulty in framing,
+were we not well accustomed to see the sun and moon move (or appear to
+move,) so that we are only called upon to conceive a slight change in
+the direction of motion, a circumstance familiar to our experience. But
+when experience affords no model on which to shape the new conception,
+how is it possible for us to form it? How, for example, can we imagine
+an end to space or time? We never saw any object without something
+beyond it, nor experienced any feeling without something following it.
+When, therefore, we attempt to conceive the last point of space, we have
+the idea irresistibly raised of other points beyond it. When we try to
+imagine the last instant of time, we cannot help conceiving another
+instant after it. Nor is there any necessity to assume, as is done by a
+modern school of metaphysicians, a peculiar fundamental law of the mind
+to account for the feeling of infinity inherent in our conceptions of
+space and time; that apparent infinity is sufficiently accounted for by
+simpler and universally acknowledged laws.
+
+Now, in the case of a geometrical axiom, such, for example, as that two
+straight lines cannot inclose a space,--a truth which is testified to us
+by our very earliest impressions of the external world,--how is it
+possible (whether those external impressions be or be not the ground of
+our belief) that the reverse of the proposition _could_ be otherwise
+than inconceivable to us? What analogy have we, what similar order of
+facts in any other branch of our experience, to facilitate to us the
+conception of two straight lines inclosing a space? Nor is even this
+all. I have already called attention to the peculiar property of our
+impressions of form, that the ideas or mental images exactly resemble
+their prototypes, and adequately represent them for the purposes of
+scientific observation. From this, and from the intuitive character of
+the observation, which in this case reduces itself to simple inspection,
+we cannot so much as call up in our imagination two straight lines, in
+order to attempt to conceive them inclosing a space, without by that
+very act repeating the scientific experiment which establishes the
+contrary. Will it really be contended that the inconceivableness of the
+thing, in such circumstances, proves anything against the experimental
+origin of the conviction? Is it not clear that in whichever mode our
+belief in the proposition may have originated, the impossibility of our
+conceiving the negative of it must, on either hypothesis, be the same?
+As, then, Dr. Whewell exhorts those who have any difficulty in
+recognising the distinction held by him between necessary and contingent
+truths, to study geometry,--a condition which I can assure him I have
+conscientiously fulfilled,--I, in return, with equal confidence, exhort
+those who agree with him, to study the general laws of association;
+being convinced that nothing more is requisite than a moderate
+familiarity with those laws, to dispel the illusion which ascribes a
+peculiar necessity to our earliest inductions from experience, and
+measures the possibility of things in themselves, by the human capacity
+of conceiving them.
+
+I hope to be pardoned for adding, that Dr. Whewell himself has both
+confirmed by his testimony the effect of habitual association in giving
+to an experimental truth the appearance of a necessary one, and afforded
+a striking instance of that remarkable law in his own person. In his
+_Philosophy of the Inductive Sciences_ he continually asserts, that
+propositions which not only are not self-evident, but which we know to
+have been discovered gradually, and by great efforts of genius and
+patience, have, when once established, appeared so self-evident that,
+but for historical proof, it would have been impossible to conceive that
+they had not been recognised from the first by all persons in a sound
+state of their faculties. "We now despise those who, in the Copernican
+controversy, could not conceive the apparent motion of the sun on the
+heliocentric hypothesis; or those who, in opposition to Galileo, thought
+that a uniform force might be that which generated a velocity
+proportional to the space; or those who held there was something absurd
+in Newton's doctrine of the different refrangibility of differently
+coloured rays; or those who imagined that when elements combine, their
+sensible qualities must be manifest in the compound; or those who were
+reluctant to give up the distinction of vegetables into herbs, shrubs,
+and trees. We cannot help thinking that men must have been singularly
+dull of comprehension, to find a difficulty in admitting what is to us
+so plain and simple. We have a latent persuasion that we in their place
+should have been wiser and more clear-sighted; that we should have taken
+the right side, and given our assent at once to the truth. Yet in
+reality such a persuasion is a mere delusion. The persons who, in such
+instances as the above, were on the losing side, were very far, in most
+cases, from being persons more prejudiced, or stupid, or narrow-minded,
+than the greater part of mankind now are; and the cause for which they
+fought was far from being a manifestly bad one, till it had been so
+decided by the result of the war.... So complete has been the victory of
+truth in most of these instances, that at present we can hardly imagine
+the struggle to have been necessary. _The very essence of these triumphs
+is, that they lead us to regard the views we reject as not only false
+but inconceivable._"[29]
+
+This last proposition is precisely what I contend for; and I ask no
+more, in order to overthrow the whole theory of its author on the nature
+of the evidence of axioms. For what is that theory? That the truth of
+axioms cannot have been learnt from experience, because their falsity is
+inconceivable. But Dr. Whewell himself says, that we are continually
+led, by the natural progress of thought, to regard as inconceivable what
+our forefathers not only conceived but believed, nay even (he might
+have added) were unable to conceive the reverse of. He cannot intend to
+justify this mode of thought: he cannot mean to say, that we can be
+right in regarding as inconceivable what others have conceived, and as
+self-evident what to others did not appear evident at all. After so
+complete an admission that inconceivableness is an accidental thing, not
+inherent in the phenomenon itself, but dependent on the mental history
+of the person who tries to conceive it, how can he ever call upon us to
+reject a proposition as impossible on no other ground than its
+inconceivableness? Yet he not only does so, but has unintentionally
+afforded some of the most remarkable examples which can be cited of the
+very illusion which he has himself so clearly pointed out. I select as
+specimens, his remarks on the evidence of the three laws of motion, and
+of the atomic theory.
+
+With respect to the laws of motion, Dr. Whewell says: "No one can doubt
+that, in historical fact, these laws were collected from experience.
+That such is the case, is no matter of conjecture. We know the time, the
+persons, the circumstances, belonging to each step of each
+discovery."[30] After this testimony, to adduce evidence of the fact
+would be superfluous. And not only were these laws by no means
+intuitively evident, but some of them were originally paradoxes. The
+first law was especially so. That a body, once in motion, would continue
+for ever to move in the same direction with undiminished velocity unless
+acted upon by some new force, was a proposition which mankind found for
+a long time the greatest difficulty in crediting. It stood opposed to
+apparent experience of the most familiar kind, which taught that it was
+the nature of motion to abate gradually, and at last terminate of
+itself. Yet when once the contrary doctrine was firmly established,
+mathematicians, as Dr. Whewell observes, speedily began to believe that
+laws, thus contradictory to first appearances, and which, even after
+full proof had been obtained, it had required generations to render
+familiar to the minds of the scientific world, were under "a
+demonstrable necessity, compelling them to be such as they are and no
+other;" and he himself, though not venturing "absolutely to pronounce"
+that _all_ these laws "can be rigorously traced to an absolute necessity
+in the nature of things,"[31] does actually so think of the law just
+mentioned; of which he says: "Though the discovery of the first law of
+motion was made, historically speaking, by means of experiment, we have
+now attained a point of view in which we see that it might have been
+certainly known to be true, independently of experience."[32] Can there
+be a more striking exemplification than is here afforded, of the effect
+of association which we have described? Philosophers, for generations,
+have the most extraordinary difficulty in putting certain ideas
+together; they at last succeed in doing so; and after a sufficient
+repetition of the process, they first fancy a natural bond between the
+ideas, then experience a growing difficulty, which at last, by the
+continuation of the same progress, becomes an impossibility, of severing
+them from one another. If such be the progress of an experimental
+conviction of which the date is of yesterday, and which is in opposition
+to first appearances, how must it fare with those which are conformable
+to appearances familiar from the first dawn of intelligence, and of the
+conclusiveness of which, from the earliest records of human thought, no
+sceptic has suggested even a momentary doubt?
+
+The other instance which I shall quote is a truly astonishing one, and
+may be called the _reductio ad absurdum_ of the theory of
+inconceivableness. Speaking of the laws of chemical composition, Dr.
+Whewell says:[33] "That they could never have been clearly understood,
+and therefore never firmly established, without laborious and exact
+experiments, is certain; but yet we may venture to say, that being once
+known, they possess an evidence beyond that of mere experiment. _For how
+in fact can we conceive combinations, otherwise than as definite in kind
+and quality?_ If we were to suppose each element ready to combine with
+any other indifferently, and indifferently in any quantity, we should
+have a world in which all would be confusion and indefiniteness. There
+would be no fixed kinds of bodies. Salts, and stones, and ores, would
+approach to and graduate into each other by insensible degrees. Instead
+of this, we know that the world consists of bodies distinguishable from
+each other by definite differences, capable of being classified and
+named, and of having general propositions asserted concerning them. And
+as _we cannot conceive a world in which this should not be the case_, it
+would appear that we cannot conceive a state of things in which the laws
+of the combination of elements should not be of that definite and
+measured kind which we have above asserted."
+
+That a philosopher of Dr. Whewell's eminence should gravely assert that
+we cannot conceive a world in which the simple elements should combine
+in other than definite proportions; that by dint of meditating on a
+scientific truth, the original discoverer of which was still living, he
+should have rendered the association in his own mind between the idea of
+combination and that of constant proportions so familiar and intimate as
+to be unable to conceive the one fact without the other; is so signal an
+instance of the mental law for which I am contending, that one word more
+in illustration must be superfluous.
+
+In the latest and most complete elaboration of his metaphysical system
+(the _Philosophy of Discovery_), as well as in the earlier discourse on
+the _Fundamental Antithesis of Philosophy_, reprinted as an appendix to
+that work, Dr. Whewell, while very candidly admitting that his language
+was open to misconception, disclaims having intended to say that mankind
+in general can _now_ perceive the law of definite proportions in
+chemical combination to be a necessary truth. All he meant was that
+philosophical chemists in a future generation may possibly see this.
+"Some truths may be seen by intuition, but yet the intuition of them may
+be a rare and a difficult attainment."[34] And he explains that the
+inconceivableness which, according to his theory, is the test of
+axioms, "depends entirely upon the clearness of the Ideas which the
+axioms involve. So long as those Ideas are vague and indistinct, the
+contrary of an Axiom may be assented to, though it cannot be distinctly
+conceived. It may be assented to, not because it is possible, but
+because we do not see clearly what is possible. To a person who is only
+beginning to think geometrically, there may appear nothing absurd in the
+assertion, that two straight lines may inclose a space. And in the same
+manner, to a person who is only beginning to think of mechanical truths,
+it may not appear to be absurd, that in mechanical processes, Reaction
+should be greater or less than Action; and so, again, to a person who
+has not thought steadily about Substance, it may not appear
+inconceivable, that by chemical operations, we should generate new
+matter, or destroy matter which already exists."[35] Necessary truths,
+therefore, are not those of which we cannot conceive, but "those of
+which we cannot _distinctly_ conceive, the contrary."[36] So long as our
+ideas are indistinct altogether, we do not know what is or is not
+capable of being distinctly conceived; but, by the ever increasing
+distinctness with which scientific men apprehend the general conceptions
+of science, they in time come to perceive that there are certain laws of
+nature, which, though historically and as a matter of fact they were
+learnt from experience, we cannot, now that we know them, distinctly
+conceive to be other than they are.
+
+The account which I should give of this progress of the scientific mind
+is somewhat different. After a general law of nature has been
+ascertained, men's minds do not at first acquire a complete facility of
+familiarly representing to themselves the phenomena of nature in the
+character which that law assigns to them. The habit which constitutes
+the scientific cast of mind, that of conceiving facts of all
+descriptions conformably to the laws which regulate them--phenomena of
+all descriptions according to the relations which have been ascertained
+really to exist between them; this habit, in the case of newly
+discovered relations, comes only by degrees. So long as it is not
+thoroughly formed, no necessary character is ascribed to the new truth.
+But in time, the philosopher attains a state of mind in which his mental
+picture of nature spontaneously represents to him all the phenomena with
+which the new theory is concerned, in the exact light in which the
+theory regards them: all images or conceptions derived from any other
+theory, or from the confused view of the facts which is anterior to any
+theory, having entirely disappeared from his mind. The mode of
+representing facts which results from the theory, has now become, to his
+faculties, the only natural mode of conceiving them. It is a known
+truth, that a prolonged habit of arranging phenomena in certain groups,
+and explaining them by means of certain principles, makes any other
+arrangement or explanation of these facts be felt as unnatural: and it
+may at last become as difficult to him to represent the facts to himself
+in any other mode, as it often was, originally, to represent them in
+that mode.
+
+But, further, if the theory is true, as we are supposing it to be, any
+other mode in which he tries, or in which he was formerly accustomed, to
+represent the phenomena, will be seen by him to be inconsistent with the
+facts that suggested the new theory--facts which now form a part of his
+mental picture of nature. And since a contradiction is always
+inconceivable, his imagination rejects these false theories, and
+declares itself incapable of conceiving them. Their inconceivableness to
+him does not, however, result from anything in the theories themselves,
+intrinsically and _a priori_ repugnant to the human faculties; it
+results from the repugnance between them and a portion of the facts;
+which facts as long as he did not know, or did not distinctly realize in
+his mental representations, the false theory did not appear other than
+conceivable; it becomes inconceivable, merely from the fact that
+contradictory elements cannot be combined in the same conception.
+Although, then, his real reason for rejecting theories at variance with
+the true one, is no other than that they clash with his experience, he
+easily falls into the belief, that he rejects them because they are
+inconceivable, and that he adopts the true theory because it is
+self-evident, and does not need the evidence of experience at all.
+
+This I take to be the real and sufficient explanation of the paradoxical
+truth, on which so much stress is laid by Dr. Whewell, that a
+scientifically cultivated mind is actually, in virtue of that
+cultivation, unable to conceive suppositions which a common man
+conceives without the smallest difficulty. For there is nothing
+inconceivable in the suppositions themselves; the impossibility is in
+combining them with facts inconsistent with them, as part of the same
+mental picture; an obstacle of course only felt by those who know the
+facts, and are able to perceive the inconsistency. As far as the
+suppositions themselves are concerned, in the case of many of Dr.
+Whewell's necessary truths the negative of the axiom is, and probably
+will be as long as the human race lasts, as easily conceivable as the
+affirmative. There is no axiom (for example) to which Dr. Whewell
+ascribes a more thorough character of necessity and self-evidence, than
+that of the indestructibility of matter. That this is a true law of
+nature I fully admit; but I imagine there is no human being to whom the
+opposite supposition is inconceivable--who has any difficulty in
+imagining a portion of matter annihilated: inasmuch as its apparent
+annihilation, in no respect distinguishable from real by our unassisted
+senses, takes place every time that water dries up, or fuel is consumed.
+Again, the law that bodies combine chemically in definite proportions is
+undeniably true; but few besides Dr. Whewell have reached the point
+which he seems personally to have arrived at, (though he only dares
+prophesy similar success to the multitude after the lapse of
+generations,) that of being unable to conceive a world in which the
+elements are ready to combine with one another "indifferently in any
+quantity;" nor is it likely that we shall ever rise to this sublime
+height of inability, so long as all the mechanical mixtures in our
+planet, whether solid, liquid, or aeriform, exhibit to our daily
+observation the very phenomenon declared to be inconceivable.
+
+According to Dr. Whewell, these and similar laws of nature cannot be
+drawn from experience, inasmuch as they are, on the contrary, assumed
+in the interpretation of experience. Our inability to "add to or
+diminish the quantity of matter in the world," is a truth which "neither
+is nor can be derived from experience; for the experiments which we make
+to verify it presuppose its truth.... When men began to use the balance
+in chemical analysis, they did not prove by trial, but took for granted,
+as self-evident, that the weight of the whole must be found in the
+aggregate weight of the elements."[37] True, it is assumed; but, I
+apprehend, no otherwise than as all experimental inquiry assumes
+provisionally some theory or hypothesis, which is to be finally held
+true or not, according as the experiments decide. The hypothesis chosen
+for this purpose will naturally be one which groups together some
+considerable number of facts already known. The proposition that the
+material of the world, as estimated by weight, is neither increased nor
+diminished by any of the processes of nature or art, had many
+appearances in its favour to begin with. It expressed truly a great
+number of familiar facts. There were other facts which it had the
+appearance of conflicting with, and which made its truth, as an
+universal law of nature, at first doubtful. Because it was doubtful,
+experiments were devised to verify it. Men assumed its truth
+hypothetically, and proceeded to try whether, on more careful
+examination, the phenomena which apparently pointed to a different
+conclusion, would not be found to be consistent with it. This turned out
+to be the case; and from that time the doctrine took its place as an
+universal truth, but as one proved to be such by experience. That the
+theory itself preceded the proof of its truth--that it had to be
+conceived before it could be proved, and in order that it might be
+proved--does not imply that it was self-evident, and did not need proof.
+Otherwise all the true theories in the sciences are necessary and
+self-evident; for no one knows better than Dr. Whewell that they all
+began by being assumed, for the purpose of connecting them by deductions
+with those facts of experience on which, as evidence, they now
+confessedly rest.[38]
+
+
+
+
+CHAPTER VI.
+
+THE SAME SUBJECT CONTINUED.
+
+
+Sec. 1. In the examination which formed the subject of the last chapter,
+into the nature of the evidence of those deductive sciences which are
+commonly represented to be systems of necessary truth, we have been led
+to the following conclusions. The results of those sciences are indeed
+necessary, in the sense of necessarily following from certain first
+principles, commonly called axioms and definitions; that is, of being
+certainly true if those axioms and definitions are so; for the word
+necessity, even in this acceptation of it, means no more than certainty.
+But their claim to the character of necessity in any sense beyond this,
+as implying an evidence independent of and superior to observation and
+experience, must depend on the previous establishment of such a claim in
+favour of the definitions and axioms themselves. With regard to axioms,
+we found that, considered as experimental truths, they rest on
+superabundant and obvious evidence. We inquired, whether, since this is
+the case, it be imperative to suppose any other evidence of those truths
+than experimental evidence, any other origin for our belief of them than
+an experimental origin. We decided, that the burden of proof lies with
+those who maintain the affirmative, and we examined, at considerable
+length, such arguments as they have produced. The examination having led
+to the rejection of those arguments, we have thought ourselves warranted
+in concluding that axioms are but a class, the most universal class, of
+inductions from experience; the simplest and easiest cases of
+generalization from the facts furnished to us by our senses or by our
+internal consciousness.
+
+While the axioms of demonstrative sciences thus appeared to be
+experimental truths, the definitions, as they are incorrectly called, in
+those sciences, were found by us to be generalizations from experience
+which are not even, accurately speaking, truths; being propositions in
+which, while we assert of some kind of object, some property or
+properties which observation shows to belong to it, we at the same time
+deny that it possesses any other properties, though in truth other
+properties do in every individual instance accompany, and in almost all
+instances modify, the property thus exclusively predicated. The denial,
+therefore, is a mere fiction, or supposition, made for the purpose of
+excluding the consideration of those modifying circumstances, when their
+influence is of too trifling amount to be worth considering, or
+adjourning it, when important, to a more convenient moment.
+
+From these considerations it would appear that Deductive or
+Demonstrative Sciences are all, without exception, Inductive Sciences;
+that their evidence is that of experience; but that they are also, in
+virtue of the peculiar character of one indispensable portion of the
+general formulae according to which their inductions are made,
+Hypothetical Sciences. Their conclusions are only true on certain
+suppositions, which are, or ought to be, approximations to the truth,
+but are seldom, if ever, exactly true; and to this hypothetical
+character is to be ascribed the peculiar certainty, which is supposed to
+be inherent in demonstration.
+
+What we have now asserted, however, cannot be received as universally
+true of Deductive or Demonstrative Sciences, until verified by being
+applied to the most remarkable of all those sciences, that of Numbers;
+the theory of the Calculus; Arithmetic and Algebra. It is harder to
+believe of the doctrines of this science than of any other, either that
+they are not truths _a priori_, but experimental truths, or that their
+peculiar certainty is owing to their being not absolute but only
+conditional truths. This, therefore, is a case which merits examination
+apart; and the more so, because on this subject we have a double set of
+doctrines to contend with; that of the _a priori_ philosophers on one
+side; and on the other, a theory the most opposite to theirs, which was
+at one time very generally received, and is still far from being
+altogether exploded, among metaphysicians.
+
+
+Sec. 2. This theory attempts to solve the difficulty apparently inherent in
+the case, by representing the propositions of the science of numbers as
+merely verbal, and its processes as simple transformations of language,
+substitutions of one expression for another. The proposition, Two and
+one are equal to three, according to these writers, is not a truth, is
+not the assertion of a really existing fact, but a definition of the
+word three; a statement that mankind have agreed to use the name three
+as a sign exactly equivalent to two and one; to call by the former name
+whatever is called by the other more clumsy phrase. According to this
+doctrine, the longest process in algebra is but a succession of changes
+in terminology, by which equivalent expressions are substituted one for
+another; a series of translations of the same fact, from one into
+another language; though how, after such a series of translations, the
+fact itself comes out changed (as when we demonstrate a new geometrical
+theorem by algebra,) they have not explained; and it is a difficulty
+which is fatal to their theory.
+
+It must be acknowledged that there are peculiarities in the processes of
+arithmetic and algebra which render the theory in question very
+plausible, and have not unnaturally made those sciences the stronghold
+of Nominalism. The doctrine that we can discover facts, detect the
+hidden processes of nature, by an artful manipulation of language, is so
+contrary to common sense, that a person must have made some advances in
+philosophy to believe it: men fly to so paradoxical a belief to avoid,
+as they think, some even greater difficulty, which the vulgar do not
+see. What has led many to believe that reasoning is a mere verbal
+process, is, that no other theory seemed reconcileable with the nature
+of the Science of Numbers. For we do not carry any ideas along with us
+when we use the symbols of arithmetic or of algebra. In a geometrical
+demonstration we have a mental diagram, if not one on paper; AB, AC, are
+present to our imagination as lines, intersecting other lines, forming
+an angle with one another, and the like; but not so _a_ and _b_. These
+may represent lines or any other magnitudes, but those magnitudes are
+never thought of; nothing is realized in our imagination but _a_ and
+_b_. The ideas which, on the particular occasion, they happen to
+represent, are banished from the mind during every intermediate part of
+the process, between the beginning, when the premises are translated
+from things into signs, and the end, when the conclusion is translated
+back from signs into things. Nothing, then, being in the reasoner's mind
+but the symbols, what can seem more inadmissible than to contend that
+the reasoning process has to do with anything more? We seem to have come
+to one of Bacon's Prerogative Instances; an _experimentum crucis_ on the
+nature of reasoning itself.
+
+Nevertheless, it will appear on consideration, that this apparently so
+decisive instance is no instance at all; that there is in every step of
+an arithmetical or algebraical calculation a real induction, a real
+inference of facts from facts; and that what disguises the induction is
+simply its comprehensive nature, and the consequent extreme generality
+of the language. All numbers must be numbers of something: there are no
+such things as numbers in the abstract. _Ten_ must mean ten bodies, or
+ten sounds, or ten beatings of the pulse. But though numbers must be
+numbers of something, they may be numbers of anything. Propositions,
+therefore, concerning numbers, have the remarkable peculiarity that they
+are propositions concerning all things whatever; all objects, all
+existences of every kind, known to our experience. All things possess
+quantity; consist of parts which can be numbered; and in that character
+possess all the properties which are called properties of numbers. That
+half of four is two, must be true whatever the word four represents,
+whether four hours, four miles, or four pounds weight. We need only
+conceive a thing divided into four equal parts, (and all things may be
+conceived as so divided,) to be able to predicate of it every property
+of the number four, that is, every arithmetical proposition in which the
+number four stands on one side of the equation. Algebra extends the
+generalization still farther: every number represents that particular
+number of all things without distinction, but every algebraical symbol
+does more, it represents all numbers without distinction. As soon as we
+conceive a thing divided into equal parts, without knowing into what
+number of parts, we may call it _a_ or _x_, and apply to it, without
+danger of error, every algebraical formula in the books. The
+proposition, _2(a + b) = 2a + 2b_, is a truth co-extensive with all
+nature. Since then algebraical truths are true of all things whatever,
+and not, like those of geometry, true of lines only or angles only, it
+is no wonder that the symbols should not excite in our minds ideas of
+any things in particular. When we demonstrate the forty-seventh
+proposition of Euclid, it is not necessary that the words should raise
+in us an image of all right-angled triangles, but only of some one
+right-angled triangle: so in algebra we need not, under the symbol _a_,
+picture to ourselves all things whatever, but only some one thing; why
+not, then, the letter itself? The mere written characters, _a_, _b_,
+_x_, _y_, _z_, serve as well for representatives of Things in general,
+as any more complex and apparently more concrete conception. That we are
+conscious of them however in their character of things, and not of mere
+signs, is evident from the fact that our whole process of reasoning is
+carried on by predicating of them the properties of things. In resolving
+an algebraic equation, by what rules do we proceed? By applying at each
+step to _a_, _b_, and _x_, the proposition that equals added to equals
+make equals; that equals taken from equals leave equals; and other
+propositions founded on these two. These are not properties of language,
+or of signs as such, but of magnitudes, which is as much as to say, of
+all things. The inferences, therefore, which are successively drawn, are
+inferences concerning things, not symbols; though as any Things whatever
+will serve the turn, there is no necessity for keeping the idea of the
+Thing at all distinct, and consequently the process of thought may, in
+this case, be allowed without danger to do what all processes of
+thought, when they have been performed often, will do if permitted,
+namely, to become entirely mechanical. Hence the general language of
+algebra comes to be used familiarly without exciting ideas, as all
+other general language is prone to do from mere habit, though in no
+other case than this can it be done with complete safety. But when we
+look back to see from whence the probative force of the process is
+derived, we find that at every single step, unless we suppose ourselves
+to be thinking and talking of the things, and not the mere symbols, the
+evidence fails.
+
+There is another circumstance, which, still more than that which we have
+now mentioned, gives plausibility to the notion that the propositions of
+arithmetic and algebra are merely verbal. That is, that when considered
+as propositions respecting Things, they all have the appearance of being
+identical propositions. The assertion, Two and one are equal to three,
+considered as an assertion respecting objects, as for instance "Two
+pebbles and one pebble are equal to three pebbles," does not affirm
+equality between two collections of pebbles, but absolute identity. It
+affirms that if we put one pebble to two pebbles, those very pebbles are
+three. The objects, therefore, being the very same, and the mere
+assertion that "objects are themselves" being insignificant, it seems
+but natural to consider the proposition, Two and one are equal to three,
+as asserting mere identity of signification between the two names.
+
+This, however, though it looks so plausible, will not bear examination.
+The expression "two pebbles and one pebble," and the expression, "three
+pebbles," stand indeed for the same aggregation of objects, but they by
+no means stand for the same physical fact. They are names of the same
+objects, but of those objects in two different states: though they
+_de_note the same things, their _con_notation is different. Three
+pebbles in two separate parcels, and three pebbles in one parcel, do not
+make the same impression on our senses; and the assertion that the very
+same pebbles may by an alteration of place and arrangement be made to
+produce either the one set of sensations or the other, though a very
+familiar proposition, is not an identical one. It is a truth known to us
+by early and constant experience: an inductive truth; and such truths
+are the foundation of the science of Number. The fundamental truths of
+that science all rest on the evidence of sense; they are proved by
+showing to our eyes and our fingers that any given number of objects,
+ten balls for example, may by separation and re-arrangement exhibit to
+our senses all the different sets of numbers the sum of which is equal
+to ten. All the improved methods of teaching arithmetic to children
+proceed on a knowledge of this fact. All who wish to carry the child's
+_mind_ along with them in learning arithmetic; all who wish to teach
+numbers, and not mere ciphers--now teach it through the evidence of the
+senses, in the manner we have described.
+
+We may, if we please, call the proposition, "Three is two and one," a
+definition of the number three, and assert that arithmetic, as it has
+been asserted that geometry, is a science founded on definitions. But
+they are definitions in the geometrical sense, not the logical;
+asserting not the meaning of a term only, but along with it an observed
+matter of fact. The proposition, "A circle is a figure bounded by a line
+which has all its points equally distant from a point within it," is
+called the definition of a circle; but the proposition from which so
+many consequences follow, and which is really a first principle in
+geometry, is, that figures answering to this description exist. And thus
+we may call "Three is two and one" a definition of three; but the
+calculations which depend on that proposition do not follow from the
+definition itself, but from an arithmetical theorem presupposed in it,
+namely, that collections of objects exist, which while they impress the
+senses thus,
+
+  o o
+   o,
+
+may be separated into two parts, thus,
+
+  o o     o.
+
+This proposition being granted, we term all such parcels Threes, after
+which the enunciation of the above mentioned physical fact will serve
+also for a definition of the word Three.
+
+The Science of Number is thus no exception to the conclusion we
+previously arrived at, that the processes even of deductive sciences are
+altogether inductive, and that their first principles are
+generalizations from experience. It remains to be examined whether this
+science resembles geometry in the further circumstance, that some of its
+inductions are not exactly true; and that the peculiar certainty
+ascribed to it, on account of which its propositions are called
+Necessary Truths, is fictitious and hypothetical, being true in no other
+sense than that those propositions legitimately follow from the
+hypothesis of the truth of premises which are avowedly mere
+approximations to truth.
+
+
+Sec. 3. The inductions of arithmetic are of two sorts: first, those which
+we have just expounded, such as One and one are two, Two and one are
+three, &c., which may be called the definitions of the various numbers,
+in the improper or geometrical sense of the word Definition; and
+secondly, the two following axioms: The sums of equals are equal, The
+differences of equals are equal. These two are sufficient; for the
+corresponding propositions respecting unequals may be proved from these,
+by a _reductio ad absurdum_.
+
+These axioms, and likewise the so-called definitions, are, as has
+already been said, results of induction; true of all objects whatever,
+and, as it may seem, exactly true, without the hypothetical assumption
+of unqualified truth where an approximation to it is all that exists.
+The conclusions, therefore, it will naturally be inferred, are exactly
+true, and the science of number is an exception to other demonstrative
+sciences in this, that the categorical certainty which is predicable of
+its demonstrations is independent of all hypothesis.
+
+On more accurate investigation, however, it will be found that, even in
+this case, there is one hypothetical element in the ratiocination. In
+all propositions concerning numbers, a condition is implied, without
+which none of them would be true; and that condition is an assumption
+which maybe false. The condition, is that 1 = 1; that all the numbers
+are numbers of the same or of equal units. Let this be doubtful, and not
+one of the propositions of arithmetic will hold true. How can we know
+that one pound and one pound make two pounds, if one of the pounds may
+be troy, and the other avoirdupois? They may not make two pounds of
+either, or of any weight. How can we know that a forty-horse power is
+always equal to itself, unless we assume that all horses are of equal
+strength? It is certain that 1 is always equal in _number_ to 1; and
+where the mere number of objects, or of the parts of an object, without
+supposing them to be equivalent in any other respect, is all that is
+material, the conclusions of arithmetic, so far as they go to that
+alone, are true without mixture of hypothesis. There are a few such
+cases; as, for instance, an inquiry into the amount of the population of
+any country. It is indifferent to that inquiry whether they are grown
+people or children, strong or weak, tall or short; the only thing we
+want to ascertain is their number. But whenever, from equality or
+inequality of number, equality or inequality in any other respect is to
+be inferred, arithmetic carried into such inquiries becomes as
+hypothetical a science as geometry. All units must be assumed to be
+equal in that other respect; and this is never accurately true, for one
+actual pound weight is not exactly equal to another, nor one measured
+mile's length to another; a nicer balance, or more accurate measuring
+instruments, would always detect some difference.
+
+What is commonly called mathematical certainty, therefore, which
+comprises the twofold conception of unconditional truth and perfect
+accuracy, is not an attribute of all mathematical truths, but of those
+only which relate to pure Number, as distinguished from Quantity in the
+more enlarged sense; and only so long as we abstain from supposing that
+the numbers are a precise index to actual quantities. The certainty
+usually ascribed to the conclusions of geometry, and even to those of
+mechanics, is nothing whatever but certainty of inference. We can have
+full assurance of particular results under particular suppositions, but
+we cannot have the same assurance that these suppositions are accurately
+true, nor that they include all the data which may exercise an influence
+over the result in any given instance.
+
+
+Sec. 4. It appears, therefore, that the method of all Deductive Sciences is
+hypothetical. They proceed by tracing the consequences of certain
+assumptions; leaving for separate consideration whether the assumptions
+are true or not, and if not exactly true, whether they are a
+sufficiently near approximation to the truth. The reason is obvious.
+Since it is only in questions of pure number that the assumptions are
+exactly true, and even there, only so long as no conclusions except
+purely numerical ones are to be founded on them; it must, in all other
+cases of deductive investigation, form a part of the inquiry, to
+determine how much the assumptions want of being exactly true in the
+case in hand. This is generally a matter of observation, to be repeated
+in every fresh case; or if it has to be settled by argument instead of
+observation, may require in every different case different evidence, and
+present every degree of difficulty from the lowest to the highest. But
+the other part of the process--namely, to determine what else may be
+concluded if we find, and in proportion as we find, the assumptions to
+be true--may be performed once for all, and the results held ready to be
+employed as the occasions turn up for use. We thus do all beforehand
+that can be so done, and leave the least possible work to be performed
+when cases arise and press for a decision. This inquiry into the
+inferences which can be drawn from assumptions, is what properly
+constitutes Demonstrative Science.
+
+It is of course quite as practicable to arrive at new conclusions from
+facts assumed, as from facts observed; from fictitious, as from real,
+inductions. Deduction, as we have seen, consists of a series of
+inferences in this form--_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_,
+therefore _a_ is a mark of _d_, which last may be a truth inaccessible
+to direct observation. In like manner it is allowable to say, _suppose_
+that _a_ were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a
+mark of _d_, which last conclusion was not thought of by those who laid
+down the premises. A system of propositions as complicated as geometry
+might be deduced from assumptions which are false; as was done by
+Ptolemy, Descartes, and others, in their attempts to explain
+synthetically the phenomena of the solar system on the supposition that
+the apparent motions of the heavenly bodies were the real motions, or
+were produced in some way more or less different from the true one.
+Sometimes the same thing is knowingly done, for the purpose of showing
+the falsity of the assumption; which is called a _reductio ad absurdum_.
+In such cases, the reasoning is as follows: _a_ is a mark of _b_, and
+_b_ of _c_; now if _c_ were also a mark of _d_, _a_ would be a mark of
+_d_; but _d_ is known to be a mark of the absence of _a_; consequently
+_a_ would be a mark of its own absence, which is a contradiction;
+therefore _c_ is not a mark of _d_.
+
+
+Sec. 5. It has even been held by some writers, that all ratiocination rests
+in the last resort on a _reductio ad absurdum_; since the way to enforce
+assent to it, in case of obscurity, would be to show that if the
+conclusion be denied we must deny some one at least of the premises,
+which, as they are all supposed true, would be a contradiction. And in
+accordance with this, many have thought that the peculiar nature of the
+evidence of ratiocination consisted in the impossibility of admitting
+the premises and rejecting the conclusion without a contradiction in
+terms. This theory, however, is inadmissible as an explanation of the
+grounds on which ratiocination itself rests. If any one denies the
+conclusion notwithstanding his admission of the premises, he is not
+involved in any direct and express contradiction until he is compelled
+to deny some premise; and he can only be forced to do this by a
+_reductio ad absurdum_, that is, by another ratiocination: now, if he
+denies the validity of the reasoning process itself, he can no more be
+forced to assent to the second syllogism than to the first. In truth,
+therefore, no one is ever forced to a contradiction in terms: he can
+only be forced to a contradiction (or rather an infringement) of the
+fundamental maxim of ratiocination, namely, that whatever has a mark,
+has what it is a mark of; or, (in the case of universal propositions,)
+that whatever is a mark of anything, is a mark of whatever else that
+thing is a mark of. For in the case of every correct argument, as soon
+as thrown into the syllogistic form, it is evident without the aid of
+any other syllogism, that he who, admitting the premises, fails to draw
+the conclusion, does not conform to the above axiom.
+
+We have now proceeded as far in the theory of Deduction as we can
+advance in the present stage of our inquiry. Any further insight into
+the subject requires that the foundation shall have been laid of the
+philosophic theory of Induction itself; in which theory that of
+deduction, as a mode of induction, which we have now shown it to be,
+will assume spontaneously the place which belongs to it, and will
+receive its share of whatever light may be thrown upon the great
+intellectual operation of which it forms so important a part.
+
+
+
+
+CHAPTER VII.
+
+EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.
+
+
+Sec. 1. Polemical discussion is foreign to the plan of this work. But an
+opinion which stands in need of much illustration, can often receive it
+most effectually, and least tediously, in the form of a defence against
+objections. And on subjects concerning which speculative minds are still
+divided, a writer does but half his duty by stating his own doctrine, if
+he does not also examine, and to the best of his ability judge, those of
+other thinkers.
+
+In the dissertation which Mr. Herbert Spencer has prefixed to his, in
+many respects, highly philosophical treatise on the Mind,[39] he
+criticises some of the doctrines of the two preceding chapters, and
+propounds a theory of his own on the subject of first principles. Mr.
+Spencer agrees with me in considering axioms to be "simply our earliest
+inductions from experience." But he differs from me "widely as to the
+worth of the test of inconceivableness." He thinks that it is the
+ultimate test of all beliefs. He arrives at this conclusion by two
+steps. First, we never can have any stronger ground for believing
+anything, than that the belief of it "invariably exists." Whenever any
+fact or proposition is invariably believed; that is, if I understand Mr.
+Spencer rightly, believed by all persons, and by oneself at all times;
+it is entitled to be received as one of the primitive truths, or
+original premises of our knowledge. Secondly, the criterion by which we
+decide whether anything is invariably believed to be true, is our
+inability to conceive it as false. "The inconceivability of its negation
+is the test by which we ascertain whether a given belief invariably
+exists or not." "For our primary beliefs, the fact of invariable
+existence, tested by an abortive effort to cause their non-existence, is
+the only reason assignable." He thinks this the sole ground of our
+belief in our own sensations. If I believe that I feel cold, I only
+receive this as true because I cannot conceive that I am not feeling
+cold. "While the proposition remains true, the negation of it remains
+inconceivable." There are numerous other beliefs which Mr. Spencer
+considers to rest on the same basis; being chiefly those, or a part of
+those, which the metaphysicians of the Reid and Stewart school consider
+as truths of immediate intuition. That there exists a material world;
+that this is the very world which we directly and immediately perceive,
+and not merely the hidden cause of our perceptions; that Space, Time,
+Force, Extension, Figure, are not modes of our consciousness, but
+objective realities; are regarded by Mr. Spencer as truths known by the
+inconceivableness of their negatives. We cannot, he says, by any effort,
+conceive these objects of thought as mere states of our mind; as not
+having an existence external to us. Their real existence is, therefore,
+as certain as our sensations themselves. The truths which are the
+subject of direct knowledge, being, according to this doctrine, known to
+be truths only by the inconceivability of their negation; and the truths
+which are not the object of direct knowledge, being known as inferences
+from those which are; and those inferences being believed to follow from
+the premises, only because we cannot conceive them not to follow;
+inconceivability is thus the ultimate ground of all assured beliefs.
+
+Thus far, there is no very wide difference between Mr. Spencer's
+doctrine and the ordinary one of philosophers of the intuitive school,
+from Descartes to Dr. Whewell; but at this point Mr. Spencer diverges
+from them. For he does not, like them, set up the test of
+inconceivability as infallible. On the contrary, he holds that it may be
+fallacious, not from any fault in the test itself, but because "men have
+mistaken for inconceivable things, some things which were not
+inconceivable." And he himself, in this very book, denies not a few
+propositions usually regarded as among the most marked examples of
+truths whose negations are inconceivable. But occasional failure, he
+says, is incident to all tests. If such failure vitiates "the test of
+inconceivableness," it "must similarly vitiate all tests whatever. We
+consider an inference logically drawn from established premises to be
+true. Yet in millions of cases men have been wrong in the inferences
+they have thought thus drawn. Do we therefore argue that it is absurd to
+consider an inference true on no other ground than that it is logically
+drawn from established premises? No: we say that though men may have
+taken for logical inferences, inferences that were not logical, there
+nevertheless _are_ logical inferences, and that we are justified in
+assuming the truth of what seem to us such, until better instructed.
+Similarly, though men may have thought some things inconceivable which
+were not so, there may still be inconceivable things; and the inability
+to conceive the negation of a thing, may still be our best warrant for
+believing it.... Though occasionally it may prove an imperfect test,
+yet, as our most certain beliefs are capable of no better, to doubt any
+one belief because we have no higher guarantee for it, is really to
+doubt all beliefs." Mr. Spencer's doctrine, therefore, does not erect
+the curable, but only the incurable limitations of the human conceptive
+faculty, into laws of the outward universe.
+
+
+Sec. 2. The doctrine, that "a belief which is proved by the
+inconceivableness of its negation to invariably exist, is true," Mr.
+Spencer enforces by two arguments, one of which may be distinguished as
+positive, and the other as negative.
+
+The positive argument is, that every such belief represents the
+aggregate of all past experience. "Conceding the entire truth of" the
+"position, that during any phase of human progress, the ability or
+inability to form a specific conception wholly depends on the
+experiences men have had; and that, by a widening of their experiences,
+they may, by and by, be enabled to conceive things before inconceivable
+to them; it may still be argued that as, at any time, the best warrant
+men can have for a belief is the perfect agreement of all pre-existing
+experience in support of it, it follows that, at any time, the
+inconceivableness of its negation is the deepest test any belief admits
+of.... Objective facts are ever impressing themselves upon us; our
+experience is a register of these objective facts; and the
+inconceivableness of a thing implies that it is wholly at variance with
+the register. Even were this all, it is not clear how, if every truth is
+primarily inductive, any better test of truth could exist. But it must
+be remembered that whilst many of these facts, impressing themselves
+upon us, are occasional; whilst others again are very general; some are
+universal and unchanging. These universal and unchanging facts are, by
+the hypothesis, certain to establish beliefs of which the negations are
+inconceivable; whilst the others are not certain to do this; and if they
+do, subsequent facts will reverse their action. Hence if, after an
+immense accumulation of experiences, there remain beliefs of which the
+negations are still inconceivable, most, if not all of them, must
+correspond to universal objective facts. If there be ... certain
+absolute uniformities in nature; if these uniformities produce, as they
+must, absolute uniformities in our experience; and if ... these absolute
+uniformities in our experience disable us from conceiving the negations
+of them; then answering to each absolute uniformity in nature which we
+can cognize, there must exist in us a belief of which the negation is
+inconceivable, and which is absolutely true. In this wide range of cases
+subjective inconceivableness must correspond to objective impossibility.
+Further experience will produce correspondence where it may not yet
+exist; and we may expect the correspondence to become ultimately
+complete. In nearly all cases this test of inconceivableness must be
+valid now;" (I wish I could think we were so nearly arrived at
+omniscience) "and where it is not, it still expresses the net result of
+our experience up to the present time; which is the most that any test
+can do."
+
+To this I answer: Even if it were true that inconceivableness represents
+"the net result" of all past experience, why should we stop at the
+representative when we can get at the thing represented? If our
+incapacity to conceive the negation of a given supposition is proof of
+its truth, because proving that our experience has hitherto been
+uniform in its favour, the real evidence for the supposition is not the
+inconceivableness, but the uniformity of experience. Now this, which is
+the substantial and only proof, is directly accessible. We are not
+obliged to presume it from an incidental consequence. If all past
+experience is in favour of a belief, let this be stated, and the belief
+openly rested on that ground: after which the question arises, what that
+fact may be worth as evidence of its truth? For uniformity of experience
+is evidence in very different degrees: in some cases it is strong
+evidence, in others weak, in others it scarcely amounts to evidence at
+all. That all metals sink in water, was an uniform experience, from the
+origin of the human race to the discovery of potassium in the present
+century by Sir Humphry Davy. That all swans are white, was an uniform
+experience down to the discovery of Australia. In the few cases in which
+uniformity of experience does amount to the strongest possible proof, as
+with such propositions as these, Two straight lines cannot inclose a
+space, Every event has a cause, it is not because their negations are
+inconceivable, which is not always the fact; but because the experience,
+which has been thus uniform, pervades all nature. It will be shown in
+the following Book that none of the conclusions either of induction or
+of deduction can be considered certain, except as far as their truth is
+shown to be inseparably bound up with truths of this class.
+
+I maintain then, first, that uniformity of past experience is very far
+from being universally a criterion of truth. But secondly,
+inconceivableness is still farther from being a test even of that test.
+Uniformity of contrary experience is only one of many causes of
+inconceivability. Tradition handed down from a period of more limited
+knowledge, is one of the commonest. The mere familiarity of one mode of
+production of a phenomenon, often suffices to make every other mode
+appear inconceivable. Whatever connects two ideas by a strong
+association may, and continually does, render their separation in
+thought impossible; as Mr. Spencer, in other parts of his speculations,
+frequently recognises. It was not for want of experience that the
+Cartesians were unable to conceive that one body could produce motion
+in another without contact. They had as much experience of other modes
+of producing motion, as they had of that mode. The planets had revolved,
+and heavy bodies had fallen, every hour of their lives. But they fancied
+these phenomena to be produced by a hidden machinery which they did not
+see, because without it they were unable to conceive what they did see.
+The inconceivableness, instead of representing their experience,
+dominated and overrode their experience. It is needless to dwell farther
+on what I have termed the positive argument of Mr. Spencer in support of
+his criterion of truth. I pass to his negative argument, on which he
+lays more stress.
+
+
+Sec. 3. The negative argument is, that, whether inconceivability be good
+evidence or bad, no stronger evidence is to be obtained. That what is
+inconceivable cannot be true, is postulated in every act of thought. It
+is the foundation of all our original premises. Still more it is assumed
+in all conclusions from those premises. The invariability of belief,
+tested by the inconceivableness of its negation, "is our sole warrant
+for every demonstration. Logic is simply a systematization of the
+process by which we indirectly obtain this warrant for beliefs that do
+not directly possess it. To gain the strongest conviction possible
+respecting any complex fact, we either analytically descend from it by
+successive steps, each of which we unconsciously test by the
+inconceivableness of its negation, until we reach some axiom or truth
+which we have similarly tested; or we synthetically ascend from such
+axiom or truth by such steps. In either case we connect some isolated
+belief, with a belief which invariably exists, by a series of
+intermediate beliefs which invariably exist." The following passage sums
+up the whole theory: "When we perceive that the negation of the belief
+is inconceivable, we have all possible warrant for asserting the
+invariability of its existence: and in asserting this, we express alike
+our logical justification of it, and the inexorable necessity we are
+under of holding it.... We have seen that this is the assumption on
+which every conclusion whatever ultimately rests. We have no other
+guarantee for the reality of consciousness, of sensations, of personal
+existence; we have no other guarantee for any axiom; we have no other
+guarantee for any step in a demonstration. Hence, as being taken for
+granted in every act of the understanding, it must be regarded as the
+Universal Postulate." But as this postulate which we are under an
+"inexorable necessity" of holding true, is sometimes false; as "beliefs
+that once were shown by the inconceivableness of their negations to
+invariably exist, have since been found untrue," and as "beliefs that
+now possess this character may some day share the same fate;" the canon
+of belief laid down by Mr. Spencer is, that "the most certain
+conclusion" is that "which involves the postulate the fewest times."
+Reasoning, therefore, never ought to prevail against one of the
+immediate beliefs (the belief in Matter, in the outward reality of
+Extension, Space, and the like), because each of these involves the
+postulate only once; while an argument, besides involving it in the
+premises, involves it again in every step of the ratiocination, no one
+of the successive acts of inference being recognised as valid except
+because we cannot conceive the conclusion not to follow from the
+premises.
+
+It will be convenient to take the last part of this argument first. In
+every reasoning, according to Mr. Spencer, the assumption of the
+postulate is renewed at every step. At each inference we judge that the
+conclusion follows from the premises, our sole warrant for that judgment
+being that we cannot conceive it not to follow. Consequently if the
+postulate is fallible, the conclusions of reasoning are more vitiated by
+that uncertainty than direct intuitions; and the disproportion is
+greater, the more numerous the steps of the argument.
+
+To test this doctrine, let us first suppose an argument consisting only
+of a single step, which would be represented by one syllogism. This
+argument does rest on an assumption, and we have seen in the preceding
+chapters what the assumption is. It is, that whatever has a mark, has
+what it is a mark of. The evidence of this axiom I shall not consider at
+present;[40] let us suppose it (with Mr. Spencer) to be the
+inconceivableness of its reverse.
+
+Let us now add a second step to the argument: we require, what? Another
+assumption? No: the same assumption a second time; and so on to a third,
+and a fourth. I confess I do not see how, on Mr. Spencer's own
+principles, the repetition of the assumption at all weakens the force of
+the argument. If it were necessary the second time to assume some other
+axiom, the argument would no doubt be weakened, since it would be
+necessary to its validity that both axioms should be true, and it might
+happen that one was true and not the other: making two chances of error
+instead of one. But since it is the _same_ axiom, if it is true once it
+is true every time; and if the argument, being of a hundred links,
+assumed the axiom a hundred times, these hundred assumptions would make
+but one chance of error among them all. It is satisfactory that we are
+not obliged to suppose the deductions of pure mathematics to be among
+the most uncertain of argumentative processes, which on Mr. Spencer's
+theory they could hardly fail to be, since they are the longest. But the
+number of steps in an argument does not subtract from its reliableness,
+if no new _premises_, of an uncertain character, are taken up by the
+way.
+
+To speak next of the premises. Our assurance of their truth, whether
+they be generalities or individual facts, is grounded, in Mr. Spencer's
+opinion, on the inconceivableness of their being false. It is necessary
+to advert to a double meaning of the word inconceivable, which Mr.
+Spencer is aware of, and would sincerely disclaim founding an argument
+upon, but from which his case derives no little advantage
+notwithstanding. By inconceivableness is sometimes meant, inability to
+form or get rid of an _idea_; sometimes, inability to form or get rid of
+a _belief_. The former meaning is the most conformable to the analogy of
+language; for a conception always means an idea, and never a belief.
+The wrong meaning of "inconceivable" is, however, fully as frequent in
+philosophical discussion as the right meaning, and the intuitive school
+of metaphysicians could not well do without either. To illustrate the
+difference, we will take two contrasted examples. The early physical
+speculators considered antipodes incredible, because inconceivable. But
+antipodes were not inconceivable in the primitive sense of the word. An
+idea of them could be formed without difficulty: they could be
+completely pictured to the mental eye. What was difficult, and as it
+then seemed, impossible, was to apprehend them as believable. The idea
+could be put together, of men sticking on by their feet to the under
+side of the earth; but the belief _would_ follow, that they must fall
+off. Antipodes were not unimaginable, but they were unbelievable.
+
+On the other hand, when I endeavour to conceive an end to extension, the
+two ideas refuse to come together. When I attempt to form a conception
+of the last point of space, I cannot help figuring to myself a vast
+space beyond that last point. The combination is, under the conditions
+of our experience, unimaginable. This double meaning of inconceivable it
+is very important to bear in mind, for the argument from
+inconceivableness almost always turns on the alternate substitution of
+each of those meanings for the other.
+
+In which of these two senses does Mr. Spencer employ the term, when he
+makes it a test of the truth of a proposition that its negation is
+inconceivable? Until Mr. Spencer expressly stated the contrary, I
+inferred from the course of his argument, that he meant unbelievable. He
+has, however, in a paper published in the fifth number of the
+_Fortnightly Review_, disclaimed this meaning, and declared that by an
+inconceivable proposition he means, now and always, "one of which the
+terms cannot, by any effort, be brought before consciousness in that
+relation which the proposition asserts between them--a proposition of
+which the subject and predicate offer an insurmountable resistance to
+union in thought." We now, therefore, know positively that Mr. Spencer
+always endeavours to use the word inconceivable in this, its proper,
+sense: but it may yet be questioned whether his endeavour is always
+successful; whether the other, and popular use of the word does not
+sometimes creep in with its associations, and prevent him from
+maintaining a clear separation between the two. When, for example, he
+says, that when I feel cold, I cannot conceive that I am not feeling
+cold, this expression cannot be translated into, "I cannot conceive
+myself not feeling cold," for it is evident that I can: the word
+conceive, therefore, is here used to express the recognition of a matter
+of fact--the perception of truth or falsehood; which I apprehend to be
+exactly the meaning of an act of belief, as distinguished from simple
+conception. Again, Mr. Spencer calls the attempt to conceive something
+which is inconceivable, "an abortive effort to cause the non-existence"
+not of a conception or mental representation, but of a belief. There is
+need, therefore, to revise a considerable part of Mr. Spencer's
+language, if it is to be kept always consistent with his definition of
+inconceivability. But in truth the point is of little importance; since
+inconceivability, in Mr. Spencer's theory, is only a test of truth,
+inasmuch as it is a test of believability. The inconceivableness of a
+supposition is the extreme case of its unbelievability. This is the very
+foundation of Mr. Spencer's doctrine. The invariability of the belief is
+with him the real guarantee. The attempt to conceive the negative, is
+made in order to test the inevitableness of the belief. It should be
+called, an attempt to _believe_ the negative. When Mr. Spencer says that
+while looking at the sun a man cannot conceive that he is looking into
+darkness, he should have said that a man cannot _believe_ that he is
+doing so. For it is surely possible, in broad daylight, to _imagine_
+oneself looking into darkness.[41] As Mr. Spencer himself says, speaking
+of the belief of our own existence: "That he _might_ not exist, he can
+conceive well enough; but that he _does_ not exist, he finds it
+impossible to conceive," _i.e._ to believe. So that the statement
+resolves itself into this: That I exist, and that I have sensations, I
+believe, because I cannot believe otherwise. And in this case every one
+will admit that the necessity is real. Any one's present sensations, or
+other states of subjective consciousness, that one person inevitably
+believes. They are facts known _per se_: it is impossible to ascend
+beyond them. Their negative is really unbelievable, and therefore there
+is never any question about believing it. Mr. Spencer's theory is not
+needed for these truths.
+
+But according to Mr. Spencer there are other beliefs, relating to other
+things than our own subjective feelings, for which we have the same
+guarantee--which are, in a similar manner, invariable and necessary.
+With regard to these other beliefs, they cannot be necessary, since they
+do not always exist. There have been, and are, many persons who do not
+believe the reality of an external world, still less the reality of
+extension and figure as the forms of that external world; who do not
+believe that space and time have an existence independent of the
+mind--nor any other of Mr. Spencer's objective intuitions. The negations
+of these alleged invariable beliefs are not unbelievable, for they are
+believed. It may be maintained, without obvious error, that we cannot
+_imagine_ tangible objects as mere states of our own and other people's
+consciousness; that the perception of them irresistibly suggests to us
+the _idea_ of something external to ourselves: and I am not in a
+condition to say that this is not the fact (though I do not think any
+one is entitled to affirm it of any person besides himself). But many
+thinkers have believed, whether they could conceive it or not, that what
+we represent to ourselves as material objects, are mere modifications of
+consciousness; complex feelings of touch and of muscular action. Mr.
+Spencer may think the inference correct from the unimaginable to the
+unbelievable, because he holds that belief itself is but the persistence
+of an idea, and that what we can succeed in imagining, we cannot at the
+moment help apprehending as believable. But of what consequence is it
+what we apprehend at the moment, if the moment is in contradiction to
+the permanent state of our mind? A person who has been frightened when
+an infant by stories of ghosts, though he disbelieves them in after
+years (and perhaps disbelieved them at first), may be unable all his
+life to be in a dark place, in circumstances stimulating to the
+imagination, without mental discomposure. The idea of ghosts, with all
+its attendant terrors, is irresistibly called up in his mind by the
+outward circumstances. Mr. Spencer may say, that while he is under the
+influence of this terror he does not disbelieve in ghosts, but has a
+temporary and uncontrollable belief in them. Be it so; but allowing it
+to be so, which would it be truest to say of this man on the whole--that
+he believes in ghosts, or that he does not believe in them? Assuredly
+that he does not believe in them. The case is similar with those who
+disbelieve a material world. Though they cannot get rid of the idea;
+though while looking at a solid object they cannot help having the
+conception, and therefore, according to Mr. Spencer's metaphysics, the
+momentary belief, of its externality; even at that moment they would
+sincerely deny holding that belief: and it would be incorrect to call
+them other than disbelievers of the doctrine. The belief therefore is
+not invariable; and the test of inconceivableness fails in the only
+cases to which there could ever be any occasion to apply it.
+
+That a thing may be perfectly believable, and yet may not have become
+conceivable, and that we may habitually believe one side of an
+alternative, and conceive only in the other, is familiarly exemplified
+in the state of mind of educated persons respecting sunrise and sunset.
+All educated persons either know by investigation, or believe on the
+authority of science, that it is the earth and not the sun which moves:
+but there are probably few who habitually _conceive_ the phenomenon
+otherwise than as the ascent or descent of the sun. Assuredly no one can
+do so without a prolonged trial; and it is probably not easier now than
+in the first generation after Copernicus. Mr. Spencer does not say, "In
+looking at sunrise it is impossible not to conceive that it is the sun
+which moves, therefore this is what everybody believes, and we have all
+the evidence for it that we can have for any truth." Yet this would be
+an exact parallel to his doctrine about the belief in matter.
+
+The existence of matter, and other Noumena, as distinguished from the
+phenomenal world, remains a question of argument, as it was before; and
+the very general, but neither necessary nor universal, belief in them,
+stands as a psychological phenomenon to be explained, either on the
+hypothesis of its truth, or on some other. The belief is not a
+conclusive proof of its own truth, unless there are no such things as
+_idola tribus_; but, being a fact, it calls on antagonists to show, from
+what except the real existence of the thing believed, so general and
+apparently spontaneous a belief can have originated. And its opponents
+have never hesitated to accept this challenge.[42] The amount of their
+success in meeting it will probably determine the ultimate verdict of
+philosophers on the question.
+
+
+Sec. 4. Sir William Hamilton holds as I do, that inconceivability is no
+criterion of impossibility. "There is no ground for inferring a certain
+fact to be impossible, merely from our inability to conceive its
+possibility." "Things there are which _may_, nay _must_, be true, of
+which the understanding is wholly unable to construe to itself the
+possibility."[43] Sir William Hamilton is however a firm believer in the
+_a priori_ character of many axioms, and of the sciences deduced from
+them; and is so far from considering those axioms to rest on the
+evidence of experience, that he declares certain of them to be true even
+of Noumena--of the Unconditioned--of which it is one of the principal
+aims of his philosophy to prove that the nature of our faculties debars
+us from having any knowledge. The axioms to which he attributes this
+exceptional emancipation from the limits which confine all our other
+possibilities of knowledge; the chinks through which, as he represents,
+one ray of light finds its way to us from behind the curtain which veils
+from us the mysterious world of Things in themselves,--are the two
+principles, which he terms, after the schoolmen, the Principle of
+Contradiction, and the Principle of Excluded Middle: the first, that two
+contradictory propositions cannot both be true; the second, that they
+cannot both be false. Armed with these logical weapons, we may boldly
+face Things in themselves, and tender to them the double alternative,
+sure that they must absolutely elect one or the other side, though we
+may be for ever precluded from discovering which. To take his favourite
+example, we cannot conceive the infinite divisibility of matter, and we
+cannot conceive a minimum, or end to divisibility: yet one or the other
+must be true.
+
+As I have hitherto said nothing of the two axioms in question, those of
+Contradiction and of Excluded Middle, it is not unseasonable to consider
+them here. The former asserts that an affirmative proposition and the
+corresponding negative proposition cannot both be true; which has
+generally been held to be intuitively evident. Sir William Hamilton and
+the Germans consider it to be the statement in words of a form or law of
+our thinking faculty. Other philosophers, not less deserving of
+consideration, deem it to be an identical proposition; an assertion
+involved in the meaning of terms; a mode of defining Negation, and the
+word Not.
+
+I am able to go one step with these last. An affirmative assertion and
+its negative are not two independent assertions, connected with each
+other only as mutually incompatible. That if the negative be true, the
+affirmative must be false, really is a mere identical proposition; for
+the negative proposition asserts nothing but the falsity of the
+affirmative, and has no other sense or meaning whatever. The Principium
+Contradictionis should therefore put off the ambitious phraseology which
+gives it the air of a fundamental antithesis pervading nature, and
+should be enunciated in the simpler form, that the same proposition
+cannot at the same time be false and true. But I can go no farther with
+the Nominalists; for I cannot look upon this last as a merely verbal
+proposition. I consider it to be, like other axioms, one of our first
+and most familiar generalizations from experience. The original
+foundation of it I take to be, that Belief and Disbelief are two
+different mental states, excluding one another. This we know by the
+simplest observation of our own minds. And if we carry our observation
+outwards, we also find that light and darkness, sound and silence,
+motion and quiescence, equality and inequality, preceding and following,
+succession and simultaneousness, any positive phenomenon whatever and
+its negative, are distinct phenomena, pointedly contrasted, and the one
+always absent where the other is present. I consider the maxim in
+question to be a generalization from all these facts.
+
+In like manner as the Principle of Contradiction (that one of two
+contradictories must be false) means that an assertion cannot be _both_
+true and false, so the Principle of Excluded Middle, or that one of two
+contradictories must be true, means that an assertion must be _either_
+true or false: either the affirmative is true, or otherwise the negative
+is true, which means that the affirmative is false. I cannot help
+thinking this principle a surprising specimen of a so-called necessity
+of Thought, since it is not even true, unless with a large
+qualification. A proposition must be either true or false, _provided_
+that the predicate be one which can in any intelligible sense be
+attributed to the subject; (and as this is always assumed to be the case
+in treatises on logic, the axiom is always laid down there as of
+absolute truth). "Abracadabra is a second intention" is neither true nor
+false. Between the true and the false there is a third possibility, the
+Unmeaning: and this alternative is fatal to Sir William Hamilton's
+extension of the maxim to Noumena. That Matter must either have a
+minimum of divisibility or be infinitely divisible, is more than we can
+ever know. For in the first place, Matter, in any other than the
+phenomenal sense of the term, may not exist: and it will scarcely be
+said that a non-entity must be either infinitely or finitely
+divisible.[44] In the second place, though matter, considered as the
+occult cause of our sensations, do really exist, yet what we call
+divisibility may be an attribute only of our sensations of sight and
+touch, and not of their uncognizable cause. Divisibility may not be
+predicable at all, in any intelligible sense, of Things in themselves,
+nor therefore of Matter in itself; and the assumed necessity of being
+either infinitely or finitely divisible, may be an inapplicable
+alternative.
