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diff --git a/30866.txt b/30866.txt new file mode 100644 index 0000000..99e8202 --- /dev/null +++ b/30866.txt @@ -0,0 +1,5193 @@ +The Project Gutenberg EBook of Analysis of Mr. Mill's System of Logic, by +William Stebbing + +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: Analysis of Mr. Mill's System of Logic + +Author: William Stebbing + +Release Date: January 6, 2010 [EBook #30866] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK MILL'S LOGIC *** + + + + +Produced by David Clarke, Martin Pettit and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive/Million Book Project) + + + + + + +ANALYSIS OF MR. MILL'S SYSTEM OF LOGIC. + + * * * * * + +WORKS BY JOHN STUART MILL, M.P. FOR WESTMINSTER. + + + A SYSTEM of LOGIC, RATIOCINATIVE and INDUCTIVE. Sixth Edition. 2 + vols. 8vo. 25_s._ + + An EXAMINATION of SIR WILLIAM HAMILTON'S PHILOSOPHY, and of the + Principal Philosophical Questions discussed in his Writings. Third + Edition, revised. 8vo. 14_s._ + + PRINCIPLES of POLITICAL ECONOMY, with some of their Applications to + Social Philosophy. Sixth Edition. 2 vols. 8vo. 30_s._ + + PRINCIPLES of POLITICAL ECONOMY. By JOHN STUART MILL, M.P. People's + Edition. Crown 8vo. 5_s._ + + CONSIDERATIONS on REPRESENTATIVE GOVERNMENT. Third Edition. 8vo. + 9_s._ + + On REPRESENTATIVE GOVERNMENT. By JOHN STUART MILL, M.P. People's + Edition. Crown 8vo. 2_s._ + + On LIBERTY. Third Edition. Post 8vo. 7_s._ 6_d._ + + On LIBERTY. By JOHN STUART MILL, M.P. People's Edition. Crown 8vo. + 1_s._ 4_d._ + + DISSERTATIONS and DISCUSSIONS, POLITICAL, PHILOSOPHICAL, and + HISTORICAL. Second Edition of VOLS. I. and II. price 24_s._; VOL. + III., price 12_s._ + + INAUGURAL ADDRESS delivered to the University of St. Andrew's, Feb. + 1, 1867. By JOHN STUART MILL, M.P. Rector of the University. + Library Edition (the Second), post 8vo. 5_s._ People's Edition, + crown 8vo. 1_s._ + + UTILITARIANISM. Second Edition. 8vo. 5_s._ + + THOUGHTS on PARLIAMENTARY REFORM. Second Edition, with SUPPLEMENT. + 8vo. 1_s._ 6_d._ + + +London: LONGMANS and CO. Paternoster Row. + + * * * * * + +ANALYSIS OF MR. MILL'S SYSTEM OF LOGIC. + +BY + +W. STEBBING, M.A. + +FELLOW OF WORCESTER COLLEGE, OXFORD. + +_NEW EDITION._ + +LONDON: +LONGMANS, GREEN, AND CO. +1867. + + +LONDON + +PRINTED BY SPOTTISWOODE AND CO. + +NEW-STREET SQUARE + + + + +PREFACE TO THE SECOND EDITION. + + +The author's aim has been to produce such a condensation of the original +work as may recall its contents to those who have read it, and may serve +those who are now reading it in the place of a full body of marginal +notes. Mr. Mill's conclusions on the true province and method of Logic +have a high substantive value, independent even of the arguments and +illustrations by which they are supported; and these conclusions may be +adequately, and, it is believed, with much practical utility, embodied +in an epitome. The processes of reasoning on which they depend, can, on +the other hand, be represented in outline only. But it is hoped that the +substance of every paragraph, necessary for the due comprehension of the +several steps by which the results have been reached, will be here +found at all events suggested. + +The author may be allowed to add, that Mr. Mill, before publication, +expressed a favourable opinion of the manner in which the work had been +executed. Without such commendation the volume would hardly have been +offered to the public. + +LONDON: _Dec. 21, 1865_. + + + + +CONTENTS. + PAGE + +INTRODUCTION 1 + + +BOOK I. + +NAMES AND PROPOSITIONS. + +CHAP. + + I. On the Necessity of commencing with an Analysis of + Language in Logic 3 + + II. Names 3 + + III. The Things denoted by Names 7 + + IV. Propositions 17 + + V. The Import of Propositions 19 + + VI. Propositions merely Verbal 24 + + VII. The Nature of Classification, and the Five Predicables 26 + + VIII. Definition 30 + + +BOOK II. + +REASONING. + + I. Inference, or Reasoning in General 35 + + II. Ratiocination, or Syllogism 36 + + III. The Functions and Logical Value of the Syllogism 39 + + IV. Trains of Reasoning, and Deductive Sciences 43 + +V. & VI. Demonstration and Necessary Truths 46 + + +BOOK III. + +INDUCTION. + + I. Preliminary Observations on Induction in general 53 + + II. Inductions improperly so called 54 + + III. The ground of Induction 57 + + IV. Laws of Nature 58 + + V. The Law of Universal Causation 60 + + VI. The Composition of Causes 66 + + VII. Observation and Experiment 67 + + VIII. & Note to IX. The Four Methods of Experimental + Enquiry 69 + + X. Plurality of Causes, and intermixture of Effects 73 + + XI. The Deductive Method 76 + + XII. & XIII. The Explanation and Examples of the Explanation + of Laws of Nature 77 + + XIV. The Limits to the Explanation of Laws of Nature; + and Hypotheses 79 + + XV. Progressive Effects, and continued Action of + Causes 81 + + XVI. Empirical Laws 83 + + XVII. Chance, and its Elimination 85 + + XVIII. The Calculation of Chances 87 + + XIX. The Extension of Derivative Laws to Adjacent Cases 89 + + XX. Analogy 91 + + XXI. The Evidence of the Law of Universal Causation 92 + + XXII. Uniformities of Coexistence not dependent on Causation 94 + + XXIII. Approximate Generalisations, and Probable Evidence 96 + + XXIV. The remaining Laws of Nature 99 + + XXV. The grounds of Disbelief 103 + + +BOOK IV. + +OPERATIONS SUBSIDIARY TO INDUCTION. + + I. Observation and Description 107 + + II. Abstraction, or the Formation of Conceptions 108 + + III. Naming as Subsidiary to Induction 111 + + IV. The Requisites of a Philosophical Language, and the + Principles of Definition 112 + + V. The Natural History of the Variation in the Meaning + of Terms 115 + + VI. Terminology and Nomenclature 117 + + VII. Classification, as Subsidiary to Induction 121 + + VIII. Classification by Series 124 + + +BOOK V. + +FALLACIES. + + I. Fallacies in general 127 + + II. Classification of Fallacies 128 + + III. Fallacies of Simple Inspection; or, a priori Fallacies 130 + + IV. Fallacies of Observation 134 + + V. Fallacies of Generalisation 137 + + VI. Fallacies of Ratiocination 141 + + VII. Fallacies of Confusion 143 + + +BOOK VI. + +ON THE LOGIC OF THE MORAL SCIENCES. + + I. Introductory Remarks 148 + + II. Liberty and Necessity 148 + + III. There is, or may be, a Science of Human Nature 150 + + IV. The Laws of Mind 151 + + V. Ethology, or the Science of the Formation of Character 153 + + VI. General Considerations on the Social Science 155 + + VII. The Chemical, or Experimental, Method in the Social + Science 156 + + VIII. The Geometrical, or Abstract Method 157 + + IX. The Physical, or Concrete Deductive Method 158 + + X. The Inverse Deductive, or Historical Method 161 + + XI. The Logic of Practice, or Art; including Morality + and Policy 165 + + + + +ANALYSIS OF MILL'S LOGIC. + + + + +INTRODUCTION. + + +No adequate definition is possible till the properties of the thing to +be defined are known. Previously we can define only the scope of the +inquiry. Now, Logic has been considered as both the science of +reasoning, i.e. the analysis of the mental process when we reason, and +the art of reasoning, i.e. the rules for the process. The term +_reasoning_, however, is not wide enough. _Reasoning_ means either +syllogising, or (and this is its truer sense) the drawing inferences +from assertions already admitted. But the Aristotelian or Scholastic +logicians included in Logic terms and propositions, and the Port Royal +logicians spoke of it as equivalent to the art of thinking. Even +popularly, accuracy of classification, and the extent of command over +premisses, are thought clearer signs of logical powers than accuracy of +deduction. On the other hand, the definition of logic as a 'science +treating of the operations of the understanding in the search of truth,' +though wide enough, would err through including truths known from +intuition; for, though doubtless many seeming intuitions are processes +of inference, questions as to what facts are _real intuitions_ belong +to Metaphysics, not to Logic. + +Logic is the science, not of Belief, but of Proof, or Evidence. Almost +all knowledge being matter of inference, the fields of Logic and of +Knowledge coincide; but the two differ in so far that Logic does not +find evidence, but only judges of it. All science is composed of data, +and conclusions thence: Logic shows what relations must subsist between +them. All inferential knowledge is true or not, according as the laws of +Logic have been obeyed or not. Logic is Bacon's _Ars Artium_, the +science of sciences. Genius sometimes employs laws unconsciously; but +only genius: as a rule, the advances of a science have been ever found +to be preceded by a fuller knowledge of the laws of Logic applicable to +it. Logic, then, may be described as the science of the operations of +the understanding which aid in the estimation of evidence. It includes +not only the process of proceeding from the known to the unknown, but, +as auxiliary thereto, Naming, Definition, and Classification. +Conception, Memory, and other like faculties, are not treated by it; but +it presupposes them. Our object, therefore, must be to analyse the +process of inference and the subsidiary operations, besides framing +canons to test any given evidence. We need not, however, carry the +analysis beyond