+
+On this question I am happy to have the full concurrence of Mr. Herbert
+Spencer, from whose paper in the _Fortnightly Review_ I extract the
+following passage. The germ of an idea identical with that of Mr.
+Spencer may be found in the present chapter, about a page back, but in
+Mr. Spencer it is not an undeveloped thought, but a philosophical
+theory.
+
+"When remembering a certain thing as in a certain place, the place and
+the thing are mentally represented together; while to think of the
+non-existence of the thing in that place, implies a consciousness in
+which the place is represented, but not the thing. Similarly, if instead
+of thinking of an object as colourless, we think of its having colour,
+the change consists in the addition to the concept of an element that
+was before absent from it--the object cannot be thought of first as red
+and then as not red, without one component of the thought being totally
+expelled from the mind by another. The law of the Excluded Middle, then,
+is simply a generalization of the universal experience that some mental
+states are directly destructive of other states. It formulates a certain
+absolutely constant law, that the appearance of any positive mode of
+consciousness cannot occur without excluding a correlative negative
+mode; and that the negative mode cannot occur without excluding the
+correlative positive mode: the antithesis of positive and negative
+being, indeed, merely an expression of this experience. Hence it follows
+that if consciousness is not in one of the two modes it must be in the
+other."[45]
+
+I must here close this supplementary chapter, and with it the Second
+Book. The theory of Induction, in the most comprehensive sense of the
+term, will form the subject of the Third.
+
+FOOTNOTES:
+
+[1] As Sir William Hamilton has pointed out, "Some A is not B" may also
+be converted in the following form: "No B is _some_ A." Some men are not
+negroes; therefore, No negroes are _some_ men (_e.g._ Europeans).
+
+[2]
+  All A is B } contraries.
+  No  A is B }
+
+  Some A is B     } subcontraries.
+  Some A is not B }
+
+  All  A is B     } contradictories.
+  Some A is not B }
+
+  No   A is B } also contradictories.
+  Some A is B }
+
+  All  A is B } and  No   A is B     } respectively subalternate.
+  Some A is B }      Some A is not B }
+
+[3] His conclusions are, "The first figure is suited to the discovery or
+proof of the properties of a thing; the second to the discovery or proof
+of the distinctions between things; the third to the discovery or proof
+of instances and exceptions; the fourth to the discovery, or exclusion,
+of the different species of a genus." The reference of syllogisms in the
+last three figures to the _dictum de omni et nullo_ is, in Lambert's
+opinion, strained and unnatural: to each of the three belongs, according
+to him, a separate axiom, co-ordinate and of equal authority with that
+_dictum_, and to which he gives the names of _dictum de diverso_ for the
+second figure, _dictum de exemplo_ for the third, and _dictum de
+reciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. Sec.
+229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74)
+takes a similar view of the subject.
+
+[4] Since this chapter was written, two treatises have appeared (or
+rather a treatise and a fragment of a treatise), which aim at a further
+improvement in the theory of the forms of ratiocination: Mr. De Morgan's
+"Formal Logic; or, the Calculus of Inference, Necessary and Probable;"
+and the "New Analytic of Logical Forms," attached as an Appendix to Sir
+William Hamilton's _Discussions on Philosophy_, and at greater length,
+to his posthumous _Lectures on Logic_.
+
+In Mr. De Morgan's volume--abounding, in its more popular parts, with
+valuable observations felicitously expressed--the principal feature of
+originality is an attempt to bring within strict technical rules the
+cases in which a conclusion can be drawn from premises of a form usually
+classed as particular. Mr. De Morgan observes, very justly, that from
+the premises Most Bs are Cs, most Bs are As, it may be concluded with
+certainty that some As are Cs, since two portions of the class B, each
+of them comprising more than half, must necessarily in part consist of
+the same individuals. Following out this line of thought, it is equally
+evident that if we knew exactly what proportion the "most" in each of
+the premises bear to the entire class B, we could increase in a
+corresponding degree the definiteness of the conclusion. Thus if 60 per
+cent of B are included in C, and 70 per cent in A, 30 per cent at least
+must be common to both; in other words, the number of As which are Cs,
+and of Cs which are As, must be at least equal to 30 per cent of the
+class B. Proceeding on this conception of "numerically definite
+propositions," and extending it to such forms as these:--"45 Xs (or
+more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
+them to be found among 70 Ys," and examining what inferences admit of
+being drawn from the various combinations which may be made of premises
+of this description, Mr. De Morgan establishes universal formulae for
+such inferences; creating for that purpose not only a new technical
+language, but a formidable array of symbols analogous to those of
+algebra.
+
+Since it is undeniable that inferences, in the cases examined by Mr. De
+Morgan, can legitimately be drawn, and that the ordinary theory takes no
+account of them, I will not say that it was not worth while to show in
+detail how these also could be reduced to formulae as rigorous as those
+of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
+more than once, as a school exercise); but I question if its results are
+worth studying and mastering for any practical purpose. The practical
+use of technical forms of reasoning is to bar out fallacies: but the
+fallacies which require to be guarded against in ratiocination properly
+so called, arise from the incautious use of the common forms of
+language; and the logician must track the fallacy into that territory,
+instead of waiting for it on a territory of his own. While he remains
+among propositions which have acquired the numerical precision of the
+Calculus of Probabilities, the enemy is left in possession of the only
+ground on which he can be formidable. And since the propositions (short
+of universal) on which a thinker has to depend, either for purposes of
+speculation or of practice, do not, except in a few peculiar cases,
+admit of any numerical precision; common reasoning cannot be translated
+into Mr. De Morgan's forms, which therefore cannot serve any purpose as
+a test of it.
+
+Sir William Hamilton's theory of the "quantification of the predicate"
+(concerning the originality of which in his case there can be no doubt,
+however Mr. De Morgan may have also, and independently, originated an
+equivalent doctrine) may be briefly described as follows:--
+
+"Logically" (I quote his own words) "we ought to take into account the
+quantity, always understood in thought, but usually, for manifest
+reasons, elided in its expression, not only of the subject, but also of
+the predicate of a judgment." All A is B, is equivalent to all A is
+_some_ B. No A is B, to No A is _any_ B. Some A is B, is tantamount to
+some A is _some_ B. Some A is not B, to Some A is _not any_ B. As in
+these forms of assertion the predicate is exactly coextensive with the
+subject, they all admit of simple conversion; and by this we obtain two
+additional forms--Some B is _all_ A, and No B is _some_ A. We may also
+make the assertion All A is all B, which will be true if the classes A
+and B are exactly coextensive. The last three forms, though conveying
+real assertions, have no place in the ordinary classification of
+Propositions. All propositions, then, being supposed to be translated
+into this language, and written each in that one of the preceding forms
+which answers to its signification, there emerges a new set of
+syllogistic rules, materially different from the common ones. A general
+view of the points of difference may be given in the words of Sir W.
+Hamilton (_Discussions_, 2nd ed. p. 651):--
+
+"The revocation of the two terms of a Proposition to their true
+relation; a proposition being always an _equation_ of its subject and
+its predicate.
+
+"The consequent reduction of the Conversion of Propositions from three
+species to one--that of Simple Conversion.
+
+"The reduction of all the _General Laws_ of Categorical Syllogisms to a
+single Canon.
+
+"The evolution from that one canon of all the Species and varieties of
+Syllogisms.
+
+"The abrogation of all the _Special Laws_ of Syllogism.
+
+"A demonstration of the exclusive possibility of Three syllogistic
+Figures; and (on new grounds) the scientific and final abolition of the
+Fourth.
+
+"A manifestation that Figure is an unessential variation in syllogistic
+form; and the consequent absurdity of Reducing the syllogisms of the
+other figures to the first.
+
+"An enouncement of _one Organic Principle_ for each Figure.
+
+"A determination of the true number of the Legitimate Moods; with
+
+"Their amplification in number (thirty-six);
+
+"Their numerical equality under all the figures; and
+
+"Their relative equivalence, or virtual identity, throughout every
+schematic difference.
+
+"That, in the second and third figures, the extremes holding both the
+same relation to the middle term, there is not, as in the first, an
+opposition and subordination between a term major and a term minor,
+mutually containing and contained, in the counter wholes of Extension
+and Comprehension.
+
+"Consequently, in the second and third figures, there is no determinate
+major and minor premise, and there are two indifferent conclusions:
+whereas in the first the premises are determinate, and there is a single
+proximate conclusion."
+
+This doctrine, like that of Mr. De Morgan previously noticed, is a real
+addition to the syllogistic theory; and has moreover this advantage over
+Mr. De Morgan's "numerically definite Syllogism," that the forms it
+supplies are really available as a test of the correctness of
+ratiocination; since propositions in the common form may always have
+their predicates quantified, and so be made amenable to Sir W.
+Hamilton's rules. Considered however as a contribution to the _Science_
+of Logic, that is, to the analysis of the mental processes concerned in
+reasoning, the new doctrine appears to me, I confess, not merely
+superfluous, but erroneous; since the form in which it clothes
+propositions does not, like the ordinary form, express what is in the
+mind of the speaker when he enunciates the proposition. I cannot think
+Sir William Hamilton right in maintaining that the quantity of the
+predicate is "always understood in thought." It is implied, but is not
+present to the mind of the person who asserts the proposition. The
+quantification of the predicate, instead of being a means of bringing
+out more clearly the meaning of the proposition, actually leads the mind
+out of the proposition, into another order of ideas. For when we say,
+All men are mortal, we simply mean to affirm the attribute mortality of
+all men; without thinking at all of the _class_ mortal in the concrete,
+or troubling ourselves about whether it contains any other beings or
+not. It is only for some artificial purpose that we ever look at the
+proposition in the aspect in which the predicate also is thought of as a
+class-name, either including the subject only, or the subject and
+something more. (See above, p. 104.)
+
+For a fuller discussion of this subject, see the twenty-second chapter
+of a work already referred to, "An Examination of Sir William Hamilton's
+Philosophy."
+
+[5] Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though
+his theory of the syllogism coincides with all that is essential of
+mine, thinks it a logical fallacy to present the two axioms in the text,
+as the regulating principles of syllogism. He charges me with falling
+into the error pointed out by Archbishop Whately and myself, of
+confounding exact likeness with literal identity; and maintains, that we
+ought not to say that Socrates possesses _the same_ attributes which are
+connoted by the word Man, but only that he possesses attributes _exactly
+like_ them: according to which phraseology, Socrates, and the attribute
+mortality, are not two things coexisting with the same thing, as the
+axiom asserts, but two things coexisting with two different things.
+
+The question between Mr. Spencer and me is merely one of language; for
+neither of us (if I understand Mr. Spencer's opinions rightly) believes
+an attribute to be a real thing, possessed of objective existence; we
+believe it to be a particular mode of naming our sensations, or our
+expectations of sensation, when looked at in their relation to an
+external object which excites them. The question raised by Mr. Spencer
+does not, therefore, concern the properties of any really existing
+thing, but the comparative appropriateness, for philosophical purposes,
+of two different modes of using a name. Considered in this point of
+view, the phraseology I have employed, which is that commonly used by
+philosophers, seems to me to be the best. Mr. Spencer is of opinion that
+because Socrates and Alcibiades are not the same man, the attribute
+which constitutes them men should not be called the same attribute; that
+because the humanity of one man and that of another express themselves
+to our senses not by the same individual sensations but by sensations
+exactly alike, humanity ought to be regarded as a different attribute in
+every different man. But on this showing, the humanity even of any one
+man should be considered as different attributes now and half-an-hour
+hence; for the sensations by which it will then manifest itself to my
+organs will not be a continuation of my present sensations, but a
+repetition of them; fresh sensations, not identical with, but only
+exactly like the present. If every general conception, instead of being
+"the One in the Many," were considered to be as many different
+conceptions as there are things to which it is applicable, there would
+be no such thing as general language. A name would have no general
+meaning if _man_ connoted one thing when predicated of John, and
+another, though closely resembling, thing when predicated of William.
+Accordingly a recent pamphlet asserts the impossibility of general
+knowledge on this precise ground.
+
+The meaning of any general name is some outward or inward phenomenon,
+consisting, in the last resort, of feelings; and these feelings, if
+their continuity is for an instant broken, are no longer the same
+feelings, in the sense of individual identity. What, then, is the common
+something which gives a meaning to the general name? Mr. Spencer can
+only say, it is the similarity of the feelings; and I rejoin, the
+attribute is precisely that similarity. The names of attributes are in
+their ultimate analysis names for the resemblances of our sensations (or
+other feelings). Every general name, whether abstract or concrete,
+denotes or connotes one or more of those resemblances. It will not,
+probably, be denied, that if a hundred sensations are undistinguishably
+alike, their resemblance ought to be spoken of as one resemblance, and
+not a hundred resemblances which merely _resemble_ one another. The
+things compared are many, but the something common to all of them must
+be conceived as one, just as the name is conceived as one, though
+corresponding to numerically different sensations of sound each time it
+is pronounced. The general term _man_ does not connote the sensations
+derived once from one man, which, once gone, can no more occur again
+than the same flash of lightning. It connotes the general type of the
+sensations derived always from all men, and the power (always thought of
+as one) of producing sensations of that type. And the axiom might be
+thus worded: Two _types of sensation_ each of which coexists with a
+third type, coexist with another; or Two _powers_ each of which coexists
+with a third power coexist with one another.
+
+Mr. Spencer has misunderstood me in another particular. He supposes that
+the coexistence spoken of in the axiom, of two things with the same
+third thing, means simultaneousness in time. The coexistence meant is
+that of being jointly attributes of the same subject. The attribute of
+being born without teeth, and the attribute of having thirty-two teeth
+in mature age, are in this sense coexistent, both being attributes of
+man, though _ex vi termini_ never of the same man at the same time.
+
+[6] Supra, p. 128.
+
+[7] _Logic_, p. 239 (9th ed.).
+
+[8] It is hardly necessary to say, that I am not contending for any such
+absurdity as that we _actually_ "ought to have known" and considered the
+case of every individual man, past, present, and future, before
+affirming that all men are mortal: although this interpretation has
+been, strangely enough, put upon the preceding observations. There is no
+difference between me and Archbishop Whately, or any other defender of
+the syllogism, on the practical part of the matter; I am only pointing
+out an inconsistency in the logical theory of it, as conceived by almost
+all writers. I do not say that a person who affirmed, before the Duke of
+Wellington was born, that all men are mortal, _knew_ that the Duke of
+Wellington was mortal; but I do say that he _asserted_ it; and I ask for
+an explanation of the apparent logical fallacy, of adducing in proof of
+the Duke of Wellington's mortality, a general statement which
+presupposes it. Finding no sufficient resolution of this difficulty in
+any of the writers on Logic, I have attempted to supply one.
+
+[9] The language of ratiocination would, I think, be brought into closer
+agreement with the real nature of the process, if the general
+propositions employed in reasoning, instead of being in the form All men
+are mortal, or Every man is mortal, were expressed in the form Any man
+is mortal. This mode of expression, exhibiting as the type of all
+reasoning from experience "The men A, B, C, &c. are so and so, therefore
+_any_ man is so and so," would much better manifest the true idea--that
+inductive reasoning is always, at bottom, inference from particulars to
+particulars, and that the whole function of general propositions in
+reasoning, is to vouch for the legitimacy of such inferences.
+
+[10] Review of Quetelet on Probabilities, _Essays_, p. 367.
+
+[11] _Philosophy of Discovery_, p. 289.
+
+[12] _Theory of Reasoning_, ch. iv. to which I may refer for an able
+statement and enforcement of the grounds of the doctrine.
+
+[13] It is very probable that the doctrine is not new, and that it was,
+as Sir John Herschel thinks, substantially anticipated by Berkeley. But
+I certainly am not aware that it is (as has been affirmed by one of my
+ablest and most candid critics) "among the standing marks of what is
+called the empirical philosophy."
+
+[14] _Logic_, book iv. ch. i. sect. 1.
+
+[15] See the important chapter on Belief, in Professor Bain's great
+treatise, _The Emotions and the Will_, pp. 581-4.
+
+[16] A writer in the "British Quarterly Review" (August 1846), in a
+review of this treatise, endeavours to show that there is no _petitio
+principii_ in the syllogism, by denying that the proposition, All men
+are mortal, asserts or assumes that Socrates is mortal. In support of
+this denial, he argues that we may, and in fact do, admit the general
+proposition that all men are mortal, without having particularly
+examined the case of Socrates, and even without knowing whether the
+individual so named is a man or something else. But this of course was
+never denied. That we can and do draw conclusions concerning cases
+specifically unknown to us, is the datum from which all who discuss this
+subject must set out. The question is, in what terms the evidence, or
+ground, on which we draw these conclusions, may best be
+designated--whether it is most correct to say, that the unknown case is
+proved by known cases, or that it is proved by a general proposition
+including both sets of cases, the unknown and the known? I contend for
+the former mode of expression. I hold it an abuse of language to say,
+that the proof that Socrates is mortal, is that all men are mortal. Turn
+it in what way we will, this seems to me to be asserting that a thing is
+the proof of itself. Whoever pronounces the words, All men are mortal,
+has affirmed that Socrates is mortal, though he may never have heard of
+Socrates; for since Socrates, whether known to be so or not, really is a
+man, he is included in the words, All men, and in every assertion of
+which they are the subject. If the reviewer does not see that there is a
+difficulty here, I can only advise him to reconsider the subject until
+he does: after which he will be a better judge of the success or failure
+of an attempt to remove the difficulty. That he had reflected very
+little on the point when he wrote his remarks, is shown by his oversight
+respecting the _dictum de omni et nullo_. He acknowledges that this
+maxim as commonly expressed,--"Whatever is true of a class, is true of
+everything included in the class," is a mere identical proposition,
+since the class _is_ nothing but the things included in it. But he
+thinks this defect would be cured by wording the maxim thus,--"Whatever
+is true of a class, is true of everything which _can be shown_ to be a
+member of the class:" as if a thing could "be shown" to be a member of
+the class without being one. If a class means the sum of all the things
+included in the class, the things which can "be shown" to be included in
+it are part of the sum, and the _dictum_ is as much an identical
+proposition with respect to them as to the rest. One would almost
+imagine that, in the reviewer's opinion, things are not members of a
+class until they are called up publicly to take their place in it--that
+so long, in fact, as Socrates is not known to be a man, he _is not_ a
+man, and any assertion which can be made concerning men does not at all
+regard him, nor is affected as to its truth or falsity by anything in
+which he is concerned.
+
+The difference between the reviewer's theory and mine may be thus
+stated. Both admit that when we say, All men are mortal, we make an
+assertion reaching beyond the sphere of our knowledge of individual
+cases; and that when a new individual, Socrates, is brought within the
+field of our knowledge by means of the minor premise, we learn that we
+have already made an assertion respecting Socrates without knowing it:
+our own general formula being, to that extent, for the first time
+_interpreted_ to us. But according to the reviewer's theory, the smaller
+assertion is proved by the larger: while I contend, that both assertions
+are proved together, by the same evidence, namely, the grounds of
+experience on which the general assertion was made, and by which it must
+be justified.
+
+The reviewer says, that if the major premise included the conclusion,
+"we should be able to affirm the conclusion without the intervention of
+the minor premise; but every one sees that that is impossible." A
+similar argument is urged by Mr. De Morgan (_Formal Logic_, p. 259):
+"The whole objection tacitly assumes the superfluity of the minor; that
+is, tacitly assumes we know Socrates[46] to be a man as soon as we know
+him to be Socrates." The objection would be well grounded if the
+assertion that the major premise includes the conclusion, meant that it
+individually specifies all it includes. As however the only indication
+it gives is a description by marks, we have still to compare any new
+individual with the marks; and to show that this comparison has been
+made, is the office of the minor. But since, by supposition, the new
+individual has the marks, whether we have ascertained him to have them
+or not; if we have affirmed the major premise, we have asserted him to
+be mortal. Now my position is that this assertion cannot be a necessary
+part of the argument. It cannot be a necessary condition of reasoning
+that we should begin by making an assertion, which is afterwards to be
+employed in proving a part of itself. I can conceive only one way out of
+this difficulty, viz. that what really forms the proof is _the other_
+part of the assertion; the portion of it, the truth of which has been
+ascertained previously: and that the unproved part is bound up in one
+formula with the proved part in mere anticipation, and as a memorandum
+of the nature of the conclusions which we are prepared to prove.
+
+With respect to the minor premise in its formal shape, the minor as it
+stands in the syllogism, predicating of Socrates a definite class name,
+I readily admit that it is no more a necessary part of reasoning than
+the major. When there is a major, doing its work by means of a class
+name, minors are needed to interpret it: but reasoning can be carried on
+without either the one or the other. They are not the conditions of
+reasoning, but a precaution against erroneous reasoning. The only minor
+premise necessary to reasoning in the example under consideration, is,
+Socrates is _like_ A, B, C, and the other individuals who are known to
+have died. And this is the only universal type of that step in the
+reasoning process which is represented by the minor. Experience,
+however, of the uncertainty of this loose mode of inference, teaches the
+expediency of determining beforehand what _kind_ of likeness to the
+cases observed, is necessary to bring an unobserved case within the same
+predicate; and the answer to this question is the major. Thus the
+syllogistic major and the syllogistic minor start into existence
+together, and are called forth by the same exigency. When we conclude
+from personal experience without referring to any record--to any general
+theorems, either written, or traditional, or mentally registered by
+ourselves as conclusions of our own drawing, we do not use, in our
+thoughts, either a major or a minor, such as the syllogism puts into
+words. When, however, we revise this rough inference from particulars to
+particulars, and substitute a careful one, the revision consists in
+selecting two syllogistic premises. But this neither alters nor adds to
+the evidence we had before; it only puts us in a better position for
+judging whether our inference from particulars to particulars is well
+grounded.
+
+[17] Infra, book iii. ch. ii.
+
+[18] Infra, book iii. ch. iv. Sec. 3, and elsewhere.
+
+[19] _Mechanical Euclid_, pp. 149 _et seqq._
+
+[20] We might, it is true, insert this property into the definition of
+parallel lines, framing the definition so as to require, both that when
+produced indefinitely they shall never meet, and also that any straight
+line which intersects one of them shall, if prolonged, meet the other.
+But by doing this we by no means get rid of the assumption; we are still
+obliged to take for granted the geometrical truth, that all straight
+lines in the same plane, which have the former of these properties, have
+also the latter. For if it were possible that they should not, that is,
+if any straight lines other than those which are parallel according to
+the definition, had the property of never meeting although indefinitely
+produced, the demonstrations of the subsequent portions of the theory of
+parallels could not be maintained.
+
+[21] Some persons find themselves prevented from believing that the
+axiom, Two straight lines cannot inclose a space, could ever become
+known to us through experience, by a difficulty which may be stated as
+follows. If the straight lines spoken of are those contemplated in the
+definition--lines absolutely without breadth and absolutely
+straight;--that such are incapable of inclosing a space is not proved by
+experience, for lines such as these do not present themselves in our
+experience. If, on the other hand, the lines meant are such straight
+lines as we do meet with in experience, lines straight enough for
+practical purposes, but in reality slightly zigzag, and with some,
+however trifling, breadth; as applied to these lines the axiom is not
+true, for two of them may, and sometimes do, inclose a small portion of
+space. In neither case, therefore, does experience prove the axiom.
+
+Those who employ this argument to show that geometrical axioms cannot be
+proved by induction, show themselves unfamiliar with a common and
+perfectly valid mode of inductive proof; proof by approximation. Though
+experience furnishes us with no lines so unimpeachably straight that two
+of them are incapable of inclosing the smallest space, it presents us
+with gradations of lines possessing less and less either of breadth or
+of flexure, of which series the straight line of the definition is the
+ideal limit. And observation shows that just as much, and as nearly, as
+the straight lines of experience approximate to having no breadth or
+flexure, so much and so nearly does the space-inclosing power of any two
+of them approach to zero. The inference that if they had no breadth or
+flexure at all, they would inclose no space at all, is a correct
+inductive inference from these facts, conformable to one of the four
+Inductive Methods hereinafter characterized, the Method of Concomitant
+Variations; of which the mathematical Doctrine of Limits presents the
+extreme case.
+
+[22] Whewell's _History of Scientific Ideas_, i. 140.
+
+[23] Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
+unreasonable to contend that we know by experience, that our idea of a
+line exactly resembles a real line. "It does not appear," he says, "how
+we can compare our ideas with the realities, since we know the realities
+only by our ideas." We know the realities (I conceive) by our senses.
+Dr. Whewell surely does not hold the "doctrine of perception by means of
+ideas," which Reid gave himself so much trouble to refute.
+
+If Dr. Whewell doubts whether we compare our ideas with the
+corresponding sensations, and assume that they resemble, let me ask on
+what evidence do we judge that a portrait of a person not present is
+like the original. Surely because it is like our idea, or mental image
+of the person, and because our idea is like the man himself.
+
+Dr. Whewell also says, that it does not appear why this resemblance of
+ideas to the sensations of which they are copies, should be spoken of as
+if it were a peculiarity of one class of ideas, those of space. My reply
+is, that I do not so speak of it. The peculiarity I contend for is only
+one of degree. All our ideas of sensation of course resemble the
+corresponding sensations, but they do so with very different degrees of
+exactness and of reliability. No one, I presume, can recal in
+imagination a colour or an odour with the same distinctness and accuracy
+with which almost every one can mentally reproduce an image of a
+straight line or a triangle. To the extent, however, of their
+capabilities of accuracy, our recollections of colours or of odours may
+serve as subjects of experimentation, as well as those of lines and
+spaces, and may yield conclusions which will be true of their external
+prototypes. A person in whom, either from natural gift or from
+cultivation, the impressions of colour were peculiarly vivid and
+distinct, if asked which of two blue flowers was of the darkest tinge,
+though he might never have compared the two, or even looked at them
+together, might be able to give a confident answer on the faith of his
+distinct recollection of the colours; that is, he might examine his
+mental pictures, and find there a property of the outward objects. But
+in hardly any case except that of simple geometrical forms, could this
+be done by mankind generally, with a degree of assurance equal to that
+which is given by a contemplation of the objects themselves. Persons
+differ most widely in the precision of their recollection, even of
+forms: one person, when he has looked any one in the face for half a
+minute, can draw an accurate likeness of him from memory; another may
+have seen him every day for six months, and hardly know whether his nose
+is long or short. But everybody has a perfectly distinct mental image of
+a straight line, a circle, or a rectangle. And every one concludes
+confidently from these mental images to the corresponding outward
+things. The truth is, that we may, and continually do, study nature in
+our recollections, when the objects themselves are absent; and in the
+case of geometrical forms we can perfectly, but in most other cases only
+imperfectly, trust our recollections.
+
+[24] _History of Scientific Ideas_, i. 65-67.
+
+[25] Ibid. 60.
+
+[26] _History of Scientific Ideas_, i. 58, 59.
+
+[27] "If all mankind had spoken one language, we cannot doubt that there
+would have been a powerful, perhaps a universal, school of philosophers,
+who would have believed in the inherent connexion between names and
+things, who would have taken the sound _man_ to be the mode of agitating
+the air which is essentially communicative of the ideas of reason,
+cookery, bipedality, &c."--De Morgan, _Formal Logic_, p. 246.
+
+[28] It would be difficult to name a man more remarkable at once for the
+greatness and the wide range of his mental accomplishments, than
+Leibnitz. Yet this eminent man gave as a reason for rejecting Newton's
+scheme of the solar system, that God _could not_ make a body revolve
+round a distant centre, unless either by some impelling mechanism, or by
+miracle:--"Tout ce qui n'est pas explicable" says he in a letter to the
+Abbe Conti, "par la nature des creatures, est miraculeux. Il ne suffit
+pas de dire: Dieu a fait une telle loi de nature; donc la chose est
+naturelle. Il faut que la loi soit executable par les natures des
+creatures. Si Dieu donnait cette loi, par exemple, a un corps libre, de
+tourner a l'entour d'un certain centre, _il faudrait ou qu'il y joignit
+d'autres corps qui par leur impulsion l'obligeassent de rester toujours
+dans son orbite circulaire, ou qu'il mit un ange a ses trousses, ou
+enfin il faudrait qu'il y concourut extraordinairement_; car
+naturellement il s'ecartera par la tangente."--_Works of Leibnitz_, ed.
+Dutens, iii. 446.
+
+[29] _Novum Organum Renovatum_, pp. 32, 33.
+
+[30] _History of Scientific Ideas_, i. 264.
+
+[31] _Hist. Sc. Id._, i. 263.
+
+[32] Ibid. 240.
+
+[33] _Hist. Sc. Id._, ii. 25, 26.
+
+[34] _Phil. of Disc._, p. 339.
+
+[35] _Phil. of Disc._, p. 338.
+
+[36] Ib. p. 463.
+
+[37] _Phil. of Disc._, pp. 472, 473.
+
+[38] The _Quarterly Review_ for June 1841, contained an article of great
+ability on Dr. Whewell's two great works (since acknowledged and
+reprinted in Sir John Herschel's Essays) which maintains, on the subject
+of axioms, the doctrine advanced in the text, that they are
+generalizations from experience, and supports that opinion by a line of
+argument strikingly coinciding with mine. When I state that the whole of
+the present chapter (except the last four pages, added in the fifth
+edition) was written before I had seen the article, (the greater part,
+indeed, before it was published,) it is not my object to occupy the
+reader's attention with a matter so unimportant as the degree of
+originality which may or may not belong to any portion of my own
+speculations, but to obtain for an opinion which is opposed to reigning
+doctrines, the recommendation derived from a striking concurrence of
+sentiment between two inquirers entirely independent of one another. I
+embrace the opportunity of citing from a writer of the extensive
+acquirements in physical and metaphysical knowledge and the capacity of
+systematic thought which the article evinces, passages so remarkably in
+unison with my own views as the following:--
+
+"The truths of geometry are summed up and embodied in its definitions
+and axioms.... Let us turn to the axioms, and what do we find? A string
+of propositions concerning magnitude in the abstract, which are equally
+true of space, time, force, number, and every other magnitude
+susceptible of aggregation and subdivision. Such propositions, where
+they are not mere definitions, as some of them are, carry their
+inductive origin on the face of their enunciation.... Those which
+declare that two straight lines cannot inclose a space, and that two
+straight lines which cut one another cannot both be parallel to a third,
+are in reality the only ones which express characteristic properties of
+space, and these it will be worth while to consider more nearly. Now the
+only clear notion we can form of straightness is uniformity of
+direction, for space in its ultimate analysis is nothing but an
+assemblage of distances and directions. And (not to dwell on the notion
+of continued contemplation, _i.e._, mental experience, as included in
+the very idea of uniformity; nor on that of transfer of the
+contemplating being from point to point, and of experience, during such
+transfer, of the homogeneity of the interval passed over) we cannot even
+propose the proposition in an intelligible form to any one whose
+experience ever since he was born has not assured him of the fact. The
+unity of direction, or that we cannot march from a given point by more
+than one path direct to the same object, is matter of practical
+experience long before it can by possibility become matter of abstract
+thought. _We cannot attempt mentally to exemplify the conditions of the
+assertion in an imaginary case opposed to it, without violating our
+habitual recollection of this experience, and defacing our mental
+picture of space as grounded on it._ What but experience, we may ask,
+can possibly assure us of the homogeneity of the parts of distance,
+time, force, and measurable aggregates in general, on which the truth of
+the other axioms depends? As regards the latter axiom, after what has
+been said it must be clear that the very same course of remarks equally
+applies to its case, and that its truth is quite as much forced on the
+mind as that of the former by daily and hourly experience, ...
+_including always, be it observed, in our notion of experience, that
+which is gained by contemplation of the inward picture which the mind
+forms to itself in any proposed case, or which it arbitrarily selects as
+an example--such picture, in virtue of the extreme simplicity of these
+primary relations, being called up by the imagination with as much
+vividness and clearness as could be done by any external impression,
+which is the only meaning we can attach to the word intuition, as
+applied to such relations_."
+
+And again, of the axioms of mechanics:--"As we admit no such
+propositions, other than as truths inductively collected from
+observation, even in geometry itself, it can hardly be expected that, in
+a science of obviously contingent relations, we should acquiesce in a
+contrary view. Let us take one of these axioms and examine its evidence:
+for instance, that equal forces perpendicularly applied at the opposite
+ends of equal arms of a straight lever will balance each other. What but
+experience, we may ask, in the first place, can possibly inform us that
+a force so applied will have any tendency to turn the lever on its
+centre at all? or that force can be so transmitted along a rigid line
+perpendicular to its direction, as to act elsewhere in space than along
+its own line of action? Surely this is so far from being self-evident
+that it has even a paradoxical appearance, which is only to be removed
+by giving our lever thickness, material composition, and molecular
+powers. Again, we conclude, that the two forces, being equal and applied
+under precisely similar circumstances, must, if they exert any effort at
+all to turn the lever, exert equal and opposite efforts: but what _a
+priori_ reasoning can possibly assure us that they _do_ act under
+precisely similar circumstances? that points which differ in place _are_
+similarly circumstanced as regards the exertion of force? that universal
+space may not have relations to universal force--or, at all events, that
+the organization of the material universe may not be such as to place
+that portion of space occupied by it in such relations to the forces
+exerted in it, as may invalidate the absolute similarity of
+circumstances assumed? Or we may argue, what have we to do with the
+notion of angular movement in the lever at all? The case is one of rest,
+and of quiescent destruction of force by force. Now how is this
+destruction effected? Assuredly by the counter-pressure which supports
+the fulcrum. But would not this destruction equally arise, and by the
+same amount of counter-acting force, if each force simply pressed its
+own half of the lever against the fulcrum? And what can assure us that
+it is not so, except removal of one or other force, and consequent
+tilting of the lever? The other fundamental axiom of statics, that the
+pressure on the point of support is the sum of the weights ... is merely
+a scientific transformation and more refined mode of stating a coarse
+and obvious result of universal experience, viz. that the weight of a
+rigid body is the same, handle it or suspend it in what position or by
+what point we will, and that whatever sustains it sustains its total
+weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever
+made a trial for the purpose of showing that the pressure on the support
+is equal to the sum of the weights.' ... But it is precisely because in
+every action of his life from earliest infancy he has been continually
+making the trial, and seeing it made by every other living being about
+him, that he never dreams of staking its result on one additional
+attempt made with scientific accuracy. This would be as if a man should
+resolve to decide by experiment whether his eyes were useful for the
+purpose of seeing, by hermetically sealing himself up for half an hour
+in a metal case."
+
+On the "paradox of universal propositions obtained by experience," the
+same writer says: "If there be necessary and universal truths
+expressible in propositions of axiomatic simplicity and obviousness, and
+having for their subject-matter the elements of all our experience and
+all our knowledge, surely these are the truths which, if experience
+suggest to us any truths at all, it ought to suggest most readily,
+clearly, and unceasingly. If it were a truth, universal and necessary,
+that a net is spread over the whole surface of every planetary globe, we
+should not travel far on our own without getting entangled in its
+meshes, and making the necessity of some means of extrication an axiom
+of locomotion.... There is, therefore, nothing paradoxical, but the
+reverse, in our being led by observation to a recognition of such
+truths, as _general_ propositions, coextensive at least with all human
+experience. That they pervade all the objects of experience, must ensure
+their continual suggestion _by_ experience; that they are true, must
+ensure that consistency of suggestion, that iteration of uncontradicted
+assertion, which commands implicit assent, and removes all occasion of
+exception; that they are simple, and admit of no misunderstanding, must
+secure their admission by every mind."
+
+"A truth, necessary and universal, relative to any object of our
+knowledge, must verify itself in every instance where that object is
+before our contemplation, and if at the same time it be simple and
+intelligible, its verification must be obvious. _The sentiment of such a
+truth cannot, therefore, but be present to our minds whenever that
+object is contemplated, and must therefore make a part of the mental
+picture or idea of that object which we may on any occasion summon
+before our imagination.... All propositions, therefore, become not only
+untrue but inconceivable_, if ... axioms be violated in their
+enunciation."
+
+Another eminent mathematician had previously sanctioned by his authority
+the doctrine of the origin of geometrical axioms in experience.
+"Geometry is thus founded likewise on observation; but of a kind so
+familiar and obvious, that the primary notions which it furnishes might
+seem intuitive."--_Sir John Leslie_, quoted by Sir William Hamilton,
+_Discourses_, &c. p. 272.
+
+[39] _Principles of Psychology._
+
+[40] Mr. Spencer is mistaken in supposing me to claim any peculiar
+"necessity" for this axiom as compared with others. I have corrected the
+expressions which led him into that misapprehension of my meaning.
+
+[41] Mr. Spencer makes a distinction between conceiving myself looking
+into darkness, and conceiving _that I am_ then and there looking into
+darkness. To me it seems that this change of the expression to the form
+_I am_, just marks the transition from conception to belief, and that
+the phrase "to conceive that _I am_," or "that anything _is_," is not
+consistent with using the word conceive in its rigorous sense.
+
+[42] I have myself accepted the contest, and fought it out on this
+battleground, in the eleventh chapter of _An Examination of Sir William
+Hamilton's Philosophy_.
+
+[43] _Discussions_, &c., 2nd ed. p. 624.
+
+[44] If it be said that the _existence_ of matter is among the things
+proved by the principle of Excluded Middle, that principle must prove
+also the existence of dragons and hippogriffs, because they must be
+either scaly or not scaly, creeping or not creeping, and so forth.
+
+[45] For further considerations respecting the axioms of Contradiction
+and Excluded Middle, see the twenty-first chapter of _An Examination of
+Sir William Hamilton's Philosophy_.
+
+[46] Mr. De Morgan says "Plato," but to prevent confusion I have kept to
+my own _exemplum_.
+
+
+
+
+BOOK III.
+
+OF INDUCTION.
+
+
+"According to the doctrine now stated, the highest, or rather the only
+proper object of physics, is to ascertain those established conjunctions
+of successive events, which constitute the order of the universe; to
+record the phenomena which it exhibits to our observations, or which it
+discloses to our experiments; and to refer these phenomena to their
+general laws."--D. STEWART, _Elements of the Philosophy of the Human
+Mind_, vol. ii. chap. iv. sect. 1.
+
+
+
+
+CHAPTER I.
+
+PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.
+
+
+Sec. 1. The portion of the present inquiry upon which we are now about to
+enter, may be considered as the principal, both from its surpassing in
+intricacy all the other branches, and because it relates to a process
+which has been shown in the preceding Book to be that in which the
+investigation of nature essentially consists. We have found that all
+Inference, consequently all Proof, and all discovery of truths not
+self-evident, consists of inductions, and the interpretation of
+inductions: that all our knowledge, not intuitive, comes to us
+exclusively from that source. What Induction is, therefore, and what
+conditions render it legitimate, cannot but be deemed the main question
+of the science of logic--the question which includes all others. It is,
+however, one which professed writers on logic have almost entirely
+passed over. The generalities of the subject have not been altogether
+neglected by metaphysicians; but, for want of sufficient acquaintance
+with the processes by which science has actually succeeded in
+establishing general truths, their analysis of the inductive operation,
+even when unexceptionable as to correctness, has not been specific
+enough to be made the foundation of practical rules, which might be for
+induction itself what the rules of the syllogism are for the
+interpretation of induction: while those by whom physical science has
+been carried to its present state of improvement--and who, to arrive at
+a complete theory of the process, needed only to generalize, and adapt
+to all varieties of problems, the methods which they themselves employed
+in their habitual pursuits--never until very lately made any serious
+attempt to philosophize on the subject, nor regarded the mode in which
+they arrived at their conclusions as deserving of study, independently
+of the conclusions themselves.
+
+
+Sec. 2. For the purposes of the present inquiry, Induction may be defined,
+the operation of discovering and proving general propositions. It is
+true that (as already shown) the process of indirectly ascertaining
+individual facts, is as truly inductive as that by which we establish
+general truths. But it is not a different kind of induction; it is a
+form of the very same process: since, on the one hand, generals are but
+collections of particulars, definite in kind but indefinite in number;
+and on the other hand, whenever the evidence which we derive from
+observation of known cases justifies us in drawing an inference
+respecting even one unknown case, we should on the same evidence be
+justified in drawing a similar inference with respect to a whole class
+of cases. The inference either does not hold at all, or it holds in all
+cases of a certain description; in all cases which, in certain definable
+respects, resemble those we have observed.
+
+If these remarks are just; if the principles and rules of inference are
+the same whether we infer general propositions or individual facts; it
+follows that a complete logic of the sciences would be also a complete
+logic of practical business and common life. Since there is no case of
+legitimate inference from experience, in which the conclusion may not
+legitimately be a general proposition; an analysis of the process by
+which general truths are arrived at, is virtually an analysis of all
+induction whatever. Whether we are inquiring into a scientific principle
+or into an individual fact, and whether we proceed by experiment or by
+ratiocination, every step in the train of inferences is essentially
+inductive, and the legitimacy of the induction depends in both cases on
+the same conditions.
+
+True it is that in the case of the practical inquirer, who is
+endeavouring to ascertain facts not for the purposes of science but for
+those of business, such for instance as the advocate or the judge, the
+chief difficulty is one in which the principles of induction will afford
+him no assistance. It lies not in making his inductions, but in the
+selection of them; in choosing from among all general propositions
+ascertained to be true, those which furnish marks by which he may trace
+whether the given subject possesses or not the predicate in question. In
+arguing a doubtful question of fact before a jury, the general
+propositions or principles to which the advocate appeals are mostly, in
+themselves, sufficiently trite, and assented to as soon as stated: his
+skill lies in bringing his case under those propositions or principles;
+in calling to mind such of the known or received maxims of probability
+as admit of application to the case in hand, and selecting from among
+them those best adapted to his object. Success is here dependent on
+natural or acquired sagacity, aided by knowledge of the particular
+subject, and of subjects allied with it. Invention, though it can be
+cultivated, cannot be reduced to rule; there is no science which will
+enable a man to bethink himself of that which will suit his purpose.
+
+But when he _has_ thought of something, science can tell him whether
+that which he has thought of will suit his purpose or not. The inquirer
+or arguer must be guided by his own knowledge and sagacity in the choice
+of the inductions out of which he will construct his argument. But the
+validity of the argument when constructed, depends on principles and
+must be tried by tests which are the same for all descriptions of
+inquiries, whether the result be to give A an estate, or to enrich
+science with a new general truth. In the one case and in the other, the
+senses, or testimony, must decide on the individual facts; the rules of
+the syllogism will determine whether, those facts being supposed
+correct, the case really falls within the formulae of the different
+inductions under which it has been successively brought; and finally,
+the legitimacy of the inductions themselves must be decided by other
+rules, and these it is now our purpose to investigate. If this third
+part of the operation be, in many of the questions of practical life,
+not the most, but the least arduous portion of it, we have seen that
+this is also the case in some great departments of the field of science;
+in all those which are principally deductive, and most of all in
+mathematics; where the inductions themselves are few in number, and so
+obvious and elementary that they seem to stand in no need of the
+evidence of experience, while to combine them so as to prove a given
+theorem or solve a problem, may call for the utmost powers of invention
+and contrivance with which our species is gifted.
+
+If the identity of the logical processes which prove particular facts
+and those which establish general scientific truths, required any
+additional confirmation, it would be sufficient to consider that in many
+branches of science, single facts have to be proved, as well as
+principles; facts as completely individual as any that are debated in a
+court of justice; but which are proved in the same manner as the other
+truths of the science, and without disturbing in any degree the
+homogeneity of its method. A remarkable example of this is afforded by
+astronomy. The individual facts on which that science grounds its most
+important deductions, such facts as the magnitudes of the bodies of the
+solar system, their distances from one another, the figure of the earth,
+and its rotation, are scarcely any of them accessible to our means of
+direct observation: they are proved indirectly, by the aid of inductions
+founded on other facts which we can more easily reach. For example, the
+distance of the moon from the earth was determined by a very circuitous
+process. The share which direct observation had in the work consisted in
+ascertaining, at one and the same instant, the zenith distances of the
+moon, as seen from two points very remote from one another on the
+earth's surface. The ascertainment of these angular distances
+ascertained their supplements; and since the angle at the earth's centre
+subtended by the distance between the two places of observation was
+deducible by spherical trigonometry from the latitude and longitude of
+those places, the angle at the moon subtended by the same line became
+the fourth angle of a quadrilateral of which the other three angles were
+known. The four angles being thus ascertained, and two sides of the
+quadrilateral being radii of the earth; the two remaining sides and the
+diagonal, or in other words, the moon's distance from the two places of
+observation and from the centre of the earth, could be ascertained, at
+least in terms of the earth's radius, from elementary theorems of
+geometry. At each step in this demonstration we take in a new
+induction, represented, in the aggregate of its results, by a general
+proposition.
+
+Not only is the process by which an individual astronomical fact was
+thus ascertained, exactly similar to those by which the same science
+establishes its general truths, but also (as we have shown to be the
+case in all legitimate reasoning) a general proposition might have been
+concluded instead of a single fact. In strictness, indeed, the result of
+the reasoning _is_ a general proposition; a theorem respecting the
+distance, not of the moon in particular, but of any inaccessible object:
+showing in what relation that distance stands to certain other
+quantities. And although the moon is almost the only heavenly body the
+distance of which from the earth can really be thus ascertained, this is
+merely owing to the accidental circumstances of the other heavenly
+bodies, which render them incapable of affording such data as the
+application of the theorem requires; for the theorem itself is as true
+of them as it is of the moon.[1]
+
+We shall fall into no error, then, if in treating of Induction, we
+limit our attention to the establishment of general propositions. The
+principles and rules of Induction as directed to this end, are the
+principles and rules of all Induction; and the logic of Science is the
+universal Logic, applicable to all inquiries in which man can engage.
+
+
+
+
+CHAPTER II.
+
+OF INDUCTIONS IMPROPERLY SO CALLED.
+
+
+Sec. 1. Induction, then, is that operation of the mind, by which we infer
+that what we know to be true in a particular case or cases, will be true
+in all cases which resemble the former in certain assignable respects.
+In other words, Induction is the process by which we conclude that what
+is true of certain individuals of a class is true of the whole class, or
+that what is true at certain times will be true in similar circumstances
+at all times.
+
+This definition excludes from the meaning of the term Induction, various
+logical operations, to which it is not unusual to apply that name.
+
+Induction, as above defined, is a process of inference; it proceeds from
+the known to the unknown; and any operation involving no inference, any
+process in which what seems the conclusion is no wider than the premises
+from which it is drawn, does not fall within the meaning of the term.
+Yet in the common books of Logic we find this laid down as the most
+perfect, indeed the only quite perfect, form of induction. In those
+books, every process which sets out from a less general and terminates
+in a more general expression,--which admits of being stated in the form,
+"This and that A are B, therefore every A is B,"--is called an
+induction, whether anything be really concluded or not: and the
+induction is asserted not to be perfect, unless every single individual
+of the class A is included in the antecedent, or premise: that is,
+unless what we affirm of the class has already been ascertained to be
+true of every individual in it, so that the nominal conclusion is not
+really a conclusion, but a mere reassertion of the premises. If we were
+to say, All the planets shine by the sun's light, from observation of
+each separate planet, or All the Apostles were Jews, because this is
+true of Peter, Paul, John, and every other apostle,--these, and such as
+these, would, in the phraseology in question, be called perfect, and the
+only perfect, Inductions. This, however, is a totally different kind of
+induction from ours; it is not an inference from facts known to facts
+unknown, but a mere short-hand registration of facts known. The two
+simulated arguments which we have quoted, are not generalizations; the
+propositions purporting to be conclusions from them, are not really
+general propositions. A general proposition is one in which the
+predicate is affirmed or denied of an unlimited number of individuals;
+namely, all, whether few or many, existing or capable of existing, which
+possess the properties connoted by the subject of the proposition. "All
+men are mortal" does not mean all now living, but all men past, present,
+and to come. When the signification of the term is limited so as to
+render it a name not for any and every individual falling under a
+certain general description, but only for each of a number of
+individuals designated as such, and as it were counted off individually,
+the proposition, though it may be general in its language, is no general
+proposition, but merely that number of singular propositions, written in
+an abridged character. The operation may be very useful, as most forms
+of abridged notation are; but it is no part of the investigation of
+truth, though often bearing an important part in the preparation of the
+materials for that investigation.
+
+As we may sum up a definite number of singular propositions in one
+proposition, which will be apparently, but not really, general, so we
+may sum up a definite number of general propositions in one proposition,
+which will be apparently, but not really, more general. If by a separate
+induction applied to every distinct species of animals, it has been
+established that each possesses a nervous system, and we affirm
+thereupon that all animals have a nervous system; this looks like a
+generalization, though as the conclusion merely affirms of all what has
+already been affirmed of each, it seems to tell us nothing but what we
+knew before. A distinction however must be made. If in concluding that
+all animals have a nervous system, we mean the same thing and no more as
+if we had said "all known animals," the proposition is not general, and
+the process by which it is arrived at is not induction. But if our
+meaning is that the observations made of the various species of animals
+have discovered to us a law of animal nature, and that we are in a
+condition to say that a nervous system will be found even in animals yet
+undiscovered, this indeed is an induction; but in this case the general
+proposition contains more than the sum of the special propositions from
+which it is inferred. The distinction is still more forcibly brought out
+when we consider, that if this real generalization be legitimate at all,
+its legitimacy probably does not require that we should have examined
+without exception every known species. It is the number and nature of
+the instances, and not their being the whole of those which happen to be
+known, that makes them sufficient evidence to prove a general law: while
+the more limited assertion, which stops at all known animals, cannot be
+made unless we have rigorously verified it in every species. In like
+manner (to return to a former example) we might have inferred, not that
+all _the_ planets, but that all _planets_, shine by reflected light: the
+former is no induction; the latter is an induction, and a bad one, being
+disproved by the case of double stars--self-luminous bodies which are
+properly planets, since they revolve round a centre.
+
+
+Sec. 2. There are several processes used in mathematics which require to be
+distinguished from Induction, being not unfrequently called by that
+name, and being so far similar to Induction properly so called, that the
+propositions they lead to are really general propositions. For example,
+when we have proved with respect to the circle, that a straight line
+cannot meet it in more than two points, and when the same thing has been
+successively proved of the ellipse, the parabola, and the hyperbola, it
+may be laid down as an universal property of the sections of the cone.
+The distinction drawn in the two previous examples can have no place
+here, there being no difference between all _known_ sections of the
+cone and _all_ sections, since a cone demonstrably cannot be intersected
+by a plane except in one of these four lines. It would be difficult,
+therefore, to refuse to the proposition arrived at, the name of a
+generalization, since there is no room for any generalization beyond it.
+But there is no induction, because there is no inference: the conclusion
+is a mere summing up of what was asserted in the various propositions
+from which it is drawn. A case somewhat, though not altogether, similar,
+is the proof of a geometrical theorem by means of a diagram. Whether the
+diagram be on paper or only in the imagination, the demonstration (as
+formerly observed[2]) does not prove directly the general theorem; it
+proves only that the conclusion, which the theorem asserts generally, is
+true of the particular triangle or circle exhibited in the diagram; but
+since we perceive that in the same way in which we have proved it of
+that circle, it might also be proved of any other circle, we gather up
+into one general expression all the singular propositions susceptible of
+being thus proved, and embody them in an universal proposition. Having
+shown that the three angles of the triangle ABC are together equal to
+two right angles, we conclude that this is true of every other triangle,
+not because it is true of ABC, but for the same reason which proved it
+to be true of ABC. If this were to be called Induction, an appropriate
+name for it would be, induction by parity of reasoning. But the term
+cannot properly belong to it; the characteristic quality of Induction is
+wanting, since the truth obtained, though really general, is not
+believed on the evidence of particular instances. We do not conclude
+that all triangles have the property because some triangles have, but
+from the ulterior demonstrative evidence which was the ground of our
+conviction in the particular instances.
+
+There are nevertheless, in mathematics, some examples of so-called
+Induction, in which the conclusion does bear the appearance of a
+generalization grounded on some of the particular cases included in it.
+A mathematician, when he has calculated a sufficient number of the
+terms of an algebraical or arithmetical series to have ascertained what
+is called the _law_ of the series, does not hesitate to fill up any
+number of the succeeding terms without repeating the calculations. But I
+apprehend he only does so when it is apparent from _a priori_
+considerations (which might be exhibited in the form of demonstration)
+that the mode of formation of the subsequent terms, each from that which
+preceded it, must be similar to the formation of the terms which have
+been already calculated. And when the attempt has been hazarded without
+the sanction of such general considerations, there are instances on
+record in which it has led to false results.
+
+It is said that Newton discovered the binomial theorem by induction; by
+raising a binomial successively to a certain number of powers, and
+comparing those powers with one another until he detected the relation
+in which the algebraic formula of each power stands to the exponent of
+that power, and to the two terms of the binomial. The fact is not
+improbable: but a mathematician like Newton, who seemed to arrive _per
+saltum_ at principles and conclusions that ordinary mathematicians only
+reached by a succession of steps, certainly could not have performed the
+comparison in question without being led by it to the _a priori_ ground
+of the law; since any one who understands sufficiently the nature of
+multiplication to venture upon multiplying several lines of symbols at
+one operation, cannot but perceive that in raising a binomial to a
+power, the coefficients must depend on the laws of permutation and
+combination: and as soon as this is recognised, the theorem is
+demonstrated. Indeed, when once it was seen that the law prevailed in a
+few of the lower powers, its identity with the law of permutation would
+at once suggest the considerations which prove it to obtain universally.
+Even, therefore, such cases as these, are but examples of what I have
+called Induction by parity of reasoning, that is, not really Induction,
+because not involving inference of a general proposition from particular
+instances.
+
+
+Sec. 3. There remains a third improper use of the term Induction, which it
+is of real importance to clear up, because the theory of Induction has
+been, in no ordinary degree, confused by it, and because the confusion
+is exemplified in the most recent and elaborate treatise on the
+inductive philosophy which exists in our language. The error in question
+is that of confounding a mere description, by general terms, of a set of
+observed phenomena, with an induction from them.
+
+Suppose that a phenomenon consists of parts, and that these parts are
+only capable of being observed separately, and as it were piecemeal.
+When the observations have been made, there is a convenience (amounting
+for many purposes to a necessity) in obtaining a representation of the
+phenomenon as a whole, by combining, or as we may say, piecing these
+detached fragments together. A navigator sailing in the midst of the
+ocean discovers land: he cannot at first, or by any one observation,
+determine whether it is a continent or an island; but he coasts along
+it, and after a few days finds himself to have sailed completely round
+it: he then pronounces it an island. Now there was no particular time or
+place of observation at which he could perceive that this land was
+entirely surrounded by water: he ascertained the fact by a succession of
+partial observations, and then selected a general expression which
+summed up in two or three words the whole of what he so observed. But is
+there anything of the nature of an induction in this process? Did he
+infer anything that had not been observed, from something else which
+had? Certainly not. He had observed the whole of what the proposition
+asserts. That the land in question is an island, is not an inference
+from the partial facts which the navigator saw in the course of his
+circumnavigation; it is the facts themselves; it is a summary of those
+facts; the description of a complex fact, to which those simpler ones
+are as the parts of a whole.
+
+Now there is, I conceive, no difference in kind between this simple
+operation, and that by which Kepler ascertained the nature of the
+planetary orbits: and Kepler's operation, all at least that was
+characteristic in it, was not more an inductive act than that of our
+supposed navigator.
+
+The object of Kepler was to determine the real path described by each
+of the planets, or let us say by the planet Mars (since it was of that
+body that he first established the two of his three laws which did not
+require a comparison of planets). To do this there was no other mode
+than that of direct observation: and all which observation could do was
+to ascertain a great number of the successive places of the planet; or
+rather, of its apparent places. That the planet occupied successively
+all these positions, or at all events, positions which produced the same
+impressions on the eye, and that it passed from one of these to another
+insensibly, and without any apparent breach of continuity; thus much the
+senses, with the aid of the proper instruments, could ascertain. What
+Kepler did more than this, was to find what sort of a curve these
+different points would make, supposing them to be all joined together.
+He expressed the whole series of the observed places of Mars by what Dr.
+Whewell calls the general conception of an ellipse. This operation was
+far from being as easy as that of the navigator who expressed the series
+of his observations on successive points of the coast by the general
+conception of an island. But it is the very same sort of operation; and
+if the one is not an induction but a description, this must also be true
+of the other.
+
+The only real induction concerned in the case, consisted in inferring
+that because the observed places of Mars were correctly represented by
+points in an imaginary ellipse, therefore Mars would continue to revolve
+in that same ellipse; and in concluding (before the gap had been filled
+up by further observations) that the positions of the planet during the
+time which intervened between two observations, must have coincided with
+the intermediate points of the curve. For these were facts which had not
+been directly observed. They were inferences from the observations;
+facts inferred, as distinguished from facts seen. But these inferences
+were so far from being a part of Kepler's philosophical operation, that
+they had been drawn long before he was born. Astronomers had long known
+that the planets periodically returned to the same places. When this had
+been ascertained, there was no induction left for Kepler to make, nor
+did he make any further induction. He merely applied his new conception
+to the facts inferred, as he did to the facts observed. Knowing already
+that the planets continued to move in the same paths; when he found that
+an ellipse correctly represented the past path, he knew that it would
+represent the future path. In finding a compendious expression for the
+one set of facts, he found one for the other: but he found the
+expression only, not the inference; nor did he (which is the true test
+of a general truth) add anything to the power of prediction already
+possessed.
+
+
+Sec. 4. The descriptive operation which enables a number of details to be
+summed up in a single proposition, Dr. Whewell, by an aptly chosen
+expression, has termed the Colligation of Facts. In most of his
+observations concerning that mental process I fully agree, and would
+gladly transfer all that portion of his book into my own pages. I only
+think him mistaken in setting up this kind of operation, which according
+to the old and received meaning of the term, is not induction at all, as
+the type of induction generally; and laying down, throughout his work,
+as principles of induction, the principles of mere colligation.
+
+Dr. Whewell maintains that the general proposition which binds together
+the particular facts, and makes them, as it were, one fact, is not the
+mere sum of those facts, but something more, since there is introduced a
+conception of the mind, which did not exist in the facts themselves.
+"The particular facts," says he,[3] "are not merely brought together,
+but there is a new element added to the combination by the very act of
+thought by which they are combined.... When the Greeks, after long
+observing the motions of the planets, saw that these motions might be
+rightly considered as produced by the motion of one wheel revolving in
+the inside of another wheel, these wheels were creations of their minds,
+added to the facts which they perceived by sense. And even if the
+wheels were no longer supposed to be material, but were reduced to mere
+geometrical spheres or circles, they were not the less products of the
+mind alone,--something additional to the facts observed. The same is the
+case in all other discoveries. The facts are known, but they are
+insulated and unconnected, till the discoverer supplies from his own
+store a principle of connexion. The pearls are there, but they will not
+hang together till some one provides the string."
+
+Let me first remark that Dr. Whewell, in this passage, blends together,
+indiscriminately, examples of both the processes which I am endeavouring
+to distinguish from one another. When the Greeks abandoned the
+supposition that the planetary motions were produced by the revolution
+of material wheels, and fell back upon the idea of "mere geometrical
+spheres or circles," there was more in this change of opinion than the
+mere substitution of an ideal curve for a physical one. There was the
+abandonment of a theory, and the replacement of it by a mere
+description. No one would think of calling the doctrine of material
+wheels a mere description. That doctrine was an attempt to point out the
+force by which the planets were acted upon, and compelled to move in
+their orbits. But when, by a great step in philosophy, the materiality
+of the wheels was discarded, and the geometrical forms alone retained,
+the attempt to account for the motions was given up, and what was left
+of the theory was a mere description of the orbits. The assertion that
+the planets were carried round by wheels revolving in the inside of
+other wheels, gave place to the proposition, that they moved in the same
+lines which would be traced by bodies so carried: which was a mere mode
+of representing the sum of the observed facts; as Kepler's was another
+and a better mode of representing the same observations.
+
+It is true that for these simply descriptive operations, as well as for
+the erroneous inductive one, a conception of the mind was required. The
+conception of an ellipse must have presented itself to Kepler's mind,
+before he could identify the planetary orbits with it. According to Dr.
+Whewell, the conception was something added to the facts. He expresses
+himself as if Kepler had put something into the facts by his mode of
+conceiving them. But Kepler did no such thing. The ellipse was in the
+facts before Kepler recognised it; just as the island was an island
+before it had been sailed round. Kepler did not _put_ what he had
+conceived into the facts, but _saw_ it in them. A conception implies,
+and corresponds to, something conceived: and though the conception
+itself is not in the facts, but in our mind, yet if it is to convey any
+knowledge relating to them, it must be a conception _of_ something which
+really is in the facts, some property which they actually possess, and
+which they would manifest to our senses, if our senses were able to take
+cognizance of it. If, for instance, the planet left behind it in space a
+visible track, and if the observer were in a fixed position at such a
+distance from the plane of the orbit as would enable him to see the
+whole of it at once, he would see it to be an ellipse; and if gifted
+with appropriate instruments and powers of locomotion, he could prove it
+to be such by measuring its different dimensions. Nay, further: if the
+track were visible, and he were so placed that he could see all parts of
+it in succession, but not all of them at once, he might be able, by
+piecing together his successive observations, to discover both that it
+was an ellipse and that the planet moved in it. The case would then
+exactly resemble that of the navigator who discovers the land to be an
+island by sailing round it. If the path was visible, no one I think
+would dispute that to identify it with an ellipse is to describe it: and
+I cannot see why any difference should be made by its not being directly
+an object of sense, when every point in it is as exactly ascertained as
+if it were so.
+
+Subject to the indispensable condition which has just been stated, I
+cannot conceive that the part which conceptions have in the operation of
+studying facts, has ever been overlooked or undervalued. No one ever
+disputed that in order to reason about anything we must have a
+conception of it; or that when we include a multitude of things under a
+general expression, there is implied in the expression a conception of
+something common to those things. But it by no means follows that the
+conception is necessarily pre-existent, or constructed by the mind out
+of its own materials. If the facts are rightly classed under the
+conception, it is because there is in the facts themselves something of
+which the conception is itself a copy; and which if we cannot directly
+perceive, it is because of the limited power of our organs, and not
+because the thing itself is not there. The conception itself is often
+obtained by abstraction from the very facts which, in Dr. Whewell's
+language, it is afterwards called in to connect. This he himself admits,
+when he observes, (which he does on several occasions,) how great a
+service would be rendered to the science of physiology by the
+philosopher "who should establish a precise, tenable, and consistent
+conception of life."[4] Such a conception can only be abstracted from
+the phenomena of life itself; from the very facts which it is put in
+requisition to connect. In other cases, no doubt, instead of collecting
+the conception from the very phenomena which we are attempting to
+colligate, we select it from among those which have been previously
+collected by abstraction from other facts. In the instance of Kepler's
+laws, the latter was the case. The facts being out of the reach of being
+observed, in any such manner as would have enabled the senses to
+identify directly the path of the planet, the conception requisite for
+framing a general description of that path could not be collected by
+abstraction from the observations themselves; the mind had to supply
+hypothetically, from among the conceptions it had obtained from other
+portions of its experience, some one which would correctly represent the
+series of the observed facts. It had to frame a supposition respecting
+the general course of the phenomenon, and ask itself, If this be the
+general description, what will the details be? and then compare these
+with the details actually observed. If they agreed, the hypothesis would
+serve for a description of the phenomenon: if not, it was necessarily
+abandoned, and another tried. It is such a case as this which gives rise
+to the doctrine that the mind, in framing the descriptions, adds
+something of its own which it does not find in the facts.
+
+Yet it is a fact surely, that the planet does describe an ellipse; and a
+fact which we could see, if we had adequate visual organs and a suitable
+position. Not having these advantages, but possessing the conception of
+an ellipse, or (to express the meaning in less technical language)
+knowing what an ellipse was, Kepler tried whether the observed places of
+the planet were consistent with such a path. He found they were so; and
+he, consequently, asserted as a fact that the planet moved in an
+ellipse. But this fact, which Kepler did not add to, but found in, the
+motions of the planet, namely, that it occupied in succession the
+various points in the circumference of a given ellipse, was the very
+fact, the separate parts of which had been separately observed; it was
+the sum of the different observations.
+
+Having stated this fundamental difference between my opinion and that of
+Dr. Whewell, I must add, that his account of the manner in which a
+conception is selected, suitable to express the facts, appears to me
+perfectly just. The experience of all thinkers will, I believe, testify
+that the process is tentative; that it consists of a succession of
+guesses; many being rejected, until one at last occurs fit to be chosen.
+We know from Kepler himself that before hitting upon the "conception" of
+an ellipse, he tried nineteen other imaginary paths, which, finding them
+inconsistent with the observations, he was obliged to reject. But as Dr.
+Whewell truly says, the successful hypothesis, though a guess, ought
+generally to be called, not a lucky, but a skilful guess. The guesses
+which serve to give mental unity and wholeness to a chaos of scattered
+particulars, are accidents which rarely occur to any minds but those
+abounding in knowledge and disciplined in intellectual combinations.
+
+How far this tentative method, so indispensable as a means to the
+colligation of facts for purposes of description, admits of application
+to Induction itself, and what functions belong to it in that department,
+will be considered in the chapter of the present Book which relates to
+Hypotheses. On the present occasion we have chiefly to distinguish this
+process of Colligation from Induction properly so called; and that the
+distinction may be made clearer, it is well to advert to a curious and
+interesting remark, which is as strikingly true of the former operation,
+as it appears to me unequivocally false of the latter.
+
+In different stages of the progress of knowledge, philosophers have
+employed, for the colligation of the same order of facts, different
+conceptions. The early rude observations of the heavenly bodies, in
+which minute precision was neither attained nor sought, presented
+nothing inconsistent with the representation of the path of a planet as
+an exact circle, having the earth for its centre. As observations
+increased in accuracy, and facts were disclosed which were not
+reconcileable with this simple supposition; for the colligation of those
+additional facts, the supposition was varied; and varied again and again
+as facts became more numerous and precise. The earth was removed from
+the centre to some other point within the circle; the planet was
+supposed to revolve in a smaller circle called an epicycle, round an
+imaginary point which revolved in a circle round the earth: in
+proportion as observation elicited fresh facts contradictory to these
+representations, other epicycles and other excentrics were added,
+producing additional complication; until at last Kepler swept all these
+circles away, and substituted the conception of an exact ellipse. Even
+this is found not to represent with complete correctness the accurate
+observations of the present day, which disclose many slight deviations
+from an orbit exactly elliptical. Now Dr. Whewell has remarked that
+these successive general expressions, though apparently so conflicting,
+were all correct: they all answered the purpose of colligation; they all
+enabled the mind to represent to itself with facility, and by a
+simultaneous glance, the whole body of facts at the time ascertained:
+each in its turn served as a correct description of the phenomena, so
+far as the senses had up to that time taken cognizance of them. If a
+necessity afterwards arose for discarding one of these general
+descriptions of the planet's orbit, and framing a different imaginary
+line, by which to express the series of observed positions, it was
+because a number of new facts had now been added, which it was necessary
+to combine with the old facts into one general description. But this did
+not affect the correctness of the former expression, considered as a
+general statement of the only facts which it was intended to represent.
+And so true is this, that, as is well remarked by M. Comte, these
+ancient generalizations, even the rudest and most imperfect of them,
+that of uniform movement in a circle, are so far from being entirely
+false, that they are even now habitually employed by astronomers when
+only a rough approximation to correctness is required. "L'astronomie
+moderne, en detruisant sans retour les hypotheses primitives, envisagees
+comme lois reelles du monde, a soigneusement maintenu leur valeur
+positive et permanente, la propriete de representer commodement les
+phenomenes quand il s'agit d'une premiere ebauche. Nos ressources a cet
+egard sont meme bien plus etendues, precisement a cause que nous ne nous
+faisons aucune illusion sur la realite des hypotheses; ce qui nous
+permet d'employer sans scrupule, en chaque cas, celle que nous jugeons
+la plus avantageuse."[5]
+
+Dr. Whewell's remark, therefore, is philosophically correct. Successive
+expressions for the colligation of observed facts, or in other words,
+successive descriptions of a phenomenon as a whole, which has been
+observed only in parts, may, though conflicting, be all correct as far
+as they go. But it would surely be absurd to assert this of conflicting
+inductions.
+
+The scientific study of facts may be undertaken for three different
+purposes: the simple description of the facts; their explanation; or
+their prediction: meaning by prediction, the determination of the
+conditions under which similar facts may be expected again to occur. To
+the first of these three operations the name of Induction does not
+properly belong: to the other two it does. Now, Dr. Whewell's
+observation is true of the first alone. Considered as a mere
+description, the circular theory of the heavenly motions represents
+perfectly well their general features: and by adding epicycles without
+limit, those motions, even as now known to us, might be expressed with
+any degree of accuracy that might be required. The elliptical theory, as
+a mere description, would have a great advantage in point of simplicity,
+and in the consequent facility of conceiving it and reasoning about it;
+but it would not really be more true than the other. Different
+descriptions, therefore, may be all true: but not, surely, different
+explanations. The doctrine that the heavenly bodies moved by a virtue
+inherent in their celestial nature; the doctrine that they were moved by
+impact, (which led to the hypothesis of vortices as the only impelling
+force capable of whirling bodies in circles,) and the Newtonian
+doctrine, that they are moved by the composition of a centripetal with
+an original projectile force; all these are explanations, collected by
+real induction from supposed parallel cases; and they were all
+successively received by philosophers, as scientific truths on the
+subject of the heavenly bodies. Can it be said of these, as was said of
+the different descriptions, that they are all true as far as they go? Is
+it not clear that only one can be true in any degree, and the other two
+must be altogether false? So much for explanations: let us now compare
+different predictions: the first, that eclipses will occur when one
+planet or satellite is so situated as to cast its shadow upon another;
+the second, that they will occur when some great calamity is impending
+over mankind. Do these two doctrines only differ in the degree of their
+truth, as expressing real facts with unequal degrees of accuracy?
+Assuredly the one is true, and the other absolutely false.[6]
+
+In every way, therefore, it is evident that to explain induction as the
+colligation of facts by means of appropriate conceptions, that is,
+conceptions which will really express them, is to confound mere
+description of the observed facts with inference from those facts, and
+ascribe to the latter what is a characteristic property of the former.
+
+There is, however, between Colligation and Induction, a real
+correlation, which it is important to conceive correctly. Colligation is
+not always induction; but induction is always colligation. The assertion
+that the planets move in ellipses, was but a mode of representing
+observed facts; it was but a colligation; while the assertion that they
+are drawn, or tend, towards the sun, was the statement of a new fact,
+inferred by induction. But the induction, once made, accomplishes the
+purposes of colligation likewise. It brings the same facts, which Kepler
+had connected by his conception of an ellipse, under the additional
+conception of bodies acted upon by a central force, and serves therefore
+as a new bond of connexion for those facts; a new principle for their
+classification.
+
+Further, the descriptions which are improperly confounded with
+induction, are nevertheless a necessary preparation for induction; no
+less necessary than correct observation of the facts themselves. Without
+the previous colligation of detached observations by means of one
+general conception, we could never have obtained any basis for an
+induction, except in the case of phenomena of very limited compass. We
+should not be able to affirm any predicates at all, of a subject
+incapable of being observed otherwise than piecemeal: much less could we
+extend those predicates by induction to other similar subjects.
+Induction, therefore, always presupposes, not only that the necessary
+observations are made with the necessary accuracy, but also that the
+results of these observations are, so far as practicable, connected
+together by general descriptions, enabling the mind to represent to
+itself as wholes whatever phenomena are capable of being so represented.
+
+
+Sec. 5. Dr. Whewell has replied at some length to the preceding
+observations, re-stating his opinions, but without (as far as I can
+perceive) adding anything material to his former arguments. Since,
+however, mine have not had the good fortune to make any impression upon
+him, I will subjoin a few remarks, tending to show more clearly in what
+our difference of opinion consists, as well as, in some measure, to
+account for it.
+
+Nearly all the definitions of induction, by writers of authority, make
+it consist in drawing inferences from known cases to unknown; affirming
+of a class, a predicate which has been found true of some cases
+belonging to the class; concluding, because some things have a certain
+property, that other things which resemble them have the same
+property--or because a thing has manifested a property at a certain
+time, that it has and will have that property at other times.
+
+It will scarcely be contended that Kepler's operation was an Induction
+in this sense of the term. The statement, that Mars moves in an
+elliptical orbit, was no generalization from individual cases to a class
+of cases. Neither was it an extension to all time, of what had been
+found true at some particular time. The whole amount of generalization
+which the case admitted of, was already completed, or might have been
+so. Long before the elliptic theory was thought of, it had been
+ascertained that the planets returned periodically to the same apparent
+places; the series of these places was, or might have been, completely
+determined, and the apparent course of each planet marked out on the
+celestial globe in an uninterrupted line. Kepler did not extend an
+observed truth to other cases than those in which it had been observed:
+he did not widen the _subject_ of the proposition which expressed the
+observed facts. The alteration he made was in the predicate. Instead of
+saying, the successive places of Mars are so and so, he summed them up
+in the statement, that the successive places of Mars are points in an
+ellipse. It is true, this statement, as Dr. Whewell says, was not the
+sum of the observations _merely_; it was the sum of the observations
+_seen under a new point of view_.[7] But it was not the sum of _more_
+than the observations, as a real induction is. It took in no cases but
+those which had been actually observed, or which could have been
+inferred from the observations before the new point of view presented
+itself. There was not that transition from known cases to unknown,
+which constitutes Induction in the original and acknowledged meaning of
+the term.
+
+Old definitions, it is true, cannot prevail against new knowledge: and
+if the Keplerian operation, as a logical process, be really identical
+with what takes place in acknowledged induction, the definition of
+induction ought to be so widened as to take it in; since scientific
+language ought to adapt itself to the true relations which subsist
+between the things it is employed to designate. Here then it is that I
+am at issue with Dr. Whewell. He does think the operations identical. He
+allows of no logical process in any case of induction, other than what
+there was in Kepler's case, namely, guessing until a guess is found
+which tallies with the facts; and accordingly, as we shall see
+hereafter, he rejects all canons of induction, because it is not by
+means of them that we guess. Dr. Whewell's theory of the logic of
+science would be very perfect if it did not pass over altogether the
+question of Proof. But in my apprehension there is such a thing as
+proof, and inductions differ altogether from descriptions in their
+relation to that element. Induction is proof; it is inferring something
+unobserved from something observed: it requires, therefore, an
+appropriate test of proof; and to provide that test, is the special
+purpose of inductive logic. When, on the contrary, we merely collate
+known observations, and, in Dr. Whewell's phraseology, connect them by
+means of a new conception; if the conception does serve to connect the
+observations, we have all we want. As the proposition in which it is
+embodied pretends to no other truth than what it may share with many
+other modes of representing the same facts, to be consistent with the
+facts is all it requires: it neither needs nor admits of proof; though
+it may serve to prove other things, inasmuch as, by placing the facts in
+mental connexion with other facts, not previously seen to resemble them,
+it assimilates the case to another class of phenomena, concerning which
+real Inductions have already been made. Thus Kepler's so-called law
+brought the orbit of Mars into the class ellipse, and by doing so,
+proved all the properties of an ellipse to be true of the orbit: but in
+this proof Kepler's law supplied the minor premise, and not (as is the
+case with real Inductions) the major.
+
+Dr. Whewell calls nothing Induction where there is not a new mental
+conception introduced, and everything induction where there is. But this
+is to confound two very different things, Invention and Proof. The
+introduction of a new conception belongs to Invention: and invention may
+be required in any operation, but is the essence of none. A new
+conception may be introduced for descriptive purposes, and so it may for
+inductive purposes. But it is so far from constituting induction, that
+induction does not necessarily stand in need of it. Most inductions
+require no conception but what was present in every one of the
+particular instances on which the induction is grounded. That all men
+are mortal is surely an inductive conclusion; yet no new conception is
+introduced by it. Whoever knows that any man has died, has all the
+conceptions involved in the inductive generalization. But Dr. Whewell
+considers the process of invention which consists in framing a new
+conception consistent with the facts, to be not merely a necessary part
+of all induction, but the whole of it.
+
+The mental operation which extracts from a number of detached
+observations certain general characters in which the observed phenomena
+resemble one another, or resemble other known facts, is what Bacon,
+Locke, and most subsequent metaphysicians, have understood by the word
+Abstraction. A general expression obtained by abstraction, connecting
+known facts by means of common characters, but without concluding from
+them to unknown, may, I think, with strict logical correctness, be
+termed a Description; nor do I know in what other way things can ever be
+described. My position, however, does not depend on the employment of
+that particular word; I am quite content to use Dr. Whewell's term
+Colligation, or the more general phrases, "mode of representing, or of
+expressing, phenomena:" provided it be clearly seen that the process is
+not Induction, but something radically different.
+
+What more may usefully be said on the subject of Colligation, or of the
+correlative expression invented by Dr. Whewell, the Explication of
+Conceptions, and generally on the subject of ideas and mental
+representations as connected with the study of facts, will find a more
+appropriate place in the Fourth Book, on the Operations Subsidiary to
+Induction: to which I must refer the reader for the removal of any
+difficulty which the present discussion may have left.
+
+
+
+
+CHAPTER III.
+
+OF THE GROUND OF INDUCTION.
+
+
+Sec. 1. Induction properly so called, as distinguished from those mental
+operations, sometimes though improperly designated by the name, which I
+have attempted in the preceding chapter to characterize, may, then, be
+summarily defined as Generalization from Experience. It consists in
+inferring from some individual instances in which a phenomenon is
+observed to occur, that it occurs in all instances of a certain class;
+namely, in all which _resemble_ the former, in what are regarded as the
+material circumstances.
+
+In what way the material circumstances are to be distinguished from
+those which are immaterial, or why some of the circumstances are
+material and others not so, we are not yet ready to point out. We must
+first observe, that there is a principle implied in the very statement
+of what Induction is; an assumption with regard to the course of nature
+and the order of the universe; namely, that there are such things in
+nature as parallel cases; that what happens once, will, under a
+sufficient degree of similarity of circumstances, happen again, and not
+only again, but as often as the same circumstances recur. This, I say,
+is an assumption, involved in every case of induction. And, if we
+consult the actual course of nature, we find that the assumption is
+warranted. The universe, so far as known to us, is so constituted, that
+whatever is true in any one case, is true in all cases of a certain
+description; the only difficulty is, to find what description.
+
+This universal fact, which is our warrant for all inferences from
+experience, has been described by different philosophers in different
+forms of language: that the course of nature is uniform; that the
+universe is governed by general laws; and the like. One of the most
+usual of these modes of expression, but also one of the most inadequate,
+is that which has been brought into familiar use by the metaphysicians
+of the school of Reid and Stewart. The disposition of the human mind to
+generalize from experience,--a propensity considered by these
+philosophers as an instinct of our nature,--they usually describe under
+some such name as "our intuitive conviction that the future will
+resemble the past." Now it has been well pointed out by Mr. Bailey,[8]
+that (whether the tendency be or not an original and ultimate element of
+our nature), Time, in its modifications of past, present, and future,
+has no concern either with the belief itself, or with the grounds of it.
+We believe that fire will burn to-morrow, because it burned to-day and
+yesterday; but we believe, on precisely the same grounds, that it burned
+before we were born, and that it burns this very day in Cochin-China. It
+is not from the past to the future, as past and future, that we infer,
+but from the known to the unknown; from facts observed to facts
+unobserved; from what we have perceived, or been directly conscious of,
+to what has not come within our experience. In this last predicament is
+the whole region of the future; but also the vastly greater portion of
+the present and of the past.
+
+Whatever be the most proper mode of expressing it, the proposition that
+the course of nature is uniform, is the fundamental principle, or
+general axiom, of Induction. It would yet be a great error to offer this
+large generalization as any explanation of the inductive process. On the
+contrary, I hold it to be itself an instance of induction, and induction
+by no means of the most obvious kind. Far from being the first induction
+we make, it is one of the last, or at all events one of those which are
+latest in attaining strict philosophical accuracy. As a general maxim,
+indeed, it has scarcely entered into the minds of any but philosophers;
+nor even by them, as we shall have many opportunities of remarking, have
+its extent and limits been always very justly conceived. The truth is,
+that this great generalization is itself founded on prior
+generalizations. The obscurer laws of nature were discovered by means
+of it, but the more obvious ones must have been understood and assented
+to as general truths before it was ever heard of. We should never have
+thought of affirming that all phenomena take place according to general
+laws, if we had not first arrived, in the case of a great multitude of
+phenomena, at some knowledge of the laws themselves; which could be done
+no otherwise than by induction. In what sense, then, can a principle,
+which is so far from being our earliest induction, be regarded as our
+warrant for all the others? In the only sense, in which (as we have
+already seen) the general propositions which we place at the head of our
+reasonings when we throw them into syllogisms, ever really contribute to
+their validity. As Archbishop Whately remarks, every induction is a
+syllogism with the major premise suppressed; or (as I prefer expressing
+it) every induction may be thrown into the form of a syllogism, by
+supplying a major premise. If this be actually done, the principle which
+we are now considering, that of the uniformity of the course of nature,
+will appear as the ultimate major premise of all inductions, and will,
+therefore, stand to all inductions in the relation in which, as has been
+shown at so much length, the major proposition of a syllogism always
+stands to the conclusion; not contributing at all to prove it, but being
+a necessary condition of its being proved; since no conclusion is
+proved, for which there cannot be found a true major premise.[9]
+
+The statement, that the uniformity of the course of nature is the
+ultimate major premise in all cases of induction, may be thought to
+require some explanation. The immediate major premise in every inductive
+argument, it certainly is not. Of that, Archbishop Whately's must be
+held to be the correct account. The induction, "John, Peter, &c. are
+mortal, therefore all mankind are mortal," may, as he justly says, be
+thrown into a syllogism by prefixing as a major premise (what is at any
+rate a necessary condition of the validity of the argument) namely, that
+what is true of John, Peter, &c. is true of all mankind. But how came we
+by this major premise? It is not self-evident; nay, in all cases of
+unwarranted generalization, it is not true. How, then, is it arrived at?
+Necessarily either by induction or ratiocination; and if by induction,
+the process, like all other inductive arguments, may be thrown into the
+form of a syllogism. This previous syllogism it is, therefore, necessary
+to construct. There is, in the long run, only one possible construction.
+The real proof that what is true of John, Peter, &c. is true of all
+mankind, can only be, that a different supposition would be inconsistent
+with the uniformity which we know to exist in the course of nature.
+Whether there would be this inconsistency or not, may be a matter of
+long and delicate inquiry; but unless there would, we have no sufficient
+ground for the major of the inductive syllogism. It hence appears, that
+if we throw the whole course of any inductive argument into a series of
+syllogisms, we shall arrive by more or fewer steps at an ultimate
+syllogism, which will have for its major premise the principle, or
+axiom, of the uniformity of the course of nature.[10]
+
+It was not to be expected that in the case of this axiom, any more than
+of other axioms, there should be unanimity among thinkers with respect
+to the grounds on which it is to be received as true. I have already
+stated that I regard it as itself a generalization from experience.
+Others hold it to be a principle which, antecedently to any verification
+by experience, we are compelled by the constitution of our thinking
+faculty to assume as true. Having so recently, and at so much length,
+combated a similar doctrine as applied to the axioms of mathematics, by
+arguments which are in a great measure applicable to the present case, I
+shall defer the more particular discussion of this controverted point in
+regard to the fundamental axiom of induction, until a more advanced
+period of our inquiry.[11] At present it is of more importance to
+understand thoroughly the import of the axiom itself. For the
+proposition, that the course of nature is uniform, possesses rather the
+brevity suitable to popular, than the precision requisite in
+philosophical language: its terms require to be explained, and a
+stricter than their ordinary signification given to them, before the
+truth of the assertion can be admitted.
+
+
+Sec. 2. Every person's consciousness assures him that he does not always
+expect uniformity in the course of events; he does not always believe
+that the unknown will be similar to the known, that the future will
+resemble the past. Nobody believes that the succession of rain and fine
+weather will be the same in every future year as in the present. Nobody
+expects to have the same dreams repeated every night. On the contrary,
+everybody mentions it as something extraordinary, if the course of
+nature is constant, and resembles itself, in these particulars. To look
+for constancy where constancy is not to be expected, as for instance
+that a day which has once brought good fortune will always be a
+fortunate day, is justly accounted superstition.
+
+The course of nature, in truth, is not only uniform, it is also
+infinitely various. Some phenomena are always seen to recur in the very
+same combinations in which we met with them at first; others seem
+altogether capricious; while some, which we had been accustomed to
+regard as bound down exclusively to a particular set of combinations, we
+unexpectedly find detached from some of the elements with which we had
+hitherto found them conjoined, and united to others of quite a contrary
+description. To an inhabitant of Central Africa, fifty years ago, no
+fact probably appeared to rest on more uniform experience than this,
+that all human beings are black. To Europeans, not many years ago, the
+proposition, All swans are white, appeared an equally unequivocal
+instance of uniformity in the course of nature. Further experience has
+proved to both that they were mistaken; but they had to wait fifty
+centuries for this experience. During that long time, mankind believed
+in an uniformity of the course of nature where no such uniformity really
+existed.
+
+According to the notion which the ancients entertained of induction, the
+foregoing were cases of as legitimate inference as any inductions
+whatever. In these two instances, in which, the conclusion being false,
+the ground of inference must have been insufficient, there was,
+nevertheless, as much ground for it as this conception of induction
+admitted of. The induction of the ancients has been well described by
+Bacon, under the name of "Inductio per enumerationem simplicem, ubi non
+reperitur instantia contradictoria." It consists in ascribing the
+character of general truths to all propositions which are true in every
+instance that we happen to know of. This is the kind of induction which
+is natural to the mind when unaccustomed to scientific methods. The
+tendency, which some call an instinct, and which others account for by
+association, to infer the future from the past, the known from the
+unknown, is simply a habit of expecting that what has been found true
+once or several times, and never yet found false, will be found true
+again. Whether the instances are few or many, conclusive or
+inconclusive, does not much affect the matter: these are considerations
+which occur only on reflection; the unprompted tendency of the mind is
+to generalize its experience, provided this points all in one direction;
+provided no other experience of a conflicting character comes unsought.
+The notion of seeking it, of experimenting for it, of _interrogating_
+nature (to use Bacon's expression) is of much later growth. The
+observation of nature, by uncultivated intellects, is purely passive:
+they accept the facts which present themselves, without taking the
+trouble of searching for more: it is a superior mind only which asks
+itself what facts are needed to enable it to come to a safe conclusion,
+and then looks out for these.
+
+But though we have always a propensity to generalize from unvarying
+experience, we are not always warranted in doing so. Before we can be at
+liberty to conclude that something is universally true because we have
+never known an instance to the contrary, we must have reason to believe
+that if there were in nature any instances to the contrary, we should
+have known of them. This assurance, in the great majority of cases, we
+cannot have, or can have only in a very moderate degree. The possibility
+of having it, is the foundation on which we shall see hereafter that
+induction by simple enumeration may in some remarkable cases amount
+practically to proof.[12] No such assurance, however, can be had, on any
+of the ordinary subjects of scientific inquiry. Popular notions are
+usually founded on induction by simple enumeration; in science it
+carries us but a little way. We are forced to begin with it; we must
+often rely on it provisionally, in the absence of means of more
+searching investigation. But, for the accurate study of nature, we
+require a surer and a more potent instrument.
+
+It was, above all, by pointing out the insufficiency of this rude and
+loose conception of Induction, that Bacon merited the title so generally
+awarded to him, of Founder of the Inductive Philosophy. The value of his
+own contributions to a more philosophical theory of the subject has
+certainly been exaggerated. Although (along with some fundamental
+errors) his writings contain, more or less fully developed, several of
+the most important principles of the Inductive Method, physical
+investigation has now far outgrown the Baconian conception of Induction.
+Moral and political inquiry, indeed, are as yet far behind that
+conception. The current and approved modes of reasoning on these
+subjects are still of the same vicious description against which Bacon
+protested; the method almost exclusively employed by those professing to
+treat such matters inductively, is the very _inductio per enumerationem
+simplicem_ which he condemns; and the experience which we hear so
+confidently appealed to by all sects, parties, and interests, is still,
+in his own emphatic words, _mera palpatio_.
+
+
+Sec. 3. In order to a better understanding of the problem which the
+logician must solve if he would establish a scientific theory of
+Induction, let us compare a few cases of incorrect inductions with
+others which are acknowledged to be legitimate. Some, we know, which
+were believed for centuries to be correct, were nevertheless incorrect.
+That all swans are white, cannot have been a good induction, since the
+conclusion has turned out erroneous. The experience, however, on which
+the conclusion rested, was genuine. From the earliest records, the
+testimony of the inhabitants of the known world was unanimous on the
+point. The uniform experience, therefore, of the inhabitants of the
+known world, agreeing in a common result, without one known instance of
+deviation from that result, is not always sufficient to establish a
+general conclusion.
+
+But let us now turn to an instance apparently not very dissimilar to
+this. Mankind were wrong, it seems, in concluding that all swans were
+white: are we also wrong, when we conclude that all men's heads grow
+above their shoulders, and never below, in spite of the conflicting
+testimony of the naturalist Pliny? As there were black swans, though
+civilized people had existed for three thousand years on the earth
+without meeting with them, may there not also be "men whose heads do
+grow beneath their shoulders," notwithstanding a rather less perfect
+unanimity of negative testimony from observers? Most persons would
+answer No; it was more credible that a bird should vary in its colour,
+than that men should vary in the relative position of their principal
+organs. And there is no doubt that in so saying they would be right: but
+to say why they are right, would be impossible, without entering more
+deeply than is usually done, into the true theory of Induction.
+
+Again, there are cases in which we reckon with the most unfailing
+confidence upon uniformity, and other cases in which we do not count
+upon it at all. In some we feel complete assurance that the future will
+resemble the past, the unknown be precisely similar to the known. In
+others, however invariable may be the result obtained from the instances
+which have been observed, we draw from them no more than a very feeble
+presumption that the like result will hold in all other cases. That a
+straight line is the shortest distance between two points, we do not
+doubt to be true even in the region of the fixed stars. When a chemist
+announces the existence and properties of a newly-discovered substance,
+if we confide in his accuracy, we feel assured that the conclusions he
+has arrived at will hold universally, though the induction be founded
+but on a single instance. We do not withhold our assent, waiting for a
+repetition of the experiment; or if we do, it is from a doubt whether
+the one experiment was properly made, not whether if properly made it
+would be conclusive. Here, then, is a general law of nature, inferred
+without hesitation from a single instance; an universal proposition from
+a singular one. Now mark another case, and contrast it with this. Not
+all the instances which have been observed since the beginning of the
+world, in support of the general proposition that all crows are black,
+would be deemed a sufficient presumption of the truth of the
+proposition, to outweigh the testimony of one unexceptionable witness
+who should affirm that in some region of the earth not fully explored,
+he had caught and examined a crow, and had found it to be grey.
+
+Why is a single instance, in some cases, sufficient for a complete
+induction, while in others, myriads of concurring instances, without a
+single exception known or presumed, go such a very little way towards
+establishing an universal proposition? Whoever can answer this question
+knows more of the philosophy of logic than the wisest of the ancients,
+and has solved the problem of induction.
+
+
+
+
+CHAPTER IV.
+
+OF LAWS OF NATURE.
+
+
+Sec. 1. In the contemplation of that uniformity in the course of nature,
+which is assumed in every inference from experience, one of the first
+observations that present themselves is, that the uniformity in question
+is not properly uniformity, but uniformities. The general regularity
+results from the coexistence of partial regularities. The course of
+nature in general is constant, because the course of each of the various
+phenomena that compose it is so. A certain fact invariably occurs
+whenever certain circumstances are present, and does not occur when they
+are absent; the like is true of another fact; and so on. From these
+separate threads of connexion between parts of the great whole which we
+term nature, a general tissue of connexion unavoidably weaves itself, by
+which the whole is held together. If A is always accompanied by D, B by
+E, and C by F, it follows that A B is accompanied by D E, A C by D F, B
+C by E F, and finally A B C by D E F; and thus the general character of
+regularity is produced, which, along with and in the midst of infinite
+diversity, pervades all nature.
+
+The first point, therefore, to be noted in regard to what is called the
+uniformity of the course of nature, is, that it is itself a complex
+fact, compounded of all the separate uniformities which exist in respect
+to single phenomena. These various uniformities, when ascertained by
+what is regarded as a sufficient induction, we call in common parlance,
+Laws of Nature. Scientifically speaking, that title is employed in a
+more restricted sense, to designate the uniformities when reduced to
+their most simple expression. Thus in the illustration already employed,
+there were seven uniformities; all of which, if considered sufficiently
+certain, would in the more lax application of the term, be called laws
+of nature. But of the seven, three alone are properly distinct and
+independent: these being presupposed, the others follow of course. The
+three first, therefore, according to the stricter acceptation, are
+called laws of nature; the remainder not; because they are in truth mere
+_cases_ of the three first; virtually included in them; said, therefore,
+to _result_ from them: whoever affirms those three has already affirmed
+all the rest.
+
+To substitute real examples for symbolical ones, the following are three
+uniformities, or call them laws of nature: the law that air has weight,
+the law that pressure on a fluid is propagated equally in all
+directions, and the law that pressure in one direction, not opposed by
+equal pressure in the contrary direction, produces motion, which does
+not cease until equilibrium is restored. From these three uniformities
+we should be able to predict another uniformity, namely, the rise of the
+mercury in the Torricellian tube. This, in the stricter use of the
+phrase, is not a law of nature. It is the result of laws of nature. It
+is a _case_ of each and every one of the three laws: and is the only
+occurrence by which they could all be fulfilled. If the mercury were not
+sustained in the barometer, and sustained at such a height that the
+column of mercury were equal in weight to a column of the atmosphere of
+the same diameter; here would be a case, either of the air not pressing
+upon the surface of the mercury with the force which is called its
+weight, or of the downward pressure on the mercury not being propagated
+equally in an upward direction, or of a body pressed in one direction
+and not in the direction opposite, either not moving in the direction in
+which it is pressed, or stopping before it had attained equilibrium. If
+we knew, therefore, the three simple laws, but had never tried the
+Torricellian experiment, we might _deduce_ its result from those laws.
+The known weight of the air, combined with the position of the
+apparatus, would bring the mercury within the first of the three
+inductions; the first induction would bring it within the second, and
+the second within the third, in the manner which we characterized in
+treating of Ratiocination. We should thus come to know the more complex
+uniformity, independently of specific experience, through our knowledge
+of the simpler ones from which it results; though, for reasons which
+will appear hereafter, _verification_ by specific experience would still
+be desirable, and might possibly be indispensable.
+
+Complex uniformities which, like this, are mere cases of simpler ones,
+and have, therefore, been virtually affirmed in affirming those, may
+with propriety be called _laws_, but can scarcely, in the strictness of
+scientific speech, be termed Laws of Nature. It is the custom in
+science, wherever regularity of any kind can be traced, to call the
+general proposition which expresses the nature of that regularity, a
+law; as when, in mathematics, we speak of the law of decrease of the
+successive terms of a converging series. But the expression _law of
+nature_ has generally been employed with a sort of tacit reference to
+the original sense of the word law, namely, the expression of the will
+of a superior. When, therefore, it appeared that any of the uniformities
+which were observed in nature, would result spontaneously from certain
+other uniformities, no separate act of creative will being supposed
+necessary for the production of the derivative uniformities, these have
+not usually been spoken of as laws of nature. According to one mode of
+expression, the question, What are the laws of nature? may be stated
+thus:--What are the fewest and simplest assumptions, which being
+granted, the whole existing order of nature would result? Another mode
+of stating it would be thus: What are the fewest general propositions
+from which all the uniformities which exist in the universe might be
+deductively inferred?
+
+Every great advance which marks an epoch in the progress of science, has
+consisted in a step made towards the solution of this problem. Even a
+simple colligation of inductions already made, without any fresh
+extension of the inductive inference, is already an advance in that
+direction. When Kepler expressed the regularity which exists in the
+observed motions of the heavenly bodies, by the three general
+propositions called his laws, he, in so doing, pointed out three simple
+suppositions which, instead of a much greater number, would suffice to
+construct the whole scheme of the heavenly motions, so far as it was
+known up to that time. A similar and still greater step was made when
+these laws, which at first did not seem to be included in any more
+general truths, were discovered to be cases of the three laws of motion,
+as obtaining among bodies which mutually tend towards one another with a
+certain force, and have had a certain instantaneous impulse originally
+impressed upon them. After this great discovery, Kepler's three
+propositions, though still called laws, would hardly, by any person
+accustomed to use language with precision, be termed laws of nature:
+that phrase would be reserved for the simpler and more general laws into
+which Newton is said to have resolved them.
+
+According to this language, every well-grounded inductive generalization
+is either a law of nature, or a result of laws of nature, capable, if
+those laws are known, of being predicted from them. And the problem of
+Inductive Logic may be summed up in two questions: how to ascertain the
+laws of nature; and how, after having ascertained them, to follow them
+into their results. On the other hand, we must not suffer ourselves to
+imagine that this mode of statement amounts to a real analysis, or to
+anything but a mere verbal transformation of the problem; for the
+expression, Laws of Nature, _means_ nothing but the uniformities which
+exist among natural phenomena (or, in other words, the results of
+induction), when reduced to their simplest expression. It is, however,
+something to have advanced so far, as to see that the study of nature is
+the study of laws, not _a_ law; of uniformities, in the plural number:
+that the different natural phenomena have their separate rules or modes
+of taking place, which, though much intermixed and entangled with one
+another, may, to a certain extent, be studied apart: that (to resume our
+former metaphor) the regularity which exists in nature is a web composed
+of distinct threads, and only to be understood by tracing each of the
+threads separately; for which purpose it is often necessary to unravel
+some portion of the web, and exhibit the fibres apart. The rules of
+experimental inquiry are the contrivances for unravelling the web.
+
+
+Sec. 2. In thus attempting to ascertain the general order of nature by
+ascertaining the particular order of the occurrence of each one of the
+phenomena of nature, the most scientific proceeding can be no more than
+an improved form of that which was primitively pursued by the human
+understanding, while undirected by science. When mankind first formed
+the idea of studying phenomena according to a stricter and surer method
+than that which they had in the first instance spontaneously adopted,
+they did not, conformably to the well-meant but impracticable precept of
+Descartes, set out from the supposition that nothing had been already
+ascertained. Many of the uniformities existing among phenomena are so
+constant, and so open to observation, as to force themselves upon
+involuntary recognition. Some facts are so perpetually and familiarly
+accompanied by certain others, that mankind learnt, as children learn,
+to expect the one where they found the other, long before they knew how
+to put their expectation into words by asserting, in a proposition, the
+existence of a connexion between those phenomena. No science was needed
+to teach that food nourishes, that water drowns, or quenches thirst,
+that the sun gives light and heat, that bodies fall to the ground. The
+first scientific inquirers assumed these and the like as known truths,
+and set out from them to discover others which were unknown: nor were
+they wrong in so doing, subject, however, as they afterwards began to
+see, to an ulterior revision of these spontaneous generalizations
+themselves, when the progress of knowledge pointed out limits to them,
+or showed their truth to be contingent on some circumstance not
+originally attended to. It will appear, I think, from the subsequent
+part of our inquiry, that there is no logical fallacy in this mode of
+proceeding; but we may see already that any other mode is rigorously
+impracticable: since it is impossible to frame any scientific method of
+induction, or test of the correctness of inductions, unless on the
+hypothesis that some inductions deserving of reliance have been already
+made.
+
+Let us revert, for instance, to one of our former illustrations, and
+consider why it is that, with exactly the same amount of evidence, both
+negative and positive, we did not reject the assertion that there are
+black swans, while we should refuse credence to any testimony which
+asserted that there were men wearing their heads underneath their
+shoulders. The first assertion was more credible than the latter. But
+why more credible? So long as neither phenomenon had been actually
+witnessed, what reason was there for finding the one harder to be
+believed than the other? Apparently because there is less constancy in
+the colours of animals, than in the general structure of their anatomy.
+But how do we know this? Doubtless, from experience. It appears, then,
+that we need experience to inform us, in what degree, and in what cases,
+or sort of cases, experience is to be relied on. Experience must be
+consulted in order to learn from it under what circumstances arguments
+from it will be valid. We have no ulterior test to which we subject
+experience in general; but we make experience its own test. Experience
+testifies, that among the uniformities which it exhibits or seems to
+exhibit, some are more to be relied on than others; and uniformity,
+therefore, may be presumed, from any given number of instances, with a
+greater degree of assurance, in proportion as the case belongs to a
+class in which the uniformities have hitherto been found more uniform.
+
+This mode of correcting one generalization by means of another, a
+narrower generalization by a wider, which common sense suggests and
+adopts in practice, is the real type of scientific Induction. All that
+art can do is but to give accuracy and precision to this process, and
+adapt it to all varieties of cases, without any essential alteration in
+its principle.
+
+There are of course no means of applying such a test as that above
+described, unless we already possess a general knowledge of the
+prevalent character of the uniformities existing throughout nature. The
+indispensable foundation, therefore, of a scientific formula of
+induction, must be a survey of the inductions to which mankind have been
+conducted in unscientific practice; with the special purpose of
+ascertaining what kinds of uniformities have been found perfectly
+invariable, pervading all nature, and what are those which have been
+found to vary with difference of time, place, or other changeable
+circumstances.
+
+
+Sec. 3. The necessity of such a survey is confirmed by the consideration,
+that the stronger inductions are the touchstone to which we always
+endeavour to bring the weaker. If we find any means of deducing one of
+the less strong inductions from stronger ones, it acquires, at once, all
+the strength of those from which it is deduced; and even adds to that
+strength; since the independent experience on which the weaker induction
+previously rested, becomes additional evidence of the truth of the
+better established law in which it is now found to be included. We may
+have inferred, from historical evidence, that the uncontrolled power of
+a monarch, of an aristocracy, or of the majority, will often be abused:
+but we are entitled to rely on this generalization with much greater
+assurance when it is shown to be a corollary from still better
+established facts; the very low degree of elevation of character ever
+yet attained by the average of mankind, and the little efficacy, for the
+most part, of the modes of education hitherto practised, in maintaining
+the predominance of reason and conscience over the selfish propensities.
+It is at the same time obvious that even these more general facts derive
+an accession of evidence from the testimony which history bears to the
+effects of despotism. The strong induction becomes still stronger when a
+weaker one has been bound up with it.
+
+On the other hand, if an induction conflicts with stronger inductions,
+or with conclusions capable of being correctly deduced from them, then,
+unless on reconsideration it should appear that some of the stronger
+inductions have been expressed with greater universality than their
+evidence warrants, the weaker one must give way. The opinion so long
+prevalent that a comet, or any other unusual appearance in the heavenly
+regions, was the precursor of calamities to mankind, or to those at
+least who witnessed it; the belief in the veracity of the oracles
+of Delphi or Dodona; the reliance on astrology, or on the
+weather-prophecies in almanacs, were doubtless inductions supposed to be
+grounded on experience:[13] and faith in such delusions seems quite
+capable of holding out against a great multitude of failures, provided
+it be nourished by a reasonable number of casual coincidences between
+the prediction and the event. What has really put an end to these
+insufficient inductions, is their inconsistency with the stronger
+inductions subsequently obtained by scientific inquiry, respecting the
+causes on which terrestrial events really depend; and where those
+scientific truths have not yet penetrated, the same or similar delusions
+still prevail.
+
+It may be affirmed as a general principle, that all inductions, whether
+strong or weak, which can be connected by ratiocination, are
+confirmatory of one another; while any which lead deductively to
+consequences that are incompatible, become mutually each other's test,
+showing that one or other must be given up, or at least more guardedly
+expressed. In the case of inductions which confirm each other, the one
+which becomes a conclusion from ratiocination rises to at least the
+level of certainty of the weakest of those from which it is deduced;
+while in general all are more or less increased in certainty. Thus the
+Torricellian experiment, though a mere case of three more general laws,
+not only strengthened greatly the evidence on which those laws rested,
+but converted one of them (the weight of the atmosphere) from a doubtful
+generalization into a completely established doctrine.
+
+If, then, a survey of the uniformities which have been ascertained to
+exist in nature, should point out some which, as far as any human
+purpose requires certainty, may be considered quite certain and quite
+universal; then by means of these uniformities we may be able to raise
+multitudes of other inductions to the same point in the scale. For if we
+can show, with respect to any inductive inference, that either it must
+be true, or one of these certain and universal inductions must admit of
+an exception; the former generalization will attain the same certainty,
+and indefeasibleness within the bounds assigned to it, which are the
+attributes of the latter. It will be proved to be a law; and if not a
+result of other and simpler laws, it will be a law of nature.
+
+There are such certain and universal inductions; and it is because there
+are such, that a Logic of Induction is possible.
+
+
+
+
+CHAPTER V.
+
+OF THE LAW OF UNIVERSAL CAUSATION.
+
+
+Sec. 1. The phenomena of nature exist in two distinct relations to one
+another; that of simultaneity, and that of succession. Every phenomenon
+is related, in an uniform manner, to some phenomena that coexist with
+it, and to some that have preceded and will follow it.
+
+Of the uniformities which exist among synchronous phenomena, the most
+important, on every account, are the laws of number; and next to them
+those of space, or, in other words, of extension and figure. The laws of
+number are common to synchronous and successive phenomena. That two and
+two make four, is equally true whether the second two follow the first
+two or accompany them. It is as true of days and years as of feet and
+inches. The laws of extension and figure (in other words, the theorems
+of geometry, from its lowest to its highest branches) are, on the
+contrary, laws of simultaneous phenomena only. The various parts of
+space, and of the objects which are said to fill space, coexist; and the
+unvarying laws which are the subject of the science of geometry, are an
+expression of the mode of their coexistence.
+
+This is a class of laws, or in other words, of uniformities, for the
+comprehension and proof of which it is not necessary to suppose any
+lapse of time, any variety of facts or events succeeding one another. If
+all the objects in the universe were unchangeably fixed, and had
+remained in that condition from eternity, the propositions of geometry
+would still be true of those objects. All things which possess
+extension, or, in other words, which fill space, are subject to
+geometrical laws. Possessing extension, they possess figure; possessing
+figure, they must possess some figure in particular, and have all the
+properties which geometry assigns to that figure. If one body be a
+sphere and another a cylinder, of equal height and diameter, the one
+will be exactly two-thirds of the other, let the nature and quality of
+the material be what it will. Again, each body, and each point of a
+body, must occupy some place or position among other bodies; and the
+position of two bodies relatively to each other, of whatever nature the
+bodies be, may be unerringly inferred from the position of each of them
+relatively to any third body.
+
+In the laws of number, then, and in those of space, we recognise in the
+most unqualified manner, the rigorous universality of which we are in
+quest. Those laws have been in all ages the type of certainty, the
+standard of comparison for all inferior degrees of evidence. Their
+invariability is so perfect, that it renders us unable even to conceive
+any exception to them; and philosophers have been led, though (as I have
+endeavoured to show) erroneously, to consider their evidence as lying
+not in experience, but in the original constitution of the intellect. If
+therefore, from the laws of space and number, we were able to deduce
+uniformities of any other description, this would be conclusive evidence
+to us that those other uniformities possessed the same rigorous
+certainty. But this we cannot do. From laws of space and number alone,
+nothing can be deduced but laws of space and number.
+
+Of all truths relating to phenomena, the most valuable to us are those
+which relate to the order of their succession. On a knowledge of these
+is founded every reasonable anticipation of future facts, and whatever
+power we possess of influencing those facts to our advantage. Even the
+laws of geometry are chiefly of practical importance to us as being a
+portion of the premises from which the order of the succession of
+phenomena may be inferred. Inasmuch as the motion of bodies, the action
+of forces, and the propagation of influences of all sorts, take place in
+certain lines and over definite spaces, the properties of those lines
+and spaces are an important part of the laws to which those phenomena
+are themselves subject. Again, motions, forces or other influences, and
+times, are numerable quantities; and the properties of number are
+applicable to them as to all other things. But though the laws of number
+and space are important elements in the ascertainment of uniformities
+of succession, they can do nothing towards it when taken by themselves.
+They can only be made instrumental to that purpose when we combine with
+them additional premises, expressive of uniformities of succession
+already known. By taking, for instance, as premises these propositions,
+that bodies acted upon by an instantaneous force move with uniform
+velocity in straight lines; that bodies acted upon by a continuous force
+move with accelerated velocity in straight lines; and that bodies acted
+upon by two forces in different directions move in the diagonal of a
+parallelogram, whose sides represent the direction and quantity of those
+forces; we may by combining these truths with propositions relating to
+the properties of straight lines and of parallelograms, (as that a
+triangle is half a parallelogram of the same base and altitude,) deduce
+another important uniformity of succession, viz., that a body moving
+round a centre of force describes areas proportional to the times. But
+unless there had been laws of succession in our premises, there could
+have been no truths of succession in our conclusions. A similar remark
+might be extended to every other class of phenomena really peculiar;
+and, had it been attended to, would have prevented many chimerical
+attempts at demonstrations of the indemonstrable, and explanations which
+do not explain.
+
+It is not, therefore, enough for us that the laws of space, which are
+only laws of simultaneous phenomena, and the laws of number, which
+though true of successive phenomena do not relate to their succession,
+possess the rigorous certainty and universality of which we are in
+search. We must endeavour to find some law of succession which has those
+same attributes, and is therefore fit to be made the foundation of
+processes for discovering, and of a test for verifying, all other
+uniformities of succession. This fundamental law must resemble the
+truths of geometry in their most remarkable peculiarity, that of never
+being, in any instance whatever, defeated or suspended by any change of
+circumstances.
+
+Now among all those uniformities in the succession of phenomena, which
+common observation is sufficient to bring to light, there are very few
+which have any, even apparent, pretension to this rigorous
+indefeasibility: and of those few, one only has been found capable of
+completely sustaining it. In that one, however, we recognise a law which
+is universal also in another sense; it is coextensive with the entire
+field of successive phenomena, all instances whatever of succession
+being examples of it. This law is the Law of Causation. The truth that
+every fact which has a beginning has a cause, is coextensive with human
+experience.
+
+This generalization may appear to some minds not to amount to much,
+since after all it asserts only this: "it is a law; that every event
+depends on some law:" "it is a law, that there is a law for everything."
+We must not, however, conclude that the generality of the principle is
+merely verbal; it will be found on inspection to be no vague or
+unmeaning assertion, but a most important and really fundamental truth.
+
+
+Sec. 2. The notion of Cause being the root of the whole theory of
+Induction, it is indispensable that this idea should, at the very outset
+of our inquiry, be, with the utmost practicable degree of precision,
+fixed and determined. If, indeed, it were necessary for the purpose of
+inductive logic that the strife should be quelled, which has so long
+raged among the different schools of metaphysicians, respecting the
+origin and analysis of our idea of causation; the promulgation, or at
+least the general reception, of a true theory of induction, might be
+considered desperate for a long time to come. But the science of the
+Investigation of Truth by means of Evidence, is happily independent of
+many of the controversies which perplex the science of the ultimate
+constitution of the human mind, and is under no necessity of pushing the
+analysis of mental phenomena to that extreme limit which alone ought to
+satisfy a metaphysician.
+
+I premise, then, that when in the course of this inquiry I speak of the
+cause of any phenomenon, I do not mean a cause which is not itself a
+phenomenon; I make no research into the ultimate or ontological cause of
+anything. To adopt a distinction familiar in the writings of the Scotch
+metaphysicians, and especially of Reid, the causes with which I concern
+myself are not _efficient_, but _physical_ causes. They are causes in
+that sense alone, in which one physical fact is said to be the cause of
+another. Of the efficient causes of phenomena, or whether any such
+causes exist at all, I am not called upon to give an opinion. The notion
+of causation is deemed, by the schools of metaphysics most in vogue at
+the present moment, to imply a mysterious and most powerful tie, such as
+cannot, or at least does not, exist between any physical fact and that
+other physical fact on which it is invariably consequent, and which is
+popularly termed its cause: and thence is deduced the supposed necessity
+of ascending higher, into the essences and inherent constitution of
+things, to find the true cause, the cause which is not only followed by,
+but actually produces, the effect. No such necessity exists for the
+purposes of the present inquiry, nor will any such doctrine be found in
+the following pages. The only notion of a cause, which the theory of
+induction requires, is such a notion as can be gained from experience.
+The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it; independently of all
+consideration respecting the ultimate mode of production of phenomena,
+and of every other question regarding the nature of "Things in
+themselves."
+
+Between the phenomena, then, which exist at any instant, and the
+phenomena which exist at the succeeding instant, there is an invariable
+order of succession; and, as we said in speaking of the general
+uniformity of the course of nature, this web is composed of separate
+fibres; this collective order is made up of particular sequences,
+obtaining invariably among the separate parts. To certain facts, certain
+facts always do, and, as we believe, will continue to, succeed. The
+invariable antecedent is termed the cause; the invariable consequent,
+the effect. And the universality of the law of causation consists in
+this, that every consequent is connected in this manner with some
+particular antecedent, or set of antecedents. Let the fact be what it
+may, if it has begun to exist, it was preceded by some fact or facts,
+with which it is invariably connected. For every event there exists some
+combination of objects or events, some given concurrence of
+circumstances, positive and negative, the occurrence of which is always
+followed by that phenomenon. We may not have found out what this
+concurrence of circumstances may be; but we never doubt that there is
+such a one, and that it never occurs without having the phenomenon in
+question as its effect or consequence. On the universality of this truth
+depends the possibility of reducing the inductive process to rules. The
+undoubted assurance we have that there is a law to be found if we only
+knew how to find it, will be seen presently to be the source from which
+the canons of the Inductive Logic derive their validity.
+
+
+Sec. 3. It is seldom, if ever, between a consequent and a single
+antecedent, that this invariable sequence subsists. It is usually
+between a consequent and the sum of several antecedents; the concurrence
+of all of them being requisite to produce, that is, to be certain of
+being followed by, the consequent. In such cases it is very common to
+single out one only of the antecedents under the denomination of Cause,
+calling the others merely Conditions. Thus, if a person eats of a
+particular dish, and dies in consequence, that is, would not have died
+if he had not eaten of it, people would be apt to say that eating of
+that dish was the cause of his death. There needs not, however, be any
+invariable connexion between eating of the dish and death; but there
+certainly is, among the circumstances which took place, some combination
+or other on which death is invariably consequent: as, for instance, the
+act of eating of the dish, combined with a particular bodily
+constitution, a particular state of present health, and perhaps even a
+certain state of the atmosphere; the whole of which circumstances
+perhaps constituted in this particular case the _conditions_ of the
+phenomenon, or, in other words, the set of antecedents which determined
+it, and but for which it would not have happened. The real Cause, is the
+whole of these antecedents; and we have, philosophically speaking, no
+right to give the name of cause to one of them, exclusively of the
+others. What, in the case we have supposed, disguises the incorrectness
+of the expression, is this: that the various conditions, except the
+single one of eating the food, were not _events_ (that is, instantaneous
+changes, or successions of instantaneous changes) but _states_,
+possessing more or less of permanency; and might therefore have preceded
+the effect by an indefinite length of duration, for want of the event
+which was requisite to complete the required concurrence of conditions:
+while as soon as that event, eating the food, occurs, no other cause is
+waited for, but the effect begins immediately to take place: and hence
+the appearance is presented of a more immediate and close connexion
+between the effect and that one antecedent, than between the effect and
+the remaining conditions. But though we may think proper to give the
+name of cause to that one condition, the fulfilment of which completes
+the tale, and brings about the effect without further delay; this
+condition has really no closer relation to the effect than any of the
+other conditions has. The production of the consequent required that
+they should all _exist_ immediately previous, though not that they
+should all _begin_ to exist immediately previous. The statement of the
+cause is incomplete, unless in some shape or other we introduce all the
+conditions. A man takes mercury, goes out of doors, and catches cold. We
+say, perhaps, that the cause of his taking cold was exposure to the air.
+It is clear, however, that his having taken mercury may have been a
+necessary condition of catching cold; and though it might consist with
+usage to say that the cause of his attack was exposure to the air, to be
+accurate we ought to say that the cause was exposure to the air while
+under the effect of mercury.
+
+If we do not, when aiming at accuracy, enumerate all the conditions, it
+is only because some of them will in most cases be understood without
+being expressed, or because for the purpose in view they may without
+detriment be overlooked. For example, when we say, the cause of a man's
+death was that his foot slipped in climbing a ladder, we omit as a
+thing unnecessary to be stated the circumstance of his weight, though
+quite as indispensable a condition of the effect which took place. When
+we say that the assent of the crown to a bill makes it law, we mean that
+the assent, being never given until all the other conditions are
+fulfilled, makes up the sum of the conditions, though no one now regards
+it as the principal one. When the decision of a legislative assembly has
+been determined by the casting vote of the chairman, we sometimes say
+that this one person was the cause of all the effects which resulted
+from the enactment. Yet we do not really suppose that his single vote
+contributed more to the result than that of any other person who voted
+in the affirmative; but, for the purpose we have in view, which is to
+insist on his individual responsibility, the part which any other person
+had in the transaction is not material.
+
+In all these instances the fact which was dignified with the name of
+cause, was the one condition which came last into existence. But it must
+not be supposed that in the employment of the term this or any other
+rule is always adhered to. Nothing can better show the absence of any
+scientific ground for the distinction between the cause of a phenomenon
+and its conditions, than the capricious manner in which we select from
+among the conditions that which we choose to denominate the cause.
+However numerous the conditions may be, there is hardly any of them
+which may not, according to the purpose of our immediate discourse,
+obtain that nominal pre-eminence. This will be seen by analysing the
+conditions of some one familiar phenomenon. For example, a stone thrown
+into water falls to the bottom. What are the conditions of this event?
+In the first place there must be a stone, and water, and the stone must
+be thrown into the water; but these suppositions forming part of the
+enunciation of the phenomenon itself, to include them also among the
+conditions would be a vicious tautology; and this class of conditions,
+therefore, have never received the name of cause from any but the
+Aristotelians, by whom they were called the _material_ cause, _causa
+materialis_. The next condition is, there must be an earth: and
+accordingly it is often said, that the fall of a stone is caused by the
+earth; or by a power or property of the earth, or a force exerted by the
+earth, all of which are merely roundabout ways of saying that it is
+caused by the earth; or, lastly, the earth's attraction; which also is
+only a technical mode of saying that the earth causes the motion, with
+the additional particularity that the motion is towards the earth, which
+is not a character of the cause, but of the effect. Let us now pass to
+another condition. It is not enough that the earth should exist; the
+body must be within that distance from it, in which the earth's
+attraction preponderates over that of any other body. Accordingly we may
+say, and the expression would be confessedly correct, that the cause of
+the stone's falling is its being _within the sphere_ of the earth's
+attraction. We proceed to a further condition. The stone is immersed in
+water: it is therefore a condition of its reaching the ground, that its
+specific gravity exceed that of the surrounding fluid, or in other words
+that it surpass in weight an equal volume of water. Accordingly any one
+would be acknowledged to speak correctly who said, that the cause of the
+stone's going to the bottom is its exceeding in specific gravity the
+fluid in which it is immersed.
+
+Thus we see that each and every condition of the phenomenon may be taken
+in its turn, and, with equal propriety in common parlance, but with
+equal impropriety in scientific discourse, may be spoken of as if it
+were the entire cause. And in practice, that particular condition is
+usually styled the cause, whose share in the matter is superficially the
+most conspicuous, or whose requisiteness to the production of the effect
+we happen to be insisting on at the moment. So great is the force of
+this last consideration, that it sometimes induces us to give the name
+of cause even to one of the negative conditions. We say, for example,
+The army was surprised because the sentinel was off his post. But since
+the sentinel's absence was not what created the enemy, or put the
+soldiers asleep, how did it cause them to be surprised? All that is
+really meant is, that the event would not have happened if he had been
+at his duty. His being off his post was no producing cause, but the mere
+absence of a preventing cause: it was simply equivalent to his
+non-existence. From nothing, from a mere negation, no consequences can
+proceed. All effects are connected, by the law of causation, with some
+set of _positive_ conditions; negative ones, it is true, being almost
+always required in addition. In other words, every fact or phenomenon
+which has a beginning, invariably arises when some certain combination
+of positive facts exists, provided certain other positive facts do not
+exist.
+
+There is, no doubt, a tendency (which our first example, that of death
+from taking a particular food, sufficiently illustrates) to associate
+the idea of causation with the proximate antecedent _event_, rather than
+with any of the antecedent _states_, or permanent facts, which may
+happen also to be conditions of the phenomenon; the reason being that
+the event not only exists, but begins to exist immediately previous;
+while the other conditions may have pre-existed for an indefinite time.
+And this tendency shows itself very visibly in the different logical
+fictions which are resorted to, even by men of science, to avoid the
+necessity of giving the name of cause to anything which had existed for
+an indeterminate length of time before the effect. Thus, rather than say
+that the earth causes the fall of bodies, they ascribe it to a _force_
+exerted by the earth, or an _attraction_ by the earth, abstractions
+which they can represent to themselves as exhausted by each effort, and
+therefore constituting at each successive instant a fresh fact,
+simultaneous with, or only immediately preceding, the effect. Inasmuch
+as the coming of the circumstance which completes the assemblage of
+conditions, is a change or event, it thence happens that an event is
+always the antecedent in closest apparent proximity to the consequent:
+and this may account for the illusion which disposes us to look upon the
+proximate event as standing more peculiarly in the position of a cause
+than any of the antecedent states. But even this peculiarity, of being
+in closer proximity to the effect than any other of its conditions, is,
+as we have already seen, far from being necessary to the common notion
+of a cause; with which notion, on the contrary, any one of the
+conditions, either positive or negative, is found, on occasion,
+completely to accord.[14]
+
+The cause, then, philosophically speaking, is the sum total of the
+conditions, positive and negative taken together; the whole of the
+contingencies of every description, which being realized, the consequent
+invariably follows. The negative conditions, however, of any
+phenomenon, a special enumeration of which would generally be very
+prolix, may be all summed up under one head, namely, the absence of
+preventing or counteracting causes. The convenience of this mode of
+expression is mainly grounded on the fact, that the effects of any cause
+in counteracting another cause may in most cases be, with strict
+scientific exactness, regarded as a mere extension of its own proper and
+separate effects. If gravity retards the upward motion of a projectile,
+and deflects it into a parabolic trajectory, it produces, in so doing,
+the very same kind of effect, and even (as mathematicians know) the
+same quantity of effect, as it does in its ordinary operation of causing
+the fall of bodies when simply deprived of their support. If an alkaline
+solution mixed with an acid destroys its sourness, and prevents it from
+reddening vegetable blues, it is because the specific effect of the
+alkali is to combine with the acid, and form a compound with totally
+different qualities. This property, which causes of all descriptions
+possess, of preventing the effects of other causes by virtue (for the
+most part) of the same laws according to which they produce their
+own,[15] enables us, by establishing the general axiom that all causes
+are liable to be counteracted in their effects by one another, to
+dispense with the consideration of negative conditions entirely, and
+limit the notion of cause to the assemblage of the positive conditions
+of the phenomenon: one negative condition invariably understood, and the
+same in all instances (namely, the absence of counteracting causes)
+being sufficient, along with the sum of the positive conditions, to make
+up the whole set of circumstances on which the phenomenon is dependent.
+
+
+Sec. 4. Among the positive conditions, as we have seen that there are some
+to which, in common parlance, the term cause is more readily and
+frequently awarded, so there are others to which it is, in ordinary
+circumstances, refused. In most cases of causation a distinction is
+commonly drawn between something which acts, and some other thing which
+is acted upon; between an _agent_ and a _patient_. Both of these, it
+would be universally allowed, are conditions of the phenomenon; but it
+would be thought absurd to call the latter the cause, that title being
+reserved for the former. The distinction, however, vanishes on
+examination, or rather is found to be only verbal; arising from an
+incident of mere expression, namely, that the object said to be acted
+upon, and which is considered as the scene in which the effect takes
+place, is commonly included in the phrase by which the effect is spoken
+of, so that if it were also reckoned as part of the cause, the seeming
+incongruity would arise of its being supposed to cause itself. In the
+instance which we have already had, of falling bodies, the question was
+thus put: What is the cause which makes a stone fall? and if the answer
+had been "the stone itself," the expression would have been in apparent
+contradiction to the meaning of the word cause. The stone, therefore, is
+conceived as the patient, and the earth (or, according to the common and
+most unphilosophical practice, some occult quality of the earth) is
+represented as the agent or cause. But that there is nothing fundamental
+in the distinction may be seen from this, that it is quite possible to
+conceive the stone as causing its own fall, provided the language
+employed be such as to save the mere verbal incongruity. We might say
+that the stone moves towards the earth by the properties of the matter
+composing it; and according to this mode of presenting the phenomenon,
+the stone itself might without impropriety be called the agent; though,
+to save the established doctrine of the inactivity of matter, men
+usually prefer here also to ascribe the effect to an occult quality, and
+say that the cause is not the stone itself, but the _weight_ or
+_gravitation_ of the stone.