what is necessary for the practical uses of Logic; for +one step in analysis is good without a second, and our purpose is simply +to see the difference between good and ill processes of inference. +Minuter analysis befits Metaphysics; though even that science, when +stepping beyond the interrogation of our consciousness, or rather of our +memory, is, as all other sciences, amenable to Logic. + + + + +BOOK I + +NAMES AND PROPOSITIONS. + + + + +CHAPTER I. + +ON THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE IN LOGIC. + + +The fact of Logic being a portion of the art of thinking, and of +thought's chief instrument being words, is one reason why we must first +inquire into the right use of words. But further, the import of +propositions cannot really be examined apart from that of words; and +(since whatever can be an object of belief assumes the form of a +proposition, and in propositions all truth and error lie) this is a +paramount reason why we must, as a preliminary, consider the import of +names, the neglecting which, and confining ourselves to things, would +indeed be to discard all past experience. The right method is, to take +men's classifications of things as shown by names, correcting them as we +proceed. + + + + +CHAPTER II. + +NAMES. + + +Hobbes's assertion that a name is a sign, not of a thing, but of our +conception of it, is untrue (unless he merely mean that the conception, +and not the thing itself, is imparted to the hearer); for we intend by +a name, not only to make men conceive what we conceive, but to inform +them what we believe as to the things themselves. + +Names may be divided according to five principles of classification. The +_first_ way of dividing them is into General (not as equivalent to +Collective) and Individual names; the _second_, into Concrete, i.e. the +names of objects, and Abstract, i.e. the names of attributes (though +Locke improperly extends the term to all names gained by abstraction, +that is, to all general names). An abstract name is sometimes general, +e.g. colour, and sometimes singular, e.g. milk-whiteness. It may be +objected to calling attributes abstract, that also concrete adjectives, +e.g. white, are attributes. But a word is the name of the things of +which it can be predicated. Hence, white is the name of all things so +coloured, given indeed because of the quality, but really the name of +the thing, and no more the name of the quality than are names generally, +since every one of them, if it signifies anything at all, must imply an +attribute. + +The _third_ division is into Connotative and Non-connotative (the latter +being wrongly called Absolute). By _connotative_ are meant, not (as Mr. +James Mill explains it) words which, pointing directly to one thing, +tacitly refer to another, but words which denote a subject and imply an +attribute; while _non-connotatives_ signify a subject only, or attribute +only. All concrete general names are connotative. They are also called +_denominative_, because the subject denoted receives a common name (e.g. +snow is named white) from the attribute connoted. Even some abstracts +are connotative, for attributes may have attributes ascribed to them, +and a word which denotes attributes may connote an attribute of them; +e.g. fault connotes hurtfulness. Proper names, on the other hand, though +concrete, are not connotative. They are merely distinguishing marks, +given perhaps originally for a reason, but, when once given, independent +of it, since the reason is proved to be no part of the sense of the word +by the fact that the name is still used when the reason is forgotten. +But other individual names are connotative. Some of these, viz. those +connoting some attribute or some set of attributes possessed by one +object only, e.g. Sun, God, are really general names, though happening +to be predicable only of a single object. But there are also real +connotative individual names, part of whose meaning is, that there +exists only one individual with the connoted attribute, e.g. The first +Emperor, The father of Socrates; and it is so with many-worded names, +made up of a general name limited by other words, e.g. The present Prime +Minister of England. In short, the meaning of all names, which have any +meaning, resides, not in what they denote, but in what they connote. +There perpetually, however, arises a difficulty of deciding how much +they do connote, that is, what difference in the object would make a +difference in the name. This vagueness comes from our learning the +connotation, through a rude generalisation and analysis, from the +objects denoted. Thus, men use a name without any precise reference to