+
+Those who have contended for a radical distinction between agent and
+patient, have generally conceived the agent as that which causes some
+state of, or some change in the state of, another object which is called
+the patient. But a little reflection will show that the licence we
+assume of speaking of phenomena as _states_ of the various objects which
+take part in them, (an artifice of which so much use has been made by
+some philosophers, Brown in particular, for the apparent explanation of
+phenomena,) is simply a sort of logical fiction, useful sometimes as one
+among several modes of expression, but which should never be supposed to
+be the enunciation of a scientific truth. Even those attributes of an
+object which might seem with greatest propriety to be called states of
+the object itself, its sensible qualities, its colour, hardness, shape,
+and the like, are in reality (as no one has pointed out more clearly
+than Brown himself) phenomena of causation, in which the substance is
+distinctly the agent, or producing cause, the patient being our own
+organs, and those of other sentient beings. What we call states of
+objects, are always sequences into which the objects enter, generally as
+antecedents or causes; and things are never more active than in the
+production of those phenomena in which they are said to be acted upon.
+Thus, in the example of a stone falling to the earth, according to the
+theory of gravitation the stone is as much an agent as the earth, which
+not only attracts, but is itself attracted by, the stone. In the case of
+a sensation produced in our organs, the laws of our organization, and
+even those of our minds, are as directly operative in determining the
+effect produced, as the laws of the outward object. Though we call
+prussic acid the agent of a person's death, the whole of the vital and
+organic properties of the patient are as actively instrumental as the
+poison, in the chain of effects which so rapidly terminates his sentient
+existence. In the process of education, we may call the teacher the
+agent, and the scholar only the material acted upon; yet in truth all
+the facts which pre-existed in the scholar's mind exert either
+co-operating or counteracting agencies in relation to the teacher's
+efforts. It is not light alone which is the agent in vision, but light
+coupled with the active properties of the eye and brain, and with those
+of the visible object. The distinction between agent and patient is
+merely verbal: patients are always agents; in a great proportion,
+indeed, of all natural phenomena, they are so to such a degree as to
+react forcibly on the causes which acted upon them: and even when this
+is not the case, they contribute, in the same manner as any of the other
+conditions, to the production of the effect of which they are vulgarly
+treated as the mere theatre. All the positive conditions of a phenomenon
+are alike agents, alike active; and in any expression of the cause which
+professes to be complete, none of them can with reason be excluded,
+except such as have already been implied in the words used for
+describing the effect; nor by including even these would there be
+incurred any but a merely verbal impropriety.
+
+
+Sec. 5. It now remains to advert to a distinction which is of first-rate
+importance both for clearing up the notion of cause, and for obviating a
+very specious objection often made against the view which we have taken
+of the subject.
+
+When we define the cause of anything (in the only sense in which the
+present inquiry has any concern with causes) to be "the antecedent which
+it invariably follows," we do not use this phrase as exactly synonymous
+with "the antecedent which it invariably _has_ followed in our past
+experience." Such a mode of conceiving causation would be liable to the
+objection very plausibly urged by Dr. Reid, namely, that according to
+this doctrine night must be the cause of day, and day the cause of
+night; since these phenomena have invariably succeeded one another from
+the beginning of the world. But it is necessary to our using the word
+cause, that we should believe not only that the antecedent always _has_
+been followed by the consequent, but that, as long as the present
+constitution of things[16] endures, it always _will_ be so. And this
+would not be true of day and night. We do not believe that night will be
+followed by day under all imaginable circumstances, but only that it
+will be so _provided_ the sun rises above the horizon. If the sun ceased
+to rise, which, for aught we know, may be perfectly compatible with the
+general laws of matter, night would be, or might be, eternal. On the
+other hand, if the sun is above the horizon, his light not extinct, and
+no opaque body between us and him, we believe firmly that unless a
+change takes place in the properties of matter, this combination of
+antecedents will be followed by the consequent, day; that if the
+combination of antecedents could be indefinitely prolonged, it would be
+always day; and that if the same combination had always existed, it
+would always have been day, quite independently of night as a previous
+condition. Therefore is it that we do not call night the cause, nor even
+a condition, of day. The existence of the sun (or some such luminous
+body), and there being no opaque medium in a straight line[17] between
+that body and the part of the earth where we are situated, are the sole
+conditions; and the union of these, without the addition of any
+superfluous circumstance, constitutes the cause. This is what writers
+mean when they say that the notion of cause involves the idea of
+necessity. If there be any meaning which confessedly belongs to the term
+necessity, it is _unconditionalness_. That which is necessary, that
+which _must_ be, means that which will be, whatever supposition we may
+make in regard to all other things. The succession of day and night
+evidently is not necessary in this sense. It is conditional on the
+occurrence of other antecedents. That which will be followed by a given
+consequent when, and only when, some third circumstance also exists, is
+not the cause, even though no case should ever have occurred in which
+the phenomenon took place without it.
+
+Invariable sequence, therefore, is not synonymous with causation, unless
+the sequence, besides being invariable, is unconditional. There are
+sequences, as uniform in past experience as any others whatever, which
+yet we do not regard as cases of causation, but as conjunctions in some
+sort accidental. Such, to an accurate thinker, is that of day and night.
+The one might have existed for any length of time, and the other not
+have followed the sooner for its existence; it follows only if certain
+other antecedents exist; and where those antecedents existed, it would
+follow in any case. No one, probably, ever called night the cause of
+day; mankind must so soon have arrived at the very obvious
+generalization, that the state of general illumination which we call day
+would follow from the presence of a sufficiently luminous body, whether
+darkness had preceded or not.
+
+We may define, therefore, the cause of a phenomenon, to be the
+antecedent, or the concurrence of antecedents, on which it is invariably
+and _unconditionally_ consequent. Or if we adopt the convenient
+modification of the meaning of the word cause, which confines it to the
+assemblage of positive conditions without the negative, then instead of
+"unconditionally," we must say, "subject to no other than negative
+conditions."
+
+To some it may appear, that the sequence between night and day being
+invariable in our experience, we have as much ground in this case as
+experience can give in any case, for recognising the two phenomena as
+cause and effect; and that to say that more is necessary--to require a
+belief that the succession is unconditional, or in other words that it
+would be invariable under all changes of circumstances, is to
+acknowledge in causation an element of belief not derived from
+experience. The answer to this is, that it is experience itself which
+teaches us that one uniformity of sequence is conditional and another
+unconditional. When we judge that the succession of night and day is a
+derivative sequence, depending on something else, we proceed on grounds
+of experience. It is the evidence of experience which convinces us that
+day could equally exist without being followed by night, and that night
+could equally exist without being followed by day. To say that these
+beliefs are "not generated by our mere observation of sequence,"[18] is
+to forget that twice in every twenty-four hours, when the sky is clear,
+we have an _experimentum crucis_ that the cause of day is the sun. We
+have an experimental knowledge of the sun which justifies us on
+experimental grounds in concluding, that if the sun were always above
+the horizon there would be day, though there had been no night, and that
+if the sun were always below the horizon there would be night, though
+there had been no day. We thus know from experience that the succession
+of night and day is not unconditional. Let me add, that the antecedent
+which is only conditionally invariable, is not the invariable
+antecedent. Though a fact may, in experience, have always been followed
+by another fact, yet if the remainder of our experience teaches us that
+it might not always be so followed, or if the experience itself is such
+as leaves room for a possibility that the known cases may not correctly
+represent all possible cases, the hitherto invariable antecedent is not
+accounted the cause; but why? Because we are not sure that it _is_ the
+invariable antecedent.
+
+Such cases of sequence as that of day and night not only do not
+contradict the doctrine which resolves causation into invariable
+sequence, but are necessarily implied in that doctrine. It is evident,
+that from a limited number of unconditional sequences, there will
+result a much greater number of conditional ones. Certain causes being
+given, that is, certain antecedents which are unconditionally followed
+by certain consequents; the mere coexistence of these causes will give
+rise to an unlimited number of additional uniformities. If two causes
+exist together, the effects of both will exist together; and if many
+causes coexist, these causes (by what we shall term hereafter the
+intermixture of their laws) will give rise to new effects, accompanying
+or succeeding one another in some particular order, which order will be
+invariable while the causes continue to coexist, but no longer. The
+motion of the earth in a given orbit round the sun, is a series of
+changes which follow one another as antecedents and consequents, and
+will continue to do so while the sun's attraction, and the force with
+which the earth tends to advance in a direct line through space,
+continue to coexist in the same quantities as at present. But vary
+either of these causes, and this particular succession of motions would
+cease to take place. The series of the earth's motions, therefore,
+though a case of sequence invariable within the limits of human
+experience, is not a case of causation. It is not unconditional.
+
+This distinction between the relations of succession which so far as we
+know are unconditional, and those relations, whether of succession or of
+coexistence, which, like the earth's motions, or the succession of day
+and night, depend on the existence or on the coexistence of other
+antecedent facts--corresponds to the great division which Dr. Whewell
+and other writers have made of the field of science, into the
+investigation of what they term the Laws of Phenomena, and the
+investigation of causes; a phraseology, as I conceive, not
+philosophically sustainable, inasmuch as the ascertainment of causes,
+such causes as the human faculties can ascertain, namely, causes which
+are themselves phenomena, is, therefore, merely the ascertainment of
+other and more universal Laws of Phenomena. And let me here observe,
+that Dr. Whewell, and in some degree even Sir John Herschel, seem to
+have misunderstood the meaning of those writers who, like M. Comte,
+limit the sphere of scientific investigation to Laws of Phenomena, and
+speak of the inquiry into causes as vain and futile. The causes which M.
+Comte designates as inaccessible, are efficient causes. The
+investigation of physical, as opposed to efficient, causes (including
+the study of all the active forces in Nature, considered as facts of
+observation) is as important a part of M. Comte's conception of science
+as of Dr. Whewell's. His objection to the _word_ cause is a mere matter
+of nomenclature, in which, as a matter of nomenclature, I consider him
+to be entirely wrong. "Those," it is justly remarked by Mr. Bailey,[19]
+"who, like M. Comte, object to designate _events_ as causes, are
+objecting without any real ground to a mere but extremely convenient
+generalization, to a very useful common name, the employment of which
+involves, or needs involve, no particular theory." To which it may be
+added, that by rejecting this form of expression, M. Comte leaves
+himself without any term for marking a distinction which, however
+incorrectly expressed, is not only real, but is one of the fundamental
+distinctions in science; indeed it is on this alone, as we shall
+hereafter find, that the possibility rests of framing a rigorous Canon
+of Induction. And as things left without a name are apt to be forgotten,
+a Canon of that description is not one of the many benefits which the
+philosophy of Induction has received from M. Comte's great powers.
+
+
+Sec. 6. Does a cause always stand with its effect in the relation of
+antecedent and consequent? Do we not often say of two simultaneous facts
+that they are cause and effect--as when we say that fire is the cause of
+warmth, the sun and moisture the cause of vegetation, and the like?
+Since a cause does not necessarily perish because its effect has been
+produced, the two things do very generally coexist; and there are some
+appearances, and some common expressions, seeming to imply not only that
+causes may, but that they must, be contemporaneous with their effects.
+_Cessante causa cessat et effectus_, has been a dogma of the schools:
+the necessity for the continued existence of the cause in order to the
+continuance of the effect, seems to have been once a generally received
+doctrine. Kepler's numerous attempts to account for the motions of the
+heavenly bodies on mechanical principles, were rendered abortive by his
+always supposing that the agency which set those bodies in motion must
+continue to operate in order to keep up the motion which it at first
+produced. Yet there were at all times many familiar instances of the
+continuance of effects, long after their causes had ceased. A _coup de
+soleil_ gives a person a brain fever: will the fever go off as soon as
+he is moved out of the sunshine? A sword is run through his body: must
+the sword remain in his body in order that he may continue dead? A
+ploughshare once made, remains a ploughshare, without any continuance of
+heating and hammering, and even after the man who heated and hammered it
+has been gathered to his fathers. On the other hand, the pressure which
+forces up the mercury in an exhausted tube must be continued in order to
+sustain it in the tube. This (it may be replied) is because another
+force is acting without intermission, the force of gravity, which would
+restore it to its level, unless counterpoised by a force equally
+constant. But again; a tight bandage causes pain, which pain will
+sometimes go off as soon as the bandage is removed. The illumination
+which the sun diffuses over the earth ceases when the sun goes down.
+
+There is, therefore, a distinction to be drawn. The conditions which are
+necessary for the first production of a phenomenon, are occasionally
+also necessary for its continuance; though more commonly its continuance
+requires no condition except negative ones. Most things, once produced,
+continue as they are, until something changes or destroys them; but some
+require the permanent presence of the agencies which produced them at
+first. These may, if we please, be considered as instantaneous
+phenomena, requiring to be renewed at each instant by the cause by which
+they were at first generated. Accordingly, the illumination of any given
+point of space has always been looked upon as an instantaneous fact,
+which perishes and is perpetually renewed as long as the necessary
+conditions subsist. If we adopt this language we avoid the necessity of
+admitting that the continuance of the cause is ever required to maintain
+the effect. We may say, it is not required to maintain, but to
+reproduce, the effect, or else to counteract some force tending to
+destroy it. And this may be a convenient phraseology. But it is only a
+phraseology. The fact remains, that in some cases (though these are a
+minority) the continuance of the conditions which produced an effect is
+necessary to the continuance of the effect.
+
+As to the ulterior question, whether it is strictly necessary that the
+cause, or assemblage of conditions, should precede, by ever so short an
+instant, the production of the effect, (a question raised and argued
+with much ingenuity by Sir John Herschel in an Essay already
+quoted,[20]) the inquiry is of no consequence for our present purpose.
+There certainly are cases in which the effect follows without any
+interval perceptible by our faculties: and when there is an interval, we
+cannot tell by how many intermediate links imperceptible to us that
+interval may really be filled up. But even granting that an effect may
+commence simultaneously with its cause, the view I have taken of
+causation is in no way practically affected. Whether the cause and its
+effect be necessarily successive or not, the beginning of a phenomenon
+is what implies a cause, and causation is the law of the succession of
+phenomena. If these axioms be granted, we can afford, though I see no
+necessity for doing so, to drop the words antecedent and consequent as
+applied to cause and effect. I have no objection to define a cause, the
+assemblage of phenomena, which occurring, some other phenomenon
+invariably commences, or has its origin. Whether the effect coincides in
+point of time with, or immediately follows, the hindmost of its
+conditions, is immaterial. At all events it does not precede it; and
+when we are in doubt, between two coexistent phenomena, which is cause
+and which effect, we rightly deem the question solved if we can
+ascertain which of them preceded the other.
+
+
+Sec. 7. It continually happens that several different phenomena, which are
+not in the slightest degree dependent or conditional on one another, are
+found all to depend, as the phrase is, on one and the same agent; in
+other words, one and the same phenomenon is seen to be followed by
+several sorts of effects quite heterogeneous, but which go on
+simultaneously one with another; provided, of course, that all other
+conditions requisite for each of them also exist. Thus, the sun produces
+the celestial motions, it produces daylight, and it produces heat. The
+earth causes the fall of heavy bodies, and it also, in its capacity of a
+great magnet, causes the phenomena of the magnetic needle. A crystal of
+galena causes the sensations of hardness, of weight, of cubical form, of
+grey colour, and many others between which we can trace no
+interdependence. The purpose to which the phraseology of Properties and
+Powers is specially adapted, is the expression of this sort of cases.
+When the same phenomenon is followed (either subject or not to the
+presence of other conditions) by effects of different and dissimilar
+orders, it is usual to say that each different sort of effect is
+produced by a different property of the cause. Thus we distinguish the
+attractive or gravitative property of the earth, and its magnetic
+property: the gravitative, luminiferous, and calorific properties of the
+sun: the colour, shape, weight, and hardness of a crystal. These are
+mere phrases, which explain nothing, and add nothing to our knowledge of
+the subject; but, considered as abstract names denoting the connexion
+between the different effects produced and the object which produces
+them, they are a very powerful instrument of abridgment, and of that
+acceleration of the process of thought which abridgment accomplishes.
+
+This class of considerations leads to a conception which we shall find
+to be of great importance, that of a Permanent Cause, or original
+natural agent. There exist in nature a number of permanent causes, which
+have subsisted ever since the human race has been in existence, and for
+an indefinite and probably an enormous length of time previous. The sun,
+the earth, and planets, with their various constituents, air, water, and
+other distinguishable substances, whether simple or compound, of which
+nature is made up, are such Permanent Causes. These have existed, and
+the effects or consequences which they were fitted to produce have taken
+place (as often as the other conditions of the production met,) from the
+very beginning of our experience. But we can give no account of the
+origin of the Permanent Causes themselves. Why these particular natural
+agents existed originally and no others, or why they are commingled in
+such and such proportions, and distributed in such and such a manner
+throughout space, is a question we cannot answer. More than this: we can
+discover nothing regular in the distribution itself; we can reduce it to
+no uniformity, to no law. There are no means by which, from the
+distribution of these causes or agents in one part of space, we could
+conjecture whether a similar distribution prevails in another. The
+coexistence, therefore, of Primeval Causes, ranks, to us, among merely
+casual concurrences: and all those sequences or coexistences among the
+effects of several such causes, which, though invariable while those
+causes coexist, would, if the coexistence terminated, terminate along
+with it, we do not class as cases of causation, or laws of nature: we
+can only calculate on finding these sequences or coexistences where we
+know by direct evidence, that the natural agents on the properties of
+which they ultimately depend, are distributed in the requisite manner.
+These Permanent Causes are not always objects; they are sometimes
+events, that is to say, periodical cycles of events, that being the only
+mode in which events can possess the property of permanence. Not only,
+for instance, is the earth itself a permanent cause, or primitive
+natural agent, but the earth's rotation is so too: it is a cause which
+has produced, from the earliest period, (by the aid of other necessary
+conditions,) the succession of day and night, the ebb and flow of the
+sea, and many other effects, while, as we can assign no cause (except
+conjecturally) for the rotation itself, it is entitled to be ranked as a
+primeval cause. It is, however, only the _origin_ of the rotation which
+is mysterious to us: once begun, its continuance is accounted for by the
+first law of motion (that of the permanence of rectilinear motion once
+impressed) combined with the gravitation of the parts of the earth
+towards one another.
+
+All phenomena without exception which begin to exist, that is, all
+except the primeval causes, are effects either immediate or remote of
+those primitive facts, or of some combination of them. There is no Thing
+produced, no event happening, in the known universe, which is not
+connected by an uniformity, or invariable sequence, with some one or
+more of the phenomena which preceded it; insomuch that it will happen
+again as often as those phenomena occur again, and as no other
+phenomenon having the character of a counteracting cause shall coexist.
+These antecedent phenomena, again, were connected in a similar manner
+with some that preceded them; and so on, until we reach, as the ultimate
+step attainable by us, either the properties of some one primeval cause,
+or the conjunction of several. The whole of the phenomena of nature were
+therefore the necessary, or in other words, the unconditional,
+consequences of some former collocation of the Permanent Causes.
+
+The state of the whole universe at any instant, we believe to be the
+consequence of its state at the previous instant; insomuch that one who
+knew all the agents which exist at the present moment, their collocation
+in space, and all their properties, in other words, the laws of their
+agency, could predict the whole subsequent history of the universe, at
+least unless some new volition of a power capable of controlling the
+universe should supervene.[21] And if any particular state of the
+entire universe could ever recur a second time, all subsequent states
+would return too, and history would, like a circulating decimal of many
+figures, periodically repeat itself:--
+
+    Jam redit et virgo, redeunt Saturnia regna....
+    Alter erit tum Tiphys, et altera quae vehat Argo
+    Delectos heroas; erunt quoque altera bella,
+    Atque iterum ad Trojam magnus mittetur Achilles.
+
+And though things do not really revolve in this eternal round, the whole
+series of events in the history of the universe, past and future, is not
+the less capable, in its own nature, of being constructed _a priori_ by
+any one whom we can suppose acquainted with the original distribution of
+all natural agents, and with the whole of their properties, that is, the
+laws of succession existing between them and their effects: saving the
+far more than human powers of combination and calculation which would be
+required, even in one possessing the data, for the actual performance of
+the task.
+
+
+Sec. 8. Since everything which occurs is determined by laws of causation
+and collocations of the original causes, it follows that the
+coexistences which are observable among effects cannot be themselves the
+subject of any similar set of laws, distinct from laws of causation.
+Uniformities there are, as well of coexistence as of succession, among
+effects; but these must in all cases be a mere result either of the
+identity or of the coexistence of their causes: if the causes did not
+coexist, neither could the effects. And these causes being also effects
+of prior causes, and these of others, until we reach the primeval
+causes, it follows that (except in the case of effects which can be
+traced immediately or remotely to one and the same cause) the
+coexistences of phenomena can in no case be universal, unless the
+coexistences of the primeval causes to which the effects are ultimately
+traceable, can be reduced to an universal law: but we have seen that
+they cannot. There are, accordingly, no original and independent, in
+other words no unconditional, uniformities of coexistence, between
+effects of different causes; if they coexist, it is only because the
+causes have casually coexisted. The only independent and unconditional
+coexistences which are sufficiently invariable to have any claim to the
+character of laws, are between different and mutually independent
+effects of the same cause; in other words, between different properties
+of the same natural agent. This portion of the Laws of Nature will be
+treated of in the latter part of the present Book, under the name of the
+Specific Properties of Kinds.
+
+
+Sec. 9. It is proper in this place to advert to a rather ancient doctrine
+respecting causation, which has been revived during the last few years
+in many quarters, and at present gives more signs of life than any other
+theory of causation at variance with that set forth in the preceding
+pages.
+
+According to the theory in question, Mind, or, to speak more precisely,
+Will, is the only cause of phenomena. The type of Causation, as well as
+the exclusive source from which we derive the idea, is our own voluntary
+agency. Here, and here only (it is said) we have direct evidence of
+causation. We know that we can move our bodies. Respecting the phenomena
+of inanimate nature, we have no other direct knowledge than that of
+antecedence and sequence. But in the case of our voluntary actions, it
+is affirmed that we are conscious of power, before we have experience of
+results. An act of volition, whether followed by an effect or not, is
+accompanied by a consciousness of effort, "of force exerted, of power in
+action, which is necessarily causal, or causative." This feeling of
+energy or force, inherent in an act of will, is knowledge _a priori_;
+assurance, prior to experience, that we have the power of causing
+effects. Volition, therefore, it is asserted, is something more than an
+unconditional antecedent; it is a cause, in a different sense from that
+in which physical phenomena are said to cause one another: it is an
+Efficient Cause. From this the transition is easy to the further
+doctrine, that Volition is the _sole_ Efficient Cause of all phenomena.
+"It is inconceivable that dead force could continue unsupported for a
+moment beyond its creation. We cannot even conceive of change or
+phenomena without the energy of a mind." "The word _action_" itself,
+says another writer of the same school, "has no real significance except
+when applied to the doings of an intelligent agent. Let any one
+conceive, if he can, of any power, energy, or force, inherent in a lump
+of matter." Phenomena may have the semblance of being produced by
+physical causes, but they are in reality produced, say these writers, by
+the immediate agency of mind. All things which do not proceed from a
+human (or, I suppose, an animal) will, proceed, they say, directly from
+divine will. The earth is not moved by the combination of a centripetal
+and a projectile force; this is but a mode of speaking, which serves to
+facilitate our conceptions. It is moved by the direct volition of an
+omnipotent Being, in a path coinciding with that which we deduce from
+the hypothesis of these two forces.
+
+As I have so often observed, the general question of the existence of
+Efficient Causes does not fall within the limits of our subject: but a
+theory which represents them as capable of being subjects of human
+knowledge, and which passes off as efficient causes what are only
+physical or phenomenal causes, belongs as much to Logic as to
+Metaphysics, and is a fit subject for discussion here.
+
+To my apprehension, a volition is not an efficient, but simply a
+physical, cause. Our will causes our bodily actions in the same sense,
+and in no other, in which cold causes ice, or a spark causes an
+explosion of gunpowder. The volition, a state of our mind, is the
+antecedent; the motion of our limbs in conformity to the volition, is
+the consequent. This sequence I conceive to be not a subject of direct
+consciousness, in the sense intended by the theory. The antecedent,
+indeed, and the consequent, are subjects of consciousness. But the
+connexion between them is a subject of experience. I cannot admit that
+our consciousness of the volition contains in itself any _a priori_
+knowledge that the muscular motion will follow. If our nerves of motion
+were paralysed, or our muscles stiff and inflexible, and had been so all
+our lives, I do not see the slightest ground for supposing that we
+should ever (unless by information from other people) have known
+anything of volition as a physical power, or been conscious of any
+tendency in feelings of our mind to produce motions of our body, or of
+other bodies. I will not undertake to say whether we should in that case
+have had the physical feeling which I suppose is meant when these
+writers speak of "consciousness of effort:" I see no reason why we
+should not; since that physical feeling is probably a state of nervous
+sensation beginning and ending in the brain, without involving the
+motory apparatus: but we certainly should not have designated it by any
+term equivalent to effort, since effort implies consciously aiming at an
+end, which we should not only in that case have had no reason to do, but
+could not even have had the idea of doing. If conscious at all of this
+peculiar sensation, we should have been conscious of it, I conceive,
+only as a kind of uneasiness, accompanying our feelings of desire.
+
+It is well argued by Sir William Hamilton against the theory in
+question, that it "is refuted by the consideration, that between the
+overt fact of corporeal movement of which we are cognisant, and the
+internal act of mental determination of which we are also cognisant,
+there intervenes a numerous series of intermediate agencies of which we
+have no knowledge; and, consequently, that we can have no consciousness
+of any causal connexion between the extreme links of this chain, the
+volition to move and the limb moving, as this hypothesis asserts. No one
+is immediately conscious, for example, of moving his arm through his
+volition. Previously to this ultimate movement, muscles, nerves, a
+multitude of solid and fluid parts, must be set in motion by the will,
+but of this motion we know, from consciousness, absolutely nothing. A
+person struck with paralysis is conscious of no inability in his limb to
+fulfil the determinations of his will; and it is only after having
+willed, and finding that his limbs do not obey his volition, that he
+learns by this experience, that the external movement does not follow
+the internal act. But as the paralytic learns after the volition that
+his limbs do not obey his mind; so it is only after volition that the
+man in health learns, that his limbs do obey the mandates of his
+will."[22]
+
+Those against whom I am contending have never produced, and do not
+pretend to produce, any positive evidence[23] that the power of our will
+to move our bodies would be known to us independently of experience.
+What they have to say on the subject is, that the production of physical
+events by a will seems to carry its own explanation with it, while the
+action of matter upon matter seems to require something else to explain
+it; and is even, according to them, "inconceivable" on any other
+supposition than that some will intervenes between the apparent cause
+and its apparent effect. They thus rest their case on an appeal to the
+inherent laws of our conceptive faculty; mistaking, as I apprehend, for
+the laws of that faculty its acquired habits, grounded on the
+spontaneous tendencies of its uncultured state. The succession between
+the will to move a limb and the actual motion, is one of the most direct
+and instantaneous of all sequences which come under our observation, and
+is familiar to every moment's experience from our earliest infancy; more
+familiar than any succession of events exterior to our bodies, and
+especially more so than any other case of the apparent origination (as
+distinguished from the mere communication) of motion. Now, it is the
+natural tendency of the mind to be always attempting to facilitate its
+conception of unfamiliar facts by assimilating them to others which are
+familiar. Accordingly, our voluntary acts, being the most familiar to us
+of all cases of causation, are, in the infancy and early youth of the
+human race, spontaneously taken as the type of causation in general, and
+all phenomena are supposed to be directly produced by the will of some
+sentient being. This original Fetichism I shall not characterize in the
+words of Hume, or of any follower of Hume, but in those of a religious
+metaphysician, Dr. Reid, in order more effectually to show the unanimity
+which exists on the subject among all competent thinkers.
+
+"When we turn our attention to external objects, and begin to exercise
+our rational faculties about them, we find that there are some motions
+and changes in them which we have power to produce, and that there are
+many which must have some other cause. Either the objects must have life
+and active power, as we have, or they must be moved or changed by
+something that has life and active power, as external objects are moved
+by us.
+
+"Our first thoughts seem to be, that the objects in which we perceive
+such motion have understanding and active power as we have. 'Savages,'
+says the Abbe Raynal, 'wherever they see motion which they cannot
+account for, there they suppose a soul.' All men may be considered as
+savages in this respect, until they are capable of instruction, and of
+using their faculties in a more perfect manner than savages do.
+
+"The Abbe Raynal's observation is sufficiently confirmed, both from
+fact, and from the structure of all languages.
+
+"Rude nations do really believe sun, moon, and stars, earth, sea, and
+air, fountains, and lakes, to have understanding and active power. To
+pay homage to them, and implore their favour, is a kind of idolatry
+natural to savages.
+
+"All languages carry in their structure the marks of their being formed
+when this belief prevailed. The distinction of verbs and participles
+into active and passive, which is found in all languages, must have been
+originally intended to distinguish what is really active from what is
+merely passive; and in all languages, we find active verbs applied to
+those objects, in which, according to the Abbe Raynal's observation,
+savages suppose a soul.
+
+"Thus we say the sun rises and sets, and comes to the meridian, the moon
+changes, the sea ebbs and flows, the winds blow. Languages were formed
+by men who believed these objects to have life and active power in
+themselves. It was therefore proper and natural to express their motions
+and changes by active verbs.
+
+"There is no surer way of tracing the sentiments of nations before they
+have records, than by the structure of their language, which,
+notwithstanding the changes produced in it by time, will always retain
+some signatures of the thoughts of those by whom it was invented. When
+we find the same sentiments indicated in the structure of all languages,
+those sentiments must have been common to the human species when
+languages were invented.
+
+"When a few, of superior intellectual abilities, find leisure for
+speculation, they begin to philosophize, and soon discover, that many of
+those objects which at first they believed to be intelligent and active
+are really lifeless and passive. This is a very important discovery. It
+elevates the mind, emancipates from many vulgar superstitions, and
+invites to further discoveries of the same kind.
+
+"As philosophy advances, life and activity in natural objects retires,
+and leaves them dead and inactive. Instead of moving voluntarily, we
+find them to be moved necessarily; instead of acting, we find them to be
+acted upon; and Nature appears as one great machine, where one wheel is
+turned by another, that by a third; and how far this necessary
+succession may reach, the philosopher does not know."[24]
+
+There is, then, a spontaneous tendency of the intellect to account to
+itself for all cases of causation by assimilating them to the
+intentional acts of voluntary agents like itself. This is the
+instinctive philosophy of the human mind in its earliest stage, before
+it has become familiar with any other invariable sequences than those
+between its own volitions or those of other human beings and their
+voluntary acts. As the notion of fixed laws of succession among external
+phenomena gradually establishes itself, the propensity to refer all
+phenomena to voluntary agency slowly gives way before it. The
+suggestions, however, of daily life continuing to be more powerful than
+those of scientific thought, the original instinctive philosophy
+maintains its ground in the mind, underneath the growths obtained by
+cultivation, and keeps up a constant resistance to their throwing their
+roots deep into the soil. The theory against which I am contending
+derives its nourishment from that substratum. Its strength does not lie
+in argument, but in its affinity to an obstinate tendency of the infancy
+of the human mind.
+
+That this tendency, however, is not the result of an inherent mental
+law, is proved by superabundant evidence. The history of science, from
+its earliest dawn, shows that mankind have not been unanimous in
+thinking either that the action of matter upon matter was not
+conceivable, or that the action of mind upon matter was. To some
+thinkers, and some schools of thinkers, both in ancient and in modern
+times, this last has appeared much more inconceivable than the former.
+Sequences entirely physical and material, as soon as they had become
+sufficiently familiar to the human mind, came to be thought perfectly
+natural, and were regarded not only as needing no explanation
+themselves, but as being capable of affording it to others, and even of
+serving as the ultimate explanation of things in general.
+
+One of the ablest recent supporters of the Volitional theory has
+furnished an explanation, at once historically true and philosophically
+acute, of the failure of the Greek philosophers in physical inquiry, in
+which, as I conceive, he unconsciously depicts his own state of mind.
+"Their stumbling-block was one as to the nature of the evidence they had
+to expect for their conviction.... They had not seized the idea that
+they must not expect to understand the processes of outward causes, but
+only their results: and consequently, the whole physical philosophy of
+the Greeks was an attempt to identify mentally the effect with its
+cause, to feel after some not only necessary but natural connexion,
+where they meant by natural that which would _per se_ carry some
+presumption to their own mind.... They wanted to see some _reason_ why
+the physical antecedent should produce this particular consequent, and
+their only attempts were in directions where they could find such
+reasons."[25] In other words, they were not content merely to know that
+one phenomenon was always followed by another; they thought that they
+had not attained the true aim of science, unless they could perceive
+something in the nature of the one phenomenon from which it might have
+been known or presumed _previous to trial_ that it would be followed by
+the other: just what the writer, who has so clearly pointed out their
+error, thinks that he perceives in the nature of the phenomenon
+Volition. And to complete the statement of the case, he should have
+added that these early speculators not only made this their aim, but
+were quite satisfied with their success in it; not only sought for
+causes which should carry in their mere statement evidence of their
+efficiency, but fully believed that they had found such causes. The
+reviewer can see plainly that this was an error, because _he_ does not
+believe that there exist any relations between material phenomena which
+can account for their producing one another: but the very fact of the
+persistency of the Greeks in this error, shows that their minds were in
+a very different state: they were able to derive from the assimilation
+of physical facts to other physical facts, the kind of mental
+satisfaction which we connect with the word explanation, and which the
+reviewer would have us think can only be found in referring phenomena to
+a will. When Thales and Hippo held that moisture was the universal
+cause, and external element, of which all other things were but the
+infinitely various sensible manifestations; when Anaximenes predicated
+the same thing of air, Pythagoras of numbers, and the like, they all
+thought that they had found a real explanation; and were content to rest
+in this explanation as ultimate. The ordinary sequences of the external
+universe appeared to them, no less than to their critic, to be
+inconceivable without the supposition of some universal agency to
+connect the antecedents with the consequents; but they did not think
+that Volition, exerted by minds, was the only agency which fulfilled
+this requirement. Moisture, or air, or numbers, carried to their minds a
+precisely similar impression of making intelligible what was otherwise
+inconceivable, and gave the same full satisfaction to the demands of
+their conceptive faculty.
+
+It was not the Greeks alone, who "wanted to see some reason why the
+physical antecedent should produce this particular consequent," some
+connexion "which would _per se_ carry some presumption to their own
+mind." Among modern philosophers, Leibnitz laid it down as a
+self-evident principle that all physical causes without exception must
+contain in their own nature something which makes it intelligible that
+they should be able to produce the effects which they do produce. Far
+from admitting Volition as the only kind of cause which carried internal
+evidence of its own power, and as the real bond of connexion between
+physical antecedents and their consequents, he demanded some naturally
+and _per se_ efficient physical antecedent as the bond of connexion
+between Volition itself and its effects. He distinctly refused to admit
+the will of God as a sufficient explanation of anything except miracles;
+and insisted upon finding something that would account _better_ for the
+phenomena of nature than a mere reference to divine volition.[26]
+
+Again, and conversely, the action of mind upon matter (which, we are now
+told, not only needs no explanation itself, but is the explanation of
+all other effects), has appeared to some thinkers to be itself the grand
+inconceivability. It was to get over this very difficulty that the
+Cartesians invented the system of Occasional Causes. They could not
+conceive that thoughts in a mind could produce movements in a body, or
+that bodily movements could produce thoughts. They could see no
+necessary connexion, no relation _a priori_, between a motion and a
+thought. And as the Cartesians, more than any other school of
+philosophical speculation before or since, made their own minds the
+measure of all things, and refused, on principle, to believe that Nature
+had done what they were unable to see any reason why she must do, they
+affirmed it to be impossible that a material and a mental fact could be
+causes one of another. They regarded them as mere Occasions on which the
+real agent, God, thought fit to exert his power as a Cause. When a man
+wills to move his foot, it is not his will that moves it, but God (they
+said) moves it on the occasion of his will. God, according to this
+system, is the only efficient cause, not _qua_ mind, or _qua_ endowed
+with volition, but _qua_ omnipotent. This hypothesis was, as I said,
+originally suggested by the supposed inconceivability of any real mutual
+action between Mind and Matter: but it was afterwards extended to the
+action of Matter upon Matter, for on a nicer examination they found this
+inconceivable too, and therefore, according to their logic, impossible.
+The _deus ex machina_ was ultimately called in to produce a spark on the
+occasion of a flint and steel coming together, or to break an egg on the
+occasion of its falling on the ground.
+
+All this, undoubtedly, shows that it is the disposition of mankind in
+general, not to be satisfied with knowing that one fact is invariably
+antecedent and another consequent, but to look out for something which
+may seem to explain their being so. But we also see that this demand may
+be completely satisfied by an agency purely physical, provided it be
+much more familiar than that which it is invoked to explain. To Thales
+and Anaximenes, it appeared inconceivable that the antecedents which we
+see in nature, should produce the consequents; but perfectly natural
+that water, or air, should produce them. The writers whom I oppose
+declare this inconceivable, but can conceive that mind, or volition, is
+_per se_ an efficient cause: while the Cartesians could not conceive
+even that, but peremptorily declared that no mode of production of any
+fact whatever was conceivable, except the direct agency of an omnipotent
+being. Thus giving additional proof of what finds new confirmation in
+every stage of the history of science: that both what persons can, and
+what they cannot, conceive, is very much an affair of accident, and
+depends altogether on their experience, and their habits of thought;
+that by cultivating the requisite associations of ideas, people may make
+themselves unable to conceive any given thing; and may make themselves
+able to conceive most things, however inconceivable these may at first
+appear: and the same facts in each person's mental history which
+determine what is or is not conceivable to him, determine also which
+among the various sequences in nature will appear to him so natural and
+plausible, as to need no other proof of their existence; to be evident
+by their own light, independent equally of experience and of
+explanation.
+
+By what rule is any one to decide between one theory of this description
+and another? The theorists do not direct us to any external evidence;
+they appeal each to his own subjective feelings. One says, the
+succession C, B, appears to me more natural, conceivable, and credible
+_per se_, than the succession A, B; you are therefore mistaken in
+thinking that B depends upon A; I am certain, though I can give no other
+evidence of it, that C comes in between A and B, and is the real and
+only cause of B. The other answers--the successions C, B, and A, B,
+appear to me equally natural and conceivable, or the latter more so than
+the former: A is quite capable of producing B without any other
+intervention. A third agrees with the first in being unable to conceive
+that A can produce B, but finds the sequence D, B, still more natural
+than C, B, or of nearer kin to the subject matter, and prefers his D
+theory to the C theory. It is plain that there is no universal law
+operating here, except the law that each person's conceptions are
+governed and limited by his individual experience and habits of thought.
+We are warranted in saying of all three, what each of them already
+believes of the other two, namely, that they exalt into an original law
+of the human intellect and of outward nature, one particular sequence of
+phenomena, which appears to them more natural and more conceivable than
+other sequences, only because it is more familiar. And from this
+judgment I am unable to except the theory, that Volition is an Efficient
+Cause.
+
+I am unwilling to leave the subject without adverting to the additional
+fallacy contained in the corollary from this theory; in the inference
+that because Volition is an efficient cause, therefore it is the only
+cause, and the direct agent in producing even what is apparently
+produced by something else. Volitions are not known to produce anything
+directly except nervous action, for the will influences even the muscles
+only through the nerves. Though it were granted, then, that every
+phenomenon has an efficient, and not merely a phenomenal cause, and that
+volition, in the case of the peculiar phenomena which are known to be
+produced by it, is that efficient cause; are we therefore to say, with
+these writers, that since we know of no other efficient cause, and ought
+not to assume one without evidence, there _is_ no other, and volition is
+the direct cause of all phenomena? A more outrageous stretch of
+inference could hardly be made. Because among the infinite variety of
+the phenomena of nature there is one, namely, a particular mode of
+action of certain nerves, which has for its cause, and as we are now
+supposing for its efficient cause, a state of our mind; and because this
+is the only efficient cause of which we are conscious, being the only
+one of which in the nature of the case we _can_ be conscious, since it
+is the only one which exists within ourselves; does this justify us in
+concluding that all other phenomena must have the same kind of efficient
+cause with that one eminently special, narrow, and peculiarly human or
+animal, phenomenon? The nearest parallel to this specimen of
+generalization is suggested by the recently revived controversy on the
+old subject of Plurality of Worlds, in which the contending parties have
+been so conspicuously successful in overthrowing one another. Here also
+we have experience only of a single case, that of the world in which we
+live, but that this is inhabited we know absolutely, and without
+possibility of doubt. Now if on this evidence any one were to infer that
+every heavenly body without exception, sun, planet, satellite, comet,
+fixed star or nebula, is inhabited, and must be so from the inherent
+constitution of things, his inference would exactly resemble that of the
+writers who conclude that because volition is the efficient cause of our
+own bodily motions, it must be the efficient cause of everything else in
+the universe. It is true there are cases in which, with acknowledged
+propriety, we generalize from a single instance to a multitude of
+instances. But they must be instances which resemble the one known
+instance, and not such as have no circumstance in common with it except
+that of being instances. I have, for example, no direct evidence that
+any creature is alive except myself: yet I attribute, with full
+assurance, life and sensation to other human beings and animals. But I
+do not conclude that all other things are alive merely because I am. I
+ascribe to certain other creatures a life like my own, because they
+manifest it by the same sort of indications by which mine is manifested.
+I find that their phenomena and mine conform to the same laws, and it is
+for this reason that I believe both to arise from a similar cause.
+Accordingly I do not extend the conclusion beyond the grounds for it.
+Earth, fire, mountains, trees, are remarkable agencies, but their
+phenomena do not conform to the same laws as my actions do, and I
+therefore do not believe earth or fire, mountains or trees, to possess
+animal life. But the supporters of the Volition Theory ask us to infer
+that volition causes everything, for no reason except that it causes one
+particular thing; although that one phenomenon, far from being a type of
+all natural phenomena, is eminently peculiar; its laws bearing scarcely
+any resemblance to those of any other phenomenon, whether of inorganic
+or of organic nature.
+
+
+NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
+
+     The author of the Second Burnett Prize Essay (Dr. Tulloch), who
+     has employed a considerable number of pages in controverting
+     the doctrines of the preceding chapter, has somewhat surprised
+     me by denying a fact, which I imagined too well known to
+     require proof--that there have been philosophers who found in
+     physical explanations of phenomena the same complete mental
+     satisfaction which we are told is only given by volitional
+     explanation, and others who denied the Volitional Theory on the
+     same ground of inconceivability on which it is defended. The
+     assertion of the Essayist is countersigned still more
+     positively by an able reviewer of the Essay:[27] "Two
+     illustrations," says the reviewer, "are advanced by Mr. Mill:
+     the case of Thales and Anaximenes, stated by him to have
+     maintained, the one Moisture and the other Air to be the origin
+     of all things; and that of Descartes and Leibnitz, whom he
+     asserts to have found the action of Mind upon Matter the grand
+     inconceivability. In counterstatement as to the first of these
+     cases the author shows--what we believe now hardly admits of
+     doubt--that the Greek philosophers distinctly recognised as
+     beyond and above their primal material source, the [Greek:
+     nous], or Divine Intelligence, as the efficient and originating
+     Source of all: and as to the second, by proof that it was the
+     _mode_, not the _fact_, of that action on matter, which was
+     represented as inconceivable."
+
+     A greater quantity of historical error has seldom been
+     comprised in a single sentence. With regard to Thales, the
+     assertion that he considered water as a mere material in the
+     hands of [Greek: nous] rests on a passage of Cicero _de Natura
+     Deorum_: and whoever will refer to any of the accurate
+     historians of philosophy, will find that they treat this as a
+     mere fancy of Cicero, resting on no authority, opposed to all
+     the evidence; and make surmises as to the manner in which
+     Cicero may have been led into the error. (See Ritter, vol. i.
+     p. 211, 2nd ed.; Brandis, vol. i. pp. 118-9, 1st ed.; Preller,
+     _Historia Philosophiae Graeco-Romanae_, p. 10. "Schiefe Ansicht,
+     durchaus zu verwerfen;" "augenscheinlich folgernd statt zu
+     berichten;" "quibus vera sententia Thaletis plane detorquetur;"
+     are the expressions of these writers.) As for Anaximenes, he,
+     even according to Cicero, maintained, not that air was the
+     material out of which God made the world, but that the air was
+     a god: "Anaximenes aera deum statuit:" or according to St.
+     Augustine, that it was the material out of which the gods were
+     made; "non tamen ab ipsis [Diis] aerem factum, sed ipsos ex
+     aere ortos credidit." Those who are not familiar with the
+     metaphysical terminology of antiquity, must not be misled by
+     finding it stated that Anaximenes attributed [Greek: psyche]
+     (translated _soul_, or _life_) to his universal element, the
+     air. The Greek philosophers acknowledged several kinds of
+     [Greek: psyche], the nutritive, the sensitive, and the
+     intellective.[28] Even the moderns with admitted correctness
+     attribute life to plants. As far as we can make out the meaning
+     of Anaximenes, he made choice of Air as the universal agent, on
+     the ground that it is perpetually in motion, without any
+     apparent cause external to itself: so that he conceived it as
+     exercising spontaneous force, and as the principle of life and
+     activity in all things, men and gods inclusive. If this be not
+     representing it as the Efficient Cause, the dispute altogether
+     has no meaning.
+
+     If either Anaximenes, or Thales, or any of their cotemporaries,
+     had held the doctrine that [Greek: nous] was the Efficient
+     Cause, that doctrine could not have been reputed, as it was
+     throughout antiquity, to have originated with Anaxagoras. The
+     testimony of Aristotle, in the first book of his Metaphysics,
+     is perfectly decisive with respect to these early speculations.
+     After enumerating four kinds of causes, or rather four
+     different meanings of the word Cause, viz. the Essence of a
+     thing, the Matter of it, the Origin of Motion (Efficient
+     Cause), and the End or Final Cause, he proceeds to say, that
+     most of the early philosophers recognised only the second kind
+     of Cause, the Matter of a thing, [Greek: tas en hyles eidei
+     monas oethesan archas einai panton]. As his first example he
+     specifies Thales, whom he describes as taking the lead in this
+     view of the subject, [Greek: ho tes toiautes archegos
+     philosophias], and goes on to Hippon, Anaximenes, Diogenes (of
+     Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.
+     Anaxagoras, however, (he proceeds to say,) taught a different
+     doctrine, as we know, and it is _alleged_ that Hermotimus of
+     Clazomenae taught it before him. Anaxagoras represented, that
+     even if these various theories of the universal material were
+     true, there would be need of some other cause to account for
+     the transformations of the material, since the material cannot
+     originate its own changes: [Greek: ou gar de to ge hypokeimenon
+     auto poiei metaballein heauto; lego d' oion oute to xylon oute
+     ho chalkos aitios tou metaballein hekateron auton, oude poiei
+     to men xylon klinen ho de chalkos andrianta, all' heteron ti
+     tes metaboles aition], viz., the other kind of cause [Greek:
+     hothen he arche tes kineseos]--an Efficient Cause. Aristotle
+     expresses great approbation of this doctrine (which he says
+     made its author appear the only sober man among persons raving,
+     [Greek: oion nephon ephane par' eike legontas tous proteron]);
+     but while describing the influence which it exercised over
+     subsequent speculation, he remarks that the philosophers
+     against whom this, as he thinks, insuperable difficulty was
+     urged, had not felt it to be any difficulty: [Greek: ouden
+     edyscheranan en heautois]. It is surely unnecessary to say more
+     in proof of the matter of fact which Dr. Tulloch and his
+     reviewer deny.
+
+     Having pointed out what he thinks the error of these early
+     speculators in not recognising the need of an efficient cause,
+     Aristotle goes on to mention two other efficient causes to
+     which they might have had recourse, instead of intelligence:
+     [Greek: tyche], chance, and [Greek: to automaton], spontaneity.
+     He indeed puts these aside as not sufficiently worthy causes
+     for the order in the universe, [Greek: oud' au to automato kai
+     te tyche tosouton epitrepsai pragma kalos eichen]: but he does
+     not reject them as incapable of producing any effect, but only
+     as incapable of producing _that_ effect. He himself recognises
+     [Greek: tyche] and [Greek: to automaton] as co-ordinate agents
+     with Mind in producing the phenomena of the universe; the
+     department allotted to them being composed of all the classes
+     of phenomena which are not supposed to follow any uniform law.
+     By thus including Chance among efficient causes, Aristotle fell
+     into an error which philosophy has now outgrown, but which is
+     by no means so alien to the spirit even of modern speculation
+     as it may at first sight appear. Up to quite a recent period
+     philosophers went on ascribing, and many of them have not yet
+     ceased to ascribe, a real existence to the results of
+     abstraction. Chance could make out as good a title to that
+     dignity as many other of the mind's abstract creations: it had
+     had a name given to it, and why should it not be a reality? As
+     for [Greek: to automaton], it is recognised even yet as one of
+     the modes of origination of phenomena, by all those thinkers
+     who maintain what is called the Freedom of the Will. The same
+     self-determining power which that doctrine attributes to
+     volitions, was supposed by the ancients to be possessed also by
+     some other natural phenomena: a circumstance which throws
+     considerable light on more than one of the supposed invincible
+     necessities of belief. I have introduced it here, because this
+     belief of Aristotle, or rather of the Greek philosophers
+     generally, is as fatal as the doctrines of Thales and the Ionic
+     school, to the theory that the human mind is compelled by its
+     constitution to conceive volition as the origin of all force,
+     and the efficient cause of all phenomena.[29]
+
+     With regard to the modern philosophers (Leibnitz and the
+     Cartesians) whom I had cited as having maintained that the
+     action of mind upon matter, so far from being the only
+     conceivable origin of material phenomena, is itself
+     inconceivable; the attempt to rebut this argument by asserting
+     that the mode, not the fact, of the action of mind on matter
+     was represented as inconceivable, is an abuse of the privilege
+     of writing confidently about authors without reading them: for
+     any knowledge whatever of Leibnitz would have taught those who
+     thus speak of him, that the inconceivability of the mode, and
+     the impossibility of the thing, were in his mind convertible
+     expressions. What was his famous Principle of the Sufficient
+     Reason, the very corner stone of his philosophy, from which the
+     Preestablished Harmony, the doctrine of Monads, and all the
+     opinions most characteristic of Leibnitz, were corollaries? It
+     was, that nothing exists, the existence of which is not capable
+     of being proved and explained _a priori_; the proof and
+     explanation in the case of contingent facts being derived from
+     the nature of their causes; which could not be the causes
+     unless there was something in their nature showing them to be
+     capable of producing those particular effects. And this
+     "something" which accounts for the production of physical
+     effects, he was able to find in many physical causes, but could
+     not find it in any finite minds, which therefore he
+     unhesitatingly asserted to be incapable of producing any
+     physical effects whatever. "On ne saurait concevoir," he says,
+     "une action reciproque de la matiere et de l'intelligence l'une
+     sur l'autre," and there is therefore (he contends) no choice
+     but between the Occasional Causes of the Cartesians, and his
+     own Preestablished Harmony, according to which there is no more
+     connexion between our volitions and our muscular actions than
+     there is between two clocks which are wound up to strike at the
+     same instant. But he felt no similar difficulty as to physical
+     causes: and throughout his speculations, as in the passage I
+     have already cited respecting gravitation, he distinctly
+     refuses to consider as part of the order of nature any fact
+     which is not explicable from the nature of its physical cause.
+
+     With regard to the Cartesians (not Descartes; I did not make
+     that mistake, though the reviewer of Dr. Tulloch's Essay
+     attributes it to me) I take a passage almost at random from
+     Malebranche, who is the best known of the Cartesians, and,
+     though not the inventor of the system of Occasional Causes, is
+     its principal expositor. In Part 2, chap. 3, of his Sixth Book,
+     having first said that matter cannot have the power of moving
+     itself, he proceeds to argue that neither can mind have the
+     power of moving it. "Quand on examine l'idee que l'on a de tous
+     les esprits finis, on ne voit point de liaison necessaire entre
+     leur volonte et le mouvement de quelque corps que ce soit, on
+     voit au contraire qu'il n'y en a point, et qu'il n'y en peut
+     avoir;" (there is nothing in the idea of finite mind which can
+     account for its causing the motion of a body;) "on doit aussi
+     conclure, si on veut raisonner selon ses lumieres, qu'il n'y a
+     aucun esprit cree qui puisse remuer quelque corps que ce soit
+     comme cause veritable ou principale, de meme que l'on a dit
+     qu'aucun corps ne se pouvait remuer soi-meme:" thus the idea of
+     Mind is according to him as incompatible as the idea of Matter
+     with the exercise of active force. But when, he continues, we
+     consider not a created but a Divine Mind, the case is altered;
+     for the idea of a Divine Mind includes omnipotence; and the
+     idea of omnipotence does contain the idea of being able to move
+     bodies. Thus it is the nature of omnipotence which renders the
+     motion of bodies even by the divine mind credible or
+     conceivable, while, so far as depended on the mere nature of
+     mind, it would have been inconceivable and incredible. If
+     Malebranche had not believed in an omnipotent being, he would
+     have held all action of mind on body to be a demonstrated
+     impossibility.[30]
+
+     A doctrine more precisely the reverse of the Volitional theory
+     of causation cannot well be imagined. The volitional theory is,
+     that we know by intuition or by direct experience the action of
+     our own mental volitions on matter; that we may hence infer all
+     other action upon matter to be that of volition, and might thus
+     know, without any other evidence, that matter is under the
+     government of a divine mind. Leibnitz and the Cartesians, on
+     the contrary, maintain that our volitions do not and cannot act
+     upon matter, and that it is only the existence of an
+     all-governing Being, and that Being omnipotent, which can
+     account for the sequence between our volitions and our bodily
+     actions. When we consider that each of these two theories,
+     which, as theories of causation, stand at the opposite extremes
+     of possible divergence from one another, invokes not only as
+     its evidence, but as its sole evidence, the absolute
+     inconceivability of any theory but itself, we are enabled to
+     measure the worth of this kind of evidence; and when we find
+     the Volitional theory entirely built upon the assertion that by
+     our mental constitution we are compelled to recognise our
+     volitions as efficient causes, and then find other thinkers
+     maintaining that we know that they are not, and cannot be such
+     causes, and cannot conceive them to be so, I think we have a
+     right to say, that this supposed law of our mental constitution
+     does not exist.
+
+     Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this,
+     that Leibnitz and the Cartesians were Theists, and believed the
+     will of God to be an efficient cause. Doubtless they did, and
+     the Cartesians even believed, though Leibnitz did not, that it
+     is the only such cause. Dr. Tulloch mistakes the nature of the
+     question. I was not writing on Theism, as Dr. Tulloch is, but
+     against a particular theory of causation, which if it be
+     unfounded, can give no effective support to Theism or to
+     anything else. I found it asserted that volition is the only
+     efficient cause, on the ground that no other efficient cause is
+     conceivable. To this assertion I oppose the instances of
+     Leibnitz and of the Cartesians, who affirmed with equal
+     positiveness that volition as an efficient cause is itself not
+     conceivable, and that omnipotence, which renders all things
+     conceivable, can alone take away the impossibility. This I
+     thought, and think, a conclusive answer to the argument on
+     which this theory of causation avowedly depends. But I
+     certainly did not imagine that Theism was bound up with that
+     theory; nor expected to be charged with denying Leibnitz and
+     the Cartesians to be Theists because I denied that they held
+     the theory.
+
+
+
+
+CHAPTER VI.
+
+ON THE COMPOSITION OF CAUSES.
+
+
+Sec. 1. To complete the general notion of causation on which the rules of
+experimental inquiry into the laws of nature must be founded, one
+distinction still remains to be pointed out: a distinction so radical,
+and of so much importance, as to require a chapter to itself.
+
+The preceding discussions have rendered us familiar with the case in
+which several agents, or causes, concur as conditions to the production
+of an effect: a case, in truth, almost universal, there being very few
+effects to the production of which no more than one agent contributes.
+Suppose, then, that two different agents, operating jointly, are
+followed, under a certain set of collateral conditions, by a given
+effect. If either of these agents, instead of being joined with the
+other, had operated alone, under the same set of conditions in all other
+respects, some effect would probably have followed; which would have
+been different from the joint effect of the two, and more or less
+dissimilar to it. Now, if we happen to know what would be the effect of
+each cause when acting separately from the other, we are often able to
+arrive deductively, or _a priori_, at a correct prediction of what will
+arise from their conjunct agency. To enable us to do this, it is only
+necessary that the same law which expresses the effect of each cause
+acting by itself, shall also correctly express the part due to that
+cause, of the effect which follows from the two together. This condition
+is realized in the extensive and important class of phenomena commonly
+called mechanical, namely the phenomena of the communication of motion
+(or of pressure, which is tendency to motion) from one body to another.
+In this important class of cases of causation, one cause never, properly
+speaking, defeats or frustrates another; both have their full effect.
+If a body is propelled in two directions by two forces, one tending to
+drive it to the north and the other to the east, it is caused to move in
+a given time exactly as far in both directions as the two forces would
+separately have carried it; and is left precisely where it would have
+arrived if it had been acted upon first by one of the two forces, and
+afterwards by the other. This law of nature is called, in dynamics, the
+principle of the Composition of Forces: and in imitation of that
+well-chosen expression, I shall give the name of the Composition of
+Causes to the principle which is exemplified in all cases in which the
+joint effect of several causes is identical with the sum of their
+separate effects.
+
+This principle, however, by no means prevails in all departments of the
+field of nature. The chemical combination of two substances produces, as
+is well known, a third substance with properties entirely different from
+those of either of the two substances separately, or both of them taken
+together. Not a trace of the properties of hydrogen or of oxygen is
+observable in those of their compound, water. The taste of sugar of lead
+is not the sum of the tastes of its component elements, acetic acid and
+lead or its oxide; nor is the colour of blue vitriol a mixture of the
+colours of sulphuric acid and copper. This explains why mechanics is a
+deductive or demonstrative science, and chemistry not. In the one, we
+can compute the effects of all combinations of causes, whether real or
+hypothetical, from the laws which we know to govern those causes when
+acting separately; because they continue to observe the same laws when
+in combination which they observed when separate: whatever would have
+happened in consequence of each cause taken by itself, happens when they
+are together, and we have only to cast up the results. Not so in the
+phenomena which are the peculiar subject of the science of chemistry.
+There, most of the uniformities to which the causes conformed when
+separate, cease altogether when they are conjoined; and we are not, at
+least in the present state of our knowledge, able to foresee what result
+will follow from any new combination, until we have tried the specific
+experiment.
+
+If this be true of chemical combinations, it is still more true of those
+far more complex combinations of elements which constitute organized
+bodies; and in which those extraordinary new uniformities arise, which
+are called the laws of life. All organized bodies are composed of parts
+similar to those composing inorganic nature, and which have even
+themselves existed in an inorganic state; but the phenomena of life,
+which result from the juxtaposition of those parts in a certain manner,
+bear no analogy to any of the effects which would be produced by the
+action of the component substances considered as mere physical agents.
+To whatever degree we might imagine our knowledge of the properties of
+the several ingredients of a living body to be extended and perfected,
+it is certain that no mere summing up of the separate actions of those
+elements will ever amount to the action of the living body itself. The
+tongue, for instance, is, like all other parts of the animal frame,
+composed of gelatine, fibrin, and other products of the chemistry of
+digestion, but from no knowledge of the properties of those substances
+could we ever predict that it could taste, unless gelatine or fibrin
+could themselves taste; for no elementary fact can be in the conclusion,
+which was not in the premises.
+
+There are thus two different modes of the conjunct action of causes;
+from which arise two modes of conflict, or mutual interference, between
+laws of nature. Suppose, at a given point of time and space, two or more
+causes, which, if they acted separately, would produce effects contrary,
+or at least conflicting with each other; one of them tending to undo,
+wholly or partially, what the other tends to do. Thus, the expansive
+force of the gases generated by the ignition of gunpowder tends to
+project a bullet towards the sky, while its gravity tends to make it
+fall to the ground. A stream running into a reservoir at one end tends
+to fill it higher and higher, while a drain at the other extremity tends
+to empty it. Now, in such cases as these, even if the two causes which
+are in joint action exactly annul one another, still the laws of both
+are fulfilled; the effect is the same as if the drain had been open for
+half an hour first,[31] and the stream had flowed in for as long
+afterwards. Each agent produced the same amount of effect as if it had
+acted separately, though the contrary effect which was taking place
+during the same time obliterated it as fast as it was produced. Here
+then are two causes, producing by their joint operation an effect which
+at first seems quite dissimilar to those which they produce separately,
+but which on examination proves to be really the sum of those separate
+effects. It will be noticed that we here enlarge the idea of the sum of
+two effects, so as to include what is commonly called their difference,
+but which is in reality the result of the addition of opposites; a
+conception to which mankind are indebted for that admirable extension of
+the algebraical calculus, which has so vastly increased its powers as an
+instrument of discovery, by introducing into its reasonings (with the
+sign of subtraction prefixed, and under the name of Negative Quantities)
+every description whatever of positive phenomena, provided they are of
+such a quality in reference to those previously introduced, that to add
+the one is equivalent to subtracting an equal quantity of the other.
+
+There is, then, one mode of the mutual interference of laws of nature,
+in which, even when the concurrent causes annihilate each other's
+effects, each exerts its full efficacy according to its own law, its law
+as a separate agent. But in the other description of cases, the agencies
+which are brought together cease entirely, and a totally different set
+of phenomena arise: as in the experiment of two liquids which, when
+mixed in certain proportions, instantly become, not a larger amount of
+liquid, but a solid mass.
+
+
+Sec. 2. This difference between the case in which the joint effect of
+causes is the sum of their separate effects, and the case in which it
+is heterogeneous to them; between laws which work together without
+alteration, and laws which, when called upon to work together, cease and
+give place to others; is one of the fundamental distinctions in nature.
+The former case, that of the Composition of Causes, is the general one;
+the other is always special and exceptional. There are no objects which
+do not, as to some of their phenomena, obey the principle of the
+Composition of Causes; none that have not some laws which are rigidly
+fulfilled in every combination into which the objects enter. The weight
+of a body, for instance, is a property which it retains in all the
+combinations in which it is placed. The weight of a chemical compound,
+or of an organized body, is equal to the sum of the weights of the
+elements which compose it. The weight either of the elements or of the
+compound will vary, if they be carried farther from their centre of
+attraction, or brought nearer to it; but whatever affects the one
+affects the other. They always remain precisely equal. So again, the
+component parts of a vegetable or animal substance do not lose their
+mechanical and chemical properties as separate agents, when, by a
+peculiar mode of juxtaposition, they, as an aggregate whole, acquire
+physiological or vital properties in addition. Those bodies continue, as
+before, to obey mechanical and chemical laws, in so far as the operation
+of those laws is not counteracted by the new laws which govern them as
+organized beings. When, in short, a concurrence of causes takes place
+which calls into action new laws bearing no analogy to any that we can
+trace in the separate operation of the causes, the new laws, while they
+supersede one portion of the previous laws, may coexist with another
+portion, and may even compound the effect of those previous laws with
+their own.
+
+Again, laws which were themselves generated in the second mode, may
+generate others in the first. Though there are laws which, like those of
+chemistry and physiology, owe their existence to a breach of the
+principle of Composition of Causes, it does not follow that these
+peculiar, or as they might be termed, _heteropathic_ laws, are not
+capable of composition with one another. The causes which by one
+combination have had their laws altered, may carry their new laws with
+them unaltered into their ulterior combinations. And hence there is no
+reason to despair of ultimately raising chemistry and physiology to the
+condition of deductive sciences; for though it is impossible to deduce
+all chemical and physiological truths from the laws or properties of
+simple substances or elementary agents, they may possibly be deducible
+from laws which commence when these elementary agents are brought
+together into some moderate number of not very complex combinations. The
+Laws of Life will never be deducible from the mere laws of the
+ingredients, but the prodigiously complex Facts of Life may all be
+deducible from comparatively simple laws of life; which laws (depending
+indeed on combinations, but on comparatively simple combinations, of
+antecedents) may, in more complex circumstances, be strictly compounded
+with one another, and with the physical and chemical laws of the
+ingredients. The details of the vital phenomena, even now, afford
+innumerable exemplifications of the Composition of Causes; and in
+proportion as these phenomena are more accurately studied, there appears
+more reason to believe that the same laws which operate in the simpler
+combinations of circumstances do, in fact, continue to be observed in
+the more complex. This will be found equally true in the phenomena of
+mind; and even in social and political phenomena, the results of the
+laws of mind. It is in the case of chemical phenomena that the least
+progress has yet been made in bringing the special laws under general
+ones from which they may be deduced; but there are even in chemistry
+many circumstances to encourage the hope that such general laws will
+hereafter be discovered. The different actions of a chemical compound
+will never, undoubtedly, be found to be the sums of the actions of its
+separate elements; but there may exist, between the properties of the
+compound and those of its elements, some constant relation, which, if
+discoverable by a sufficient induction, would enable us to foresee the
+sort of compound which will result from a new combination before we have
+actually tried it, and to judge of what sort of elements some new
+substance is compounded before we have analysed it. The law of definite
+proportions, first discovered in its full generality by Dalton, is a
+complete solution of this problem in one, though but a secondary aspect,
+that of quantity: and in respect to quality, we have already some
+partial generalizations sufficient to indicate the possibility of
+ultimately proceeding farther. We can predicate some common properties
+of the kind of compounds which result from the combination, in each of
+the small number of possible proportions, of any acid whatever with any
+base. We have also the curious law, discovered by Berthollet, that two
+soluble salts mutually decompose one another whenever the new
+combinations which result produce an insoluble compound, or one less
+soluble than the two former. Another uniformity is that called the law
+of isomorphism; the identity of the crystalline forms of substances
+which possess in common certain peculiarities of chemical composition.
+Thus it appears that even heteropathic laws, such laws of combined
+agency as are not compounded of the laws of the separate agencies, are
+yet, at least in some cases, derived from them according to a fixed
+principle. There may, therefore, be laws of the generation of laws from
+others dissimilar to them; and in chemistry, these undiscovered laws of
+the dependence of the properties of the compound on the properties of
+its elements, may, together with the laws of the elements themselves,
+furnish the premises by which the science is perhaps destined one day to
+be rendered deductive.
+
+It would seem, therefore, that there is no class of phenomena in which
+the Composition of Causes does not obtain: that as a general rule,
+causes in combination produce exactly the same effects as when acting
+singly: but that this rule, though general, is not universal: that in
+some instances, at some particular points in the transition from
+separate to united action, the laws change, and an entirely new set of
+effects are either added to, or take the place of, those which arise
+from the separate agency of the same causes: the laws of these new
+effects being again susceptible of composition, to an indefinite extent,
+like the laws which they superseded.
+
+
+Sec. 3. That effects are proportional to their causes is laid down by some
+writers as an axiom in the theory of causation; and great use is
+sometimes made of this principle in reasonings respecting the laws of
+nature, though it is incumbered with many difficulties and apparent
+exceptions, which much ingenuity has been expended in showing not to be
+real ones. This proposition, in so far as it is true, enters as a
+particular case into the general principle of the Composition of Causes;
+the causes compounded being, in this instance, homogeneous; in which
+case, if in any, their joint effect might be expected to be identical
+with the sum of their separate effects. If a force equal to one hundred
+weight will raise a certain body along an inclined plane, a force equal
+to two hundred weight will raise two bodies exactly similar, and thus
+the effect is proportional to the cause. But does not a force equal to
+two hundred weight actually contain in itself two forces each equal to
+one hundred weight, which, if employed apart, would separately raise the
+two bodies in question? The fact, therefore, that when exerted jointly
+they raise both bodies at once, results from the Composition of Causes,
+and is a mere instance of the general fact that mechanical forces are
+subject to the law of Composition. And so in every other case which can
+be supposed. For the doctrine of the proportionality of effects to their
+causes cannot of course be applicable to cases in which the augmentation
+of the cause alters the _kind_ of effect; that is, in which the surplus
+quantity superadded to the cause does not become compounded with it, but
+the two together generate an altogether new phenomenon. Suppose that the
+application of a certain quantity of heat to a body merely increases its
+bulk, that a double quantity melts it, and a triple quantity decomposes
+it: these three effects being heterogeneous, no ratio, whether
+corresponding or not to that of the quantities of heat applied, can be
+established between them. Thus the supposed axiom of the proportionality
+of effects to their causes fails at the precise point where the
+principle of the Composition of Causes also fails; viz., where the
+concurrence of causes is such as to determine a change in the properties
+of the body generally, and render it subject to new laws, more or less
+dissimilar to those to which it conformed in its previous state. The
+recognition, therefore, of any such law of proportionality, is
+superseded by the more comprehensive principle, in which as much of it
+as is true is implicitly asserted.
+
+The general remarks on causation, which seemed necessary as an
+introduction to the theory of the inductive process, may here terminate.
+That process is essentially an inquiry into cases of causation. All the
+uniformities which exist in the succession of phenomena, and most of the
+uniformities in their coexistence, are either, as we have seen,
+themselves laws of causation, or consequences resulting from, and
+corollaries capable of being deduced from, such laws. If we could
+determine what causes are correctly assigned to what effects, and what
+effects to what causes, we should be virtually acquainted with the whole
+course of nature. All those uniformities which are mere results of
+causation, might then be explained and accounted for; and every
+individual fact or event might be predicted, provided we had the
+requisite data, that is, the requisite knowledge of the circumstances
+which, in the particular instance, preceded it.
+
+To ascertain, therefore, what are the laws of causation which exist in
+nature; to determine the effect of every cause, and the causes of all
+effects,--is the main business of Induction; and to point out how this
+is done is the chief object of Inductive Logic.
+
+
+
+
+CHAPTER VII.
+
+OF OBSERVATION AND EXPERIMENT.
+
+
+Sec. 1. It results from the preceding exposition, that the process of
+ascertaining what consequents, in nature, are invariably connected with
+what antecedents, or in other words what phenomena are related to each
+other as causes and effects, is in some sort a process of analysis. That
+every fact which begins to exist has a cause, and that this cause must
+be found somewhere among the facts which immediately preceded the
+occurrence, may be taken for certain. The whole of the present facts are
+the infallible result of all past facts, and more immediately of all the
+facts which existed at the moment previous. Here, then, is a great
+sequence, which we know to be uniform. If the whole prior state of the
+entire universe could again recur, it would again be followed by the
+present state. The question is, how to resolve this complex uniformity
+into the simpler uniformities which compose it, and assign to each
+portion of the vast antecedent the portion of the consequent which is
+attendant on it.
+
+This operation, which we have called analytical, inasmuch as it is the
+resolution of a complex whole into the component elements, is more than
+a merely mental analysis. No mere contemplation of the phenomena, and
+partition of them by the intellect alone, will of itself accomplish the
+end we have now in view. Nevertheless, such a mental partition is an
+indispensable first step. The order of nature, as perceived at a first
+glance, presents at every instant a chaos followed by another chaos. We
+must decompose each chaos into single facts. We must learn to see in the
+chaotic antecedent a multitude of distinct antecedents, in the chaotic
+consequent a multitude of distinct consequents. This, supposing it done,
+will not of itself tell us on which of the antecedents each consequent
+is invariably attendant. To determine that point, we must endeavour to
+effect a separation of the facts from one another, not in our minds
+only, but in nature. The mental analysis, however, must take place
+first. And every one knows that in the mode of performing it, one
+intellect differs immensely from another. It is the essence of the act
+of observing; for the observer is not he who merely sees the thing which
+is before his eyes, but he who sees what parts that thing is composed
+of. To do this well is a rare talent. One person, from inattention, or
+attending only in the wrong place, overlooks half of what he sees:
+another sets down much more than he sees, confounding it with what he
+imagines, or with what he infers; another takes note of the _kind_ of
+all the circumstances, but being inexpert in estimating their degree,
+leaves the quantity of each vague and uncertain; another sees indeed the
+whole, but makes such an awkward division of it into parts, throwing
+things into one mass which require to be separated, and separating
+others which might more conveniently be considered as one, that the
+result is much the same, sometimes even worse, than if no analysis had
+been attempted at all. It would be possible to point out what qualities
+of mind, and modes of mental culture, fit a person for being a good
+observer: that, however, is a question not of Logic, but of the Theory
+of Education, in the most enlarged sense of the term. There is not
+properly an Art of Observing. There may be rules for observing. But
+these, like rules for inventing, are properly instructions for the
+preparation of one's own mind; for putting it into the state in which it
+will be most fitted to observe, or most likely to invent. They are,
+therefore, essentially rules of self-education, which is a different
+thing from Logic. They do not teach how to do the thing, but how to make
+ourselves capable of doing it. They are an art of strengthening the
+limbs, not an art of using them.
+
+The extent and minuteness of observation which may be requisite, and the
+degree of decomposition to which it may be necessary to carry the mental
+analysis, depend on the particular purpose in view. To ascertain the
+state of the whole universe at any particular moment is impossible, but
+would also be useless. In making chemical experiments, we do not think
+it necessary to note the position of the planets; because experience has
+shown, as a very superficial experience is sufficient to show, that in
+such cases that circumstance is not material to the result: and,
+accordingly, in the ages when men believed in the occult influences of
+the heavenly bodies, it might have been unphilosophical to omit
+ascertaining the precise condition of those bodies at the moment of the
+experiment. As to the degree of minuteness of the mental subdivision; if
+we were obliged to break down what we observe into its very simplest
+elements, that is, literally into single facts, it would be difficult to
+say where we should find them: we can hardly ever affirm that our
+divisions of any kind have reached the ultimate unit. But this too is
+fortunately unnecessary. The only object of the mental separation is to
+suggest the requisite physical separation, so that we may either
+accomplish it ourselves, or seek for it in nature; and we have done
+enough when we have carried the subdivision as far as the point at which
+we are able to see what observations or experiments we require. It is
+only essential, at whatever point our mental decomposition of facts may
+for the present have stopped, that we should hold ourselves ready and
+able to carry it farther as occasion requires, and should not allow the
+freedom of our discriminating faculty to be imprisoned by the swathes
+and bands of ordinary classification; as was the case with all early
+speculative inquirers, not excepting the Greeks, to whom it seldom
+occurred that what was called by one abstract name might, in reality, be
+several phenomena, or that there was a possibility of decomposing the
+facts of the universe into any elements but those which ordinary
+language already recognised.
+
+
+Sec. 2. The different antecedents and consequents, being, then, supposed to
+be, so far as the case requires, ascertained and discriminated from one
+another; we are to inquire which is connected with which. In every
+instance which comes under our observation, there are many antecedents
+and many consequents. If those antecedents could not be severed from
+one another except in thought, or if those consequents never were found
+apart, it would be impossible for us to distinguish (_a posteriori_ at
+least) the real laws, or to assign to any cause its effect, or to any
+effect its cause. To do so, we must be able to meet with some of the
+antecedents apart from the rest, and observe what follows from them; or
+some of the consequents, and observe by what they are preceded. We must,
+in short, follow the Baconian rule of _varying the circumstances_. This
+is, indeed, only the first rule of physical inquiry, and not, as some
+have thought, the sole rule; but it is the foundation of all the rest.
+
+For the purpose of varying the circumstances, we may have recourse
+(according to a distinction commonly made) either to observation or to
+experiment; we may either _find_ an instance in nature, suited to our
+purposes, or, by an artificial arrangement of circumstances, _make_ one.
+The value of the instance depends on what it is in itself, not on the
+mode in which it is obtained: its employment for the purposes of
+induction depends on the same principles in the one case and in the
+other; as the uses of money are the same whether it is inherited or
+acquired. There is, in short, no difference in kind, no real logical
+distinction, between the two processes of investigation. There are,
+however, practical distinctions to which it is of considerable
+importance to advert.
+
+
+Sec. 3. The first and most obvious distinction between Observation and
+Experiment is, that the latter is an immense extension of the former. It
+not only enables us to produce a much greater number of variations in
+the circumstances than nature spontaneously offers, but also, in
+thousands of cases, to produce the precise _sort_ of variation which we
+are in want of for discovering the law of the phenomenon; a service
+which nature, being constructed on a quite different scheme from that of
+facilitating our studies, is seldom so friendly as to bestow upon us.
+For example, in order to ascertain what principle in the atmosphere
+enables it to sustain life, the variation we require is that a living
+animal should be immersed in each component element of the atmosphere
+separately. But nature does not supply either oxygen or azote in a
+separate state. We are indebted to artificial experiment for our
+knowledge that it is the former, and not the latter, which supports
+respiration; and for our knowledge of the very existence of the two
+ingredients.
+
+Thus far the advantage of experimentation over simple observation is
+universally recognised: all are aware that it enables us to obtain
+innumerable combinations of circumstances which are not to be found in
+nature, and so add to nature's experiments a multitude of experiments of
+our own. But there is another superiority (or, as Bacon would have
+expressed it, another prerogative) of instances artificially obtained
+over spontaneous instances,--of our own experiments over even the same
+experiments when made by nature,--which is not of less importance, and
+which is far from being felt and acknowledged in the same degree.
+
+When we can produce a phenomenon artificially, we can take it, as it
+were, home with us, and observe it in the midst of circumstances with
+which in all other respects we are accurately acquainted. If we desire
+to know what are the effects of the cause A, and are able to produce A
+by means at our disposal, we can generally determine at our own
+discretion, so far as is compatible with the nature of the phenomenon A,
+the whole of the circumstances which shall be present along with it: and
+thus, knowing exactly the simultaneous state of everything else which is
+within the reach of A's influence, we have only to observe what
+alteration is made in that state by the presence of A.
+
+For example, by the electric machine we can produce in the midst of
+known circumstances, the phenomena which nature exhibits on a grander
+scale in the form of lightning and thunder. Now let any one consider
+what amount of knowledge of the effects and laws of electric agency
+mankind could have obtained from the mere observation of thunder-storms,
+and compare it with that which they have gained, and may expect to gain,
+from electrical and galvanic experiments. This example is the more
+striking, now that we have reason to believe that electric action is of
+all natural phenomena (except heat) the most pervading and universal,
+which, therefore, it might antecedently have been supposed could stand
+least in need of artificial means of production to enable it to be
+studied; while the fact is so much the contrary, that without the
+electric machine, the Leyden jar, and the voltaic battery, we probably
+should never have suspected the existence of electricity as one of the
+great agents in nature; the few electric phenomena we should have known
+of would have continued to be regarded either as supernatural, or as a
+sort of anomalies and eccentricities in the order of the universe.
+
+When we have succeeded in insulating the phenomenon which is the subject
+of inquiry, by placing it among known circumstances, we may produce
+further variations of circumstances to any extent, and of such kinds as
+we think best calculated to bring the laws of the phenomenon into a
+clear light. By introducing one well-defined circumstance after another
+into the experiment, we obtain assurance of the manner in which the
+phenomenon behaves under an indefinite variety of possible
+circumstances. Thus, chemists, after having obtained some
+newly-discovered substance in a pure state, (that is, having made sure
+that there is nothing present which can interfere with and modify its
+agency,) introduce various other substances, one by one, to ascertain
+whether it will combine with them, or decompose them, and with what
+result; and also apply heat, or electricity, or pressure, to discover
+what will happen to the substance under each of these circumstances.
+
+But if, on the other hand, it is out of our power to produce the
+phenomenon, and we have to seek for instances in which nature produces
+it, the task before us is very different. Instead of being able to
+choose what the concomitant circumstances shall be, we now have to
+discover what they are; which, when we go beyond the simplest and most
+accessible cases, it is next to impossible to do, with any precision and
+completeness. Let us take, as an exemplification of a phenomenon which
+we have no means of fabricating artificially, a human mind. Nature
+produces many; but the consequence of our not being able to produce
+them by art is, that in every instance in which we see a human mind
+developing itself, or acting upon other things, we see it surrounded and
+obscured by an indefinite multitude of unascertainable circumstances,
+rendering the use of the common experimental methods almost delusive. We
+may conceive to what extent this is true, if we consider, among other
+things, that whenever nature produces a human mind, she produces, in
+close connexion with it, a body; that is, a vast complication of
+physical facts, in no two cases perhaps exactly similar, and most of
+which (except the mere structure, which we can examine in a sort of
+coarse way after it has ceased to act), are radically out of the reach
+of our means of exploration. If, instead of a human mind, we suppose the
+subject of investigation to be a human society or State, all the same
+difficulties recur in a greatly augmented degree.
+
+We have thus already come within sight of a conclusion, which the
+progress of the inquiry will, I think, bring before us with the clearest
+evidence: namely, that in the sciences which deal with phenomena in
+which artificial experiments are impossible (as in the case of
+astronomy), or in which they have a very limited range (as in mental
+philosophy, social science, and even physiology), induction from direct
+experience is practised at a disadvantage in most cases equivalent to
+impracticability: from which it follows that the methods of those
+sciences, in order to accomplish anything worthy of attainment, must be
+to a great extent, if not principally, deductive. This is already known
+to be the case with the first of the sciences we have mentioned,
+astronomy; that it is not generally recognised as true of the others, is
+probably one of the reasons why they are not in a more advanced state.
+
+
+Sec. 4. If what is called pure observation is at so great a disadvantage,
+compared with artificial experimentation, in one department of the
+direct exploration of phenomena, there is another branch in which the
+advantage is all on the side of the former.
+
+Inductive inquiry having for its object to ascertain what causes are
+connected with what effects, we may begin this search at either end of
+the road which leads from the one point to the other: we may either
+inquire into the effects of a given cause, or into the causes of a given
+effect. The fact that light blackens chloride of silver might have been
+discovered either by experiments on light, trying what effect it would
+produce on various substances, or by observing that portions of the
+chloride had repeatedly become black, and inquiring into the
+circumstances. The effect of the urali poison might have become known
+either by administering it to animals, or by examining how it happened
+that the wounds which the Indians of Guiana inflict with their arrows
+prove so uniformly mortal. Now it is manifest from the mere statement of
+the examples, without any theoretical discussion, that artificial
+experimentation is applicable only to the former of these modes of
+investigation. We can take a cause, and try what it will produce: but we
+cannot take an effect, and try what it will be produced by. We can only
+watch till we see it produced, or are enabled to produce it by accident.
+
+This would be of little importance, if it always depended on our choice
+from which of the two ends of the sequence we would undertake our
+inquiries. But we have seldom any option. As we can only travel from the
+known to the unknown, we are obliged to commence at whichever end we are
+best acquainted with. If the agent is more familiar to us than its
+effects, we watch for, or contrive, instances of the agent, under such
+varieties of circumstances as are open to us, and observe the result.
+If, on the contrary, the conditions on which a phenomenon depends are
+obscure, but the phenomenon itself familiar, we must commence our
+inquiry from the effect. If we are struck with the fact that chloride of
+silver has been blackened, and have no suspicion of the cause, we have
+no resource but to compare instances in which the fact has chanced to
+occur, until by that comparison we discover that in all those instances
+the substances had been exposed to light. If we knew nothing of the
+Indian arrows but their fatal effect, accident alone could turn our
+attention to experiments on the urali; in the regular course of
+investigation, we could only inquire, or try to observe, what had been
+done to the arrows in particular instances.
+
+Wherever, having nothing to guide us to the cause, we are obliged to set
+out from the effect, and to apply the rule of varying the circumstances
+to the consequents, not the antecedents, we are necessarily destitute of
+the resource of artificial experimentation. We cannot, at our choice,
+obtain consequents, as we can antecedents, under any set of
+circumstances compatible with their nature. There are no means of
+producing effects but through their causes, and by the supposition the
+causes of the effect in question are not known to us. We have therefore
+no expedient but to study it where it offers itself spontaneously. If
+nature happens to present us with instances sufficiently varied in their
+circumstances, and if we are able to discover, either among the
+proximate antecedents or among some other order of antecedents,
+something which is always found when the effect is found, however
+various the circumstances, and never found when it is not; we may
+discover, by mere observation without experiment, a real uniformity in
+nature.
+
+But though this is certainly the most favourable case for sciences of
+pure observation, as contrasted with those in which artificial
+experiments are possible, there is in reality no case which more
+strikingly illustrates the inherent imperfection of direct induction
+when not founded on experimentation. Suppose that, by a comparison of
+cases of the effect, we have found an antecedent which appears to be,
+and perhaps is, invariably connected with it: we have not yet proved
+that antecedent to be the cause, until we have reversed the process, and
+produced the effect by means of that antecedent. If we can produce the
+antecedent artificially, and if, when we do so, the effect follows, the
+induction is complete; that antecedent is the cause of that
+consequent.[32] But we have then added the evidence of experiment to
+that of simple observation. Until we had done so, we had only proved
+_invariable_ antecedence within the limits of experience, but not
+_unconditional_ antecedence, or causation. Until it had been shown by
+the actual production of the antecedent under known circumstances, and
+the occurrence thereupon of the consequent, that the antecedent was
+really the condition on which it depended; the uniformity of succession
+which was proved to exist between them might, for aught we knew, be
+(like the succession of day and night) not a case of causation at all;
+both antecedent and consequent might be successive stages of the effect
+of an ulterior cause. Observation, in short, without experiment
+(supposing no aid from deduction) can ascertain sequences and
+coexistences, but cannot prove causation.
+
+In order to see these remarks verified by the actual state of the
+sciences, we have only to think of the condition of natural history. In
+zoology, for example, there is an immense number of uniformities
+ascertained, some of coexistence, others of succession, to many of
+which, notwithstanding considerable variations of the attendant
+circumstances, we know not any exception: but the antecedents, for the
+most part, are such as we cannot artificially produce; or if we can, it
+is only by setting in motion the exact process by which nature produces
+them; and this being to us a mysterious process, of which the main
+circumstances are not only unknown but unobservable, we do not succeed
+in obtaining the antecedents under known circumstances. What is the
+result? That on this vast subject, which affords so much and such varied
+scope for observation, we have made most scanty progress in ascertaining
+any laws of causation. We know not with certainty, in the case of most
+of the phenomena that we find conjoined, which is the condition of the
+other; which is cause, and which effect, or whether either of them is
+so, or they are not rather conjunct effects of causes yet to be
+discovered, complex results of laws hitherto unknown.
+
+Although some of the foregoing observations may be, in technical
+strictness of arrangement, premature in this place, it seemed that a few
+general remarks on the difference between sciences of mere observation
+and sciences of experimentation, and the extreme disadvantage under
+which directly inductive inquiry is necessarily carried on in the
+former, were the best preparation for discussing the methods of direct
+induction; a preparation rendering superfluous much that must otherwise
+have been introduced, with some inconvenience, into the heart of that
+discussion. To the consideration of these methods we now proceed.
+
+
+
+
+CHAPTER VIII.
+
+OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.
+
+
+Sec. 1. The simplest and most obvious modes of singling out from among the
+circumstances which precede or follow a phenomenon, those with which it
+is really connected by an invariable law, are two in number. One is, by
+comparing together different instances in which the phenomenon occurs.
+The other is, by comparing instances in which the phenomenon does occur,
+with instances in other respects similar in which it does not. These two
+methods may be respectively denominated, the Method of Agreement, and
+the Method of Difference.
+
+In illustrating these methods, it will be necessary to bear in mind the
+twofold character of inquiries into the laws of phenomena; which may be
+either inquiries into the cause of a given effect, or into the effects
+or properties of a given cause. We shall consider the methods in their
+application to either order of investigation, and shall draw our
+examples equally from both.
+
+We shall denote antecedents by the large letters of the alphabet, and
+the consequents corresponding to them by the small. Let A, then, be an
+agent or cause, and let the object of our inquiry be to ascertain what
+are the effects of this cause. If we can either find, or produce, the
+agent A in such varieties of circumstances, that the different cases
+have no circumstance in common except A; then whatever effect we find to
+be produced in all our trials, is indicated as the effect of A. Suppose,
+for example, that A is tried along with B and C, and that the effect is
+_a b c_; and suppose that A is next tried with D and E, but without B
+and C, and that the effect is _a d e_. Then we may reason thus: _b_ and
+_c_ are not effects of A, for they were not produced by it in the second
+experiment; nor are _d_ and _e_, for they were not produced in the
+first. Whatever is really the effect of A must have been produced in
+both instances; now this condition is fulfilled by no circumstance
+except _a_. The phenomenon _a_ cannot have been the effect of B or C,
+since it was produced where they were not; nor of D or E, since it was
+produced where they were not. Therefore it is the effect of A.
+
+For example, let the antecedent A be the contact of an alkaline
+substance and an oil. This combination being tried under several
+varieties of circumstances, resembling each other in nothing else, the
+results agree in the production of a greasy and detersive or saponaceous
+substance: it is therefore concluded that the combination of an oil and
+an alkali causes the production of a soap. It is thus we inquire, by the
+Method of Agreement, into the effect of a given cause.
+
+In a similar manner we may inquire into the cause of a given effect. Let
+_a_ be the effect. Here, as shown in the last chapter, we have only the
+resource of observation without experiment: we cannot take a phenomenon
+of which we know not the origin, and try to find its mode of production
+by producing it: if we succeeded in such a random trial it could only be
+by accident. But if we can observe _a_ in two different combinations, _a
+b c_, and _a d e_; and if we know, or can discover, that the antecedent
+circumstances in these cases respectively were A B C and A D E; we may
+conclude by a reasoning similar to that in the preceding example, that A
+is the antecedent connected with the consequent _a_ by a law of
+causation. B and C, we may say, cannot be causes of _a_, since on its
+second occurrence they were not present; nor are D and E, for they were
+not present on its first occurrence. A, alone of the five circumstances,
+was found among the antecedents of _a_ in both instances.
+
+For example, let the effect _a_ be crystallization. We compare instances
+in which bodies are known to assume crystalline structure, but which
+have no other point of agreement; and we find them to have one, and as
+far as we can observe, only one, antecedent in common: the deposition of
+a solid matter from a liquid state, either a state of fusion or of
+solution. We conclude, therefore, that the solidification of a
+substance from a liquid state is an invariable antecedent of its
+crystallization.
+
+In this example we may go farther, and say, it is not only the
+invariable antecedent but the cause; or at least the proximate event
+which completes the cause. For in this case we are able, after detecting
+the antecedent A, to produce it artificially, and by finding that _a_
+follows it, verify the result of our induction. The importance of thus
+reversing the proof was strikingly manifested when by keeping a phial of
+water charged with siliceous particles undisturbed for years, a chemist
+(I believe Dr. Wollaston) succeeded in obtaining crystals of quartz: and
+in the equally interesting experiment in which Sir James Hall produced
+artificial marble, by the cooling of its materials from fusion under
+immense pressure: two admirable examples of the light which may be
+thrown upon the most secret processes of nature by well-contrived
+interrogation of her.
+
+But if we cannot artificially produce the phenomenon A, the conclusion
+that it is the cause of _a_ remains subject to very considerable doubt.
+Though an invariable, it may not be the unconditional antecedent of _a_,
+but may precede it as day precedes night or night day. This uncertainty
+arises from the impossibility of assuring ourselves that A is the _only_
+immediate antecedent common to both the instances. If we could be
+certain of having ascertained all the invariable antecedents, we might
+be sure that the unconditional invariable antecedent, or cause, must be
+found somewhere among them. Unfortunately it is hardly ever possible to
+ascertain all the antecedents, unless the phenomenon is one which we can
+produce artificially. Even then, the difficulty is merely lightened, not
+removed: men knew how to raise water in pumps long before they adverted
+to what was really the operating circumstance in the means they
+employed, namely, the pressure of the atmosphere on the open surface of
+the water. It is, however, much easier to analyse completely a set of
+arrangements made by ourselves, than the whole complex mass of the
+agencies which nature happens to be exerting at the moment of the
+production of a given phenomenon. We may overlook some of the material
+circumstances in an experiment with an electrical machine; but we shall,
+at the worst, be better acquainted with them than with those of a
+thunder-storm.
+
+The mode of discovering and proving laws of nature, which we have now
+examined, proceeds on the following axiom: Whatever circumstances can be
+excluded, without prejudice to the phenomenon, or can be absent
+notwithstanding its presence, is not connected with it in the way of
+causation. The casual circumstances being thus eliminated, if only one
+remains, that one is the cause which we are in search of: if more than
+one, they either are, or contain among them, the cause; and so, _mutatis
+mutandis_, of the effect. As this method proceeds by comparing different
+instances to ascertain in what they agree, I have termed it the Method
+of Agreement: and we may adopt as its regulating principle the following
+canon:--
+
+FIRST CANON.
+
+_If two or more instances of the phenomenon under investigation have
+only one circumstance in common, the circumstance in which alone all the
+instances agree, is the cause (or effect) of the given phenomenon._
+
+Quitting for the present the Method of Agreement, to which we shall
+almost immediately return, we proceed to a still more potent instrument
+of the investigation of nature, the Method of Difference.
+
+
+Sec. 2. In the Method of Agreement, we endeavoured to obtain instances
+which agreed in the given circumstance but differed in every other: in
+the present method we require, on the contrary, two instances resembling
+one another in every other respect, but differing in the presence or
+absence of the phenomenon we wish to study. If our object be to discover
+the effects of an agent A, we must procure A in some set of ascertained
+circumstances, as A B C, and having noted the effects produced, compare
+them with the effect of the remaining circumstances B C, when A is
+absent. If the effect of A B C is _a b c_, and the effect of B C, _b c_,
+it is evident that the effect of A is _a_. So again, if we begin at the
+other end, and desire to investigate the cause of an effect _a_, we must
+select an instance, as _a b c_, in which the effect occurs, and in which
+the antecedents were A B C, and we must look out for another instance in
+which the remaining circumstances, _b c_, occur without _a_. If the
+antecedents, in that instance, are B C, we know that the cause of _a_
+must be A: either A alone, or A in conjunction with some of the other
+circumstances present.
+
+It is scarcely necessary to give examples of a logical process to which
+we owe almost all the inductive conclusions we draw in daily life. When
+a man is shot through the heart, it is by this method we know that it
+was the gun-shot which killed him: for he was in the fulness of life
+immediately before, all circumstances being the same, except the wound.
+
+The axioms implied in this method are evidently the following. Whatever
+antecedent cannot be excluded without preventing the phenomenon, is the
+cause, or a condition, of that phenomenon: Whatever consequent can be
+excluded, with no other difference in the antecedents than the absence
+of a particular one, is the effect of that one. Instead of comparing
+different instances of a phenomenon, to discover in what they agree,
+this method compares an instance of its occurrence with an instance of
+its non-occurrence, to discover in what they differ. The canon which is
+the regulating principle of the Method of Difference may be expressed as
+follows:
+
+SECOND CANON.
+
+_If an instance in which the phenomenon under investigation occurs, and
+an instance in which it does not occur, have every circumstance in
+common save one, that one occurring only in the former; the circumstance
+in which alone the two instances differ, is the effect, or the cause, or
+an indispensable part of the cause, of the phenomenon._
+
+
+Sec. 3. The two methods which we have now stated have many features of
+resemblance, but there are also many distinctions between them. Both
+are methods of _elimination_. This term (employed in the theory of
+equations to denote the process by which one after another of the
+elements of a question is excluded, and the solution made to depend on
+the relation between the remaining elements only) is well suited to
+express the operation, analogous to this, which has been understood
+since the time of Bacon to be the foundation of experimental inquiry:
+namely, the successive exclusion of the various circumstances which are
+found to accompany a phenomenon in a given instance, in order to
+ascertain what are those among them which can be absent consistently
+with the existence of the phenomenon. The Method of Agreement stands on
+the ground that whatever can be eliminated, is not connected with the
+phenomenon by any law. The Method of Difference has for its foundation,
+that whatever cannot be eliminated, is connected with the phenomenon by
+a law.
+
+Of these methods, that of Difference is more particularly a method of
+artificial experiment; while that of Agreement is more especially the
+resource employed where experimentation is impossible. A few reflections
+will prove the fact, and point out the reason of it.
+
+It is inherent in the peculiar character of the Method of Difference,
+that the nature of the combinations which it requires is much more
+strictly defined than in the Method of Agreement. The two instances
+which are to be compared with one another must be exactly similar, in
+all circumstances except the one which we are attempting to investigate:
+they must be in the relation of A B C and B C, or of _a b c_ and _b c_.
+It is true that this similarity of circumstances needs not extend to
+such as are already known to be immaterial to the result. And in the
+case of most phenomena we learn at once, from the commonest experience,
+that most of the coexistent phenomena of the universe may be either
+present or absent without affecting the given phenomenon; or, if
+present, are present indifferently when the phenomenon does not happen
+and when it does. Still, even limiting the identity which is required
+between the two instances, A B C and B C, to such circumstances as are
+not already known to be indifferent; it is very seldom that nature
+affords two instances, of which we can be assured that they stand in
+this precise relation to one another. In the spontaneous operations of
+nature there is generally such complication and such obscurity, they are
+mostly either on so overwhelmingly large or on so inaccessibly minute a
+scale, we are so ignorant of a great part of the facts which really take
+place, and even those of which we are not ignorant are so multitudinous,
+and therefore so seldom exactly alike in any two cases, that a
+spontaneous experiment, of the kind required by the Method of
+Difference, is commonly not to be found. When, on the contrary, we
+obtain a phenomenon by an artificial experiment, a pair of instances
+such as the method requires is obtained almost as a matter of course,
+provided the process does not last a long time. A certain state of
+surrounding circumstances existed before we commenced the experiment;
+this is B C. We then introduce A; say, for instance, by merely bringing
+an object from another part of the room, before there has been time for
+any change in the other elements. It is, in short (as M. Comte
+observes), the very nature of an experiment, to introduce into the
+pre-existing state of circumstances a change perfectly definite. We
+choose a previous state of things with which we are well acquainted, so
+that no unforeseen alteration in that state is likely to pass
+unobserved; and into this we introduce, as rapidly as possible, the
+phenomenon which we wish to study; so that in general we are entitled to
+feel complete assurance that the pre-existing state, and the state which
+we have produced, differ in nothing except the presence or absence of
+that phenomenon. If a bird is taken from a cage, and instantly plunged
+into carbonic acid gas, the experimentalist may be fully assured (at all
+events after one or two repetitions) that no circumstance capable of
+causing suffocation had supervened in the interim, except the change
+from immersion in the atmosphere to immersion in carbonic acid gas.
+There is one doubt, indeed, which may remain in some cases of this
+description; the effect may have been produced not by the change, but by
+the means employed to produce the change. The possibility, however, of
+this last supposition generally admits of being conclusively tested by
+other experiments. It thus appears that in the study of the various
+kinds of phenomena which we can, by our voluntary agency, modify or
+control, we can in general satisfy the requisitions of the Method of
+Difference; but that by the spontaneous operations of nature those
+requisitions are seldom fulfilled.
+
+The reverse of this is the case with the Method of Agreement. We do not
+here require instances of so special and determinate a kind. Any
+instances whatever, in which nature presents us with a phenomenon, may
+be examined for the purposes of this method; and if all such instances
+agree in anything, a conclusion of considerable value is already
+attained. We can seldom, indeed, be sure that the one point of agreement
+is the only one; but this ignorance does not, as in the Method of
+Difference, vitiate the conclusion; the certainty of the result, as far
+as it goes, is not affected. We have ascertained one invariable
+antecedent or consequent, however many other invariable antecedents or
+consequents may still remain unascertained. If A B C, A D E, A F G, are
+all equally followed by _a_, then _a_ is an invariable consequent of A.
+If _a b c_, _a d e_, _a f g_, all number A among their antecedents, then
+A is connected as an antecedent, by some invariable law, with _a_. But
+to determine whether this invariable antecedent is a cause, or this
+invariable consequent an effect, we must be able, in addition, to
+produce the one by means of the other; or, at least, to obtain that
+which alone constitutes our assurance of having produced anything,
+namely, an instance in which the effect, _a_, has come into existence,
+with no other change in the pre-existing circumstances than the addition
+of A. And this, if we can do it, is an application of the Method of
+Difference, not of the Method of Agreement.
+
+It thus appears to be by the Method of Difference alone that we can
+ever, in the way of direct experience, arrive with certainty at causes.
+The Method of Agreement leads only to laws of phenomena (as some writers
+call them, but improperly, since laws of causation are also laws of
+phenomena): that is, to uniformities, which either are not laws of
+causation, or in which the question of causation must for the present
+remain undecided. The Method of Agreement is chiefly to be resorted to,
+as a means of suggesting applications of the Method of Difference (as in
+the last example the comparison of A B C, A D E, A F G, suggested that A
+was the antecedent on which to try the experiment whether it could
+produce _a_); or as an inferior resource, in case the Method of
+Difference is impracticable; which, as we before showed, generally
+arises from the impossibility of artificially producing the phenomena.
+And hence it is that the Method of Agreement, though applicable in
+principle to either case, is more emphatically the method of
+investigation on those subjects where artificial experimentation is
+impossible: because on those it is, generally, our only resource of a
+directly inductive nature; while, in the phenomena which we can produce
+at pleasure, the Method of Difference generally affords a more
+efficacious process, which will ascertain causes as well as mere laws.
+
+
+Sec. 4. There are, however, many cases in which, though our power of
+producing the phenomenon is complete, the Method of Difference either
+cannot be made available at all, or not without a previous employment of
+the Method of Agreement. This occurs when the agency by which we can
+produce the phenomenon is not that of one single antecedent, but a
+combination of antecedents, which we have no power of separating from
+each other, and exhibiting apart. For instance, suppose the subject of
+inquiry to be the cause of the double refraction of light. We can
+produce this phenomenon at pleasure, by employing any one of the many
+substances which are known to refract light in that peculiar manner. But
+if, taking one of those substances, as Iceland spar for example, we wish
+to determine on which of the properties of Iceland spar this remarkable
+phenomenon depends, we can make no use, for that purpose, of the Method
+of Difference; for we cannot find another substance precisely resembling
+Iceland spar except in some one property. The only mode, therefore, of
+prosecuting this inquiry is that afforded by the Method of Agreement; by
+which, in fact, through a comparison of all the known substances which
+have the property of doubly refracting light, it was ascertained that
+they agree in the circumstance of being crystalline substances; and
+though the converse does not hold, though all crystalline substances
+have not the property of double refraction, it was concluded, with
+reason, that there is a real connexion between these two properties;
+that either crystalline structure, or the cause which gives rise to that
+structure, is one of the conditions of double refraction.
+
+Out of this employment of the Method of Agreement arises a peculiar
+modification of that method, which is sometimes of great avail in the
+investigation of nature. In cases similar to the above, in which it is
+not possible to obtain the precise pair of instances which our second
+canon requires--instances agreeing in every antecedent except A, or in
+every consequent except _a_; we may yet be able, by a double employment
+of the Method of Agreement, to discover in what the instances which
+contain A or _a_, differ from those which do not.
+
+If we compare various instances in which _a_ occurs, and find that they
+all have in common the circumstance A, and (as far as can be observed)
+no other circumstance, the Method of Agreement, so far, bears testimony
+to a connexion between A and _a_. In order to convert this evidence of
+connexion into proof of causation by the direct Method of Difference, we
+ought to be able, in some one of these instances, as for example A B C,
+to leave out A, and observe whether by doing so, _a_ is prevented. Now
+supposing (what is often the case) that we are not able to try this
+decisive experiment; yet, provided we can by any means discover what
+would be its result if we could try it, the advantage will be the same.
+Suppose, then, that as we previously examined a variety of instances in
+which _a_ occurred, and found them to agree in containing A, so we now
+observe a variety of instances in which _a_ does not occur, and find
+them agree in not containing A; which establishes, by the Method of
+Agreement, the same connexion between the absence of A and the absence
+of _a_, which was before established between their presence. As, then,
+it had been shown that whenever A is present _a_ is present, so it being
+now shown that when A is taken away _a_ is removed along with it, we
+have by the one proposition A B C, _a b c_, by the other B C, _b c_,
+the positive and negative instances which the Method of Difference
+requires.
+
+This method may be called the Indirect Method of Difference, or the
+Joint Method of Agreement and Difference; and consists in a double
+employment of the Method of Agreement, each proof being independent of
+the other, and corroborating it. But it is not equivalent to a proof by
+the direct Method of Difference. For the requisitions of the Method of
+Difference are not satisfied, unless we can be quite sure either that
+the instances affirmative of _a_ agree in no antecedent whatever but A,
+or that the instances negative of _a_ agree in nothing but the negation
+of A. Now if it were possible, which it never is, to have this
+assurance, we should not need the joint method; for either of the two
+sets of instances separately would then be sufficient to prove
+causation. This indirect method, therefore, can only be regarded as a
+great extension and improvement of the Method of Agreement, but not as
+participating in the more cogent nature of the Method of Difference. The
+following may be stated as its canon:--
+
+THIRD CANON.
+
+_If two or more instances in which the phenomenon occurs have only one
+circumstance in common, while two or more instances in which it does not
+occur have nothing in common save the absence of that circumstance; the
+circumstance in which alone the two sets of instances differ, is the
+effect, or the cause, or an indispensable part of the cause, of the
+phenomenon._
+
+We shall presently see that the Joint Method of Agreement and Difference
+constitutes, in another respect not yet adverted to, an improvement upon
+the common Method of Agreement, namely, in being unaffected by a
+characteristic imperfection of that method, the nature of which still
+remains to be pointed out. But as we cannot enter into this exposition
+without introducing a new element of complexity into this long and
+intricate discussion, I shall postpone it to a subsequent chapter, and
+shall at once proceed to a statement of two other methods, which will
+complete the enumeration of the means which mankind possess for
+exploring the laws of nature by specific observation and experience.
+
+
+Sec. 5. The first of these has been aptly denominated the Method of
+Residues. Its principle is very simple. Subducting from any given
+phenomenon all the portions which, by virtue of preceding inductions,
+can be assigned to known causes, the remainder will be the effect of the
+antecedents which had been overlooked, or of which the effect was as yet
+an unknown quantity.
+
+Suppose, as before, that we have the antecedents A B C, followed by the
+consequents _a b c_, and that by previous inductions (founded, we will
+suppose, on the Method of Difference) we have ascertained the causes of
+some of these effects, or the effects of some of these causes; and are
+thence apprised that the effect of A is _a_, and that the effect of B is
+_b_. Subtracting the sum of these effects from the total phenomenon,
+there remains _c_, which now, without any fresh experiments, we may know
+to be the effect of C. This Method of Residues is in truth a peculiar
+modification of the Method of Difference. If the instance A B C, _a b
+c_, could have been compared with a single instance A B, _a b_, we
+should have proved C to be the cause of _c_, by the common process of
+the Method of Difference. In the present case, however, instead of a
+single instance A B, we have had to study separately the causes A and B,
+and to infer from the effects which they produce separately, what effect
+they must produce in the case A B C where they act together. Of the two
+instances, therefore, which the Method of Difference requires,--the one
+positive, the other negative,--the negative one, or that in which the
+given phenomenon is absent, is not the direct result of observation and
+experiment, but has been arrived at by deduction. As one of the forms of
+the Method of Difference, the Method of Residues partakes of its
+rigorous certainty, provided the previous inductions, those which gave
+the effects of A and B, were obtained by the same infallible method, and
+provided we are certain that C is the _only_ antecedent to which the
+residual phenomenon _c_ can be referred; the only agent of which we had
+not already calculated and subducted the effect. But as we can never be
+quite certain of this, the evidence derived from the Method of Residues
+is not complete unless we can obtain C artificially and try it
+separately, or unless its agency, when once suggested, can be accounted
+for, and proved deductively from known laws.
+
+Even with these reservations, the Method of Residues is one of the most
+important among our instruments of discovery. Of all the methods of
+investigating laws of nature, this is the most fertile in unexpected
+results; often informing us of sequences in which neither the cause nor
+the effect were sufficiently conspicuous to attract of themselves the
+attention of observers. The agent C may be an obscure circumstance, not
+likely to have been perceived unless sought for, nor likely to have been
+sought for until attention had been awakened by the insufficiency of the
+obvious causes to account for the whole of the effect. And _c_ may be so
+disguised by its intermixture with _a_ and _b_, that it would scarcely
+have presented itself spontaneously as a subject of separate study. Of
+these uses of the method, we shall presently cite some remarkable
+examples. The canon of the Method of Residues is as follows:--
+
+FOURTH CANON.
+
+_Subduct from any phenomenon such part as is known by previous
+inductions to be the effect of certain antecedents, and the residue of
+the phenomenon is the effect of the remaining antecedents._
+
+
+Sec. 6. There remains a class of laws which it is impracticable to
+ascertain by any of the three methods which I have attempted to
+characterize; namely, the laws of those Permanent Causes, or
+indestructible natural agents, which it is impossible either to exclude
+or to isolate; which we can neither hinder from being present, nor
+contrive that they shall be present alone. It would appear at first
+sight that we could by no means separate the effects of these agents
+from the effects of those other phenomena with which they cannot be
+prevented from coexisting. In respect, indeed, to most of the permanent
+causes, no such difficulty exists; since though we cannot eliminate
+them as coexisting facts, we can eliminate them as influencing agents,
+by simply trying our experiment in a local situation beyond the limits
+of their influence. The pendulum, for example, has its oscillations
+disturbed by the vicinity of a mountain: we remove the pendulum to a
+sufficient distance from the mountain, and the disturbance ceases: from
+these data we can determine by the Method of Difference, the amount of
+effect due to the mountain; and beyond a certain distance everything
+goes on precisely as it would do if the mountain exercised no influence
+whatever, which, accordingly, we, with sufficient reason, conclude to be
+the fact.
+
+The difficulty, therefore, in applying the methods already treated of to
+determine the effects of Permanent Causes, is confined to the cases in
+which it is impossible for us to get out of the local limits of their
+influence. The pendulum can be removed from the influence of the
+mountain, but it cannot be removed from the influence of the earth: we
+cannot take away the earth from the pendulum, nor the pendulum from the
+earth, to ascertain whether it would continue to vibrate if the action
+which the earth exerts upon it were withdrawn. On what evidence, then,
+do we ascribe its vibrations to the earth's influence? Not on any
+sanctioned by the Method of Difference; for one of the two instances,
+the negative instance, is wanting. Nor by the Method of Agreement; for
+though all pendulums agree in this, that during their oscillations the
+earth is always present, why may we not as well ascribe the phenomenon
+to the sun, which is equally a coexistent fact in all the experiments?
+It is evident that to establish even so simple a fact of causation as
+this, there was required some method over and above those which we have
+yet examined.
+
+As another example, let us take the phenomenon Heat. Independently of
+all hypothesis as to the real nature of the agency so called, this fact
+is certain, that we are unable to exhaust any body of the whole of its
+heat. It is equally certain, that no one ever perceived heat not
+emanating from a body. Being unable, then, to separate Body and Heat, we
+cannot effect such a variation of circumstances as the foregoing three
+methods require; we cannot ascertain, by those methods, what portion of
+the phenomena exhibited by any body is due to the heat contained in it.
+If we could observe a body with its heat, and the same body entirely
+divested of heat, the Method of Difference would show the effect due to
+the heat, apart from that due to the body. If we could observe heat
+under circumstances agreeing in nothing but heat, and therefore not
+characterized also by the presence of a body, we could ascertain the
+effects of heat, from an instance of heat with a body and an instance of
+heat without a body, by the Method of Agreement; or we could determine
+by the Method of Difference what effect was due to the body, when the
+remainder which was due to the heat would be given by the Method of
+Residues. But we can do none of these things; and without them the
+application of any of the three methods to the solution of this problem
+would be illusory. It would be idle, for instance, to attempt to
+ascertain the effect of heat by subtracting from the phenomena exhibited
+by a body, all that is due to its other properties; for as we have never
+been able to observe any bodies without a portion of heat in them,
+effects due to that heat might form a part of the very results, which we
+were affecting to subtract in order that the effect of heat might be
+shown by the residue.
+
+If, therefore, there were no other methods of experimental investigation
+than these three, we should be unable to determine the effects due to
+heat as a cause. But we have still a resource. Though we cannot exclude
+an antecedent altogether, we may be able to produce, or nature may
+produce for us, some modification in it. By a modification is here
+meant, a change in it, not amounting to its total removal. If some
+modification in the antecedent A is always followed by a change in the
+consequent _a_, the other consequents _b_ and _c_ remaining the same; or
+_vice versa_, if every change in _a_ is found to have been preceded by
+some modification in A, none being observable in any of the other
+antecedents; we may safely conclude that _a_ is, wholly or in part, an
+effect traceable to A, or at least in some way connected with it through
+causation. For example, in the case of heat, though we cannot expel it
+altogether from any body, we can modify it in quantity, we can increase
+or diminish it; and doing so, we find by the various methods of
+experimentation or observation already treated of, that such increase or
+diminution of heat is followed by expansion or contraction of the body.
+In this manner we arrive at the conclusion, otherwise unattainable by
+us, that one of the effects of heat is to enlarge the dimensions of
+bodies; or what is the same thing in other words, to widen the distances
+between their particles.
+
+A change in a thing, not amounting to its total removal, that is, a
+change which leaves it still the same thing it was, must be a change
+either in its quantity, or in some of its variable relations to other
+things, of which variable relations the principal is its position in
+space. In the previous example, the modification which was produced in
+the antecedent was an alteration in its quantity. Let us now suppose the
+question to be, what influence the moon exerts on the surface of the
+earth. We cannot try an experiment in the absence of the moon, so as to
+observe what terrestrial phenomena her annihilation would put an end to;
+but when we find that all the variations in the _position_ of the moon
+are followed by corresponding variations in the time and place of high
+water, the place being always either the part of the earth which is
+nearest to, or that which is most remote from, the moon, we have ample
+evidence that the moon is, wholly or partially, the cause which
+determines the tides. It very commonly happens, as it does in this
+instance, that the variations of an effect are correspondent, or
+analogous, to those of its cause; as the moon moves farther towards the
+east, the high water point does the same: but this is not an
+indispensable condition; as may be seen in the same example, for along
+with that high water point there is at the same instant another high
+water point diametrically opposite to it, and which, therefore, of
+necessity, moves towards the west, as the moon, followed by the nearer
+of the tide waves, advances towards the east: and yet both these motions
+are equally effects of the moon's motion.
+
+That the oscillations of the pendulum are caused by the earth, is proved
+by similar evidence. Those oscillations take place between equidistant
+points on the two sides of a line, which, being perpendicular to the
+earth, varies with every variation in the earth's position, either in
+space or relatively to the object. Speaking accurately, we only know by
+the method now characterized, that all terrestrial bodies tend to the
+earth, and not to some unknown fixed point lying in the same direction.
+In every twenty-four hours, by the earth's rotation, the line drawn from
+the body at right angles to the earth coincides successively with all
+the radii of a circle, and in the course of six months the place of that
+circle varies by nearly two hundred millions of miles; yet in all these
+changes of the earth's position, the line in which bodies tend to fall
+continues to be directed towards it: which proves that terrestrial
+gravity is directed to the earth, and not, as was once fancied by some,
+to a fixed point of space.
+
+The method by which these results were obtained, may be termed the
+Method of Concomitant Variations: it is regulated by the following
+canon:--
+
+FIFTH CANON.
+
+_Whatever phenomenon varies in any manner whenever another phenomenon
+varies in some particular manner, is either a cause or an effect of that
+phenomenon, or is connected with it through some fact of causation._
+
+The last clause is subjoined, because it by no means follows when two
+phenomena accompany each other in their variations, that the one is
+cause and the other effect. The same thing may, and indeed must happen,
+supposing them to be two different effects of a common cause: and by
+this method alone it would never be possible to ascertain which of the
+suppositions is the true one. The only way to solve the doubt would be
+that which we have so often adverted to, viz. by endeavouring to
+ascertain whether we can produce the one set of variations by means of
+the other. In the case of heat, for example, by increasing the
+temperature of a body we increase its bulk, but by increasing its bulk
+we do not increase its temperature; on the contrary, (as in the
+rarefaction of air under the receiver of an air-pump,) we generally
+diminish it: therefore heat is not an effect, but a cause, of increase
+of bulk. If we cannot ourselves produce the variations, we must
+endeavour, though it is an attempt which is seldom successful, to find
+them produced by nature in some case in which the pre-existing
+circumstances are perfectly known to us.
+
+It is scarcely necessary to say, that in order to ascertain the uniform
+concomitance of variations in the effect with variations in the cause,
+the same precautions must be used as in any other case of the
+determination of an invariable sequence. We must endeavour to retain all
+the other antecedents unchanged, while that particular one is subjected
+to the requisite series of variations; or in other words, that we may be
+warranted in inferring causation from concomitance of variations, the
+concomitance itself must be proved by the Method of Difference.
+
+It might at first appear that the Method of Concomitant Variations
+assumes a new axiom, or law of causation in general, namely, that every
+modification of the cause is followed by a change in the effect. And it
+does usually happen that when a phenomenon A causes a phenomenon _a_,
+any variation in the quantity or in the various relations of A, is
+uniformly followed by a variation in the quantity or relations of _a_.
+To take a familiar instance, that of gravitation. The sun causes a
+certain tendency to motion in the earth; here we have cause and effect;
+but that tendency is _towards_ the sun, and therefore varies in
+direction as the sun varies in the relation of position; and moreover
+the tendency varies in intensity, in a certain numerical correspondence
+to the sun's distance from the earth, that is, according to another
+relation of the sun. Thus we see that there is not only an invariable
+connexion between the sun and the earth's gravitation, but that two of
+the relations of the sun, its position with respect to the earth and its
+distance from the earth, are invariably connected as antecedents with
+the quantity and direction of the earth's gravitation. The cause of the
+earth's gravitating at all, is simply the sun; but the cause of its
+gravitating with a given intensity and in a given direction, is the
+existence of the sun in a given direction and at a given distance. It is
+not strange that a modified cause, which is in truth a different cause,
+should produce a different effect.
+
+Although it is for the most part true that a modification of the cause
+is followed by a modification of the effect, the Method of Concomitant
+Variations does not, however, presuppose this as an axiom. It only
+requires the converse proposition; that anything on whose modifications,
+modifications of an effect are invariably consequent, must be the cause
+(or connected with the cause) of that effect; a proposition, the truth
+of which is evident; for if the thing itself had no influence on the
+effect, neither could the modifications of the thing have any influence.
+If the stars have no power over the fortunes of mankind, it is implied
+in the very terms, that the conjunctions or oppositions of different
+stars can have no such power.
+
+Although the most striking applications of the Method of Concomitant
+Variations take place in the cases in which the Method of Difference,
+strictly so called, is impossible, its use is not confined to those
+cases; it may often usefully follow after the Method of Difference, to
+give additional precision to a solution which that has found. When by
+the Method of Difference it has first been ascertained that a certain
+object produces a certain effect, the Method of Concomitant Variations
+may be usefully called in, to determine according to what law the
+quantity or the different relations of the effect follow those of the
+cause.
+
+
+Sec. 7. The case in which this method admits of the most extensive
+employment, is that in which the variations of the cause are variations
+of quantity. Of such variations we may in general affirm with safety,
+that they will be attended not only with variations, but with similar
+variations, of the effect: the proposition, that more of the cause is
+followed by more of the effect, being a corollary from the principle of
+the Composition of Causes, which, as we have seen, is the general rule
+of causation; cases of the opposite description, in which causes change
+their properties on being conjoined with one another, being, on the
+contrary, special and exceptional. Suppose, then, that when A changes
+in quantity, _a_ also changes in quantity, and in such a manner that we
+can trace the numerical relation which the changes of the one bear to
+such changes of the other as take place within our limits of
+observation. We may then, with certain precautions, safely conclude that
+the same numerical relation will hold beyond those limits. If, for
+instance, we find that when A is double, _a_ is double; that when A is
+treble or quadruple, _a_ is treble or quadruple; we may conclude that if
+A were a half or a third, _a_ would be a half or a third, and finally,
+that if A were annihilated, _a_ would be annihilated, and that _a_ is
+wholly the effect of A, or wholly the effect of the same cause with A.
+And so with any other numerical relation according to which A and _a_
+would vanish simultaneously; as for instance, if _a_ were proportional
+to the square of A. If, on the other hand, _a_ is not wholly the effect
+of A, but yet varies when A varies, it is probably a mathematical
+function not of A alone, but of A and something else: its changes, for
+example, may be such as would occur if part of it remained constant, or
+varied on some other principle, and the remainder varied in some
+numerical relation to the variations of A. In that case, when A
+diminishes, _a_ will be seen to approach not towards zero, but towards
+some other limit: and when the series of variations is such as to
+indicate what that limit is, if constant, or the law of its variation if
+variable, the limit will exactly measure how much of _a_ is the effect
+of some other and independent cause, and the remainder will be the
+effect of A (or of the cause of A).
+
+These conclusions, however, must not be drawn without certain
+precautions. In the first place, the possibility of drawing them at all,
+manifestly supposes that we are acquainted not only with the variations,
+but with the absolute quantities both of A and _a_. If we do not know
+the total quantities, we cannot, of course, determine the real numerical
+relation according to which those quantities vary. It is therefore an
+error to conclude, as some have concluded, that because increase of heat
+expands bodies, that is, increases the distance between their particles,
+therefore the distance is wholly the effect of heat, and that if we
+could entirely exhaust the body of its heat, the particles would be in
+complete contact. This is no more than a guess, and of the most
+hazardous sort, not a legitimate induction: for since we neither know
+how much heat there is in any body, nor what is the real distance
+between any two of its particles, we cannot judge whether the
+contraction of the distance does or does not follow the diminution of
+the quantity of heat according to such a numerical relation that the two
+quantities would vanish simultaneously.
+
+In contrast with this, let us consider a case in which the absolute
+quantities are known; the case contemplated in the first law of motion;
+viz. that all bodies in motion continue to move in a straight line with
+uniform velocity until acted upon by some new force. This assertion is
+in open opposition to first appearances; all terrestrial objects, when
+in motion, gradually abate their velocity and at last stop; which
+accordingly the ancients, with their _inductio per enumerationem
+simplicem_, imagined to be the law. Every moving body, however,
+encounters various obstacles, as friction, the resistance of the
+atmosphere, &c., which we know by daily experience to be causes capable
+of destroying motion. It was suggested that the whole of the retardation
+might be owing to these causes. How was this inquired into? If the
+obstacles could have been entirely removed, the case would have been
+amenable to the Method of Difference. They could not be removed, they
+could only be diminished, and the case, therefore, admitted only of the
+Method of Concomitant Variations. This accordingly being employed, it
+was found that every diminution of the obstacles diminished the
+retardation of the motion: and inasmuch as in this case (unlike the case
+of heat) the total quantities both of the antecedent and of the
+consequent were known; it was practicable to estimate, with an approach
+to accuracy, both the amount of the retardation and the amount of the
+retarding causes, or resistances, and to judge how near they both were
+to being exhausted; and it appeared that the effect dwindled as rapidly,
+and at each step was as far on the road towards annihilation, as the
+cause was. The simple oscillation of a weight suspended from a fixed
+point, and moved a little out of the perpendicular, which in ordinary
+circumstances lasts but a few minutes, was prolonged in Borda's
+experiments to more than thirty hours, by diminishing as much as
+possible the friction at the point of suspension, and by making the body
+oscillate in a space exhausted as nearly as possible of its air. There
+could therefore be no hesitation in assigning the whole of the
+retardation of motion to the influence of the obstacles; and since,
+after subducting this retardation from the total phenomenon, the
+remainder was an uniform velocity, the result was the proposition known
+as the first law of motion.
+
+There is also another characteristic uncertainty affecting the inference
+that the law of variation which the quantities observe within our limits
+of observation, will hold beyond those limits. There is of course, in
+the first instance, the possibility that beyond the limits, and in
+circumstances therefore of which we have no direct experience, some
+counteracting cause might develop itself; either a new agent, or a new
+property of the agents concerned, which lies dormant in the
+circumstances we are able to observe. This is an element of uncertainty
+which enters largely into all our predictions of effects; but it is not
+peculiarly applicable to the Method of Concomitant Variations. The
+uncertainty, however, of which I am about to speak, is characteristic of
+that method; especially in the cases in which the extreme limits of our
+observation are very narrow, in comparison with the possible variations
+in the quantities of the phenomena. Any one who has the slightest
+acquaintance with mathematics, is aware that very different laws of
+variation may produce numerical results which differ but slightly from
+one another within narrow limits; and it is often only when the absolute
+amounts of variation are considerable, that the difference between the
+results given by one law and by another becomes appreciable. When,
+therefore, such variations in the quantity of the antecedents as we have
+the means of observing, are small in comparison with the total
+quantities, there is much danger lest we should mistake the numerical
+law, and be led to miscalculate the variations which would take place
+beyond the limits; a miscalculation which would vitiate any conclusion
+respecting the dependence of the effect upon the cause, that could be
+founded on those variations. Examples are not wanting of such mistakes.
+"The formulae," says Sir John Herschel,[33] "which have been empirically
+deduced for the elasticity of steam, (till very recently,) and those for
+the resistance of fluids, and other similar subjects," when relied on
+beyond the limits of the observations from which they were deduced,
+"have almost invariably failed to support the theoretical structures
+which have been erected on them."
+
+In this uncertainty, the conclusion we may draw from the concomitant
+variations of _a_ and A, to the existence of an invariable and exclusive
+connexion between them, or to the permanency of the same numerical
+relation between their variations when the quantities are much greater
+or smaller than those which we have had the means of observing, cannot
+be considered to rest on a complete induction. All that in such a case
+can be regarded as proved on the subject of causation is, that there is
+some connexion between the two phenomena; that A, or something which can
+influence A, must be _one_ of the causes which collectively determine
+_a_. We may, however, feel assured that the relation which we have
+observed to exist between the variations of A and _a_, will hold true in
+all cases which fall between the same extreme limits; that is, wherever
+the utmost increase or diminution in which the result has been found by
+observation to coincide with the law, is not exceeded.
+
+The four methods which it has now been attempted to describe, are the
+only possible modes of experimental inquiry--of direct induction _a
+posteriori_, as distinguished from deduction: at least, I know not, nor
+am able to imagine, any others. And even of these, the Method of
+Residues, as we have seen, is not independent of deduction; though, as
+it also requires specific experience, it may, without impropriety, be
+included among methods of direct observation and experiment.
+
+These, then, with such assistance as can be obtained from Deduction,
+compose the available resources of the human mind for ascertaining the
+laws of the succession of phenomena. Before proceeding to point out
+certain circumstances, by which the employment of these methods is
+subjected to an immense increase of complication and of difficulty, it
+is expedient to illustrate the use of the methods, by suitable examples
+drawn from actual physical investigations. These, accordingly, will form
+the subject of the succeeding chapter.
+
+
+
+
+CHAPTER IX.
+
+MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.
+
+
+Sec. 1. I shall select, as a first example, an interesting speculation of
+one of the most eminent of theoretical chemists, Baron Liebig. The
+object in view, is to ascertain the immediate cause of the death
+produced by metallic poisons.
+
+Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
+introduced into the animal organism, except in the smallest doses,
+destroy life. These facts have long been known, as insulated truths of
+the lowest order of generalization; but it was reserved for Liebig, by
+an apt employment of the first two of our methods of experimental
+inquiry, to connect these truths together by a higher induction,
+pointing out what property, common to all these deleterious substances,
+is the really operating cause of their fatal effect.
+
+When solutions of these substances are placed in sufficiently close
+contact with many animal products, albumen, milk, muscular fibre, and
+animal membranes, the acid or salt leaves the water in which it was
+dissolved, and enters into combination with the animal substance: which
+substance, after being thus acted upon, is found to have lost its
+tendency to spontaneous decomposition, or putrefaction.
+
+Observation also shows, in cases where death has been produced by these
+poisons, that the parts of the body with which the poisonous substances
+have been brought into contact, do not afterwards putrefy.
+
+And, finally, when the poison has been supplied in too small a quantity
+to destroy life, eschars are produced, that is, certain superficial
+portions of the tissues are destroyed, which are afterwards thrown off
+by the reparative process taking place in the healthy parts.
+
+These three sets of instances admit of being treated according to the
+Method of Agreement. In all of them the metallic compounds are brought
+into contact with the substances which compose the human or animal body;
+and the instances do not seem to agree in any other circumstance. The
+remaining antecedents are as different, and even opposite, as they could
+possibly be made; for in some the animal substances exposed to the
+action of the poisons are in a state of life, in others only in a state
+of organization, in others not even in that. And what is the result
+which follows in all the cases? The conversion of the animal substance
+(by combination with the poison) into a chemical compound, held together
+by so powerful a force as to resist the subsequent action of the
+ordinary causes of decomposition. Now, organic life (the necessary
+condition of sensitive life) consisting in a continual state of
+decomposition and recomposition of the different organs and tissues;
+whatever incapacitates them for this decomposition destroys life. And
+thus the proximate cause of the death produced by this description of
+poisons, is ascertained, as far as the Method of Agreement can ascertain
+it.
+
+Let us now bring our conclusion to the test of the Method of Difference.
+Setting out from the cases already mentioned, in which the antecedent is
+the presence of substances forming with the tissues a compound incapable
+of putrefaction, (and _a fortiori_ incapable of the chemical actions
+which constitute life,) and the consequent is death, either of the whole
+organism, or of some portion of it; let us compare with these cases
+other cases, as much resembling them as possible, but in which that
+effect is not produced. And, first, "many insoluble basic salts of
+arsenious acid are known not to be poisonous. The substance called
+alkargen, discovered by Bunsen, which contains a very large quantity of
+arsenic, and approaches very closely in composition to the organic
+arsenious compounds found in the body, has not the slightest injurious
+action upon the organism." Now when these substances are brought into
+contact with the tissues in any way, they do not combine with them; they
+do not arrest their progress to decomposition. As far, therefore, as
+these instances go, it appears that when the effect is absent, it is by
+reason of the absence of that antecedent which we had already good
+ground for considering as the proximate cause.
+
+But the rigorous conditions of the Method of Difference are not yet
+satisfied; for we cannot be sure that these unpoisonous bodies agree
+with the poisonous substances in every property, except the particular
+one, of entering into a difficultly decomposable compound with the
+animal tissues. To render the method strictly applicable, we need an
+instance, not of a different substance, but of one of the very same
+substances, in circumstances which would prevent it from forming, with
+the tissues, the sort of compound in question; and then, if death does
+not follow, our case is made out. Now such instances are afforded by the
+antidotes to these poisons. For example, in case of poisoning by
+arsenious acid, if hydrated peroxide of iron is administered, the
+destructive agency is instantly checked. Now this peroxide is known to
+combine with the acid, and form a compound, which, being insoluble,
+cannot act at all on animal tissues. So, again, sugar is a well-known
+antidote to poisoning by salts of copper; and sugar reduces those salts
+either into metallic copper, or into the red suboxide, neither of which
+enters into combination with animal matter. The disease called painter's
+colic, so common in manufactories of white lead, is unknown where the
+workmen are accustomed to take, as a preservative, sulphuric acid
+lemonade (a solution of sugar rendered acid by sulphuric acid). Now
+diluted sulphuric acid has the property of decomposing all compounds of
+lead with organic matter, or of preventing them from being formed.
+
+There is another class of instances, of the nature required by the
+Method of Difference, which seem at first sight to conflict with the
+theory. Soluble salts of silver, such for instance as the nitrate, have
+the same stiffening antiseptic effect on decomposing animal substances
+as corrosive sublimate and the most deadly metallic poisons; and when
+applied to the external parts of the body, the nitrate is a powerful
+caustic; depriving those parts of all active vitality, and causing them
+to be thrown off by the neighbouring living structures, in the form of
+an eschar. The nitrate and the other salts of silver ought, then, it
+would seem, if the theory be correct, to be poisonous; yet they may be
+administered internally with perfect impunity. From this apparent
+exception arises the strongest confirmation which the theory has yet
+received. Nitrate of silver, in spite of its chemical properties, does
+not poison when introduced into the stomach; but in the stomach, as in
+all animal liquids, there is common salt; and in the stomach there is
+also free muriatic acid. These substances operate as natural antidotes,
+combining with the nitrate, and if its quantity is not too great,
+immediately converting it into chloride of silver; a substance very
+slightly soluble, and therefore incapable of combining with the tissues,
+although to the extent of its solubility it has a medicinal influence,
+though an entirely different class of organic actions.
+
+The preceding instances have afforded an induction of a high order of
+conclusiveness, illustrative of the two simplest of our four methods;
+though not rising to the maximum of certainty which the Method of
+Difference, in its most perfect exemplification, is capable of
+affording. For (let us not forget) the positive instance and the
+negative one which the rigour of that method requires, ought to differ
+only in the presence or absence of one single circumstance. Now, in the
+preceding argument, they differ in the presence or absence not of a
+single _circumstance_, but of a single _substance_: and as every
+substance has innumerable properties, there is no knowing what number of
+real differences are involved in what is nominally and apparently only
+one difference. It is conceivable that the antidote, the peroxide of
+iron for example, may counteract the poison through some other of its
+properties than that of forming an insoluble compound with it; and if
+so, the theory would fall to the ground, so far as it is supported by
+that instance. This source of uncertainty, which is a serious hindrance
+to all extensive generalizations in chemistry, is however reduced in the
+present case to almost the lowest degree possible, when we find that
+not only one substance, but many substances, possess the capacity of
+acting as antidotes to metallic poisons, and that all these agree in the
+property of forming insoluble compounds with the poisons, while they
+cannot be ascertained to agree in any other property whatsoever. We have
+thus, in favour of the theory, all the evidence which can be obtained by
+what we termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference; the evidence of which, though it never can
+amount to that of the Method of Difference properly so called, may
+approach indefinitely near to it.
+
+
+Sec. 2. Let the object be[34] to ascertain the law of what is termed
+_induced_ electricity; to find under what conditions any electrified
+body, whether positively or negatively electrified, gives rise to a
+contrary electric state in some other body adjacent to it.
+
+The most familiar exemplification of the phenomenon to be investigated
+is the following. Around the prime conductors of an electrical machine,
+the atmosphere to some distance, or any conducting surface suspended in
+that atmosphere, is found to be in an electric condition opposite to
+that of the prime conductor itself. Near and around the positive prime
+conductor there is negative electricity, and near and around the
+negative prime conductor there is positive electricity. When pith balls
+are brought near to either of the conductors, they become electrified
+with the opposite electricity to it; either receiving a share from the
+already electrified atmosphere by conduction, or acted upon by the
+direct inductive influence of the conductor itself: they are then
+attracted by the conductor to which they are in opposition; or, if
+withdrawn in their electrified state, they will be attracted by any
+other oppositely charged body. In like manner the hand, if brought near
+enough to the conductor, receives or gives an electric discharge; now we
+have no evidence that a charged conductor can be suddenly discharged
+unless by the approach of a body oppositely electrified. In the case,
+therefore, of the electric machine, it appears that the accumulation of
+electricity in an insulated conductor is always accompanied by the
+excitement of the contrary electricity in the surrounding atmosphere,
+and in every conductor placed near the former conductor. It does not
+seem possible, in this case, to produce one electricity by itself.
+
+Let us now examine all the other instances which we can obtain,
+resembling this instance in the given consequent, namely, the evolution
+of an opposite electricity in the neighbourhood of an electrified body.
+As one remarkable instance we have the Leyden jar; and after the
+splendid experiments of Faraday in complete and final establishment of
+the substantial identity of magnetism and electricity, we may cite the
+magnet, both the natural and the electro-magnet, in neither of which it
+is possible to produce one kind of electricity by itself, or to charge
+one pole without charging an opposite pole with the contrary electricity
+at the same time. We cannot have a magnet with one pole: if we break a
+natural loadstone into a thousand pieces, each piece will have its two
+oppositely electrified poles complete within itself. In the voltaic
+circuit, again, we cannot have one current without its opposite. In the
+ordinary electric machine, the glass cylinder or plate, and the rubber,
+acquire opposite electricities.
+
+From all these instances, treated by the Method of Agreement, a general
+law appears to result. The instances embrace all the known modes in
+which a body can become charged with electricity; and in all of them
+there is found, as a concomitant or consequent, the excitement of the
+opposite electric state in some other body or bodies. It seems to follow
+that the two facts are invariably connected, and that the excitement of
+electricity in any body has for one of its necessary conditions the
+possibility of a simultaneous excitement of the opposite electricity in
+some neighbouring body.
+
+As the two contrary electricities can only be produced together, so
+they can only cease together. This may be shown by an application of the
+Method of Difference to the example of the Leyden jar. It needs scarcely
+be here remarked that in the Leyden jar, electricity can be accumulated
+and retained in considerable quantity, by the contrivance of having two
+conducting surfaces of equal extent, and parallel to each other through
+the whole of that extent, with a non-conducting substance such as glass
+between them. When one side of the jar is charged positively, the other
+is charged negatively, and it was by virtue of this fact that the Leyden
+jar served just now as an instance in our employment of the Method of
+Agreement. Now it is impossible to discharge one of the coatings unless
+the other can be discharged at the same time. A conductor held to the
+positive side cannot convey away any electricity unless an equal
+quantity be allowed to pass from the negative side: if one coating be
+perfectly insulated, the charge is safe. The dissipation of one must
+proceed _pari passu_ with that of the other.
+
+The law thus strongly indicated admits of corroboration by the Method of
+Concomitant Variations. The Leyden jar is capable of receiving a much
+higher charge than can ordinarily be given to the conductor of an
+electrical machine. Now in the case of the Leyden jar, the metallic
+surface which receives the induced electricity is a conductor exactly
+similar to that which receives the primary charge, and is therefore as
+susceptible of receiving and retaining the one electricity, as the
+opposite surface of receiving and retaining the other; but in the
+machine, the neighbouring body which is to be oppositely electrified is
+the surrounding atmosphere, or any body casually brought near to the
+conductor; and as these are generally much inferior in their capacity of
+becoming electrified, to the conductor itself, their limited power
+imposes a corresponding limit to the capacity of the conductor for being
+charged. As the capacity of the neighbouring body for supporting the
+opposition increases, a higher charge becomes possible: and to this
+appears to be owing the great superiority of the Leyden jar.
+
+A further and most decisive confirmation by the Method of Difference,
+is to be found in one of Faraday's experiments in the course of his
+researches on the subject of induced electricity.
+
+Since common or machine electricity, and voltaic electricity, may be
+considered for the present purpose to be identical, Faraday wished to
+know whether, as the prime conductor develops opposite electricity upon
+a conductor in its vicinity, so a voltaic current running along a wire
+would induce an opposite current upon another wire laid parallel to it
+at a short distance. Now this case is similar to the cases previously
+examined, in every circumstance except the one to which we have ascribed
+the effect. We found in the former instances that whenever electricity
+of one kind was excited in one body, electricity of the opposite kind
+must be excited in a neighbouring body. But in Faraday's experiment this
+indispensable opposition exists within the wire itself. From the nature
+of a voltaic charge, the two opposite currents necessary to the
+existence of each other are both accommodated in one wire; and there is
+no need of another wire placed beside it to contain one of them, in the
+same way as the Leyden jar must have a positive and a negative surface.
+The exciting cause can and does produce all the effect which its laws
+require, independently of any electric excitement of a neighbouring
+body. Now the result of the experiment with the second wire was, that no
+opposite current was produced. There was an instantaneous effect at the
+closing and breaking of the voltaic circuit; electric inductions
+appeared when the two wires were moved to and from one another; but
+these are phenomena of a different class. There was no induced
+electricity in the sense in which this is predicated of the Leyden jar;
+there was no sustained current running up the one wire while an opposite
+current ran down the neighbouring wire; and this alone would have been a
+true parallel case to the other.
+
+It thus appears by the combined evidence of the Method of Agreement, the
+Method of Concomitant Variations, and the most rigorous form of the
+Method of Difference, that neither of the two kinds of electricity can
+be excited without an equal excitement of the other and opposite kind:
+that both are effects of the same cause; that the possibility of the one
+is a condition of the possibility of the other, and the quantity of the
+one an impassable limit to the quantity of the other. A scientific
+result of considerable interest in itself, and illustrating those three
+methods in a manner both characteristic and easily intelligible.[35]
+
+
+Sec. 3. Our third example shall be extracted from Sir John Herschel's
+_Discourse on the Study of Natural Philosophy_, a work replete with
+happily-selected exemplifications of inductive processes from almost
+every department of physical science, and in which alone, of all books
+which I have met with, the four methods of induction are distinctly
+recognised, though not so clearly characterized and defined, nor their
+correlation so fully shown, as has appeared to me desirable. The present
+example is described by Sir John Herschel as "one of the most beautiful
+specimens" which can be cited "of inductive experimental inquiry lying
+within a moderate compass;" the theory of dew, first promulgated by the
+late Dr. Wells, and now universally adopted by scientific authorities.
+The passages in inverted commas are extracted verbatim from the
+Discourse.[36]
+
+"Suppose _dew_ were the phenomenon proposed, whose cause we would know.
+In the first place" we must determine precisely what we mean by dew:
+what the fact really is, whose cause we desire to investigate. "We must
+separate dew from rain, and the moisture of fogs, and limit the
+application of the term to what is really meant, which is the
+spontaneous appearance of moisture on substances exposed in the open air
+when no rain or _visible_ wet is falling." This answers to a preliminary
+operation which will be characterized in the ensuing book, treating of
+operations subsidiary to induction.[37]
+
+"Now, here we have analogous phenomena in the moisture which bedews a
+cold metal or stone when we breathe upon it; that which appears on a
+glass of water fresh from the well in hot weather; that which appears on
+the inside of windows when sudden rain or hail chills the external air;
+that which runs down our walls when, after a long frost, a warm moist
+thaw comes on." Comparing these cases, we find that they all contain the
+phenomenon which was proposed as the subject of investigation. Now "all
+these instances agree in one point, the coldness of the object dewed, in
+comparison with the air in contact with it." But there still remains the
+most important case of all, that of nocturnal dew: does the same
+circumstance exist in this case? "Is it a fact that the object dewed is
+colder than the air? Certainly not, one would at first be inclined to
+say; for what is to _make_ it so? But ... the experiment is easy: we
+have only to lay a thermometer in contact with the dewed substance, and
+hang one at a little distance above it, out of reach of its influence.
+The experiment has been therefore made, the question has been asked, and
+the answer has been invariably in the affirmative. Whenever an object
+contracts dew, it _is_ colder than the air."
+
+Here then is a complete application of the Method of Agreement,
+establishing the fact of an invariable connexion between the deposition
+of dew on a surface, and the coldness of that surface compared with the
+external air. But which of these is cause, and which effect? or are they
+both effects of something else? On this subject the Method of Agreement
+can afford us no light: we must call in a more potent method. "We must
+collect more facts, or, which comes to the same thing, vary the
+circumstances; since every instance in which the circumstances differ is
+a fresh fact: and especially, we must note the contrary or negative
+cases, _i.e._ where no dew is produced:" a comparison between instances
+of dew and instances of no dew, being the condition necessary to bring
+the Method of Difference into play.
+
+"Now, first, no dew is produced on the surface of polished metals, but
+it _is_ very copiously on glass, both exposed with their faces upwards,
+and in some cases the under side of a horizontal plate of glass is also
+dewed." Here is an instance in which the effect is produced, and another
+instance in which it is not produced; but we cannot yet pronounce, as
+the canon of the Method of Difference requires, that the latter instance
+agrees with the former in all its circumstances except one; for the
+differences between glass and polished metals are manifold, and the only
+thing we can as yet be sure of is, that the cause of dew will be found
+among the circumstances by which the former substance is distinguished
+from the latter. But if we could be sure that glass, and the various
+other substances on which dew is deposited, have only one quality in
+common, and that polished metals and the other substances on which dew
+is not deposited have also nothing in common but the one circumstance,
+of not having the one quality which the others have; the requisitions of
+the Method of Difference would be completely satisfied, and we should
+recognise, in that quality of the substances, the cause of dew. This,
+accordingly, is the path of inquiry which is next to be pursued.
+
+"In the cases of polished metal and polished glass, the contrast shows
+evidently that the _substance_ has much to do with the phenomenon;
+therefore let the substance _alone_ be diversified as much as possible,
+by exposing polished surfaces of various kinds. This done, a _scale of
+intensity_ becomes obvious. Those polished substances are found to be
+most strongly dewed which conduct heat worst; while those which conduct
+well, resist dew most effectually." The complication increases; here is
+the Method of Concomitant Variations called to our assistance; and no
+other method was practicable on this occasion; for the quality of
+conducting heat could not be excluded, since all substances conduct heat
+in some degree. The conclusion obtained is, that _caeteris paribus_ the
+deposition of dew is in some proportion to the power which the body
+possesses of resisting the passage of heat; and that this, therefore,
+(or something connected with this,) must be at least one of the causes
+which assist in producing the deposition of dew on the surface.
+
+"But if we expose rough surfaces instead of polished, we sometimes find
+this law interfered with. Thus, roughened iron, especially if painted
+over or blackened, becomes dewed sooner than varnished paper; the kind
+of _surface_, therefore, has a great influence. Expose, then, the _same_
+material in very diversified states as to surface," (that is, employ the
+Method of Difference to ascertain concomitance of variations,) "and
+another scale of intensity becomes at once apparent; those _surfaces_
+which _part with their heat_ most readily by radiation, are found to
+contract dew most copiously." Here, therefore, are the requisites for a
+second employment of the Method of Concomitant Variations; which in this
+case also is the only method available, since all substances radiate
+heat in some degree or other. The conclusion obtained by this new
+application of the method is, that _caeteris paribus_ the deposition of
+dew is also in some proportion to the power of radiating heat; and that
+the quality of doing this abundantly (or some cause on which that
+quality depends) is another of the causes which promote the deposition
+of dew on the substance.
+
+"Again, the influence ascertained to exist of _substance_ and _surface_
+leads us to consider that of _texture_: and here, again, we are
+presented on trial with remarkable differences, and with a third scale
+of intensity, pointing out substances of a close firm texture, such as
+stones, metals, &c., as unfavourable, but those of a loose one, as
+cloth, velvet, wool, eider-down, cotton, &c., as eminently favourable to
+the contraction of dew." The Method of Concomitant Variations is here,
+for the third time, had recourse to; and, as before, from necessity,
+since the texture of no substance is absolutely firm or absolutely
+loose. Looseness of texture, therefore, or something which is the cause
+of that quality, is another circumstance which promotes the deposition
+of dew; but this third cause resolves itself into the first, viz. the
+quality of resisting the passage of heat: for substances of loose
+texture "are precisely those which are best adapted for clothing, or for
+impeding the free passage of heat from the skin into the air, so as to
+allow their outer surfaces to be very cold, while they remain warm
+within;" and this last is, therefore, an induction (from fresh
+instances) simply _corroborative_ of a former induction.
+
+It thus appears that the instances in which much dew is deposited, which
+are very various, agree in this, and, so far as we are able to observe,
+in this only, that they either radiate heat rapidly or conduct it
+slowly: qualities between which there is no other circumstance of
+agreement, than that by virtue of either, the body tends to lose heat
+from the surface more rapidly than it can be restored from within. The
+instances, on the contrary, in which no dew, or but a small quantity of
+it, is formed, and which are also extremely various, agree (as far as we
+can observe) in nothing except in _not_ having this same property. We
+seem, therefore, to have detected the characteristic difference between
+the substances on which dew is produced, and those on which it is not
+produced. And thus have been realized the requisitions of what we have
+termed the Indirect Method of Difference, or the Joint Method of
+Agreement and Difference. The example afforded of this indirect method,
+and of the manner in which the data are prepared for it by the Methods
+of Agreement and of Concomitant Variations, is the most important of all
+the illustrations of induction afforded by this interesting speculation.
+
+We might now consider the question, on what the deposition of dew
+depends, to be completely solved, if we could be quite sure that the
+substances on which dew is produced differ from those on which it is
+not, in _nothing_ but in the property of losing heat from the surface
+faster than the loss can be repaired from within. And though we never
+can have that complete certainty, this is not of so much importance as
+might at first be supposed; for we have, at all events, ascertained
+that even if there be any other quality hitherto unobserved which is
+present in all the substances which contract dew, and absent in those
+which do not, this other property must be one which, in all that great
+number of substances, is present or absent exactly where the property of
+being a better radiator than conductor is present or absent; an extent
+of coincidence which affords a strong presumption of a community of
+cause, and a consequent invariable coexistence between the two
+properties; so that the property of being a better radiator than
+conductor, if not itself the cause, almost certainly always accompanies
+the cause, and, for purposes of prediction, no error is likely to be
+committed by treating it as if it were really such.
+
+Reverting now to an earlier stage of the inquiry, let us remember that
+we had ascertained that, in every instance where dew is formed, there is
+actual coldness of the surface below the temperature of the surrounding
+air; but we were not sure whether this coldness was the cause of dew, or
+its effect. This doubt we are now able to resolve. We have found that,
+in every such instance, the substance is one which, by its own
+properties or laws, would, if exposed in the night, become colder than
+the surrounding air. The coldness therefore being accounted for
+independently of the dew, while it is proved that there is a connexion
+between the two, it must be the dew which depends on the coldness; or in
+other words, the coldness is the cause of the dew.
+
+This law of causation, already so amply established, admits, however, of
+efficient additional corroboration in no less than three ways. First, by
+deduction from the known laws of aqueous vapour when diffused through
+air or any other gas; and though we have not yet come to the Deductive
+Method, we will not omit what is necessary to render this speculation
+complete. It is known by direct experiment that only a limited quantity
+of water can remain suspended in the state of vapour at each degree of
+temperature, and that this maximum grows less and less as the
+temperature diminishes. From this it follows, deductively, that if there
+is already as much vapour suspended as the air will contain at its
+existing temperature, any lowering of that temperature will cause a
+portion of the vapour to be condensed, and become water. But, again, we
+know deductively, from the laws of heat, that the contact of the air
+with a body colder than itself, will necessarily lower the temperature
+of the stratum of air immediately applied to its surface; and will
+therefore cause it to part with a portion of its water, which
+accordingly will, by the ordinary laws of gravitation or cohesion,
+attach itself to the surface of the body, thereby constituting dew. This
+deductive proof, it will have been seen, has the advantage of at once
+proving causation as well as coexistence; and it has the additional
+advantage that it also accounts for the exceptions to the occurrence of
+the phenomenon, the cases in which, although the body is colder than the
+air, yet no dew is deposited; by showing that this will necessarily be
+the case when the air is so under-supplied with aqueous vapour,
+comparatively to its temperature, that even when somewhat cooled by the
+contact of the colder body, it can still continue to hold in suspension
+all the vapour which was previously suspended in it: thus in a very dry
+summer there are no dews, in a very dry winter no hoar frost. Here,
+therefore, is an additional condition of the production of dew, which
+the methods we previously made use of failed to detect, and which might
+have remained still undetected, if recourse had not been had to the plan
+of deducing the effect from the ascertained properties of the agents
+known to be present.
+
+The second corroboration of the theory is by direct experiment,
+according to the canon of the Method of Difference. We can, by cooling
+the surface of any body, find in all cases some temperature, (more or
+less inferior to that of the surrounding air, according to its
+hygrometric condition,) at which dew will begin to be deposited. Here,
+too, therefore, the causation is directly proved. We can, it is true,
+accomplish this only on a small scale; but we have ample reason to
+conclude that the same operation, if conducted in Nature's great
+laboratory, would equally produce the effect.
+
+And, finally, even on that great scale we are able to verify the result.
+The case is one of those rare cases, as we have shown them to be, in
+which nature works the experiment for us in the same manner in which we
+ourselves perform it; introducing into the previous state of things a
+single and perfectly definite new circumstance, and manifesting the
+effect so rapidly that there is not time for any other material change
+in the pre-existing circumstances. "It is observed that dew is never
+copiously deposited in situations much screened from the open sky, and
+not at all in a cloudy night; but _if the clouds withdraw even for a few
+minutes, and leave a clear opening, a deposition of dew presently
+begins_, and goes on increasing.... Dew formed in clear intervals will
+often even evaporate again when the sky becomes thickly overcast." The
+proof, therefore, is complete, that the presence or absence of an
+uninterrupted communication with the sky causes the deposition or
+non-deposition of dew. Now, since a clear sky is nothing but the absence
+of clouds, and it is a known property of clouds, as of all other bodies
+between which and any given object nothing intervenes but an elastic
+fluid, that they tend to raise or keep up the superficial temperature of
+the object by radiating heat to it, we see at once that the
+disappearance of clouds will cause the surface to cool; so that Nature,
+in this case, produces a change in the antecedent by definite and known
+means, and the consequent follows accordingly: a natural experiment
+which satisfies the requisitions of the Method of Difference.[38]
+
+The accumulated proof of which the Theory of Dew has been found
+susceptible, is a striking instance of the fulness of assurance which
+the inductive evidence of laws of causation may attain, in cases in
+which the invariable sequence is by no means obvious to a superficial
+view.
+
+
+Sec. 4. The admirable physiological investigations of Dr. Brown-Sequard
+afford brilliant examples of the application of the Inductive Methods to
+a class of inquiries in which, for reasons which will presently be
+given, direct induction takes place under peculiar difficulties and
+disadvantages. As one of the most apt instances I select his speculation
+(in the Proceedings of the Royal Society for May 16, 1861) on the
+relations between muscular irritability, cadaveric rigidity, and
+putrefaction.
+
+The law which Dr. Brown-Sequard's investigation tends to establish, is
+the following:--"The greater the degree of muscular irritability at the
+time of death, the later the cadaveric rigidity sets in, and the longer
+it lasts, and the later also putrefaction appears, and the slower it
+progresses." One would say at first sight that the method here required
+must be that of Concomitant Variations. But this is a delusive
+appearance, arising from the circumstance that the conclusion to be
+tested is itself a fact of concomitant variation. For the establishment
+of that fact any of the Methods may be put in requisition, and it will
+be found that the fourth Method, though really employed, has only a
+subordinate place in this particular investigation.
+
+The evidences by which Dr. Brown-Sequard establishes the law may be
+enumerated as follows:--
+
+1st. Paralysed muscles have greater irritability than healthy muscles.
+Now, paralysed muscles are later in assuming the cadaveric rigidity than
+healthy muscles, the rigidity lasts longer, and putrefaction sets in
+later and proceeds more slowly.
+
+Both these propositions had to be proved by experiment; and for the
+experiments which prove them, science is also indebted to Dr.
+Brown-Sequard. The former of the two--that paralysed muscles have
+greater irritability than healthy muscles--he ascertained in various
+ways, but most decisively by "comparing the duration of irritability in
+a paralysed muscle and in the corresponding healthy one of the opposite
+side, while they are both submitted to the same excitation." He "often
+found in experimenting in that way, that the paralysed muscle remained
+irritable twice, three times, or even four times as long as the healthy
+one." This is a case of induction by the Method of Difference. The two
+limbs, being those of the same animal, were presumed to differ in no
+circumstance material to the case except the paralysis, to the presence
+and absence of which, therefore, the difference in the muscular
+irritability was to be attributed. This assumption of complete
+resemblance in all material circumstances save one, evidently could not
+be safely made in any one pair of experiments, because the two legs of
+any given animal might be accidentally in very different pathological
+conditions; but if, besides taking pains to avoid any such difference,
+the experiment was repeated sufficiently often in different animals to
+exclude the supposition that any abnormal circumstance could be present
+in them all, the conditions of the Method of Difference were adequately
+secured.
+
+In the same manner in which Dr. Brown-Sequard proved that paralysed
+muscles have greater irritability, he also proved the correlative
+proposition respecting cadaveric rigidity and putrefaction. Having, by
+section of the roots of the sciatic nerve, and again of a lateral half
+of the spinal cord, produced paralysis in one hind leg of an animal
+while the other remained healthy, he found that not only did muscular
+irritability last much longer in the paralysed limb, but rigidity set in
+later and ended later, and putrefaction began later and was less rapid
+than on the healthy side. This is a common case of the Method of
+Difference, requiring no comment. A further and very important
+corroboration was obtained by the same method. When the animal was
+killed, not shortly after the section of the nerve, but a month later,
+the effect was reversed; rigidity set in sooner, and lasted a shorter
+time, than in the healthy muscles. But after this lapse of time, the
+paralysed muscles, having been kept by the paralysis in a state of rest,
+had lost a great part of their irritability, and instead of more, had
+become less irritable than those on the healthy side. This gives the A B
+C, a b c, and B C, b c, of the Method of Difference. One antecedent,
+increased irritability, being changed, and the other circumstances being
+the same, the consequence did not follow; and moreover, when a new
+antecedent, contrary to the first, was supplied, it was followed by a
+contrary consequent. This instance is attended with the special
+advantage, of proving that the retardation and prolongation of the
+rigidity do not depend directly on the paralysis, since that was the
+same in both the instances; but specifically on one effect of the
+paralysis, namely, the increased irritability; since they ceased when it
+ceased, and were reversed when it was reversed.
+
+2ndly. Diminution of the temperature of muscles before death increases
+their irritability. But diminution of their temperature also retards
+cadaveric rigidity and putrefaction.
+
+Both these truths were first made known by Dr. Brown-Sequard himself,
+through experiments which conclude according to the Method of
+Difference. There is nothing in the nature of the process requiring
+specific analysis.
+
+3rdly. Muscular exercise, prolonged to exhaustion, diminishes the
+muscular irritability. This is a well-known truth, dependent on the most
+general laws of muscular action, and proved by experiments under the
+Method of Difference, constantly repeated. Now it has been shown by
+observation that overdriven cattle, if killed before recovery from their
+fatigue, become rigid and putrefy in a surprisingly short time. A
+similar fact has been observed in the case of animals hunted to death;
+cocks killed during or shortly after a fight; and soldiers slain in the
+field of battle. These various cases agree in no circumstance, directly
+connected with the muscles, except that these have just been subjected
+to exhausting exercise. Under the canon, therefore, of the Method of
+Agreement, it may be inferred that there is a connexion between the two
+facts. The Method of Agreement, indeed, as has been shown, is not
+competent to prove causation. The present case, however, is already
+known to be a case of causation, it being certain that the state of the
+body after death must somehow depend upon its state at the time of
+death. We are therefore warranted in concluding that the single
+circumstance in which all the instances agree, is the part of the
+antecedent which is the cause of that particular consequent.
+
+4thly. In proportion as the nutrition of muscles is in a good state,
+their irritability is high. This fact also rests on the general evidence
+of the laws of physiology, grounded on many familiar applications of the
+Method of Difference. Now, in the case of those who die from accident or
+violence, with their muscles in a good state of nutrition, the muscular
+irritability continues long after death, rigidity sets in late, and
+persists long without the putrefactive change. On the contrary, in cases
+of disease in which nutrition has been diminished for a long time before
+death, all these effects are reversed. These are the conditions of the
+Joint Method of Agreement and Difference. The cases of retarded and long
+continued rigidity here in question, agree only in being preceded by a
+high state of nutrition of the muscles; the cases of rapid and brief
+rigidity agree only in being preceded by a low state of muscular
+nutrition; a connexion is therefore inductively proved between the
+degree of the nutrition, and the slowness and prolongation of the
+rigidity.
+
+5thly. Convulsions, like exhausting exercise, but in a still greater
+degree, diminish the muscular irritability. Now, when death follows
+violent and prolonged convulsions, as in tetanus, hydrophobia, some
+cases of cholera, and certain poisons, rigidity sets in very rapidly,
+and after a very brief duration, gives place to putrefaction. This is
+another example of the Method of Agreement, of the same character with
+No. 3.
+
+6thly. The series of instances which we shall take last, is of a more
+complex character, and requires a more minute analysis.
+
+It has long been observed that in some cases of death by lightning,
+cadaveric rigidity either does not take place at all, or is of such
+extremely brief duration as to escape notice, and that in these cases
+putrefaction is very rapid. In other cases, however, the usual cadaveric
+rigidity appears. There must be some difference in the cause, to account
+for this difference in the effect. Now "death by lightning may be the
+result of, 1st, a syncope by fright, or in consequence of a direct or
+reflex influence of lightning on the par vagum; 2ndly, hemorrhage in or
+around the brain, or in the lungs, the pericardium, &c.; 3rdly,
+concussion, or some other alteration in the brain;" none of which
+phenomena have any known property capable of accounting for the
+suppression, or almost suppression, of the cadaveric rigidity. But the
+cause of death may also be that the lightning produces "a violent
+convulsion of every muscle in the body," of which, if of sufficient
+intensity, the known effect would be that "muscular irritability ceases
+almost at once." If Dr. Brown-Sequard's generalization is a true law,
+these will be the very cases in which rigidity is so much abridged as to
+escape notice; and the cases in which, on the contrary, rigidity takes
+place as usual, will be those in which the stroke of lightning operates
+in some of the other modes which have been enumerated. How, then, is
+this brought to the test? By experiments not on lightning, which cannot
+be commanded at pleasure, but on the same natural agency in a manageable
+form, that of artificial galvanism. Dr. Brown-Sequard galvanized the
+entire bodies of animals immediately after death. Galvanism cannot
+operate in any of the modes in which the stroke of lightning may have
+operated, except the single one of producing muscular convulsions. If,
+therefore, after the bodies have been galvanized, the duration of
+rigidity is much shortened and putrefaction much accelerated, it is
+reasonable to ascribe the same effects when produced by lightning, to
+the property which galvanism shares with lightning, and not to those
+which it does not. Now this Dr. Brown-Sequard found to be the fact. The
+galvanic experiment was tried with charges of very various degrees of
+strength; and the more powerful the charge, the shorter was found to be
+the duration of rigidity, and the more speedy and rapid the
+putrefaction. In the experiment in which the charge was strongest, and
+the muscular irritability most promptly destroyed, the rigidity only
+lasted fifteen minutes. On the principle, therefore, of the Method of
+Concomitant Variations, it maybe inferred that the duration of the
+rigidity depends on the degree of the irritability; and that if the
+charge had been as much stronger than Dr. Brown-Sequard's strongest, as
+a stroke of lightning must be stronger than any electric shock which we
+can produce artificially, the rigidity would have been shortened in a
+corresponding ratio, and might have disappeared altogether. This
+conclusion having been arrived at, the case of an electric shock,
+whether natural or artificial, becomes an instance in addition to all
+those already ascertained, of correspondence between the irritability of
+the muscle and the duration of rigidity.
+
+All these instances are summed up in the following statement:--"That
+when the degree of muscular irritability at the time of death is
+considerable, either in consequence of a good state of nutrition, as in
+persons who die in full health from an accidental cause, or in
+consequence of rest, as in cases of paralysis, or on account of the
+influence of cold, cadaveric rigidity in all these cases sets in late
+and lasts long, and putrefaction appears late, and progresses slowly:"
+but "that when the degree of muscular irritability at the time of death
+is slight, either in consequence of a bad state of nutrition, or of
+exhaustion from over-exertion, or from convulsions caused by disease or
+poison, cadaveric rigidity sets in and ceases soon, and putrefaction
+appears and progresses quickly." These facts present, in all their
+completeness, the conditions of the Joint Method of Agreement and
+Difference. Early and brief rigidity takes place in cases which agree
+only in the circumstance of a low state of muscular irritability.
+Rigidity begins late and lasts long in cases which agree only in the
+contrary circumstance, of a muscular irritability high and unusually
+prolonged. It follows that there is a connexion through causation
+between the degree of muscular irritability after death, and the
+tardiness and prolongation of the cadaveric rigidity. This
+investigation places in a strong light the value and efficacy of the
+Joint Method. For, as we have already seen, the defect of that Method
+is, that like the Method of Agreement, of which it is only an improved
+form, it cannot prove causation. But in the present case (as in one of
+the steps in the argument which led up to it) causation is already
+proved; since there could never be any doubt that the rigidity
+altogether, and the putrefaction which follows it, are caused by the
+fact of death: the observations and experiments on which this rests are
+too familiar to need analysis, and fall under the Method of Difference.
+It being, therefore, beyond doubt that the aggregate antecedent, the
+death, is the actual cause of the whole train of consequents, whatever
+of the circumstances attending the death can be shown to be followed in
+all its variations by variations in the effect under investigation, must
+be the particular feature of the fact of death on which that effect
+depends. The degree of muscular irritability at the time of death
+fulfils this condition. The only point that could be brought into
+question, would be whether the effect depended on the irritability
+itself, or on something which always accompanied the irritability: and
+this doubt is set at rest by establishing, as the instances do, that by
+whatever cause the high or low irritability is produced, the effect
+equally follows; and cannot, therefore, depend upon the causes of
+irritability, nor upon the other effects of those causes, which are as
+various as the causes themselves; but upon the irritability, solely.
+
+
+Sec. 5. The last two examples will have conveyed to any one by whom they
+have been duly followed, so clear a conception of the use and practical
+management of three of the four methods of experimental inquiry, as to
+supersede the necessity of any further exemplification of them. The
+remaining method, that of Residues, not having found a place in any of
+the preceding investigations, I shall quote from Sir John Herschel some
+examples of that method, with the remarks by which they are introduced.
+
+"It is by this process, in fact, that science, in its present advanced
+state, is chiefly promoted. Most of the phenomena which Nature presents
+are very complicated; and when the effects of all known causes are
+estimated with exactness, and subducted, the residual facts are
+constantly appearing in the form of phenomena altogether new, and
+leading to the most important conclusions.
+
+"For example: the return of the comet predicted by Professor Encke, a
+great many times in succession, and the general good agreement of its
+calculated with its observed place during any one of its periods of
+visibility, would lead us to say that its gravitation towards the sun
+and planets is the sole and sufficient cause of all the phenomena of its
+orbitual motion; but when the effect of this cause is strictly
+calculated and subducted from the observed motion, there is found to
+remain behind a _residual phenomenon_, which would never have been
+otherwise ascertained to exist, which is a small anticipation of the
+time of its reappearance, or a diminution of its periodic time, which
+cannot be accounted for by gravity, and whose cause is therefore to be
+inquired into. Such an anticipation would be caused by the resistance of
+a medium disseminated through the celestial regions; and as there are
+other good reasons for believing this to be a _vera causa_," (an
+actually existing antecedent,) "it has therefore been ascribed to such a
+resistance.[39]
+
+"M. Arago, having suspended a magnetic needle by a silk thread, and set
+it in vibration, observed, that it came much sooner to a state of rest
+when suspended over a plate of copper, than when no such plate was
+beneath it. Now, in both cases there were two _verae causae_" (antecedents
+known to exist) "why it _should_ come at length to rest, viz. the
+resistance of the air, which opposes, and at length destroys, all
+motions performed in it; and the want of perfect mobility in the silk
+thread. But the effect of these causes being exactly known by the
+observation made in the absence of the copper, and being thus allowed
+for and subducted, a residual phenomenon appeared, in the fact that a
+retarding influence was exerted by the copper itself; and this fact,
+once ascertained, speedily led to the knowledge of an entirely new and
+unexpected class of relations." This example belongs, however, not to
+the Method of Residues but to the Method of Difference, the law being
+ascertained by a direct comparison of the results of two experiments,
+which differed in nothing but the presence or absence of the plate of
+copper. To have made it exemplify the Method of Residues, the effect of
+the resistance of the air and that of the rigidity of the silk should
+have been calculated _a priori_, from the laws obtained by separate and
+foregone experiments.
+
+"Unexpected and peculiarly striking confirmations of inductive laws
+frequently occur in the form of residual phenomena, in the course of
+investigations of a widely different nature from those which gave rise
+to the inductions themselves. A very elegant example may be cited in the
+unexpected confirmation of the law of the development of heat in elastic
+fluids by compression, which is afforded by the phenomena of sound. The
+inquiry into the cause of sound had led to conclusions respecting its
+mode of propagation, from which its velocity in the air could be
+precisely calculated. The calculations were performed; but, when
+compared with fact, though the agreement was quite sufficient to show
+the general correctness of the cause and mode of propagation assigned,
+yet the _whole_ velocity could not be shown to arise from this theory.
+There was still a residual velocity to be accounted for, which placed
+dynamical philosophers for a long time in great dilemma. At length
+Laplace struck on the happy idea, that this might arise from the _heat_
+developed in the act of that condensation which necessarily takes place
+at every vibration by which sound is conveyed. The matter was subjected
+to exact calculation, and the result was at once the complete
+explanation of the residual phenomenon, and a striking confirmation of
+the general law of the development of heat by compression, under
+circumstances beyond artificial imitation."
+
+"Many of the new elements of chemistry have been detected in the
+investigation of residual phenomena. Thus Arfwedson discovered lithia by
+perceiving an excess of weight in the sulphate produced from a small
+portion of what he considered as magnesia present in a mineral he had
+analysed. It is on this principle, too, that the small concentrated
+residues of great operations in the arts are almost sure to be the
+lurking places of new chemical ingredients: witness iodine, brome,
+selenium, and the new metals accompanying platina in the experiments of
+Wollaston and Tennant. It was a happy thought of Glauber to examine what
+everybody else threw away."[40]
+
+"Almost all the greatest discoveries in Astronomy," says the same
+author,[41] "have resulted from the consideration of residual phenomena
+of a quantitative or numerical kind.... It was thus that the grand
+discovery of the precession of the equinoxes resulted as a residual
+phenomenon, from the imperfect explanation of the return of the seasons
+by the return of the sun to the same apparent place among the fixed
+stars. Thus, also, aberration and nutation resulted as residual
+phenomena from that portion of the changes of the apparent places of the
+fixed stars which was left unaccounted for by precession. And thus again
+the apparent proper motions of the stars are the observed residues of
+their apparent movements outstanding and unaccounted for by strict
+calculation of the effects of precession, nutation, and aberration. The
+nearest approach which human theories can make to perfection is to
+diminish this residue, this _caput mortuum_ of observation, as it may be
+considered, as much as practicable, and, if possible, to reduce it to
+nothing, either by showing that something has been neglected in our
+estimation of known causes, or by reasoning upon it as a new fact, and
+on the principle of the inductive philosophy ascending from the effect
+to its cause or causes."
+
+The disturbing effects mutually produced by the earth and planets upon
+each other's motions were first brought to light as residual phenomena,
+by the difference which appeared between the observed places of those
+bodies, and the places calculated on a consideration solely of their
+gravitation towards the sun. It was this which determined astronomers
+to consider the law of gravitation as obtaining between all bodies
+whatever, and therefore between all particles of matter; their first
+tendency having been to regard it as a force acting only between each
+planet or satellite and the central body to whose system it belonged.
+Again, the catastrophists, in geology, be their opinion right or wrong,
+support it on the plea, that after the effect of all causes now in
+operation has been allowed for, there remains in the existing
+constitution of the earth a large residue of facts, proving the
+existence at former periods either of other forces, or of the same
+forces in a much greater degree of intensity. To add one more example:
+those who assert, what no one has shown any real ground for believing,
+that there is in one human individual, one sex, or one race of mankind
+over another, an inherent and inexplicable superiority in mental
+faculties, could only substantiate their proposition by subtracting from
+the differences of intellect which we in fact see, all that can be
+traced by known laws either to the ascertained differences of physical
+organization, or to the differences which have existed in the outward
+circumstances in which the subjects of the comparison have hitherto been
+placed. What these causes might fail to account for, would constitute a
+residual phenomenon, which and which alone would be evidence of an
+ulterior original distinction, and the measure of its amount. But the
+assertors of such supposed differences have not provided themselves with
+these necessary logical conditions of the establishment of their
+doctrine.
+
+The spirit of the Method of Residues being, it is hoped, sufficiently
+intelligible from these examples, and the other three methods having
+already been so fully exemplified, we may here close our exposition of
+the four methods, considered as employed in the investigation of the
+simpler and more elementary order of the combinations of phenomena.
+
+
+Sec. 6. Dr. Whewell has expressed a very unfavourable opinion of the
+utility of the Four Methods, as well as of the aptness of the examples
+by which I have attempted to illustrate them. His words are these:--[42]
+
+"Upon these methods, the obvious thing to remark is, that they take for
+granted the very thing which is most difficult to discover, the
+reduction of the phenomena to formulae such as are here presented to us.
+When we have any set of complex facts offered to us; for instance, those
+which were offered in the cases of discovery which I have
+mentioned,--the facts of the planetary paths, of falling bodies, of
+refracted rays, of cosmical motions, of chemical analysis; and when, in
+any of these cases, we would discover the law of nature which governs
+them, or, if any one chooses so to term it, the feature in which all the
+cases agree, where are we to look for our A, B, C, and _a_, _b_, _c_?
+Nature does not present to us the cases in this form; and how are we to
+reduce them to this form? You say, _when_ we find the combination of A B
+C with _a b c_ and A B D with _a b d_, then we may draw our inference.
+Granted; but when and where are we to find such combinations? Even now
+that the discoveries are made, who will point out to us what are the A,
+B, C, and _a_, _b_, _c_ elements of the cases which have just been
+enumerated? Who will tell us which of the methods of inquiry those
+historically real and successful inquiries exemplify? Who will carry
+these formulae through the history of the sciences, as they have really
+grown up; and show us that these four methods have been operative in
+their formation; or that any light is thrown upon the steps of their
+progress by reference to these formulae?"
+
+He adds that, in this work, the methods have not been applied "to a
+large body of conspicuous and undoubted examples of discovery, extending
+along the whole history of science;" which ought to have been done in
+order that the methods might be shown to possess the "advantage" (which
+he claims as belonging to his own) of being those "by which all great
+discoveries in science have really been made."--(p. 277.)
+
+There is a striking similarity between the objections here made against
+Canons of Induction, and what was alleged, in the last century, by as
+able men as Dr. Whewell, against the acknowledged Canon of
+Ratiocination. Those who protested against the Aristotelian Logic said
+of the Syllogism, what Dr. Whewell says of the Inductive Methods, that
+it "takes for granted the very thing which is most difficult to
+discover, the reduction of the argument to formulae such as are here
+presented to us." The grand difficulty, they said, is to obtain your
+syllogism, not to judge of its correctness when obtained. On the matter
+of fact, both they and Dr. Whewell are right. The greatest difficulty in
+both cases is first that of obtaining the evidence, and next, of
+reducing it to the form which tests its conclusiveness. But if we try to
+reduce it without knowing _to what_, we are not likely to make much
+progress. It is a more difficult thing to solve a geometrical problem,
+than to judge whether a proposed solution is correct: but if people were
+not able to judge of the solution when found, they would have little
+chance of finding it. And it cannot be pretended that to judge of an
+induction when found, is perfectly easy, is a thing for which aids and
+instruments are superfluous; for erroneous inductions, false inferences
+from experience, are quite as common, on some subjects much commoner,
+than true ones. The business of Inductive Logic is to provide rules and
+models (such as the Syllogism and its rules are for ratiocination) to
+which if inductive arguments conform, those arguments are conclusive,
+and not otherwise. This is what the Four Methods profess to be, and what
+I believe they are universally considered to be by experimental
+philosophers, who had practised all of them long before any one sought
+to reduce the practice to theory.
+
+The assailants of the Syllogism had also anticipated Dr. Whewell in the
+other branch of his argument. They said that no discoveries were ever
+made by syllogism; and Dr. Whewell says, or seems to say, that none were
+ever made by the four Methods of Induction. To the former objectors,
+Archbishop Whately very pertinently answered, that their argument, if
+good at all, was good against the reasoning process altogether; for
+whatever cannot be reduced to syllogism, is not reasoning. And Dr.
+Whewell's argument, if good at all, is good against all inferences from
+experience. In saying that no discoveries were ever made by the four
+Methods, he affirms that none were ever made by observation and
+experiment; for assuredly if any were, it was by processes reducible to
+one or other of those methods.
+
+This difference between us accounts for the dissatisfaction which my
+examples give him; for I did not select them with a view to satisfy any
+one who required to be convinced that observation and experiment are
+modes of acquiring knowledge: I confess that in the choice of them I
+thought only of illustration, and of facilitating the _conception_ of
+the Methods by concrete instances. If it had been my object to justify
+the processes themselves as means of investigation, there would have
+been no need to look far off, or make use of recondite or complicated
+instances. As a specimen of a truth ascertained by the Method of
+Agreement, I might have chosen the proposition "Dogs bark." This dog,
+and that dog, and the other dog, answer to A B C, A D E, A F G. The
+circumstance of being a dog, answers to A. Barking answers to _a_. As a
+truth made known by the Method of Difference, "Fire burns" might have
+sufficed. Before I touch the fire I am not burnt; this is B C; I touch
+it, and am burnt; this is A B C, _a_ B C.
+
+Such familiar experimental processes are not regarded as inductions by
+Dr. Whewell; but they are perfectly homogeneous with those by which,
+even on his own showing, the pyramid of science is supplied with its
+base. In vain he attempts to escape from this conclusion by laying the
+most arbitrary restrictions on the choice of examples admissible as
+instances of Induction: they must neither be such as are still matter of
+discussion (p. 265), nor must any of them be drawn from mental and
+social subjects (p. 269), nor from ordinary observation and practical
+life (pp. 241-247). They must be taken exclusively from the
+generalizations by which scientific thinkers have ascended to great and
+comprehensive laws of natural phenomena. Now it is seldom possible, in
+these complicated inquiries, to go much beyond the initial steps,
+without calling in the instrument of Deduction, and the temporary aid of
+hypotheses; as I myself, in common with Dr. Whewell, have maintained
+against the purely empirical school. Since therefore such cases could
+not conveniently be selected to illustrate the principles of mere
+observation and experiment, Dr. Whewell is misled by their absence into
+representing the Experimental Methods as serving no purpose in
+scientific investigation; forgetting that if those methods had not
+supplied the first generalizations, there would have been no materials
+for his own conception of Induction to work upon.
+
+His challenge, however, to point out which of the four methods are
+exemplified in certain important cases of scientific inquiry, is easily
+answered. "The planetary paths," as far as they are a case of induction
+at all,[43] fall under the Method of Agreement. The law of "falling
+bodies," namely that they describe spaces proportional to the squares of
+the times, was historically a deduction from the first law of motion;
+but the experiments by which it was verified, and by which it might have
+been discovered, were examples of the Method of Agreement; and the
+apparent variation from the true law, caused by the resistance of the
+air, was cleared up by experiments _in vacuo_, constituting an
+application of the Method of Difference. The law of "refracted rays"
+(the constancy of the ratio between the sines of incidence and of
+refraction for each refracting substance) was ascertained by direct
+measurement, and therefore by the Method of Agreement. The "cosmical
+motions" were determined by highly complex processes of thought, in
+which Deduction was predominant, but the Methods of Agreement and of
+Concomitant Variations had a large part in establishing the empirical
+laws. Every case without exception of "chemical analysis" constitutes a
+well-marked example of the Method of Difference. To any one acquainted
+with the subjects--to Dr. Whewell himself, there would not be the
+smallest difficulty in setting out "the A B C and _a b c_ elements" of
+these cases.
+
+If discoveries are ever made by observation and experiment without
+Deduction, the four methods are methods of discovery: but even if they
+were not methods of discovery, it would not be the less true that they
+are the sole methods of Proof; and in that character, even the results
+of deduction are amenable to them. The great generalizations which begin
+as Hypotheses, must end by being proved, and are in reality (as will be
+shown hereafter) proved, by the Four Methods. Now it is with Proof, as
+such, that Logic is principally concerned. This distinction has indeed
+no chance of finding favour with Dr. Whewell; for it is the peculiarity
+of his system, not to recognise, in cases of Induction, any necessity
+for proof. If, after assuming an hypothesis and carefully collating it
+with facts, nothing is brought to light inconsistent with it, that is,
+if experience does not _disprove_ it, he is content: at least until a
+simpler hypothesis, equally consistent with experience, presents itself.
+If this be Induction, doubtless there is no necessity for the four
+methods. But to suppose that it is so, appears to me a radical
+misconception of the nature of the evidence of physical truths.
+
+So real and practical is the need of a test for induction, similar to
+the syllogistic test of ratiocination, that inferences which bid
+defiance to the most elementary notions of inductive logic are put forth
+without misgiving by persons eminent in physical science, as soon as
+they are off the ground on which they are conversant with the facts, and
+not reduced to judge only by the arguments; and as for educated persons
+in general, it may be doubted if they are better judges of a good or a
+bad induction than they were before Bacon wrote. The improvement in the
+results of thinking has seldom extended to the processes; or has
+reached, if any process, that of investigation only, not that of proof.
+A knowledge of many laws of nature has doubtless been arrived at, by
+framing hypotheses and finding that the facts corresponded to them; and
+many errors have been got rid of by coming to a knowledge of facts which
+were inconsistent with them, but not by discovering that the mode of
+thought which led to the errors was itself faulty, and might have been
+known to be such independently of the facts which disproved the
+specific conclusion. Hence it is, that while the thoughts of mankind
+have on many subjects worked themselves practically right, the thinking
+power remains as weak as ever: and on all subjects on which the facts
+which would check the result are not accessible, as in what relates to
+the invisible world, and even, as has been seen lately, to the visible
+world of the planetary regions, men of the greatest scientific
+acquirements argue as pitiably as the merest ignoramus. For though they
+have made many sound inductions, they have not learnt from them (and Dr.
+Whewell thinks there is no necessity that they should learn) the
+principles of inductive _evidence_.
+
+
+
+
+CHAPTER X.
+
+OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS.
+
+
+Sec. 1. In the preceding exposition of the four methods of observation and
+experiment, by which we contrive to distinguish among a mass of
+coexistent phenomena the particular effect due to a given cause, or the
+particular cause which gave birth to a given effect; it has been
+necessary to suppose, in the first instance, for the sake of
+simplification, that this analytical operation is encumbered by no other
+difficulties than what are essentially inherent in its nature; and to
+represent to ourselves, therefore, every effect, on the one hand as
+connected exclusively with a single cause, and on the other hand as
+incapable of being mixed and confounded with any other coexistent
+effect. We have regarded _a b c d e_, the aggregate of the phenomena
+existing at any moment, as consisting of dissimilar facts, _a_, _b_,
+_c_, _d_, and _e_, for each of which one, and only one, cause needs be
+sought; the difficulty being only that of singling out this one cause
+from the multitude of antecedent circumstances, A, B, C, D, and E. The
+cause indeed may not be simple; it may consist of an assemblage of
+conditions; but we have supposed that there was only one possible
+assemblage of conditions, from which the given effect could result.
+
+If such were the fact, it would be comparatively an easy task to
+investigate the laws of nature. But the supposition does not hold, in
+either of its parts. In the first place, it is not true that the same
+phenomenon is always produced by the same cause: the effect _a_ may
+sometimes arise from A, sometimes from B. And, secondly, the effects of
+different causes are often not dissimilar, but homogeneous, and marked
+out by no assignable boundaries from one another: A and B may produce
+not _a_ and _b_, but different portions of an effect _a_. The obscurity
+and difficulty of the investigation of the laws of phenomena is
+singularly increased by the necessity of adverting to these two
+circumstances; Intermixture of Effects, and Plurality of Causes. To the
+latter, being the simpler of the two considerations, we shall first
+direct our attention.
+
+It is not true, then, that one effect must be connected with only one
+cause, or assemblage of conditions; that each phenomenon can be produced
+only in one way. There are often several independent modes in which the
+same phenomenon could have originated. One fact may be the consequent in
+several invariable sequences; it may follow, with equal uniformity, any
+one of several antecedents, or collections of antecedents. Many causes
+may produce motion: many causes may produce some kinds of sensation:
+many causes may produce death. A given effect may really be produced by
+a certain cause, and yet be perfectly capable of being produced without
+it.
+
+
+Sec. 2. One of the principal consequences of this fact of Plurality of
+Causes is, to render the first of the inductive methods, that of
+Agreement, uncertain. To illustrate that method, we supposed two
+instances, A B C followed by _a b c_, and A D E followed by _a d e_.
+From these instances it might apparently be concluded that A is an
+invariable antecedent of _a_, and even that it is the unconditional
+invariable antecedent, or cause, if we could be sure that there is no
+other antecedent common to the two cases. That this difficulty may not
+stand in the way, let us suppose the two cases positively ascertained to
+have no antecedent in common except A. The moment, however, that we let
+in the possibility of a plurality of causes, the conclusion fails. For
+it involves a tacit supposition, that _a_ must have been produced in
+both instances by the same cause. If there can possibly have been two
+causes, those two may, for example, be C and E: the one may have been
+the cause of _a_ in the former of the instances, the other in the
+latter, A having no influence in either case.
+
+Suppose, for example, that two great artists, or great philosophers,
+that two extremely selfish, or extremely generous characters, were
+compared together as to the circumstances of their education and
+history, and the two cases were found to agree only in one circumstance:
+would it follow that this one circumstance was the cause of the quality
+which characterized both those individuals? Not at all; for the causes
+which may produce any type of character are innumerable; and the two
+persons might equally have agreed in their character, though there had
+been no manner of resemblance in their previous history.
+
+This, therefore, is a characteristic imperfection of the Method of
+Agreement; from which imperfection the Method of Difference is free. For
+if we have two instances, A B C and B C, of which B C gives _b c_, and A
+being added converts it into _a b c_, it is certain that in this
+instance at least, A was either the cause of _a_, or an indispensable
+portion of its cause, even though the cause which produces it in other
+instances may be altogether different. Plurality of Causes, therefore,
+not only does not diminish the reliance due to the Method of Difference,
+but does not even render a greater number of observations or experiments
+necessary: two instances, the one positive and the other negative, are
+still sufficient for the most complete and rigorous induction. Not so,
+however, with the Method of Agreement. The conclusions which that
+yields, when the number of instances compared is small, are of no real
+value, except as, in the character of suggestions, they may lead either
+to experiments bringing them to the test of the Method of Difference, or
+to reasonings which may explain and verify them deductively.
+
+It is only when the instances, being indefinitely multiplied and varied,
+continue to suggest the same result, that this result acquires any high
+degree of independent value. If there are but two instances, A B C and A
+D E, though these instances have no antecedent in common except A, yet
+as the effect may possibly have been produced in the two cases by
+different causes, the result is at most only a slight probability in
+favour of A; there may be causation, but it is almost equally probable
+that there was only a coincidence. But the oftener we repeat the
+observation, varying the circumstances, the more we advance towards a
+solution of this doubt. For if we try A F G, A H K, &c., all unlike one
+another except in containing the circumstance A, and if we find the
+effect _a_ entering into the result in all these cases, we must suppose
+one of two things, either that it is caused by A, or that it has as many
+different causes as there are instances. With each addition, therefore,
+to the number of instances, the presumption is strengthened in favour of
+A. The inquirer, of course, will not neglect, if an opportunity present
+itself, to exclude A from some one of these combinations, from A H K for
+instance, and by trying H K separately, appeal to the Method of
+Difference in aid of the Method of Agreement. By the Method of
+Difference alone can it be ascertained that A is the cause of _a_; but
+that it is either the cause, or another effect of the same cause, may be
+placed beyond any reasonable doubt by the Method of Agreement, provided
+the instances are very numerous, as well as sufficiently various.
+
+After how great a multiplication, then, of varied instances, all
+agreeing in no other antecedent except A, is the supposition of a
+plurality of causes sufficiently rebutted, and the conclusion that _a_
+is connected with A divested of the characteristic imperfection, and
+reduced to a virtual certainty? This is a question which we cannot be
+exempted from answering: but the consideration of it belongs to what is
+called the Theory of Probability, which will form the subject of a
+chapter hereafter. It is seen, however, at once, that the conclusion
+does amount to a practical certainty after a sufficient number of
+instances, and that the method, therefore, is not radically vitiated by
+the characteristic imperfection. The result of these considerations is
+only, in the first place, to point out a new source of inferiority in
+the Method of Agreement as compared with other modes of investigation,
+and new reasons for never resting contented with the results obtained by
+it, without attempting to confirm them either by the Method of
+Difference, or by connecting them deductively with some law or laws
+already ascertained by that superior method. And, in the second place,
+we learn from this the true theory of the value of mere _number_ of
+instances in inductive inquiry. The Plurality of Causes is the only
+reason why mere number is of any importance. The tendency of
+unscientific inquirers is to rely too much on number, without analysing
+the instances; without looking closely enough into their nature, to
+ascertain what circumstances are or are not eliminated by means of them.
+Most people hold their conclusions with a degree of assurance
+proportioned to the mere _mass_ of the experience on which they appear
+to rest; not considering that by the addition of instances to instances,
+all of the same kind, that is, differing from one another only in points
+already recognised as immaterial, nothing whatever is added to the
+evidence of the conclusion. A single instance eliminating some
+antecedent which existed in all the other cases, is of more value than
+the greatest multitude of instances which are reckoned by their number
+alone. It is necessary, no doubt, to assure ourselves, by repetition of
+the observation or experiment, that no error has been committed
+concerning the individual facts observed; and until we have assured
+ourselves of this, instead of varying the circumstances, we cannot too
+scrupulously repeat the same experiment or observation without any
+change. But when once this assurance has been obtained, the
+multiplication of instances which do not exclude any more circumstances
+is entirely useless, provided there have been already enough to exclude
+the supposition of Plurality of Causes.
+
+It is of importance to remark, that the peculiar modification of the
+Method of Agreement, which, as partaking in some degree of the nature of
+the Method of Difference, I have called the Joint Method of Agreement
+and Difference, is not affected by the characteristic imperfection now
+pointed out. For, in the joint method, it is supposed not only that the
+instances in which _a_ is, agree only in containing A, but also that the
+instances in which _a_ is not, agree only in not containing A. Now, if
+this be so, A must be not only the cause of _a_, but the only possible
+cause: for if there were another, as for example B, then in the
+instances in which _a_ is not, B must have been absent as well as A, and
+it would not be true that these instances agree _only_ in not containing
+A. This, therefore, constitutes an immense advantage of the joint
+method over the simple Method of Agreement. It may seem, indeed, that
+the advantage does not belong so much to the joint method, as to one of
+its two premises, (if they may be so called,) the negative premise. The
+Method of Agreement, when applied to negative instances, or those in
+which a phenomenon does _not_ take place, is certainly free from the
+characteristic imperfection which affects it in the affirmative case.
+The negative premise, it might therefore be supposed, could be worked as
+a simple case of the Method of Agreement, without requiring an
+affirmative premise to be joined with it. But though this is true in
+principle, it is generally altogether impossible to work the Method of
+Agreement by negative instances without positive ones: it is so much
+more difficult to exhaust the field of negation than that of
+affirmation. For instance, let the question be, what is the cause of the
+transparency of bodies; with what prospect of success could we set
+ourselves to inquire directly in what the multifarious substances which
+are _not_ transparent, agree? But we might hope much sooner to seize
+some point of resemblance among the comparatively few and definite
+species of objects which _are_ transparent; and this being attained, we
+should quite naturally be put upon examining whether the _absence_ of
+this one circumstance be not precisely the point in which all opaque
+substances will be found to resemble.
+
+The Joint Method of Agreement and Difference, therefore, or, as I have
+otherwise called it, the Indirect Method of Difference (because, like
+the Method of Difference properly so called, it proceeds by ascertaining
+how and in what the cases where the phenomenon is present, differ from
+those in which it is absent) is, after the Direct Method of Difference,
+the most powerful of the remaining instruments of inductive
+investigation; and in the sciences which depend on pure observation,
+with little or no aid from experiment, this method, so well exemplified
+in the speculation on the cause of dew, is the primary resource, so far
+as direct appeals to experience are concerned.
+
+
+Sec. 3. We have thus far treated Plurality of Causes only as a possible
+supposition, which, until removed, renders our inductions uncertain; and
+have only considered by what means, where the plurality does not really
+exist, we may be enabled to disprove it. But we must also consider it as
+a case actually occurring in nature, and which, as often as it does
+occur, our methods of induction ought to be capable of ascertaining and
+establishing. For this, however, there is required no peculiar method.
+When an effect is really producible by two or more causes, the process
+for detecting them is in no way different from that by which we discover
+single causes. They may (first) be discovered as separate sequences, by
+separate sets of instances. One set of observations or experiments shows
+that the sun is a cause of heat, another that friction is a source of
+it, another that percussion, another that electricity, another that
+chemical action is such a source. Or (secondly) the plurality may come
+to light in the course of collating a number of instances, when we
+attempt to find some circumstance in which they all agree, and fail in
+doing so. We find it impossible to trace, in all the cases in which the
+effect is met with, any common circumstance. We find that we can
+eliminate _all_ the antecedents; that no one of them is present in all
+the instances, no one of them indispensable to the effect. On closer
+scrutiny, however, it appears that though no one is always present, one
+or other of several always is. If, on further analysis, we can detect in
+these any common element, we may be able to ascend from them to some one
+cause which is the really operative circumstance in them all. Thus it is
+now thought that in the production of heat by friction, percussion,
+chemical action, &c., the ultimate source is one and the same. But if
+(as continually happens) we cannot take this ulterior step, the
+different antecedents must be set down provisionally as distinct causes,
+each sufficient of itself to produce the effect.
+
+We here close our remarks on the Plurality of Causes, and proceed to the
+still more peculiar and more complex case of the Intermixture of
+Effects, and the interference of causes with one another: a case
+constituting the principal part of the complication and difficulty of
+the study of nature; and with which the four only possible methods of
+directly inductive investigation by observation and experiment, are for
+the most part, as will appear presently, quite unequal to cope. The
+instrument of Deduction alone is adequate to unravel the complexities
+proceeding from this source; and the four methods have little more in
+their power than to supply premises for, and a verification of, our
+deductions.
+
+
+Sec. 4. A concurrence of two or more causes, not separately producing each
+its own effect, but interfering with or modifying the effects of one
+another, takes place, as has already been explained, in two different
+ways. In the one, which is exemplified by the joint operation of
+different forces in mechanics, the separate effects of all the causes
+continue to be produced, but are compounded with one another, and
+disappear in one total. In the other, illustrated by the case of
+chemical action, the separate effects cease entirely, and are succeeded
+by phenomena altogether different, and governed by different laws.
+
+Of these cases the former is by far the more frequent, and this case it
+is which, for the most part, eludes the grasp of our experimental
+methods. The other and exceptional case is essentially amenable to them.
+When the laws of the original agents cease entirely, and a phenomenon
+makes its appearance, which, with reference to those laws, is quite
+heterogeneous; when, for example, two gaseous substances, hydrogen and
+oxygen, on being brought together, throw off their peculiar properties,
+and produce the substance called water; in such cases the new fact may
+be subjected to experimental inquiry, like any other phenomenon; and the
+elements which are said to compose it may be considered as the mere
+agents of its production; the conditions on which it depends, the facts
+which make up its cause.
+
+The _effects_ of the new phenomenon, the _properties_ of water, for
+instance, are as easily found by experiment as the effects of any other
+cause. But to discover the _cause_ of it, that is, the particular
+conjunction of agents from which it results, is often difficult enough.
+In the first place, the origin and actual production of the phenomenon
+are most frequently inaccessible to our observation. If we could not
+have learned the composition of water until we found instances in which
+it was actually produced from oxygen and hydrogen, we should have been
+forced to wait until the casual thought struck some one of passing an
+electric spark through a mixture of the two gases, or inserting a
+lighted taper into it, merely to try what would happen. Besides, many
+substances, though they can be analysed, cannot by any known artificial
+means be recompounded. Further, even if we could have ascertained, by
+the Method of Agreement, that oxygen and hydrogen were both present when
+water is produced, no experimentation on oxygen and hydrogen separately,
+no knowledge of their laws, could have enabled us deductively to infer
+that they would produce water. We require a specific experiment on the
+two combined.
+
+Under these difficulties, we should generally have been indebted for our
+knowledge of the causes of this class of effects, not to any inquiry
+directed specifically towards that end, but either to accident, or to
+the gradual progress of experimentation on the different combinations of
+which the producing agents are susceptible; if it were not for a
+peculiarity belonging to effects of this description, that they often,
+under some particular combination of circumstances, reproduce their
+causes. If water results from the juxtaposition of hydrogen and oxygen
+whenever this can be made sufficiently close and intimate, so, on the
+other hand, if water itself be placed in certain situations, hydrogen
+and oxygen are reproduced from it: an abrupt termination is put to the
+new laws, and the agents reappear separately with their own properties
+as at first. What is called chemical analysis is the process of
+searching for the causes of a phenomenon among its effects, or rather
+among the effects produced by the action of some other causes upon it.
+
+Lavoisier, by heating mercury to a high temperature in a close vessel
+containing air, found that the mercury increased in weight, and became
+what was then called red precipitate, while the air, on being examined
+after the experiment, proved to have lost weight, and to have become
+incapable of supporting life or combustion. When red precipitate was
+exposed to a still greater heat, it became mercury again, and gave off a
+gas which did support life and flame. Thus the agents which by their
+combination produced red precipitate, namely the mercury and the gas,
+reappear as effects resulting from that precipitate when acted upon by
+heat. So, if we decompose water by means of iron filings, we produce two
+effects, rust and hydrogen: now rust is already known by experiments
+upon the component substances, to be an effect of the union of iron and
+oxygen: the iron we ourselves supplied, but the oxygen must have been
+produced from the water. The result therefore is that water has
+disappeared, and hydrogen and oxygen have appeared in its stead: or in
+other words, the original laws of these gaseous agents, which had been
+suspended by the superinduction of the new laws called the properties of
+water, have again started into existence, and the causes of water are
+found among its effects.
+
+Where two phenomena, between the laws or properties of which considered
+in themselves no connexion can be traced, are thus reciprocally cause
+and effect, each capable in its turn of being produced from the other,
+and each, when it produces the other, ceasing itself to exist (as water
+is produced from oxygen and hydrogen, and oxygen and hydrogen are
+reproduced from water); this causation of the two phenomena by one
+another, each being generated by the other's destruction, is properly
+transformation. The idea of chemical composition is an idea of
+transformation, but of a transformation which is incomplete; since we
+consider the oxygen and hydrogen to be present in the water _as_ oxygen
+and hydrogen, and capable of being discovered in it if our senses were
+sufficiently keen: a supposition (for it is no more) grounded solely on
+the fact, that the weight of the water is the sum of the separate
+weights of the two ingredients. If there had not been this exception to
+the entire disappearance, in the compound, of the laws of the separate
+ingredients; if the combined agents had not, in this one particular of
+weight, preserved their own laws, and produced a joint result equal to
+the sum of their separate results; we should never, probably, have had
+the notion now implied by the words chemical composition: and, in the
+facts of water produced from hydrogen and oxygen, and hydrogen and
+oxygen produced from water, as the transformation would have been
+complete, we should have seen only a transformation.
+
+The very promising generalization now commonly known as the Conservation
+or Persistence of Force, bears a close resemblance to what the
+conception of chemical composition would become, if divested of the one
+circumstance which now distinguishes it from simple transformation. It
+has long been known that heat is capable of producing electricity, and
+electricity heat; that mechanical motion in numerous cases produces and
+is produced by them both; and so of all other physical forces. It has of
+late become the general belief of scientific inquirers that mechanical
+force, electricity, magnetism, heat, light, and chemical action (to
+which has subsequently been added vital action) are not so much causes
+of one another as convertible into one another; and they are now
+generally spoken of as forms of one and the same force, varying only in
+its manifestations. This doctrine may be admitted, without by any means
+implying that Force is a real entity, a Thing in itself, distinct from
+all its phenomenal manifestations to our organs. Supposing the doctrine
+true, the several kinds of phenomena which it identifies in respect of
+their origin would nevertheless remain different facts; facts which
+would be causes of one another--reciprocally causes and effects, which
+is the first element in the form of causation properly called
+transformation. What the doctrine contains more than this, is, that in
+each of these cases of reciprocal causation, the causes are reproduced
+without alteration in quantity. This is what takes place in the
+transformations of matter: when water has been converted into hydrogen
+and oxygen, these can be reconverted into precisely the same quantity of
+water from which they were produced. To establish a corresponding law in
+regard to Force, it has to be proved that heat is capable of being
+converted into electricity, electricity into chemical action, chemical
+action into mechanical force, and mechanical force back again into the
+exact quantity of heat which was originally expended; and so through
+all the interchanges. Were this proved, it would establish what
+constitutes transformation, as distinguished from the simple fact of
+reciprocal causation. The fact in issue is simply the quantitative
+equivalence of all these natural agencies; whereby a given quantity of
+any one is convertible into, and interchangeable with, a given, and
+always the same, quantity of any other: this, no less, but also no more.
+It cannot yet be said that the law has been fully proved of any case,
+except that of interchange between heat and mechanical motion. It does
+seem to be ascertained, not only that these two are convertible into
+each other, but that after any number of conversions the original
+quantities reappear without addition or diminution, like the original
+quantities of hydrogen and oxygen after passing through the condition of
+water. If the same thing comes to be proved true of all the other
+forces, in relation to these two and to one another, the law of
+Conservation will be established; and it will be a legitimate mode of
+expressing the fact, to speak of Force, as we already speak of Matter,
+as indestructible. But Force will not the less remain, to the
+philosopher, a mere abstraction of the mind. All that will have been
+proved is, that in the phenomena of Nature, nothing actually ceases
+without generating a calculable, and always the same, quantity of some
+other natural phenomenon, which again, when it ceases, will in its turn
+either generate a calculable, and always the same, quantity of some
+third phenomenon, or reproduce the original quantity of the first.
+
+In these cases, where the heteropathic effect (as we called it in a
+former chapter)[44] is but a transformation of its cause, or in other
+words, where the effect and its cause are reciprocally such, and
+mutually convertible into each other; the problem of finding the cause
+resolves itself into the far easier one of finding an effect, which is
+the kind of inquiry that admits of being prosecuted by direct
+experiment. But there are other cases of heteropathic effects to which
+this mode of investigation is not applicable. Take, for instance, the
+heteropathic laws of mind; that portion of the phenomena of our mental
+nature which are analogous to chemical rather than to dynamical
+phenomena; as when a complex passion is formed by the coalition of
+several elementary impulses, or a complex emotion by several simple
+pleasures or pains, of which it is the result without being the
+aggregate, or in any respect homogeneous with them. The product, in
+these cases, is generated by its various factors; but the factors cannot
+be reproduced from the product; just as a youth can grow into an old
+man, but an old man cannot grow into a youth. We cannot ascertain from
+what simple feelings any of our complex states of mind are generated, as
+we ascertain the ingredients of a chemical compound, by making it, in
+its turn, generate them. We can only, therefore, discover these laws by
+the slow process of studying the simple feelings themselves, and
+ascertaining synthetically, by experimenting on the various combinations
+of which they are susceptible, what they, by their mutual action upon
+one another, are capable of generating.
+
+
+Sec. 5. It might have been supposed that the other, and apparently simpler
+variety of the mutual interference of causes, where each cause continues
+to produce its own proper effect according to the same laws to which it
+conforms in its separate state, would have presented fewer difficulties
+to the inductive inquirer than that of which we have just finished the
+consideration. It presents, however, so far as direct induction apart
+from deduction is concerned, infinitely greater difficulties. When a
+concurrence of causes gives rise to a new effect, bearing no relation to
+the separate effects of those causes, the resulting phenomenon stands
+forth undisguised, inviting attention to its peculiarity, and presenting
+no obstacle to our recognising its presence or absence among any number
+of surrounding phenomena. It admits therefore of being easily brought
+under the canons of Induction, provided instances can be obtained such
+as those canons require: and the non-occurrence of such instances, or
+the want of means to produce them artificially, is the real and only
+difficulty in such investigations; a difficulty not logical, but in some
+sort physical. It is otherwise with cases of what, in a preceding
+chapter, has been denominated the Composition of Causes. There, the
+effects of the separate causes do not terminate and give place to
+others, thereby ceasing to form any part of the phenomenon to be
+investigated; on the contrary, they still take place, but are
+intermingled with, and disguised by, the homogeneous and closely allied
+effects of other causes. They are no longer _a_, _b_, _c_, _d_, _e_,
+existing side by side, and continuing to be separately discernible; they
+are + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of which cancel one
+another, while many others do not appear distinguishably, but merge in
+one sum: forming altogether a result, between which and the causes
+whereby it was produced there is often an insurmountable difficulty in
+tracing by observation any fixed relation whatever.
+
+The general idea of the Composition of Causes has been seen to be, that
+though two or more laws interfere with one another, and apparently
+frustrate or modify one another's operation, yet in reality all are
+fulfilled, the collective effect being the exact sum of the effects of
+the causes taken separately. A familiar instance is that of a body kept
+in equilibrium by two equal and contrary forces. One of the forces if
+acting alone would carry the body in a given time a certain distance to
+the west, the other if acting alone would carry it exactly as far
+towards the east; and the result is the same as if it had been first
+carried to the west as far as the one force would carry it, and then
+back towards the east as far as the other would carry it, that is,
+precisely the same distance; being ultimately left where it was found at
+first.
+
+All laws of causation are liable to be in this manner counteracted, and
+seemingly frustrated, by coming into conflict with other laws, the
+separate result of which is opposite to theirs, or more or less
+inconsistent with it. And hence, with almost every law, many instances
+in which it really is entirely fulfilled, do not, at first sight, appear
+to be cases of its operation at all. It is so in the example just
+adduced: a force, in mechanics, means neither more nor less than a cause
+of motion, yet the sum of the effects of two causes of motion may be
+rest. Again, a body solicited by two forces in directions making an
+angle with one another, moves in the diagonal; and it seems a paradox to
+say that motion in the diagonal is the sum of two motions in two other
+lines. Motion, however, is but change of place, and at every instant the
+body is in the exact place it would have been in if the forces had acted
+during alternate instants instead of acting in the same instant; (saving
+that if we suppose two forces to act successively which are in truth
+simultaneous, we must of course allow them double the time.) It is
+evident, therefore, that each force has had, during each instant, all
+the effect which belonged to it; and that the modifying influence which
+one of two concurrent causes is said to exercise with respect to the
+other, may be considered as exerted not over the action of the cause
+itself, but over the effect after it is completed. For all purposes of
+predicting, calculating, or explaining their joint result, causes which
+compound their effects may be treated as if they produced simultaneously
+each of them its own effect, and all these effects coexisted visibly.
+
+Since the laws of causes are as really fulfilled when the causes are
+said to be counteracted by opposing causes, as when they are left to
+their own undisturbed action, we must be cautious not to express the
+laws in such terms as would render the assertion of their being
+fulfilled in those cases a contradiction. If, for instance, it were
+stated as a law of nature that a body to which a force is applied moves
+in the direction of the force, with a velocity proportioned to the force
+directly, and to its own mass inversely; when in point of fact some
+bodies to which a force is applied do not move at all, and those which
+do move (at least in the region of our earth) are, from the very first,
+retarded by the action of gravity and other resisting forces, and at
+last stopped altogether; it is clear that the general proposition,
+though it would be true under a certain hypothesis, would not express
+the facts as they actually occur. To accommodate the expression of the
+law to the real phenomena, we must say, not that the object moves, but
+that it _tends_ to move, in the direction and with the velocity
+specified. We might, indeed, guard our expression in a different mode,
+by saying that the body moves in that manner unless prevented, or except
+in so far as prevented, by some counteracting cause. But the body does
+not only move in that manner unless counteracted; it _tends_ to move in
+that manner even when counteracted; it still exerts, in the original
+direction, the same energy of movement as if its first impulse had been
+undisturbed, and produces, by that energy, an exactly equivalent
+quantity of effect. This is true even when the force leaves the body as
+it found it, in a state of absolute rest; as when we attempt to raise a
+body of three tons weight with a force equal to one ton. For if, while
+we are applying this force, wind or water or any other agent supplies an
+additional force just exceeding two tons, the body will be raised; thus
+proving that the force we applied exerted its full effect, by
+neutralizing an equivalent portion of the weight which it was
+insufficient altogether to overcome. And if while we are exerting this
+force of one ton upon the object in a direction contrary to that of
+gravity, it be put into a scale and weighed, it will be found to have
+lost a ton of its weight, or in other words, to press downwards with a
+force only equal to the difference of the two forces.
+
+These facts are correctly indicated by the expression _tendency_. All
+laws of causation, in consequence of their liability to be counteracted,
+require to be stated in words affirmative of tendencies only, and not of
+actual results. In those sciences of causation which have an accurate
+nomenclature, there are special words which signify a tendency to the
+particular effect with which the science is conversant; thus _pressure_,
+in mechanics, is synonymous with tendency to motion, and forces are not
+reasoned on as causing actual motion, but as exerting pressure. A
+similar improvement in terminology would be very salutary in many other
+branches of science.
+
+The habit of neglecting this necessary element in the precise expression
+of the laws of nature, has given birth to the popular prejudice that all
+general truths have exceptions; and much unmerited distrust has thence
+accrued to the conclusions of science, when they have been submitted to
+the judgment of minds insufficiently disciplined and cultivated. The
+rough generalizations suggested by common observation usually have
+exceptions; but principles of science, or in other words, laws of
+causation, have not. "What is thought to be an exception to a
+principle," (to quote words used on a different occasion,) "is always
+some other and distinct principle cutting into the former; some other
+force which impinges[45] against the first force, and deflects it from
+its direction. There are not a law and an exception to that law, the law
+acting in ninety-nine cases, and the exception in one. There are two
+laws, each possibly acting in the whole hundred cases, and bringing
+about a common effect by their conjunct operation. If the force which,
+being the less conspicuous of the two, is called the _disturbing_ force,
+prevails sufficiently over the other force in some one case, to
+constitute that case what is commonly called an exception, the same
+disturbing force probably acts as a modifying cause in many other cases
+which no one will call exceptions.
+
+"Thus if it were stated to be a law of nature that all heavy bodies fall
+to the ground, it would probably be said that the resistance of the
+atmosphere, which prevents a balloon from falling, constitutes the
+balloon an exception to that pretended law of nature. But the real law
+is, that all heavy bodies _tend_ to fall; and to this there is no
+exception, not even the sun and moon; for even they, as every astronomer
+knows, tend towards the earth, with a force exactly equal to that with
+which the earth tends towards them. The resistance of the atmosphere
+might, in the particular case of the balloon, from a misapprehension of
+what the law of gravitation is, be said to _prevail over_ the law; but
+its disturbing effect is quite as real in every other case, since though
+it does not prevent, it retards the fall of all bodies whatever. The
+rule, and the so-called exception, do not divide the cases between them;
+each of them is a comprehensive rule extending to all cases. To call one
+of these concurrent principles an exception to the other, is
+superficial, and contrary to the correct principles of nomenclature and
+arrangement. An effect of precisely the same kind, and arising from the
+same cause, ought not to be placed in two different categories, merely
+as there does or does not exist another cause preponderating over
+it."[46]
+
+
+Sec. 6. We have now to consider according to what method these complex
+effects, compounded of the effects of many causes, are to be studied;
+how we are enabled to trace each effect to the concurrence of causes in
+which it originated, and ascertain the conditions of its recurrence--the
+circumstances in which it may be expected again to occur. The conditions
+of a phenomenon which arises from a composition of causes, may be
+investigated either deductively or experimentally.
+
+The case, it is evident, is naturally susceptible of the deductive mode
+of investigation. The law of an effect of this description is a result
+of the laws of the separate causes on the combination of which it
+depends, and is therefore in itself capable of being deduced from these
+laws. This is called the method _a priori_. The other, or _a posteriori_
+method, professes to proceed according to the canons of experimental
+inquiry. Considering the whole assemblage of concurrent causes which
+produced the phenomenon, as one single cause, it attempts to ascertain
+the cause in the ordinary manner, by a comparison of instances. This
+second method subdivides itself into two different varieties. If it
+merely collates instances of the effect, it is a method of pure
+observation. If it operates upon the causes, and tries different
+combinations of them, in hopes of ultimately hitting the precise
+combination which will produce the given total effect, it is a method of
+experiment.
+
+In order more completely to clear up the nature of each of these three
+methods, and determine which of them deserves the preference, it will be
+expedient (conformably to a favourite maxim of Lord Chancellor Eldon, to
+which, though it has often incurred philosophical ridicule, a deeper
+philosophy will not refuse its sanction) to "clothe them in
+circumstances." We shall select for this purpose a case which as yet
+furnishes no very brilliant example of the success of any of the three
+methods, but which is all the more suited to illustrate the difficulties
+inherent in them. Let the subject of inquiry be, the conditions of
+health and disease in the human body; or (for greater simplicity) the
+conditions of recovery from a given disease; and in order to narrow the
+question still more, let it be limited, in the first instance, to this
+one inquiry: Is, or is not some particular medicament (mercury, for
+instance) a remedy for the given disease.
+
+Now, the deductive method would set out from known properties of
+mercury, and known laws of the human body, and by reasoning from these,
+would attempt to discover whether mercury will act upon the body when in
+the morbid condition supposed, in such a manner as to restore health.
+The experimental method would simply administer mercury in as many cases
+as possible, noting the age, sex, temperament, and other peculiarities
+of bodily constitution, the particular form or variety of the disease,
+the particular stage of its progress, &c., remarking in which of these
+cases it produced a salutary effect, and with what circumstances it was
+on those occasions combined. The method of simple observation would
+compare instances of recovery, to find whether they agreed in having
+been preceded by the administration of mercury; or would compare
+instances of recovery with instances of failure, to find cases which,
+agreeing in all other respects, differed only in the fact that mercury
+had been administered, or that it had not.
+
+
+Sec. 7. That the last of these three modes of investigation is applicable
+to the case, no one has ever seriously contended. No conclusions of
+value on a subject of such intricacy, ever were obtained in that way.
+The utmost that could result would be a vague general impression for or
+against the efficacy of mercury, of no avail for guidance unless
+confirmed by one of the other two methods. Not that the results, which
+this method strives to obtain, would not be of the utmost possible value
+if they could be obtained. If all the cases of recovery which presented
+themselves, in an examination extending to a great number of instances,
+were cases in which mercury had been administered, we might generalize
+with confidence from this experience, and should have obtained a
+conclusion of real value. But no such basis for generalization can we,
+in a case of this description, hope to obtain. The reason is that which
+we have spoken of as constituting the characteristic imperfection of the
+Method of Agreement; Plurality of Causes. Supposing even that mercury
+does tend to cure the disease, so many other causes, both natural and
+artificial, also tend to cure it, that there are sure to be abundant
+instances of recovery in which mercury has not been administered:
+unless, indeed, the practice be to administer it in all cases; on which
+supposition it will equally be found in the cases of failure.
+
+When an effect results from the union of many causes, the share which
+each has in the determination of the effect cannot in general be great:
+and the effect is not likely, even in its presence or absence, still
+less in its variations, to follow, even approximately, any one of the
+causes. Recovery from a disease is an event to which, in every case,
+many influences must concur. Mercury may be one such influence; but from
+the very fact that there are many other such, it will necessarily happen
+that although mercury is administered, the patient, for want of other
+concurring influences, will often not recover, and that he often will
+recover when it is not administered, the other favourable influences
+being sufficiently powerful without it. Neither, therefore, will the
+instances of recovery agree in the administration of mercury, nor will
+the instances of failure agree in its non-administration. It is much if,
+by multiplied and accurate returns from hospitals and the like, we can
+collect that there are rather more recoveries and rather fewer failures
+when mercury is administered than when it is not; a result of very
+secondary value even as a guide to practice, and almost worthless as a
+contribution to the theory of the subject.
+
+
+Sec. 8. The inapplicability of the method of simple observation to
+ascertain the conditions of effects dependent on many concurring
+causes, being thus recognised; we shall next inquire whether any greater
+benefit can be expected from the other branch of the _a posteriori_
+method, that which proceeds by directly trying different combinations of
+causes, either artificially produced or found in nature, and taking
+notice what is their effect: as, for example, by actually trying the
+effect of mercury, in as many different circumstances as possible. This
+method differs from the one which we have just examined, in turning our
+attention directly to the causes or agents, instead of turning it to the
+effect, recovery from the disease. And since, as a general rule, the
+effects of causes are far more accessible to our study than the causes
+of effects, it is natural to think that this method has a much better
+chance of proving successful than the former.
+
+The method now under consideration is called the Empirical Method; and
+in order to estimate it fairly, we must suppose it to be completely, not
+incompletely, empirical. We must exclude from it everything which
+partakes of the nature not of an experimental but of a deductive
+operation. If for instance we try experiments with mercury upon a person
+in health, in order to ascertain the general laws of its action upon the
+human body, and then reason from these laws to determine how it will act
+upon persons affected with a particular disease, this may be a really
+effectual method, but this is deduction. The experimental method does
+not derive the law of a complex case from the simpler laws which
+conspire to produce it, but makes its experiments directly upon the
+complex case. We must make entire abstraction of all knowledge of the
+simpler tendencies, the _modi operandi_ of mercury in detail. Our
+experimentation must aim at obtaining a direct answer to the specific
+question, Does or does not mercury tend to cure the particular disease?
+
+Let us see, therefore, how far the case admits of the observance of
+those rules of experimentation, which it is found necessary to observe
+in other cases. When we devise an experiment to ascertain the effect of
+a given agent, there are certain precautions which we never, if we can
+help it, omit. In the first place, we introduce the agent into the midst
+of a set of circumstances which we have exactly ascertained. It needs
+hardly be remarked how far this condition is from being realized in any
+case connected with the phenomena of life; how far we are from knowing
+what are all the circumstances which pre-exist in any instance in which
+mercury is administered to a living being. This difficulty, however,
+though insuperable in most cases, may not be so in all; there are
+sometimes concurrences of many causes, in which we yet know accurately
+what the causes are. Moreover, the difficulty may be attenuated by
+sufficient multiplication of experiments, in circumstances rendering it
+improbable that any of the unknown causes should exist in them all. But
+when we have got clear of this obstacle, we encounter another still more
+serious. In other cases, when we intend to try an experiment, we do not
+reckon it enough that there be no circumstance in the case the presence
+of which is unknown to us. We require also that none of the
+circumstances which we do know, shall have effects susceptible of being
+confounded with those of the agent whose properties we wish to study. We
+take the utmost pains to exclude all causes capable of composition with
+the given cause; or if forced to let in any such causes, we take care to
+make them such that we can compute and allow for their influence, so
+that the effect of the given cause may, after the subduction of those
+other effects, be apparent as a residual phenomenon.
+
+These precautions are inapplicable to such cases as we are now
+considering. The mercury of our experiment being tried with an unknown
+multitude (or even let it be a known multitude) of other influencing
+circumstances, the mere fact of their being influencing circumstances
+implies that they disguise the effect of the mercury, and preclude us
+from knowing whether it has any effect or not. Unless we already knew
+what and how much is owing to every other circumstance, (that is, unless
+we suppose the very problem solved which we are considering the means of
+solving,) we cannot tell that those other circumstances may not have
+produced the whole of the effect, independently or even in spite of the
+mercury. The Method of Difference, in the ordinary mode of its use,
+namely by comparing the state of things following the experiment with
+the state which preceded it, is thus, in the case of intermixture of
+effects, entirely unavailing; because other causes than that whose
+effect we are seeking to determine, have been operating during the
+transition. As for the other mode of employing the Method of Difference,
+namely by comparing, not the same case at two different periods, but
+different cases, this in the present instance is quite chimerical. In
+phenomena so complicated it is questionable if two cases, similar in all
+respects but one, ever occurred; and were they to occur, we could not
+possibly know that they were so exactly similar.
+
+Anything like a scientific use of the method of experiment, in these
+complicated cases, is therefore out of the question. We can in the most
+favourable cases only discover, by a succession of trials, that a
+certain cause is _very often_ followed by a certain effect. For, in one
+of these conjunct effects, the portion which is determined by any one of
+the influencing agents, is generally, as we before remarked, but small;
+and it must be a more potent cause than most, if even the tendency which
+it really exerts is not thwarted by other tendencies in nearly as many
+cases as it is fulfilled.
+
+If so little can be done by the experimental method to determine the
+conditions of an effect of many combined causes, in the case of medical
+science; still less is this method applicable to a class of phenomena
+more complicated than even those of physiology, the phenomena of
+politics and history. There, Plurality of Causes exists in almost
+boundless excess, and effects are, for the most part, inextricably
+interwoven with one another. To add to the embarrassment, most of the
+inquiries in political science relate to the production of effects of a
+most comprehensive description, such as the public wealth, public
+security, public morality, and the like: results liable to be affected
+directly or indirectly either in _plus_ or in _minus_ by nearly every
+fact which exists, or event which occurs, in human society. The vulgar
+notion, that the safe methods on political subjects are those of
+Baconian induction--that the true guide is not general reasoning, but
+specific experience--will one day be quoted as among the most
+unequivocal marks of a low state of the speculative faculties in any
+age in which it is accredited. Nothing can be more ludicrous than the
+sort of parodies on experimental reasoning which one is accustomed to
+meet with, not in popular discussion only, but in grave treatises, when
+the affairs of nations are the theme. "How," it is asked, "can an
+institution be bad, when the country has prospered under it?" "How can
+such or such causes have contributed to the prosperity of one country,
+when another has prospered without them?" Whoever makes use of an
+argument of this kind, not intending to deceive, should be sent back to
+learn the elements of some one of the more easy physical sciences. Such
+reasoners ignore the fact of Plurality of Causes in the very case which
+affords the most signal example of it. So little could be concluded, in
+such a case, from any possible collation of individual instances, that
+even the impossibility, in social phenomena, of making artificial
+experiments, a circumstance otherwise so prejudicial to directly
+inductive inquiry, hardly affords, in this case, additional reason of
+regret. For even if we could try experiments upon a nation or upon the
+human race, with as little scruple as M. Magendie tried them on dogs and
+rabbits, we should never succeed in making two instances identical in
+every respect except the presence or absence of some one definite
+circumstance. The nearest approach to an experiment in the philosophical
+sense, which takes place in politics, is the introduction of a new
+operative element into national affairs by some special and assignable
+measure of government, such as the enactment or repeal of a particular
+law. But where there are so many influences at work, it requires some
+time for the influence of any new cause upon national phenomena to
+become apparent; and as the causes operating in so extensive a sphere
+are not only infinitely numerous, but in a state of perpetual
+alteration, it is always certain that before the effect of the new cause
+becomes conspicuous enough to be a subject of induction, so many of the
+other influencing circumstances will have changed as to vitiate the
+experiment.
+
+Two, therefore, of the three possible methods for the study of phenomena
+resulting from the composition of many causes, being, from the very
+nature of the case, inefficient and illusory, there remains only the
+third,--that which considers the causes separately, and infers the
+effect from the balance of the different tendencies which produce it: in
+short, the deductive, or _a priori_ method. The more particular
+consideration of this intellectual process requires a chapter to itself.
+
+
+
+
+CHAPTER XI.
+
+OF THE DEDUCTIVE METHOD.
+
+
+Sec. 1. The mode of investigation which, from the proved inapplicability of
+direct methods of observation and experiment, remains to us as the main
+source of the knowledge we possess or can acquire respecting the
+conditions, and laws of recurrence, of the more complex phenomena, is
+called, in its most general expression, the Deductive Method; and
+consists of three operations: the first, one of direct induction; the
+second, of ratiocination; the third, of verification.
+
+I call the first step in the process an inductive operation, because
+there must be a direct induction as the basis of the whole; though in
+many particular investigations the place of the induction may be
+supplied by a prior deduction; but the premises of this prior deduction
+must have been derived from induction.
+
+The problem of the Deductive Method is, to find the law of an effect,
+from the laws of the different tendencies of which it is the joint
+result. The first requisite, therefore, is to know the laws of those
+tendencies; the law of each of the concurrent causes: and this supposes
+a previous process of observation or experiment upon each cause
+separately; or else a previous deduction, which also must depend for its
+ultimate premises on observation or experiment. Thus, if the subject be
+social or historical phenomena, the premises of the Deductive Method
+must be the laws of the causes which determine that class of phenomena;
+and those causes are human actions, together with the general outward
+circumstances under the influence of which mankind are placed, and which
+constitute man's position on the earth. The Deductive Method, applied to
+social phenomena, must begin, therefore, by investigating, or must
+suppose to have been already investigated, the laws of human action,
+and those properties of outward things by which the actions of human
+beings in society are determined. Some of these general truths will
+naturally be obtained by observation and experiment, others by
+deduction: the more complex laws of human action, for example, may be
+deduced from the simpler ones; but the simple or elementary laws will
+always, and necessarily, have been obtained by a directly inductive
+process.
+
+To ascertain, then, the laws of each separate cause which takes a share
+in producing the effect, is the first desideratum of the Deductive
+Method. To know what the causes are, which must be subjected to this
+process of study, may or may not be difficult. In the case last
+mentioned, this first condition is of easy fulfilment. That social
+phenomena depend on the acts and mental impressions of human beings,
+never could have been a matter of any doubt, however imperfectly it may
+have been known either by what laws those impressions and actions are
+governed, or to what social consequences their laws naturally lead.
+Neither, again, after physical science had attained a certain
+development, could there be any real doubt where to look for the laws on
+which the phenomena of life depend, since they must be the mechanical
+and chemical laws of the solid and fluid substances composing the
+organized body and the medium in which it subsists, together with the
+peculiar vital laws of the different tissues constituting the organic
+structure. In other cases, really far more simple than these, it was
+much less obvious in what quarter the causes were to be looked for: as
+in the case of the celestial phenomena. Until, by combining the laws of
+certain causes, it was found that those laws explained all the facts
+which experience had proved concerning the heavenly motions, and led to
+predictions which it always verified, mankind never knew that those
+_were_ the causes. But whether we are able to put the question before,
+or not until after, we have become capable of answering it, in either
+case it must be answered; the laws of the different causes must be
+ascertained, before we can proceed to deduce from them the conditions of
+the effect.
+
+The mode of ascertaining those laws neither is, nor can be, any other
+than the fourfold method of experimental inquiry, already discussed. A
+few remarks on the application of that method to cases of the
+Composition of Causes, are all that is requisite.
+
+It is obvious that we cannot expect to find the law of a tendency, by an
+induction from cases in which the tendency is counteracted. The laws of
+motion could never have been brought to light from the observation of
+bodies kept at rest by the equilibrium of opposing forces. Even where
+the tendency is not, in the ordinary sense of the word, counteracted,
+but only modified, by having its effects compounded with the effects
+arising from some other tendency or tendencies, we are still in an
+unfavourable position for tracing, by means of such cases, the law of
+the tendency itself. It would have been scarcely possible to discover
+the law that every body in motion tends to continue moving in a straight
+line, by an induction from instances in which the motion is deflected
+into a curve, by being compounded with the effect of an accelerating
+force. Notwithstanding the resources afforded in this description of
+cases by the Method of Concomitant Variations, the principles of a
+judicious experimentation prescribe that the law of each of the
+tendencies should be studied, if possible, in cases in which that
+tendency operates alone, or in combination with no agencies but those of
+which the effect can, from previous knowledge, be calculated and allowed
+for.
+
+Accordingly, in the cases, unfortunately very numerous and important, in
+which the causes do not suffer themselves to be separated and observed
+apart, there is much difficulty in laying down with due certainty the
+inductive foundation necessary to support the deductive method. This
+difficulty is most of all conspicuous in the case of physiological
+phenomena; it being seldom possible to separate the different agencies
+which collectively compose an organized body, without destroying the
+very phenomena which it is our object to investigate:
+
+    --following life, in creatures we dissect,
+    We lose it, in the moment we detect.
+
+And for this reason I am inclined to the opinion, that physiology
+(greatly and rapidly progressive as it now is) is embarrassed by
+greater natural difficulties, and is probably susceptible of a less
+degree of ultimate perfection, than even the social science; inasmuch as
+it is possible to study the laws and operations of one human mind apart
+from other minds, much less imperfectly than we can study the laws of
+one organ or tissue of the human body apart from the other organs or
+tissues.
+
+It has been judiciously remarked that pathological facts, or, to speak
+in common language, diseases in their different forms and degrees,
+afford in the case of physiological investigation the most valuable
+equivalent to experimentation properly so called; inasmuch as they often
+exhibit to us a definite disturbance in some one organ or organic
+function, the remaining organs and functions being, in the first
+instance at least, unaffected. It is true that from the perpetual
+actions and reactions which are going on among all parts of the organic
+economy, there can be no prolonged disturbance in any one function
+without ultimately involving many of the others; and when once it has
+done so, the experiment for the most part loses its scientific value.
+All depends on observing the early stages of the derangement; which,
+unfortunately, are of necessity the least marked. If, however, the
+organs and functions not disturbed in the first instance, become
+affected in a fixed order of succession, some light is thereby thrown
+upon the action which one organ exercises over another: and we
+occasionally obtain a series of effects which we can refer with some
+confidence to the original local derangement; but for this it is
+necessary that we should know that the original derangement _was_ local.
+If it was what is termed constitutional, that is, if we do not know in
+what part of the animal economy it took its rise, or the precise nature
+of the disturbance which took place in that part, we are unable to
+determine which of the various derangements was cause and which effect;
+which of them were produced by one another, and which by the direct,
+though perhaps tardy, action of the original cause.
+
+Besides natural pathological facts, we can produce pathological facts
+artificially; we can try experiments, even in the popular sense of the
+term, by subjecting the living being to some external agent, such as the
+mercury of our former example, or the section of a nerve to ascertain
+the functions of different parts of the nervous system. As this
+experimentation is not intended to obtain a direct solution of any
+practical question, but to discover general laws, from which afterwards
+the conditions of any particular effect may be obtained by deduction;
+the best cases to select are those of which the circumstances can be
+best ascertained: and such are generally not those in which there is any
+practical object in view. The experiments are best tried, not in a state
+of disease, which is essentially a changeable state, but in the
+condition of health, comparatively a fixed state. In the one, unusual
+agencies are at work, the results of which we have no means of
+predicting; in the other, the course of the accustomed physiological
+phenomena would, it may generally be presumed, remain undisturbed, were
+it not for the disturbing cause which we introduce.
+
+Such, with the occasional aid of the Method of Concomitant Variations,
+(the latter not less incumbered than the more elementary methods by the
+peculiar difficulties of the subject,) are our inductive resources for
+ascertaining the laws of the causes considered separately, when we have
+it not in our power to make trial of them in a state of actual
+separation. The insufficiency of these resources is so glaring, that no
+one can be surprised at the backward state of the science of physiology;
+in which indeed our knowledge of causes is so imperfect, that we can
+neither explain, nor could without specific experience have predicted,
+many of the facts which are certified to us by the most ordinary
+observation. Fortunately, we are much better informed as to the
+empirical laws of the phenomena, that is, the uniformities respecting
+which we cannot yet decide whether they are cases of causation, or mere
+results of it. Not only has the order in which the facts of organization
+and life successively manifest themselves, from the first germ of
+existence to death, been found to be uniform, and very accurately
+ascertainable; but, by a great application of the Method of Concomitant
+Variations to the entire facts of comparative anatomy and physiology,
+the characteristic organic structure corresponding to each class of
+functions has been determined with considerable precision. Whether these
+organic conditions are the whole of the conditions, and in many cases
+whether they are conditions at all, or mere collateral effects of some
+common cause, we are quite ignorant: nor are we ever likely to know,
+unless we could construct an organized body, and try whether it would
+live.
+
+Under such disadvantages do we, in cases of this description, attempt
+the initial, or inductive step, in the application of the Deductive
+Method to complex phenomena. But such, fortunately, is not the common
+case. In general, the laws of the causes on which the effect depends may
+be obtained by an induction from comparatively simple instances, or, at
+the worst, by deduction from the laws of simpler causes, so obtained. By
+simple instances are meant, of course, those in which the action of each
+cause was not intermixed or interfered with, or not to any great extent,
+by other causes whose laws were unknown. And only when the induction
+which furnished the premises to the Deductive method rested on such
+instances, has the application of such a method to the ascertainment of
+the laws of a complex effect, been attended with brilliant results.
+
+
+Sec. 2. When the laws of the causes have been ascertained, and the first
+stage of the great logical operation now under discussion satisfactorily
+accomplished, the second part follows; that of determining from the laws
+of the causes, what effect any given combination of those causes will
+produce. This is a process of calculation, in the wider sense of the
+term; and very often involves processes of calculation in the narrowest
+sense. It is a ratiocination; and when our knowledge of the causes is so
+perfect, as to extend to the exact numerical laws which they observe in
+producing their effects, the ratiocination may reckon among its premises
+the theorems of the science of number, in the whole immense extent of
+that science. Not only are the most advanced truths of mathematics often
+required to enable us to compute an effect, the numerical law of which
+we already know; but, even by the aid of those most advanced truths, we
+can go but a little way. In so simple a case as the common problem of
+three bodies gravitating towards one another, with a force directly as
+their mass and inversely as the square of the distance, all the
+resources of the calculus have not hitherto sufficed to obtain any
+general solution but an approximate one. In a case a little more
+complex, but still one of the simplest which arise in practice, that of
+the motion of a projectile, the causes which affect the velocity and
+range (for example) of a cannon-ball may be all known and estimated; the
+force of the gunpowder, the angle of elevation, the density of the air,
+the strength and direction of the wind; but it is one of the most
+difficult of mathematical problems to combine all these, so as to
+determine the effect resulting from their collective action.
+
+Besides the theorems of number, those of geometry also come in as
+premises, where the effects take place in space, and involve motion and
+extension, as in mechanics, optics, acoustics, astronomy. But when the
+complication increases, and the effects are under the influence of so
+many and such shifting causes as to give no room either for fixed
+numbers, or for straight lines and regular curves, (as in the case of
+physiological, to say nothing of mental and social phenomena,) the laws
+of number and extension are applicable, if at all, only on that large
+scale on which precision of details becomes unimportant. Although these
+laws play a conspicuous part in the most striking examples of the
+investigation of nature by the Deductive Method, as for example in the
+Newtonian theory of the celestial motions, they are by no means an
+indispensable part of every such process. All that is essential in it is
+reasoning from a general law to a particular case, that is, determining
+by means of the particular circumstances of that case, what result is
+required in that instance to fulfil the law. Thus in the Torricellian
+experiment, if the fact that air has weight had been previously known,
+it would have been easy, without any numerical data, to deduce from the
+general law of equilibrium, that the mercury would stand in the tube at
+such a height that the column of mercury would exactly balance a column
+of the atmosphere of equal diameter; because, otherwise, equilibrium
+would not exist.
+
+By such ratiocinations from the separate laws of the causes, we may, to
+a certain extent, succeed in answering either of the following
+questions: Given a certain combination of causes, what effect will
+follow? and, What combination of causes, if it existed, would produce a
+given effect? In the one case, we determine the effect to be expected in
+any complex circumstances of which the different elements are known: in
+the other case we learn, according to what law--under what antecedent
+conditions--a given complex effect will occur.
+
+
+Sec. 3. But (it may here be asked) are not the same arguments by which the
+methods of direct observation and experiment were set aside as illusory
+when applied to the laws of complex phenomena, applicable with equal
+force against the Method of Deduction? When in every single instance a
+multitude, often an unknown multitude, of agencies, are clashing and
+combining, what security have we that in our computation _a priori_ we
+have taken all these into our reckoning? How many must we not generally
+be ignorant of? Among those which we know, how probable that some have
+been overlooked; and, even were all included, how vain the pretence of
+summing up the effects of many causes, unless we know accurately the
+numerical law of each,--a condition in most cases not to be fulfilled;
+and even when fulfilled, to make the calculation transcends, in any but
+very simple cases, the utmost power of mathematical science with all its
+most modern improvements.
+
+These objections have real weight, and would be altogether unanswerable,
+if there were no test by which, when we employ the Deductive Method, we
+might judge whether an error of any of the above descriptions had been
+committed or not. Such a test however there is: and its application
+forms, under the name of Verification, the third essential component
+part of the Deductive Method; without which all the results it can give
+have little other value than that of conjecture. To warrant reliance on
+the general conclusions arrived at by deduction, these conclusions must
+be found, on careful comparison, to accord with the results of direct
+observation wherever it can be had. If, when we have experience to
+compare with them, this experience confirms them, we may safely trust to
+them in other cases of which our specific experience is yet to come. But
+if our deductions have led to the conclusion that from a particular
+combination of causes a given effect would result, then in all known
+cases where that combination can be shown to have existed, and where the
+effect has not followed, we must be able to show (or at least to make a
+probable surmise) what frustrated it: if we cannot, the theory is
+imperfect, and not yet to be relied upon. Nor is the verification
+complete, unless some of the cases in which the theory is borne out by
+the observed result, are of at least equal complexity with any other
+cases in which its application could be called for.
+
+If direct observation and collation of instances have furnished us with
+any empirical laws of the effect (whether true in all observed cases, or
+only true for the most part), the most effectual verification of which
+the theory could be susceptible would be, that it led deductively to
+those empirical laws; that the uniformities, whether complete or
+incomplete, which were observed to exist among the phenomena, were
+accounted for by the laws of the causes--were such as could not but
+exist if those be really the causes by which the phenomena are produced.
+Thus it was very reasonably deemed an essential requisite of any true
+theory of the causes of the celestial motions, that it should lead by
+deduction to Kepler's laws: which, accordingly, the Newtonian theory
+did.
+
+In order, therefore, to facilitate the verification of theories obtained
+by deduction, it is important that as many as possible of the empirical
+laws of the phenomena should be ascertained, by a comparison of
+instances, conformably to the Method of Agreement: as well as (it must
+be added) that the phenomena themselves should be described, in the most
+comprehensive as well as accurate manner possible; by collecting from
+the observation of parts, the simplest possible correct expressions for
+the corresponding wholes: as when the series of the observed places of a
+planet was first expressed by a circle, then by a system of epicycles,
+and subsequently by an ellipse.
+
+It is worth remarking, that complex instances which would have been of
+no use for the discovery of the simple laws into which we ultimately
+analyse their phenomena, nevertheless, when they have served to verify
+the analysis, become additional evidence of the laws themselves.
+Although we could not have got at the law from complex cases, still when
+the law, got at otherwise, is found to be in accordance with the result
+of a complex case, that case becomes a new experiment on the law, and
+helps to confirm what it did not assist to discover. It is a new trial
+of the principle in a different set of circumstances; and occasionally
+serves to eliminate some circumstance not previously excluded, and the
+exclusion of which might require an experiment impossible to be
+executed. This was strikingly conspicuous in the example formerly
+quoted, in which the difference between the observed and the calculated
+velocity of sound was ascertained to result from the heat extricated by
+the condensation which takes place in each sonorous vibration. This was
+a trial, in new circumstances, of the law of the development of heat by
+compression; and it added materially to the proof of the universality of
+that law. Accordingly any law of nature is deemed to have gained in
+point of certainty, by being found to explain some complex case which
+had not previously been thought of in connexion with it; and this indeed
+is a consideration to which it is the habit of scientific inquirers to
+attach rather too much value than too little.
+
+To the Deductive Method, thus characterized in its three constituent
+parts, Induction, Ratiocination, and Verification, the human mind is
+indebted for its most conspicuous triumphs in the investigation of
+nature. To it we owe all the theories by which vast and complicated
+phenomena are embraced under a few simple laws, which, considered as the
+laws of those great phenomena, could never have been detected by their
+direct study. We may form some conception of what the method has done
+for us, from the case of the celestial motions; one of the simplest
+among the greater instances of the Composition of Causes, since (except
+in a few cases not of primary importance) each of the heavenly bodies
+may be considered, without material inaccuracy, to be never at one time
+influenced by the attraction of more than two bodies, the sun and one
+other planet or satellite; making, with the reaction of the body itself,
+and the force generated by the body's own motion and acting in the
+direction of the tangent, only four different agents on the concurrence
+of which the motions of that body depend; a much smaller number, no
+doubt, than that by which any other of the great phenomena of nature is
+determined or modified. Yet how could we ever have ascertained the
+combination of forces on which the motions of the earth and planets are
+dependent, by merely comparing the orbits or velocities of different
+planets, or the different velocities or positions of the same planet?
+Notwithstanding the regularity which manifests itself in those motions,
+in a degree so rare among the effects of a concurrence of causes; and
+although the periodical recurrence of exactly the same effect, affords
+positive proof that all the combinations of causes which occur at all,
+recur periodically; we should not have known what the causes were, if
+the existence of agencies precisely similar on our own earth had not,
+fortunately, brought the causes themselves within the reach of
+experimentation under simple circumstances. As we shall have occasion to
+analyse, further on, this great example of the Method of Deduction, we
+shall not occupy any time with it here, but shall proceed to that
+secondary application of the Deductive Method, the result of which is
+not to prove laws of phenomena, but to explain them.
+
+
+
+
+CHAPTER XII.
+
+OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+Sec. 1. The deductive operation by which we derive the law of an effect
+from the laws of the causes, the concurrence of which gives rise to it,
+may be undertaken either for the purpose of discovering the law, or of
+explaining a law already discovered. The word _explanation_ occurs so
+continually and holds so important a place in philosophy, that a little
+time spent in fixing the meaning of it will be profitably employed.
+
+An individual fact is said to be explained, by pointing out its cause,
+that is, by stating the law or laws of causation, of which its
+production is an instance. Thus, a conflagration is explained, when it
+is proved to have arisen from a spark falling into the midst of a heap
+of combustibles. And in a similar manner, a law or uniformity in nature
+is said to be explained, when another law or laws are pointed out, of
+which that law itself is but a case, and from which it could be deduced.
+
+
+Sec. 2. There are three distinguishable sets of circumstances in which a
+law of causation may be explained from, or, as it also is often
+expressed, resolved into, other laws.
+
+The first is the case already so fully considered; an intermixture of
+laws, producing a joint effect equal to the sum of the effects of the
+causes taken separately. The law of the complex effect is explained, by
+being resolved into the separate laws of the causes which contribute to
+it. Thus, the law of the motion of a planet is resolved into the law of
+the acquired force, which tends to produce an uniform motion in the
+tangent, and the law of the centripetal force which tends to produce an
+accelerating motion towards the sun; the real motion being a compound of
+the two.
+
+It is necessary here to remark, that in this resolution of the law of a
+complex effect, the laws of which it is compounded are not the only
+elements. It is resolved into the laws of the separate causes, together
+with the fact of their coexistence. The one is as essential an
+ingredient as the other; whether the object be to discover the law of
+the effect, or only to explain it. To deduce the laws of the heavenly
+motions, we require not only to know the law of a rectilineal and that
+of a gravitative force, but the existence of both these forces in the
+celestial regions, and even their relative amount. The complex laws of
+causation are thus resolved into two distinct kinds of elements: the
+one, simpler laws of causation, the other (in the aptly selected
+expression of Dr. Chalmers) collocations; the collocations consisting in
+the existence of certain agents or powers, in certain circumstances of
+place and time. We shall hereafter have occasion to return to this
+distinction, and to dwell on it at such length as dispenses with the
+necessity of further insisting on it here. The first mode, then, of the
+explanation of Laws of Causation, is when the law of an effect is
+resolved into the various tendencies of which it is the result, together
+with the laws of those tendencies.
+
+
+Sec. 3. A second case is when, between what seemed the cause and what was
+supposed to be its effect, further observation detects an intermediate
+link; a fact caused by the antecedent, and in its turn causing the
+consequent; so that the cause at first assigned is but the remote cause,
+operating through the intermediate phenomenon. A seemed the cause of C,
+but it subsequently appeared that A was only the cause of B, and that it
+is B which was the cause of C. For example: mankind were aware that the
+act of touching an outward object caused a sensation. It was
+subsequently discovered, that after we have touched the object, and
+before we experience the sensation, some change takes place in a kind of
+thread called a nerve, which extends from our outward organs to the
+brain. Touching the object, therefore, is only the remote cause of our
+sensation; that is, not the cause, properly speaking, but the cause of
+the cause;--the real cause of the sensation is the change in the state
+of the nerve. Future experience may not only give us more knowledge than
+we now have of the particular nature of this change, but may also
+interpolate another link: between the contact (for example) of the
+object with our outward organs, and the production of the change of
+state in the nerve, there may take place some electric phenomenon; or
+some phenomenon of a nature not resembling the effects of any known
+agency. Hitherto, however, no such intermediate link has been
+discovered; and the touch of the object must be considered,
+provisionally, as the proximate cause of the affection of the nerve. The
+sequence, therefore, of a sensation of touch on contact with an object,
+is ascertained not to be an ultimate law; it is resolved, as the phrase
+is, into two other laws,--the law, that contact with an object produces
+an affection of the nerve; and the law, that an affection of the nerve
+produces sensation.
+
+To take another example: the more powerful acids corrode or blacken
+organic compounds. This is a case of causation, but of remote causation;
+and is said to be explained when it is shown that there is an
+intermediate link, namely, the separation of some of the chemical
+elements of the organic structure from the rest, and their entering into
+combination with the acid. The acid causes this separation of the
+elements, and the separation of the elements causes the disorganization,
+and often the charring of the structure. So, again, chlorine extracts
+colouring matters, (whence its efficacy in bleaching,) and purifies the
+air from infection. This law is resolved into the two following laws.
+Chlorine has a powerful affinity for bases of all kinds, particularly
+metallic bases and hydrogen. Such bases are essential elements of
+colouring matters and contagious compounds: which substances, therefore,
+are decomposed and destroyed by chlorine.
+
+
+Sec. 4. It is of importance to remark, that when a sequence of phenomena is
+thus resolved into other laws, they are always laws more general than
+itself. The law that A is followed by C, is less general than either of
+the laws which connect B with C and A with B. This will appear from very
+simple considerations.
+
+All laws of causation are liable to be counteracted or frustrated, by
+the non-fulfilment of some negative condition: the tendency, therefore,
+of B to produce C may be defeated. Now the law that A produces B, is
+equally fulfilled whether B is followed by C or not; but the law that A
+produces C by means of B, is of course only fulfilled when B is really
+followed by C, and is therefore less general than the law that A
+produces B. It is also less general than the law that B produces C. For
+B may have other causes besides A; and as A produces C only by means of
+B, while B produces C whether it has itself been produced by A or by
+anything else, the second law embraces a greater number of instances,
+covers as it were a greater space of ground, than the first.
+
+Thus, in our former example, the law that the contact of an object
+causes a change in the state of the nerve, is more general than the law
+that contact with an object causes sensation, since, for aught we know,
+the change in the nerve may equally take place when, from a
+counteracting cause, as for instance, strong mental excitement, the
+sensation does not follow; as in a battle, where wounds are sometimes
+received without any consciousness of receiving them. And again, the law
+that change in the state of a nerve produces sensation, is more general
+than the law that contact with an object produces sensation; since the
+sensation equally follows the change in the nerve when not produced by
+contact with an object, but by some other cause; as in the well-known
+case, when a person who has lost a limb, feels the same sensation which
+he has been accustomed to call a pain in the limb.
+
+Not only are the laws of more immediate sequence into which the law of a
+remote sequence is resolved, laws of greater generality than that law
+is, but (as a consequence of, or rather as implied in, their greater
+generality) they are more to be relied on; there are fewer chances of
+their being ultimately found not to be universally true. From the moment
+when the sequence of A and C is shown not to be immediate, but to
+depend on an intervening phenomenon, then, however constant and
+invariable the sequence of A and C has hitherto been found,
+possibilities arise of its failure, exceeding those which can affect
+either of the more immediate sequences, A, B, and B, C. The tendency of
+A to produce C may be defeated by whatever is capable of defeating
+either the tendency of A to produce B, or the tendency of B to produce
+C; it is therefore twice as liable to failure as either of those more
+elementary tendencies; and the generalization that A is always followed
+by C, is twice as likely to be found erroneous. And so of the converse
+generalization, that C is always preceded and caused by A; which will be
+erroneous not only if there should happen to be a second immediate mode
+of production of C itself, but moreover if there be a second mode of
+production of B, the immediate antecedent of C in the sequence.
+
+The resolution of the one generalization into the other two, not only
+shows that there are possible limitations of the former, from which its
+two elements are exempt, but shows also where these are to be looked
+for. As soon as we know that B intervenes between A and C, we also know
+that if there be cases in which the sequence of A and C does not hold,
+these are most likely to be found by studying the effects or the
+conditions of the phenomenon B.
+
+It appears, then, that in the second of the three modes in which a law
+may be resolved into other laws, the latter are more general, that is,
+extend to more cases, and are also less likely to require limitation
+from subsequent experience, than the law which they serve to explain.
+They are more nearly unconditional; they are defeated by fewer
+contingencies; they are a nearer approach to the universal truth of
+nature. The same observations are still more evidently true with regard
+to the first of the three modes of resolution. When the law of an effect
+of combined causes is resolved into the separate laws of the causes, the
+nature of the case implies that the law of the effect is less general
+than the law of any of the causes, since it only holds when they are
+combined; while the law of any one of the causes holds good both then,
+and also when that cause acts apart from the rest. It is also manifest
+that the complex law is liable to be oftener unfulfilled than any one
+of the simpler laws of which it is the result, since every contingency
+which defeats any of the laws prevents so much of the effect as depends
+on it, and thereby defeats the complex law. The mere rusting, for
+example, of some small part of a great machine, often suffices entirely
+to prevent the effect which ought to result from the joint action of all
+the parts. The law of the effect of a combination of causes is always
+subject to the whole of the negative conditions which attach to the
+action of all the causes severally.
+
+There is another and an equally strong reason why the law of a complex
+effect must be less general than the laws of the causes which conspire
+to produce it. The same causes, acting according to the same laws, and
+differing only in the proportions in which they are combined, often
+produce effects which differ not merely in quantity, but in kind. The
+combination of a centripetal with a projectile force, in the proportions
+which obtain in all the planets and satellites of our solar system,
+gives rise to an elliptical motion; but if the ratio of the two forces
+to each other were slightly altered, it is demonstrated that the motion
+produced would be in a circle, or a parabola, or an hyperbola: and it is
+thought that in the case of some comets one of these is probably the
+fact. Yet the law of the parabolic motion would be resolvable into the
+very same simple laws into which that of the elliptical motion is
+resolved, namely, the law of the permanence of rectilineal motion, and
+the law of gravitation. If, therefore, in the course of ages, some
+circumstance were to manifest itself which, without defeating the law of
+either of those forces, should merely alter their proportion to one
+another, (such as the shock of some solid body, or even the accumulating
+effect of the resistance of the medium in which astronomers have been
+led to surmise that the motions of the heavenly bodies take place,) the
+elliptical motion might be changed into a motion in some other conic
+section; and the complex law, that the planetary motions take place in
+ellipses, would be deprived of its universality, though the discovery
+would not at all detract from the universality of the simpler laws into
+which that complex law is resolved. The law, in short, of each of the
+concurrent causes remains the same, however their collocations may vary;
+but the law of their joint effect varies with every difference in the
+collocations. There needs no more to show how much more general the
+elementary laws must be, than any of the complex laws which are derived
+from them.
+
+
+Sec. 5. Besides the two modes which have been treated of, there is a third
+mode in which laws are resolved into one another; and in this it is
+self-evident that they are resolved into laws more general than
+themselves. This third mode is the _subsumption_ (as it has been called)
+of one law under another: or (what comes to the same thing) the
+gathering up of several laws into one more general law which includes
+them all. The most splendid example of this operation was when
+terrestrial gravity and the central force of the solar system were
+brought together under the general law of gravitation. It had been
+proved antecedently that the earth and the other planets tend to the
+sun; and it had been known from the earliest times that terrestrial
+bodies tend towards the earth. These were similar phenomena; and to
+enable them both to be subsumed under one law, it was only necessary to
+prove that, as the effects were similar in quality, so also they, as to
+quantity, conform to the same rules. This was first shown to be true of
+the moon, which agreed with terrestrial objects not only in tending to a
+centre, but in the fact that this centre was the earth. The tendency of
+the moon towards the earth being ascertained to vary as the inverse
+square of the distance, it was deduced from this, by direct calculation,
+that if the moon were as near to the earth as terrestrial objects are,
+and the acquired force in the direction of the tangent were suspended,
+the moon would fall towards the earth through exactly as many feet in a
+second as those objects do by virtue of their weight. Hence the
+inference was irresistible, that the moon also tends to the earth by
+virtue of its weight: and that the two phenomena, the tendency of the
+moon to the earth and the tendency of terrestrial objects to the earth,
+being not only similar in quality, but, when in the same circumstances,
+identical in quantity, are cases of one and the same law of causation.
+But the tendency of the moon to the earth, and the tendency of the earth
+and planets to the sun, were already known to be cases of the same law
+of causation: and thus the law of all these tendencies, and the law of
+terrestrial gravity, were recognised as identical, and were subsumed
+under one general law, that of gravitation.
+
+In a similar manner, the laws of magnetic phenomena have more recently
+been subsumed under known laws of electricity. It is thus that the most
+general laws of nature are usually arrived at: we mount to them by
+successive steps. For, to arrive by correct induction at laws which hold
+under such an immense variety of circumstances, laws so general as to be
+independent of any varieties of space or time which we are able to
+observe, requires for the most part many distinct sets of experiments or
+observations, conducted at different times and by different people. One
+part of the law is first ascertained, afterwards another part: one set
+of observations teaches us that the law holds good under some
+conditions, another that it holds good under other conditions, by
+combining which observations we find that it holds good under conditions
+much more general, or even universally. The general law, in this case,
+is literally the sum of all the partial ones; it is the recognition of
+the same sequence in different sets of instances; and may, in fact, be
+regarded as merely one step in the process of elimination. That tendency
+of bodies towards one another, which we now call gravity, had at first
+been observed only on the earth's surface, where it manifested itself
+only as a tendency of all bodies towards the earth, and might,
+therefore, be ascribed to a peculiar property of the earth itself: one
+of the circumstances, namely, the proximity of the earth, had not been
+eliminated. To eliminate this circumstance required a fresh set of
+instances in other parts of the universe: these we could not ourselves
+create; and though nature had created them for us, we were placed in
+very unfavourable circumstances for observing them. To make these
+observations, fell naturally to the lot of a different set of persons
+from those who studied terrestrial phenomena; and had, indeed, been a
+matter of great interest at a time when the idea of explaining celestial
+facts by terrestrial laws was looked upon as the confounding of an
+indefeasible distinction. When, however, the celestial motions were
+accurately ascertained, and the deductive processes performed, from
+which it appeared that their laws and those of terrestrial gravity
+corresponded, those celestial observations became a set of instances
+which exactly eliminated the circumstance of proximity to the earth; and
+proved that in the original case, that of terrestrial objects, it was
+not the earth, as such, that caused the motion or the pressure, but the
+circumstance common to that case with the celestial instances, namely,
+the presence of some great body within certain limits of distance.
+
+
+Sec. 6. There are, then, three modes of explaining laws of causation, or,
+which is the same thing, resolving them into other laws. First, when the
+law of an effect of combined causes is resolved into the separate laws
+of the causes, together with the fact of their combination. Secondly,
+when the law which connects any two links, not proximate, in a chain of
+causation, is resolved into the laws which connect each with the
+intermediate links. Both of these are cases of resolving one law into
+two or more; in the third, two or more are resolved into one: when,
+after the law has been shown to hold good in several different classes
+of cases, we decide that what is true in each of these classes of cases,
+is true under some more general supposition, consisting of what all
+those classes of cases have in common. We may here remark that this last
+operation involves none of the uncertainties attendant on induction by
+the Method of Agreement, since we need not suppose the result to be
+extended by way of inference to any new class of cases, different from
+those by the comparison of which it was engendered.
+
+In all these three processes, laws are, as we have seen, resolved into
+laws more general than themselves; laws extending to all the cases which
+the former extended to, and others besides. In the first two modes they
+are also resolved into laws more certain, in other words, more
+universally true than themselves; they are, in fact, proved not to be
+themselves laws of nature, the character of which is to be universally
+true, but _results_ of laws of nature, which may be only true
+conditionally, and for the most part. No difference of this sort exists
+in the third case; since here the partial laws are, in fact, the very
+same law as the general one, and any exception to them would be an
+exception to it too.
+
+By all the three processes, the range of deductive science is extended;
+since the laws, thus resolved, may be thenceforth deduced
+demonstratively from the laws into which they are resolved. As already
+remarked, the same deductive process which proves a law or fact of
+causation if unknown, serves to explain it when known.
+
+The word explanation is here used in its philosophical sense. What is
+called explaining one law of nature by another, is but substituting one
+mystery for another; and does nothing to render the general course of
+nature other than mysterious: we can no more assign a _why_ for the more
+extensive laws than for the partial ones. The explanation may substitute
+a mystery which has become familiar, and has grown to _seem_ not
+mysterious, for one which is still strange. And this is the meaning of
+explanation, in common parlance. But the process with which we are here
+concerned often does the very contrary: it resolves a phenomenon with
+which we are familiar, into one of which we previously knew little or
+nothing; as when the common fact of the fall of heavy bodies was
+resolved into the tendency of all particles of matter towards one
+another. It must be kept constantly in view, therefore, that in science,
+those who speak of explaining any phenomenon mean (or should mean)
+pointing out not some more familiar, but merely some more general,
+phenomenon, of which it is a partial exemplification; or some laws of
+causation which produce it by their joint or successive action, and from
+which, therefore, its conditions may be determined deductively. Every
+such operation brings us a step nearer towards answering the question
+which was stated in a previous chapter as comprehending the whole
+problem of the investigation of nature, viz. What are the fewest
+assumptions, which being granted, the order of nature as it exists
+would be the result? What are the fewest general propositions from which
+all the uniformities existing in nature could be deduced?
+
+The laws, thus explained or resolved, are sometimes said to be
+_accounted for_; but the expression is incorrect, if taken to mean
+anything more than what has been already stated. In minds not habituated
+to accurate thinking, there is often a confused notion that the general
+laws are the _causes_ of the partial ones; that the law of general
+gravitation, for example, causes the phenomenon of the fall of bodies to
+the earth. But to assert this, would be a misuse of the word cause:
+terrestrial gravity is not an effect of general gravitation, but a
+_case_ of it; that is, one kind of the particular instances in which
+that general law obtains. To account for a law of nature means, and can
+mean, nothing more than to assign other laws more general, together with
+collocations, which laws and collocations being supposed, the partial
+law follows without any additional supposition.
+
+
+
+
+CHAPTER XIII.
+
+MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.
+
+
+Sec. 1. The most striking example which the history of science presents, of
+the explanation of laws of causation and other uniformities of sequence
+among special phenomena, by resolving them into laws of greater
+simplicity and generality, is the great Newtonian generalization:
+respecting which typical instance so much having already been said, it
+is sufficient to call attention to the great number and variety of the
+special observed uniformities which are in this case accounted for,
+either as particular cases or as consequences of one very simple law of
+universal nature. The simple fact of a tendency of every particle of
+matter towards every other particle, varying inversely as the square of
+the distance, explains the fall of bodies to the earth, the revolutions
+of the planets and satellites, the motions (so far as known) of comets,
+and all the various regularities which have been observed in these
+special phenomena; such as the elliptical orbits, and the variations
+from exact ellipses; the relation between the solar distances of the
+planets and the duration of their revolutions; the precession of the
+equinoxes; the tides, and a vast number of minor astronomical truths.
+
+Mention has also been made in the preceding chapter of the explanation
+of the phenomena of magnetism from laws of electricity; the special laws
+of magnetic agency having been affiliated by deduction to observed laws
+of electric action, in which they have ever since been considered to be
+included as special cases. An example not so complete in itself, but
+even more fertile in consequences, having been the starting point of the
+really scientific study of physiology, is the affiliation, commenced by
+Bichat, and carried on by subsequent biologists, of the properties of
+the bodily organs, to the elementary properties of the tissues into
+which they are anatomically decomposed.
+
+Another striking instance is afforded by Dalton's generalization,
+commonly known as the atomic theory. It had been known from the very
+commencement of accurate chemical observation, that any two bodies
+combine chemically with one another in only a certain number of
+proportions; but those proportions were in each case expressed by a
+percentage--so many parts (by weight) of each ingredient, in 100 of the
+compound; (say 35 and a fraction of one element, 64 and a fraction of
+the other): in which mode of statement no relation was perceived between
+the proportion in which a given element combines with one substance, and
+that in which it combines with others. The great step made by Dalton
+consisted in perceiving, that a unit of weight might be established for
+each substance, such that by supposing the substance to enter into all
+its combinations in the ratio either of that unit, or of some low
+multiple of that unit, all the different proportions, previously
+expressed by percentages, were found to result. Thus 1 being assumed as
+the unit of hydrogen, if 8 were then taken as that of oxygen, the
+combination of one unit of hydrogen with one unit of oxygen would
+produce the exact proportion of weight between the two substances which
+is known to exist in water; the combination of one unit of hydrogen with
+two units of oxygen would produce the proportion which exists in the
+other compound of the same two elements, called peroxide of hydrogen;
+and the combinations of hydrogen and of oxygen with all other
+substances, would correspond with the supposition that those elements
+enter into combination by single units, or twos, or threes, of the
+numbers assigned to them, 1 and 8, and the other substances by ones or
+twos or threes of other determinate numbers proper to each. The result
+is that a table of the equivalent numbers, or, as they are called,
+atomic weights, of all the elementary substances, comprises in itself,
+and scientifically explains, all the proportions in which any substance,
+elementary or compound, is found capable of entering into chemical
+combination with any other substance whatever.
+
+
+Sec. 2. Some interesting cases of the explanation of old uniformities by
+newly ascertained laws are afforded by the researches of Professor
+Graham. That eminent chemist was the first who drew attention to the
+distinction which may be made of all substances into two classes, termed
+by him crystalloids and colloids; or rather, of all states of matter
+into the crystalloid and the colloidal states, for many substances are
+capable of existing in either. When in the colloidal state, their
+sensible properties are very different from those of the same substance
+when crystallized, or when in a state easily susceptible of
+crystallization. Colloid substances pass with extreme difficulty and
+slowness into the crystalline state, and are extremely inert in all the
+ordinary chemical relations. Substances in the colloid state are almost
+always, when combined with water, more or less viscous or gelatinous.
+The most prominent examples of the state are certain animal and
+vegetable substances, particularly gelatine, albumen, starch, the gums,
+caramel, tannin, and some others. Among substances not of organic
+origin, the most notable instances are hydrated silicic acid, and
+hydrated alumina, with other metallic peroxides of the aluminous class.
+
+Now it is found, that while colloidal substances are easily penetrated
+by water, and by the solutions of crystalloid substances, they are very
+little penetrable by one another: which enabled Professor Graham to
+introduce a highly effective process (termed dialysis) for separating
+the crystalloid substances contained in any liquid mixture, by passing
+them through a thin septum of colloidal matter, which does not suffer
+anything colloidal to pass, or suffers it only in very minute quantity.
+This property of colloids enabled Mr. Graham to account for a number of
+special results of observation, not previously explained.
+
+For instance, "while soluble crystalloids are always highly sapid,
+soluble colloids are singularly insipid," as might be expected; for, as
+the sentient extremities of the nerves of the palate "are probably
+protected by a colloidal membrane," impermeable to other colloids, a
+colloid, when tasted, probably never reaches those nerves. Again, "it
+has been observed that vegetable gum is not digested in the stomach; the
+coats of that organ dialyse the soluble food, absorbing crystalloids,
+and rejecting all colloids." One of the mysterious processes
+accompanying digestion, the secretion of free muriatic acid by the coats
+of the stomach, obtains a probable hypothetical explanation through the
+same law. Finally, much light is thrown upon the observed phenomena of
+osmose (the passage of fluids outward and inward through animal
+membranes) by the fact that the membranes are colloidal. In consequence,
+the water and saline solutions contained in the animal body pass easily
+and rapidly through the membranes, while the substances directly
+applicable to nutrition, which are mostly colloidal, are detained by
+them.[47]
+
+The property which salt possesses of preserving animal substances from
+putrefaction is resolved by Liebig into two more general laws, the
+strong attraction of salt for water, and the necessity of the presence
+of water as a condition of putrefaction. The intermediate phenomenon
+which is interpolated between the remote cause and the effect, can here
+be not merely inferred but seen; for it is a familiar fact, that flesh
+upon which salt has been thrown is speedily found swimming in brine.
+
+The second of the two factors (as they may be termed) into which the
+preceding law has been resolved, the necessity of water to putrefaction,
+itself affords an additional example of the Resolution of Laws. The law
+itself is proved by the Method of Difference, since flesh completely
+dried and kept in a dry atmosphere does not putrefy; as we see in the
+case of dried provisions, and human bodies in very dry climates. A
+deductive explanation of this same law results from Liebig's
+speculations. The putrefaction of animal and other azotised bodies is a
+chemical process, by which they are gradually dissipated in a gaseous
+form, chiefly in that of carbonic acid and ammonia; now to convert the
+carbon of the animal substance into carbonic acid requires oxygen, and
+to convert the azote into ammonia requires hydrogen, which are the
+elements of water. The extreme rapidity of the putrefaction of azotised
+substances, compared with the gradual decay of non-azotised bodies (such
+as wood and the like) by the action of oxygen alone, he explains from
+the general law that substances are much more easily decomposed by the
+action of two different affinities upon two of their elements, than by
+the action of only one.
+
+
+Sec. 3. Among the many important properties of the nervous system, which
+have either been first discovered or strikingly illustrated by Dr.
+Brown-Sequard, I select the reflex influence of the nervous system on
+nutrition and secretion. By reflex nervous action is meant, action which
+one part of the nervous system exerts over another part, without any
+intermediate action on the brain, and consequently without
+consciousness; or which, if it does pass through the brain, at least
+produces its effects independently of the will. There are many
+experiments which prove that irritation of a nerve in one part of the
+body may in this manner excite powerful action in another part; for
+example, food injected into the stomach through a divided oesophagus,
+nevertheless produces secretion of saliva; warm water injected into the
+bowels, and various other irritations of the lower intestines, have been
+found to excite secretion of the gastric juice, and so forth. The
+reality of the power being thus proved, its agency explains a great
+variety of apparently anomalous phenomena; of which I select the
+following from Dr. Brown-Sequard's _Lectures on the Nervous System_.
+
+The production of tears by irritation of the eye, or of the mucous
+membrane of the nose:
+
+The secretions of the eye and nose increased by exposure of other parts
+of the body to cold:
+
+Inflammation of the eye, especially when of traumatic origin, very
+frequently excites a similar affection in the other eye, which may be
+cured by section of the intervening nerve:
+
+Loss of sight sometimes produced by neuralgia; and has been known to be
+at once cured by the extirpation (for instance) of a carious tooth:
+
+Even cataract has been produced in a healthy eye by cataract in the
+other eye, or by neuralgia, or by a wound of the frontal nerve:
+
+The well-known phenomenon of a sudden stoppage of the heart's action,
+and consequent death, produced by irritation of some of the nervous
+extremities: _e.g._, by drinking very cold water; or by a blow on the
+abdomen, or other sudden excitation of the abdominal sympathetic nerve;
+though this nerve may be irritated to any extent without stopping the
+heart's action, if a section be made of the communicating nerves:
+
+The extraordinary effects produced on the internal organs by an
+extensive burn on the surface of the body; consisting in violent
+inflammation of the tissues of the abdomen, chest, or head: which, when
+death ensues from this kind of injury, is one of the most frequent
+causes of it:
+
+Paralysis and anaesthesia of one part of the body from neuralgia in
+another part; and muscular atrophy from neuralgia, even when there is no
+paralysis:
+
+Tetanus produced by the lesion of a nerve; Dr. Brown-Sequard thinks it
+highly probable that hydrophobia is a phenomenon of a similar nature:
+
+Morbid changes in the nutrition of the brain and spinal cord,
+manifesting themselves by epilepsy, chorea, hysteria, and other
+diseases, occasioned by lesion of some of the nervous extremities in
+remote places, as by worms, calculi, tumours, carious bones, and in some
+cases even by very slight irritations of the skin.
+
+
+Sec. 4. From the foregoing and similar instances, we may see the
+importance, when a law of nature previously unknown has been brought to
+light, or when new light has been thrown upon a known law by experiment,
+of examining all cases which present the conditions necessary for
+bringing that law into action; a process fertile in demonstrations of
+special laws previously unsuspected, and explanations of others already
+empirically known.
+
+For instance, Faraday discovered by experiment, that voltaic electricity
+could be evolved from a natural magnet, provided a conducting body were
+set in motion at right angles to the direction of the magnet: and this
+he found to hold not only of small magnets, but of that great magnet,
+the earth. The law being thus established experimentally, that
+electricity is evolved, by a magnet, and a conductor moving at right
+angles to the direction of its poles, we may now look out for fresh
+instances in which these conditions meet. Wherever a conductor moves or
+revolves at right angles to the direction of the earth's magnetic poles,
+there we may expect an evolution of electricity. In the northern
+regions, where the polar direction is nearly perpendicular to the
+horizon, all horizontal motions of conductors will produce electricity;
+horizontal wheels, for example, made of metal; likewise all running
+streams will evolve a current of electricity, which will circulate round
+them; and the air thus charged with electricity may be one of the causes
+of the Aurora Borealis. In the equatorial regions, on the contrary,
+upright wheels placed parallel to the equator will originate a voltaic
+circuit, and waterfalls will naturally become electric.
+
+For a second example; it has been proved, chiefly by the researches of
+Professor Graham, that gases have a strong tendency to permeate animal
+membranes, and diffuse themselves through the spaces which such
+membranes inclose, notwithstanding the presence of other gases in those
+spaces. Proceeding from this general law, and reviewing a variety of
+cases in which gases lie contiguous to membranes, we are enabled to
+demonstrate or to explain the following more special laws: 1st. The
+human or animal body, when surrounded with any gas not already contained
+within the body, absorbs it rapidly; such, for instance, as the gases of
+putrefying matters: which helps to explain malaria. 2nd. The carbonic
+acid gas of effervescing drinks, evolved in the stomach, permeates its
+membranes, and rapidly spreads through the system. 3rd. Alcohol taken
+into the stomach passes into vapour and spreads through the system with
+great rapidity; (which, combined with the high combustibility of
+alcohol, or in other words its ready combination with oxygen, may
+perhaps help to explain the bodily warmth immediately consequent on
+drinking spirituous liquors.) 4th. In any state of the body in which
+peculiar gases are formed within it, these will rapidly exhale through
+all parts of the body; and hence the rapidity with which, in certain
+states of disease, the surrounding atmosphere becomes tainted. 5th. The
+putrefaction of the interior parts of a carcase will proceed as rapidly
+as that of the exterior, from the ready passage outwards of the gaseous
+products. 6th. The exchange of oxygen and carbonic acid in the lungs is
+not prevented, but rather promoted, by the intervention of the membrane
+of the lungs and the coats of the blood-vessels between the blood and
+the air. It is necessary, however, that there should be a substance in
+the blood with which the oxygen of the air may immediately combine;
+otherwise instead of passing into the blood, it would permeate the whole
+organism: and it is necessary that the carbonic acid, as it is formed in
+the capillaries, should also find a substance in the blood with which it
+can combine; otherwise it would leave the body at all points, instead of
+being discharged through the lungs.
+
+
+Sec. 5. The following is a deduction which confirms, by explaining, the old
+but not undisputed empirical generalization, that soda powders weaken
+the human system. These powders, consisting of a mixture of tartaric
+acid with bicarbonate of soda, from which the carbonic acid is set free,
+must pass into the stomach as tartrate of soda. Now, neutral tartrates,
+citrates, and acetates of the alkalis are found, in their passage
+through the system, to be changed into carbonates; and to convert a
+tartrate into a carbonate requires an additional quantity of oxygen, the
+abstraction of which must lessen the oxygen destined for assimilation
+with the blood, on the quantity of which the vigorous action of the
+human system partly depends.
+
+The instances of new theories agreeing with and explaining old
+empiricisms, are innumerable. All the just remarks made by experienced
+persons on human character and conduct, are so many special laws, which
+the general laws of the human mind explain and resolve. The empirical
+generalizations on which the operations of the arts have usually been
+founded, are continually justified and confirmed on the one hand, or
+corrected and improved on the other, by the discovery of the simpler
+scientific laws on which the efficacy of those operations depends. The
+effects of the rotation of crops, of the various manures, and other
+processes of improved agriculture, have been for the first time resolved
+in our own day into known laws of chemical and organic action, by Davy,
+Liebig, and others. The processes of the medical art are even now mostly
+empirical: their efficacy is concluded, in each instance, from a special
+and most precarious experimental generalization: but as science advances
+in discovering the simple laws of chemistry and physiology, progress is
+made in ascertaining the intermediate links in the series of phenomena,
+and the more general laws on which they depend; and thus, while the old
+processes are either exploded, or their efficacy, in so far as real,
+explained, better processes, founded on the knowledge of proximate
+causes, are continually suggested and brought into use.[48] Many even of
+the truths of geometry were generalizations from experience before they
+were deduced from first principles. The quadrature of the cycloid is
+said to have been first effected by measurement, or rather by weighing a
+cycloidal card, and comparing its weight with that of a piece of similar
+card of known dimensions.
+
+
+Sec. 6. To the foregoing examples from physical science, let us add another
+from mental. The following is one of the simple laws of mind: Ideas of a
+pleasurable or painful character form associations more easily and
+strongly than other ideas, that is, they become associated after fewer
+repetitions, and the association is more durable. This is an
+experimental law, grounded on the Method of Difference. By deduction
+from this law, many of the more special laws which experience shows to
+exist among particular mental phenomena may be demonstrated and
+explained:--the ease and rapidity, for instance, with which thoughts
+connected with our passions or our more cherished interests are excited,
+and the firm hold which the facts relating to them have on our memory;
+the vivid recollection we retain of minute circumstances which
+accompanied any object or event that deeply interested us, and of the
+times and places in which we have been very happy or very miserable; the
+horror with which we view the accidental instrument of any occurrence
+which shocked us, or the locality where it took place, and the pleasure
+we derive from any memorial of past enjoyment; all these effects being
+proportional to the sensibility of the individual mind, and to the
+consequent intensity of the pain or pleasure from which the association
+originated. It has been suggested by the able writer of a biographical
+sketch of Dr. Priestley in a monthly periodical,[49] that the same
+elementary law of our mental constitution, suitably followed out, would
+explain a variety of mental phenomena previously inexplicable, and in
+particular some of the fundamental diversities of human character and
+genius. Associations being of two sorts, either between synchronous, or
+between successive impressions; and the influence of the law which
+renders associations stronger in proportion to the pleasurable or
+painful character of the impressions, being felt with peculiar force in
+the synchronous class of associations; it is remarked by the writer
+referred to, that in minds of strong organic sensibility synchronous
+associations will be likely to predominate, producing a tendency to
+conceive things in pictures and in the concrete, richly clothed in
+attributes and circumstances, a mental habit which is commonly called
+Imagination, and is one of the peculiarities of the painter and the
+poet; while persons of more moderate susceptibility to pleasure and pain
+will have a tendency to associate facts chiefly in the order of their
+succession, and such persons, if they possess mental superiority, will
+addict themselves to history or science rather than to creative art.
+This interesting speculation the author of the present work has
+endeavoured, on another occasion, to pursue farther, and to examine how
+far it will avail towards explaining the peculiarities of the poetical
+temperament.[50] It is at least an example which may serve, instead of
+many others, to show the extensive scope which exists for deductive
+investigation in the important and hitherto so imperfect Science of
+Mind.
+
+
+Sec. 7. The copiousness with which the discovery and explanation of special
+laws of phenomena by deduction from simpler and more general ones has
+here been exemplified, was prompted by a desire to characterize clearly,
+and place in its due position of importance, the Deductive Method;
+which, in the present state of knowledge, is destined henceforth
+irrevocably to predominate in the course of scientific investigation. A
+revolution is peaceably and progressively effecting itself in
+philosophy, the reverse of that to which Bacon has attached his name.
+That great man changed the method of the sciences from deductive to
+experimental, and it is now rapidly reverting from experimental to
+deductive. But the deductions which Bacon abolished were from premises
+hastily snatched up, or arbitrarily assumed. The principles were neither
+established by legitimate canons of experimental inquiry, nor the
+results tested by that indispensable element of a rational Deductive
+Method, verification by specific experience. Between the primitive
+method of Deduction and that which I have attempted to characterize,
+there is all the difference which exists between the Aristotelian
+physics and the Newtonian theory of the heavens.
+
+It would, however, be a mistake to expect that those great
+generalizations, from which the subordinate truths of the more backward
+sciences will probably at some future period be deduced by reasoning (as
+the truths of astronomy are deduced from the generalities of the
+Newtonian theory), will be found, in all, or even in most cases, among
+truths now known and admitted. We may rest assured, that many of the
+most general laws of nature are as yet entirely unthought of; and that
+many others, destined hereafter to assume the same character, are known,
+if at all, only as laws or properties of some limited class of
+phenomena; just as electricity, now recognised as one of the most
+universal of natural agencies, was once known only as a curious property
+which certain substances acquired by friction, of first attracting and
+then repelling light bodies. If the theories of heat, cohesion,
+crystallization, and chemical action, are destined, as there can be
+little doubt that they are, to become deductive, the truths which will
+then be regarded as the _principia_ of those sciences would probably, if
+now announced, appear quite as novel[51] as the law of gravitation
+appeared to the cotemporaries of Newton; possibly even more so, since
+Newton's law, after all, was but an extension of the law of weight--that
+is, of a generalization familiar from of old, and which already
+comprehended a not inconsiderable body of natural phenomena. The general
+laws of a similarly commanding character, which we still look forward to
+the discovery of, may not always find so much of their foundations
+already laid.
+
+These general truths will doubtless make their first appearance in the
+character of hypotheses; not proved, nor even admitting of proof, in
+the first instance, but assumed as premises for the purpose of deducing
+from them the known laws of concrete phenomena. But this, though their
+initial, cannot be their final state. To entitle an hypothesis to be
+received as one of the truths of nature, and not as a mere technical
+help to the human faculties, it must be capable of being tested by the
+canons of legitimate induction, and must actually have been submitted to
+that test. When this shall have been done, and done successfully,
+premises will have been obtained from which all the other propositions
+of the science will thenceforth be presented as conclusions, and the
+science will, by means of a new and unexpected Induction, be rendered
+Deductive.
+
+FOOTNOTES:
+
+[1] Dr. Whewell thinks it improper to apply the term Induction to any
+operation not terminating in the establishment of a general truth.
+Induction, he says (_Philosophy of Discovery_, p. 245), "is not the same
+thing as experience and observation. Induction is experience or
+observation _consciously_ looked at in a _general_ form. This
+consciousness and generality are necessary parts of that knowledge which
+is science." And he objects (p. 241) to the mode in which the word
+Induction is employed in this work, as an undue extension of that term
+"not only to the cases in which the general induction is consciously
+applied to a particular instance, but to the cases in which the
+particular instance is dealt with by means of experience in that rude
+sense in which experience can be asserted of brutes, and in which of
+course we can in no way imagine that the law is possessed or understood
+as a general proposition." This use of the term he deems a "confusion of
+knowledge with practical tendencies."
+
+I disclaim, as strongly as Dr. Whewell can do, the application of such
+terms as induction, inference, or reasoning, to operations performed by
+mere instinct, that is, from an animal impulse, without the exertion of
+any intelligence. But I perceive no ground for confining the use of
+those terms to cases in which the inference is drawn in the forms and
+with the precautions required by scientific propriety. To the idea of
+Science, an express recognition and distinct apprehension of general
+laws as such, is essential: but nine-tenths of the conclusions drawn
+from experience in the course of practical life, are drawn without any
+such recognition: they are direct inferences from known cases, to a case
+supposed to be similar. I have endeavoured to show that this is not only
+as legitimate an operation, but substantially the same operation, as
+that of ascending from known cases to a general proposition; except that
+the latter process has one great security for correctness which the
+former does not possess. In Science, the inference must necessarily pass
+through the intermediate stage of a general proposition, because Science
+wants its conclusions for record, and not for instantaneous use. But the
+inferences drawn for the guidance of practical affairs, by persons who
+would often be quite incapable of expressing in unexceptionable terms
+the corresponding generalizations, may and frequently do exhibit
+intellectual powers quite equal to any which have ever been displayed in
+Science: and if these inferences are not inductive, what are they? The
+limitation imposed on the term by Dr. Whewell seems perfectly arbitrary;
+neither justified by any fundamental distinction between what he
+includes and what he desires to exclude, nor sanctioned by usage, at
+least from the time of Reid and Stewart, the principal legislators (as
+far as the English language is concerned) of modern metaphysical
+terminology.
+
+[2] Supra, p. 214.
+
+[3] _Novum Organum Renovatum_, pp. 72, 73.
+
+[4] _Novum Organum Renovatum_, p. 32.
+
+[5] _Cours de Philosophie Positive_, vol. ii. p. 202.
+
+[6] Dr. Whewell, in his reply, contests the distinction here drawn, and
+maintains, that not only different descriptions, but different
+explanations of a phenomenon, may all be true. Of the three theories
+respecting the motions of the heavenly bodies, he says (_Philosophy of
+Discovery_, p. 231): "Undoubtedly all these explanations may be true and
+consistent with each other, and would be so if each had been followed
+out so as to show in what manner it could be made consistent with the
+facts. And this was, in reality, in a great measure done. The doctrine
+that the heavenly bodies were moved by vortices was successfully
+modified, so that it came to coincide in its results with the doctrine
+of an inverse-quadratic centripetal force.... When this point was
+reached, the vortex was merely a machinery, well or ill devised, for
+producing such a centripetal force, and therefore did not contradict the
+doctrine of a centripetal force. Newton himself does not appear to have
+been averse to explaining gravity by impulse. So little is it true that
+if one theory be true the other must be false. The attempt to explain
+gravity by the impulse of streams of particles flowing through the
+universe in all directions, which I have mentioned in the _Philosophy_,
+is so far from being inconsistent with the Newtonian theory, that it is
+founded entirely upon it. And even with regard to the doctrine, that the
+heavenly bodies move by an inherent virtue; if this doctrine had been
+maintained in any such way that it was brought to agree with the facts,
+the inherent virtue must have had its laws determined; and then it would
+have been found that the virtue had a reference to the central body; and
+so, the 'inherent virtue' must have coincided in its effect with the
+Newtonian force; and then, the two explanations would agree, except so
+far as the word 'inherent' was concerned. And if such a part of an
+earlier theory as this word _inherent_ indicates, is found to be
+untenable, it is of course rejected in the transition to later and more
+exact theories, in Inductions of this kind, as well as in what Mr. Mill
+calls Descriptions. There is, therefore, still no validity discoverable
+in the distinction which Mr. Mill attempts to draw between descriptions
+like Kepler's law of elliptical orbits, and other examples of
+induction."
+
+If the doctrine of vortices had meant, not that vortices existed, but
+only that the planets moved _in the same manner_ as if they had been
+whirled by vortices; if the hypothesis had been merely a mode of
+representing the facts, not an attempt to account for them; if, in
+short, it had been only a Description; it would, no doubt, have been
+reconcileable with the Newtonian theory. The vortices, however, were not
+a mere aid to conceiving the motions of the planets, but a supposed
+physical agent, actively impelling them; a material fact, which might be
+true or not true, but could not be both true and not true. According to
+Descartes' theory it was true, according to Newton's it was not true.
+Dr. Whewell probably means that since the phrases, centripetal and
+projectile force, do not declare the nature but only the direction of
+the forces, the Newtonian theory does not absolutely contradict any
+hypothesis which may be framed respecting the mode of their production.
+The Newtonian theory, regarded as a mere _description_ of the planetary
+motions, does not; but the Newtonian theory as an _explanation_ of them
+does. For in what does the explanation consist? In ascribing those
+motions to a general law which obtains between all particles of matter,
+and in identifying this with the law by which bodies fall to the ground.
+If the planets are kept in their orbits by a force which draws the
+particles composing them towards every other particle of matter in the
+solar system, they are not kept in those orbits by the impulsive force
+of certain streams of matter which whirl them round. The one explanation
+absolutely excludes the other. Either the planets are not moved by
+vortices, or they do not move by a law common to all matter. It is
+impossible that both opinions can be true. As well might it be said that
+there is no contradiction between the assertions, that a man died
+because somebody killed him, and that he died a natural death.
+
+So, again, the theory that the planets move by a virtue inherent in
+their celestial nature, is incompatible with either of the two others:
+either that of their being moved by vortices, or that which regards them
+as moving by a property which they have in common with the earth and all
+terrestrial bodies. Dr. Whewell says that the theory of an inherent
+virtue agrees with Newton's when the word inherent is left out, which of
+course it would be (he says) if "found to be untenable." But leave that
+out, and where is the theory? The word inherent _is_ the theory. When
+that is omitted, there remains nothing except that the heavenly bodies
+move by "a virtue," _i.e._ by a power of some sort; or by virtue of
+their celestial nature, which directly contradicts the doctrine that
+terrestrial bodies fall by the same law.
+
+If Dr. Whewell is not yet satisfied, any other subject will serve
+equally well to test his doctrine. He will hardly say that there is no
+contradiction between the emission theory and the undulatory theory of
+light; or that there can be both one and two electricities; or that the
+hypothesis of the production of the higher organic forms by development
+from the lower, and the supposition of separate and successive acts of
+creation, are quite reconcileable; or that the theory that volcanoes are
+fed from a central fire, and the doctrines which ascribe them to
+chemical action at a comparatively small depth below the earth's
+surface, are consistent with one another, and all true as far as they
+go.
+
+If different explanations of the same fact cannot both be true, still
+less, surely, can different predictions. Dr. Whewell quarrels (on what
+ground it is not necessary here to consider) with the example I had
+chosen on this point, and thinks an objection to an illustration a
+sufficient answer to a theory. Examples not liable to his objection are
+easily found, if the proposition that conflicting predictions cannot
+both be true, can be made clearer by any examples. Suppose the
+phenomenon to be a newly-discovered comet, and that one astronomer
+predicts its return once in every 300 years--another once in every 400:
+can they both be right? When Columbus predicted that by sailing
+constantly westward he should in time return to the point from which he
+set out, while others asserted that he could never do so except by
+turning back, were both he and his opponents true prophets? Were the
+predictions which foretold the wonders of railways and steamships, and
+those which averred that the Atlantic could never be crossed by steam
+navigation, nor a railway train propelled ten miles an hour, both (in
+Dr. Whewell's words) "true, and consistent with one another"?
+
+Dr. Whewell sees no distinction between holding contradictory opinions
+on a question of fact, and merely employing different analogies to
+facilitate the conception of the same fact. The case of different
+Inductions belongs to the former class, that of different Descriptions
+to the latter.
+
+[7] _Phil. of Discov._ p. 256.
+
+[8] _Essays on the Pursuit of Truth._
+
+[9] In the first edition a note was appended at this place, containing
+some criticism on Archbishop Whately's mode of conceiving the relation
+between Syllogism and Induction. In a subsequent issue of his _Logic_,
+the Archbishop made a reply to the criticism, which induced me to cancel
+part of the note, incorporating the remainder in the text. In a still
+later edition, the Archbishop observes in a tone of something like
+disapprobation, that the objections, "doubtless from their being fully
+answered and found untenable, were silently suppressed," and that hence
+he might appear to some of his readers to be combating a shadow. On this
+latter point, the Archbishop need give himself no uneasiness. His
+readers, I make bold to say, will fully credit his mere affirmation that
+the objections have actually been made.
+
+But as he seems to think that what he terms the suppression of the
+objections ought not to have been made "silently," I now break that
+silence, and state exactly what it is that I suppressed, and why. I
+suppressed that alone which might be regarded as personal criticism on
+the Archbishop. I had imputed to him the having omitted to ask himself a
+particular question. I found that he had asked himself the question, and
+could give it an answer consistent with his own theory. I had also,
+within the compass of a parenthesis, hazarded some remarks on certain
+general characteristics of Archbishop Whately as a philosopher. These
+remarks, though their tone, I hope, was neither disrespectful nor
+arrogant, I felt, on reconsideration, that I was hardly entitled to
+make; least of all, when the instance which I had regarded as an
+illustration of them, failed, as I now saw, to bear them out. The real
+matter at the bottom of the whole dispute, the different view we take of
+the function of the major premise, remains exactly where it was; and so
+far was I from thinking that my opinion had been "fully answered" and
+was "untenable," that in the same edition in which I cancelled the note,
+I not only enforced the opinion by further arguments, but answered
+(though without naming him) those of the Archbishop.
+
+For not having made this statement before, I do not think it needful to
+apologize. It would be attaching very great importance to one's smallest
+sayings, to think a formal retractation requisite every time that one
+commits an error. Nor is Archbishop Whately's well-earned fame of so
+tender a quality as to require, that in withdrawing a slight criticism
+on him I should have been bound to offer a public _amende_ for having
+made it.
+
+[10] But though it is a condition of the validity of every induction
+that there be uniformity in the course of nature, it is not a necessary
+condition that the uniformity should pervade all nature. It is enough
+that it pervades the particular class of phenomena to which the
+induction relates. An induction concerning the motions of the planets,
+or the properties of the magnet, would not be vitiated though we were to
+suppose that wind and weather are the sport of chance, provided it be
+assumed that astronomical and magnetic phenomena are under the dominion
+of general laws. Otherwise the early experience of mankind would have
+rested on a very weak foundation; for in the infancy of science it could
+not be known that _all_ phenomena are regular in their course.
+
+Neither would it be correct to say that every induction by which we
+infer any truth, implies the general fact of uniformity _as foreknown_,
+even in reference to the kind of phenomena concerned. It implies,
+_either_ that this general fact is already known, _or_ that we may now
+know it: as the conclusion, the Duke of Wellington is mortal, drawn from
+the instances A, B, and C, implies either that we have already concluded
+all men to be mortal, or that we are now entitled to do so from the same
+evidence. A vast amount of confusion and paralogism respecting the
+grounds of Induction would be dispelled by keeping in view these simple
+considerations.
+
+[11] Infra, chap. xxi.
+
+[12] Infra, chap. xxi. xxii.
+
+[13] Dr. Whewell (_Phil. of Discov._ p. 246) will not allow these and
+similar erroneous judgments to be called inductions; inasmuch as such
+superstitious fancies "were not collected from the facts by seeking a
+law of their occurrence, but were suggested by an imagination of the
+anger of superior powers, shown by such deviations from the ordinary
+course of nature." I conceive the question to be, not in what manner
+these notions were at first suggested, but by what evidence they have,
+from time to time, been supposed to be substantiated. If the believers
+in these erroneous opinions had been put on their defence, they would
+have referred to experience: to the comet which preceded the
+assassination of Julius Caesar, or to oracles and other prophecies known
+to have been fulfilled. It is by such appeals to facts that all
+analogous superstitions, even in our day, attempt to justify themselves;
+the supposed evidence of experience is necessary to their hold on the
+mind. I quite admit that the influence of such coincidences would not be
+what it is, if strength were not lent to it by an antecedent
+presumption; but this is not peculiar to such cases; preconceived
+notions of probability form part of the explanation of many other cases
+of belief on insufficient evidence. The _a priori_ prejudice does not
+prevent the erroneous opinion from being sincerely regarded as a
+legitimate conclusion from experience; though it improperly predisposes
+the mind to that interpretation of experience.
+
+Thus much in defence of the sort of examples objected to. But it would
+be easy to produce instances, equally adapted to the purpose, and in
+which no antecedent prejudice is at all concerned. "For many ages," says
+Archbishop Whately, "all farmers and gardeners were firmly
+convinced--and convinced of their knowing it by experience--that the
+crops would never turn out good unless the seed were sown during the
+increase of the moon." This was induction, but bad induction: just as a
+vicious syllogism is reasoning, but bad reasoning.
+
+[14] The assertion, that any and every one of the conditions of a
+phenomenon may be and is, on some occasions and for some purposes,
+spoken of as the cause, has been disputed by an intelligent reviewer of
+this work in the _Prospective Review_ (the predecessor of the justly
+esteemed _National Review_), who maintains that "we always apply the
+word cause rather to that element in the antecedents which exercises
+_force_, and which would _tend_ at all times to produce the same or a
+similar effect to that which, under certain conditions, it would
+actually produce." And he says, that "every one would feel" the
+expression, that the cause of a surprise was the sentinel's being off
+his post, to be incorrect; but that the "allurement or force which
+_drew_ him off his post, might be so called, because in doing so it
+removed a resisting power which would have prevented the surprise." I
+cannot think that it would be wrong to say, that the event took place
+because the sentinel was absent, and yet right to say that it took place
+because he was bribed to be absent. Since the only direct effect of the
+bribe was his absence, the bribe could be called the remote cause of the
+surprise, only on the supposition that the absence was the proximate
+cause; nor does it seem to me that any one (who had not a theory to
+support) would use the one expression and reject the other.
+
+The reviewer observes, that when a person dies of poison, his possession
+of bodily organs is a necessary condition, but that no one would ever
+speak of it as the cause. I admit the fact; but I believe the reason to
+be, that the occasion could never arise for so speaking of it; for when
+in the inaccuracy of common discourse we are led to speak of some one
+condition of a phenomenon as its cause, the condition so spoken of is
+always one which it is at least possible that the hearer may require to
+be informed of. The possession of bodily organs is a known condition,
+and to give that as the answer, when asked the cause of a person's
+death, would not supply the information sought. Once conceive that a
+doubt could exist as to his having bodily organs, or that he were to be
+compared with some being who had them not, and cases may be imagined in
+which it might be said that his possession of them was the cause of his
+death. If Faust and Mephistopheles together took poison, it might be
+said that Faust died because he was a human being, and had a body, while
+Mephistopheles survived because he was a spirit.
+
+It is for the same reason that no one (as the reviewer remarks) "calls
+the cause of a leap, the muscles or sinews of the body, though they are
+necessary conditions; nor the cause of a self-sacrifice, the knowledge
+which was necessary for it; nor the cause of writing a book, that a man
+has time for it, which is a necessary condition." These conditions
+(besides that they are antecedent _states_, and not proximate antecedent
+_events_, and are therefore never the conditions in closest apparent
+proximity to the effect) are all of them so obviously implied, that it
+is hardly possible there should exist that necessity for insisting on
+them, which alone gives occasion for speaking of a single condition as
+if it were the cause. Wherever this necessity exists in regard to some
+one condition, and does not exist in regard to any other, I conceive
+that it is consistent with usage, when scientific accuracy is not aimed
+at, to apply the name cause to that one condition. If the only condition
+which can be supposed to be unknown is a negative condition, the
+negative condition may be spoken of as the cause. It might be said that
+a person died for want of medical advice: though this would not be
+likely to be said, unless the person was already understood to be ill,
+and in order to indicate that this negative circumstance was what made
+the illness fatal, and not the weakness of his constitution, or the
+original virulence of the disease. It might be said that a person was
+drowned because he could not swim; the positive condition, namely, that
+he fell into the water, being already implied in the word drowned. And
+here let me remark, that his falling into the water is in this case the
+only positive condition: all the conditions not expressly or virtually
+included in this (as that he could not swim, that nobody helped him, and
+so forth) are negative. Yet, if it were simply said that the cause of a
+man's death was falling into the water, there would be quite as great a
+sense of impropriety in the expression, as there would be if it were
+said that the cause was his inability to swim; because, though the one
+condition is positive and the other negative, it would be felt that
+neither of them was sufficient, without the other, to produce death.
+
+With regard to the assertion that nothing is termed the cause, except
+the element which exerts active force; I wave the question as to the
+meaning of active force, and accepting the phrase in its popular sense,
+I revert to a former example, and I ask, would it be more agreeable to
+custom to say that a man fell because his foot slipped in climbing a
+ladder, or that he fell because of his weight? for his weight, and not
+the motion of his foot, was the active force which determined his fall.
+If a person walking out in a frosty day, stumbled and fell, it might be
+said that he stumbled because the ground was slippery, or because he was
+not sufficiently careful; but few people, I suppose, would say, that he
+stumbled because he walked. Yet the only active force concerned was that
+which he exerted in walking: the others were mere negative conditions;
+but they happened to be the only ones which there could be any necessity
+to state; for he walked, most likely, in exactly his usual manner, and
+the negative conditions made all the difference. Again, if a person were
+asked why the army of Xerxes defeated that of Leonidas, he would
+probably say, because they were a thousand times the number; but I do
+not think he would say, it was because they fought, though that was the
+element of active force. To borrow another example, used by Mr. Grove
+and by Mr. Baden Powell, the opening of floodgates is said to be the
+cause of the flow of water; yet the active force is exerted by the water
+itself, and opening the floodgates merely supplies a negative condition.
+The reviewer adds, "there are some conditions absolutely passive, and
+yet absolutely necessary to physical phenomena, viz. the relations of
+space and time; and to these no one ever applies the word cause without
+being immediately arrested by those who hear him." Even from this
+statement I am compelled to dissent. Few persons would feel it
+incongruous to say (for example) that a secret became known because it
+was spoken of when A. B. was within hearing; which is a condition of
+space: or that the cause why one of two particular trees is taller than
+the other, is that it has been longer planted; which is a condition of
+time.
+
+[15] There are a few exceptions; for there are some properties of
+objects which seem to be purely preventive; as the property of opaque
+bodies, by which they intercept the passage of light. This, as far as we
+are able to understand it, appears an instance not of one cause
+counteracting another by the same law whereby it produces its own
+effects, but of an agency which manifests itself in no other way than in
+defeating the effects of another agency. If we knew on what other
+relations to light, or on what peculiarities of structure, opacity
+depends, we might find that this is only an apparent, not a real,
+exception to the general proposition in the text. In any case it needs
+not affect the practical application. The formula which includes all the
+negative conditions of an effect in the single one of the absence of
+counteracting causes, is not violated by such cases as this; though, if
+all counteracting agencies were of this description, there would be no
+purpose served by employing the formula, since we should still have to
+enumerate specially the negative conditions of each phenomenon, instead
+of regarding them as implicitly contained in the positive laws of the
+various other agencies in nature.
+
+[16] I mean by this expression, the ultimate laws of nature (whatever
+they may be) as distinguished from the derivative laws and from the
+collocations. The diurnal revolution of the earth (for example) is not a
+part of the constitution of things, because nothing can be so called
+which might possibly be terminated or altered by natural causes.
+
+[17] I use the words "straight line" for brevity and simplicity. In
+reality the line in question is not exactly straight, for, from the
+effect of refraction, we actually see the sun for a short interval
+during which the opaque mass of the earth is interposed in a direct line
+between the sun and our eyes; thus realizing, though but to a limited
+extent, the coveted desideratum of seeing round a corner.
+
+[18] _Second Burnett Prize Essay_, by Principal Tulloch, p. 25.
+
+[19] _Letters on the Philosophy of the Human Mind_, First Series, p.
+219.
+
+[20] _Essays_, pp. 206-208.
+
+[21] To the universality which mankind are agreed in ascribing to the
+Law of Causation, there is one claim of exception, one disputed case,
+that of the Human Will; the determinations of which, a large class of
+metaphysicians are not willing to regard as following the causes called
+motives, according to as strict laws as those which they suppose to
+exist in the world of mere matter. This controverted point will undergo
+a special examination when we come to treat particularly of the Logic of
+the Moral Sciences (Book vi. ch. 2). In the mean time I may remark that
+these metaphysicians, who, it must be observed, ground the main part of
+their objection on the supposed repugnance of the doctrine in question
+to our consciousness, seem to me to mistake the fact which consciousness
+testifies against. What is really in contradiction to consciousness,
+they would, I think, on strict self-examination, find to be, the
+application to human actions and volitions of the ideas involved in the
+common use of the term Necessity; which I agree with them in objecting
+to. But if they would consider that by saying that a person's actions
+_necessarily_ follow from his character, all that is really meant (for
+no more is meant in any case whatever of causation) is that he
+invariably _does_ act in conformity to his character, and that any one
+who thoroughly knew his character would certainly predict how he would
+act in any supposable case; they probably would not find this doctrine
+either contrary to their experience or revolting to their feelings. And
+no more than this is contended for by any one but an Asiatic fatalist.
+
+[22] _Lectures on Metaphysics_, vol. ii. Lect. xxxix. pp. 391-2.
+
+I regret that I cannot invoke the authority of Sir William Hamilton in
+favour of my own opinions on Causation, as I can against the particular
+theory which I am now combating. But that acute thinker has a theory of
+Causation peculiar to himself, which has never yet, as far as I know,
+been analytically examined, but which, I venture to think, admits of as
+complete refutation as any one of the false or insufficient
+psychological theories which strew the ground in such numbers under his
+potent metaphysical scythe. (Since examined and controverted in the
+sixteenth chapter of _An Examination of Sir William Hamilton's
+Philosophy_).
+
+[23] Unless we are to consider as such the following statement, by one
+of the writers quoted in the text: "In the case of mental exertion, the
+result to be accomplished is preconsidered or meditated, and is
+therefore known _a priori_, or before experience."--(Bowen's _Lowell
+Lectures on the Application of Metaphysical and Ethical Science to the
+Evidence of Religion_, Boston, 1849.) This is merely saying that when we
+will a thing we have an idea of it. But to have an idea of what we wish
+to happen, does not imply a prophetic knowledge that it will happen.
+Perhaps it will be said that the _first time_ we exerted our will, when
+we had of course no experience of any of the powers residing in us, we
+nevertheless must already have known that we possessed them, since we
+cannot will that which we do not believe to be in our power. But the
+impossibility is perhaps in the words only, and not in the facts; for we
+may _desire_ what we do not know to be in our power; and finding by
+experience that our bodies move according to our _desire_, we may then,
+and only then, pass into the more complicated mental state which is
+termed will.
+
+After all, even if we had an instinctive knowledge that our actions
+would follow our will, this, as Brown remarks, would prove nothing as to
+the nature of Causation. Our knowing, previous to experience, that an
+antecedent will be followed by a certain consequent, would not prove the
+relation between them to be anything more than antecedence and
+consequence.
+
+[24] Reid's _Essays on the Active Powers_, Essay iv. ch. 3.
+
+[25] _Prospective Review_ for February 1850.
+
+[26] Vide supra, p. 270, note.
+
+[27] _Westminster Review_ for October 1855.
+
+[28] See the whole doctrine in Aristotle _de Anima_: where the [Greek:
+threptike psyche] is treated as exactly equivalent to [Greek: threptike
+dynamis].
+
+[29] It deserves notice that the parts of nature, which Aristotle
+regards as presenting evidence of design, are the Uniformities: the
+phenomena in so far as reducible to law. [Greek: Tyche] and [Greek: to
+automaton] satisfy him as explanations of the variable element in
+phenomena, but their occurring according to a fixed rule can only, to
+his conceptions, be accounted for by an Intelligent Will. The common, or
+what may be called the instinctive, religious interpretation of nature,
+is the reverse of this. The events in which men spontaneously see the
+hand of a supernatural being, are those which cannot, as they think, be
+reduced to a physical law. What they can distinctly connect with
+physical causes, and especially what they can predict, though of course
+ascribed to an Author of Nature if they already recognise such an
+author, might be conceived, they think, to arise from a blind fatality,
+and in any case do not appear to them to bear so obviously the mark of a
+divine will. And this distinction has been countenanced by eminent
+writers on Natural Theology, in particular by Dr. Chalmers: who thinks
+that though design is present everywhere, the irresistible evidence of
+it is to be found not in the _laws_ of nature but in the collocations,
+_i.e._ in the part of nature in which it is impossible to trace any law.
+A few properties of dead matter might, he thinks, conceivably account
+for the regular and invariable succession of effects and causes; but
+that the different kinds of matter have been so placed as to promote
+beneficent ends, is what he regards as the proof of a Divine Providence.
+Mr. Baden Powell, in his Essay entitled "Philosophy of Creation," has
+returned to the point of view of Aristotle and the ancients, and
+vigorously reasserts the doctrine that the indication of design in the
+universe is not special adaptations, but Uniformity and Law, these being
+the evidences of mind, and not what appears to us to be a provision for
+our uses. While I decline to express any opinion here on this _vexata
+quaestio_, I ought not to mention Mr. Powell's volume without the
+acknowledgment due to the philosophic spirit which pervades generally
+the three Essays composing it, forming in the case of one of them (the
+"Unity of Worlds") an honourable contrast with the other dissertations,
+so far as they have come under my notice, which have appeared on either
+side of that controversy.
+
+[30] In the words of Fontenelle, another celebrated Cartesian, "les
+philosophes aussi bien que le peuple avaient cru que l'ame et le corps
+agissaient reellement et physiquement l'un sur l'autre. Descartes vint,
+qui prouva que leur nature ne permettait point cette sorte de
+communication veritable, et qu'ils n'en pouvaient avoir qu'une
+apparente, dont Dieu etait le Mediateur."--_Oeuvres de Fontenelle_,
+ed. 1767, tom. v. p. 534.
+
+[31] I omit, for simplicity, to take into account the effect, in this
+latter case, of the diminution of pressure, in diminishing the flow of
+water through the drain; which evidently in no way affects the truth or
+applicability of the principle, since when the two causes act
+simultaneously the conditions of that diminution of pressure do not
+arise.
+
+[32] Unless, indeed, the consequent was generated not by the antecedent,
+but by the means employed to produce the antecedent. As, however, these
+means are under our power, there is so far a probability that they are
+also sufficiently within our knowledge, to enable us to judge whether
+that could be the case or not.
+
+[33] _Discourse on the Study of Natural Philosophy_, p. 179.
+
+[34] For this speculation, as for many other of my scientific
+illustrations, I am indebted to Professor Bain, of Aberdeen, who has
+since, in his profound treatises entitled "The Senses and the
+Intellect," and "The Emotions and the Will," carried the analytic
+investigation of the mental phenomena according to the methods of
+physical science, to the most advanced point which it has yet reached,
+and has worthily inscribed his name among the successive constructors of
+an edifice to which Hartley, Brown, and James Mill had each contributed
+their part.
+
+[35] This view of the necessary coexistence of opposite excitements
+involves a great extension of the original doctrine of two
+electricities. The early theorists assumed that, when amber was rubbed,
+the amber was made positive and the rubber negative to the same degree;
+but it never occurred to them to suppose that the existence of the amber
+charge was dependent on an opposite charge in the bodies with which the
+amber was contiguous, while the existence of the negative charge on the
+rubber was equally dependent on a contrary state of the surfaces that
+might accidentally be confronted with it; that, in fact, in a case of
+electrical excitement by friction, four charges were the minimum that
+could exist. But this double electrical action is essentially implied in
+the explanation now universally adopted in regard to the phenomena of
+the common electric machine.
+
+[36] Pp. 159-162.
+
+[37] Infra, book iv. ch. ii. On Abstraction.
+
+[38] I must, however, remark, that this example, which seems to militate
+against the assertion we made of the comparative inapplicability of the
+Method of Difference to cases of pure observation, is really one of
+those exceptions which, according to a proverbial expression, prove the
+general rule. For in this case, in which Nature, in her experiment,
+seems to have imitated the type of the experiments made by man, she has
+only succeeded in producing the likeness of man's most imperfect
+experiments; namely, those in which, though he succeeds in producing the
+phenomenon, he does so by employing complex means, which he is unable
+perfectly to analyse, and can form therefore no sufficient judgment what
+portion of the effects may be due, not to the supposed cause, but to
+some unknown agency of the means by which that cause was produced. In
+the natural experiment which we are speaking of, the means used was the
+clearing off a canopy of clouds; and we certainly do not know
+sufficiently in what this process consists, or on what it depends, to be
+certain _a priori_ that it might not operate upon the deposition of dew
+independently of any thermometric effect at the earth's surface. Even,
+therefore, in a case so favourable as this to Nature's experimental
+talents, her experiment is of little value except in corroboration of a
+conclusion already attained through other means.
+
+[39] In his subsequent work, _Outlines of Astronomy_ (Sec. 570), Sir John
+Herschel suggests another possible explanation of the acceleration of
+the revolution of a comet.
+
+[40] Discourse, pp. 156-8, and 171.
+
+[41] _Outlines of Astronomy_, Sec. 856.
+
+[42] _Philosophy of Discovery_, pp. 263, 264.
+
+[43] See, on this point, the second chapter of the present Book.
+
+[44] Ante, ch. vii. Sec. 1.
+
+[45] It seems hardly necessary to say that the word _impinge_, as a
+general term to express collision of forces, is here used by a figure of
+speech, and not as expressive of any theory respecting the nature of
+force.
+
+[46] _Essays on some Unsettled Questions of Political Economy_, Essay V.
+
+[47] _Vide_ Memoir by Thomas Graham, F.R.S., Master of the Mint, "On
+Liquid Diffusion Applied to Analysis," in the _Philosophical
+Transactions_ for 1862, reprinted in the _Journal of the Chemical
+Society_, and also separately as a pamphlet.
+
+[48] It was an old generalization in surgery, that tight bandaging had a
+tendency to prevent or dissipate local inflammation. This sequence,
+being, in the progress of physiological knowledge, resolved into more
+general laws, led to the important surgical invention made by Dr.
+Arnott, the treatment of local inflammation and tumours by means of an
+equable pressure, produced by a bladder partially filled with air. The
+pressure, by keeping back the blood from the part, prevents the
+inflammation, or the tumour, from being nourished: in the case of
+inflammation, it removes the stimulus, which the organ is unfit to
+receive; in the case of tumours, by keeping back the nutritive fluid, it
+causes the absorption of matter to exceed the supply, and the diseased
+mass is gradually absorbed and disappears.
+
+[49] Since acknowledged and reprinted in Mr. Martineau's _Miscellanies_.
+
+[50] _Dissertations and Discussions_, vol. i., fourth paper.
+
+[51] Written before the rise of the new views respecting the relation of
+heat to mechanical force; but confirmed rather than contradicted by
+them.
+
+
+END OF VOL. I.
+
+
+
+
+  LONDON:
+  SAVILL, EDWARDS AND CO., PRINTERS, CHANDOS STREET,
+  COVENT GARDEN.
+
+
+
+
+Transcriber's Notes
+
+
+Spelling irregularities where there was no obviously preferred version
+were left as is. Variants include: "alkalies" and "alkalis;" "apprise"
+and "apprize;" "coexistent" and "co-existent" (along with derivatives);
+"coextensive" and "co-extensive;" "e. g." and "e.g."; "encumbered" and
+"incumbered;" "formulae" and "formulas;" "i. e." and "i.e."; "nonentity"
+and "non-entity;" "recal" and "recall" (and derivatives); "rectilinear"
+and "rectilineal;" "stopt" and "stopped."
+
+Changed "3" to "4" on page xiii: "4. --and from descriptions."
+
+Inserted missing page number, "167," for Chapter VIII, section 7 on page
+xiii.
+
+Moved the semi-colon inside the quotation marks in the footnote on page
+14: "the Science of the Formal Laws of Thought;".
+
+Changed "sub-divisions" to "subdivisions" on page 59: "three
+subdivisions."
+
+Changed "pre-supposed" to "presupposed" on page 75: "they are
+presupposed."
+
+In the footnote to page 122, changed the Greek character upsilon with
+dasia and oxia to upsilon with psili and oxia, making the
+transliteration "deuterai ousiai."
+
+Changed "he" to "be" on page 189: "to which it may be reduced."
+
+Changed "cb." to "ch." in footnote on page 227: "Theory of Reasoning,
+ch. iv."
+
+Changed "reconcilable" to "reconcileable" on page 240: "not easily
+reconcileable."
+
+Preserved the hyphen in "counter-acting" on page 280. Usually this is
+spelled without the hyphen, but this instance is in a quotation.
+
+Moved parenthesis that was after "to" to before it on page 321: "(to
+return to a former example)."
+
+Put "i.e." in italics on page 335: "_i.e._ by a power of some sort."
+
+Changed "paralyzed" to "paralysed" on page 389: "nerves of motion were
+paralysed."
+
+The footnote from page 396 refers to the footnote on page 270. There is
+no such footnote. The intent may be to refer to the footnote on page
+268. However, the text was not changed.
+
+Added the dropped "w" in "which" on page 420: "which the progress of the
+inquiry."
+
+Changed "developes" to "develops" on page 456: "the prime conductor
+develops."
+
+Removed the additional period at the end of the footnote on page 457:
+"Pp. 159-162."
+
+Added the dropped "l" to "essential" on page 515: "an essential
+requisite."
+
+Removed extra opening quotation mark before "gum" on page 532:
+"vegetable gum is not digested."
+
+In the Latin-1 text version, the oe-ligature was replaced by the two
+characters, "oe" (or "Oe" when capitalized).
+
+
+
+
+
+End of the Project Gutenberg EBook of A System of Logic: Ratiocinative and
+Inductive, by John Stuart Mill
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