a +definite set of attributes, applying it to new objects on account of +superficial resemblance, so that at length all common meaning +disappears. Even scientific writers, from ignorance, or from the +aversion which men at large feel to the use of new names, often force +old terms to express an ever-growing number of distinctions. But every +concrete general name should be given a definite connotation with the +least possible change in the denotation; and this is what is aimed at in +every definition of a general name already in use. But we must not +confound the use of names of indeterminate connotation, which is so +great an evil, with the employment, necessitated by the paucity of names +as compared with the demand, of the same words with different +connotations in different relations. + +A _fourth_ division of names is into Positive and Negative. When the +positive is connotative, so is the corresponding negative, for the +non-possession of an attribute is itself an attribute. Names negative in +form, e.g. unpleasant, are often really positive; and others, e.g. idle, +sober, though seemingly positive, are really negative. Privatives are +names which are equivalent each to a positive and a negative name taken +together. They connote both the absence of certain attributes, and the +presence of others, whence the presence of the defaulting ones might +have been expected. Thus, blind would be applied only to a non-seeing +member of a seeing class. + +The _fifth_ division is into Relative and (that we may economise the +term Absolute for an occasion when none other is available) Non-relative +names. Correlatives, when concrete, are of course connotative. A +relation arises from two individuals being concerned in the same series +of facts, so that the signification of neither name can be explained +except by mentioning another: and any two correlatives connote, not the +same attribute indeed, but just this series of facts, which is exactly +the same in both cases. + +Some make a _sixth_ division, viz. Univocals, i.e. names predicated of +different individuals in the same sense, and AEquivocals, i.e. names +predicated of different individuals in different senses. But these are +not two kinds of names, but only two modes of using them; for an +aequivocal name is two names accidentally coinciding in sound. An +intermediate case is that of a name used analogically or metaphorically, +that is, in two senses, one its primary, the other its secondary sense. +The not perceiving that such a word is really two has produced many +fallacies. + + + + +CHAPTER III. + +THE THINGS DENOTED BY NAMES. + + +Logic is the theory of Proof, and everything provable can be exhibited +as a proposition, propositions alone being objects of belief. Therefore, +the import of propositions, that is, the import of predication, must be +ascertained. But, as to make a proposition, i.e. to predicate, is to +assert one _thing_ of another _thing_, the way to learn the import of +predication is, by discovering what are the _things_ signified by names +which are capable of being subject or predicate. It was with this object +that Aristotle formed his Categories, i.e. an attempted enumeration of +all nameable things by the _summa genera_ or highest predicates, one or +other of which must, he asserted, be predicable of everything. His, +however, is a rude catalogue, without philosophical analysis of the +rationale even of familiar distinctions. For instance, his Relation +properly includes Action, Passivity, and Local Situation, and also the +two categories of Position [Greek: pote] and [Greek: pou], while the +difference between [Greek: pou] and [Greek: keisthai] is only verbal, +and [Greek: echein] is not a _summum genus_ at all. Besides--only +substantives and attributes being there considered--there is no category +for sensation and other mental states, since, though these may rightly +be placed, so far as they express their relation, if active, to their +objects, if passive to their causes, in the Categories of Actio and +Passio, the things, viz., the mental states, do not belong there. + +The absence of a well-defined concrete name answering to the abstract +_existence_, is one great obstacle to renewing Aristotle's attempt. The +words used for the purpose commonly denote substances only, though +attributes and feelings are equally existences. Even _being_ is +inadequate, since it denotes only _some_ existences, being used by +custom as synonymous with _substance_, both material and spiritual. That +is, it is applied to what excites feelings and has attributes, but not +to feelings and attributes themselves; and if we called extension, +virtue, &c., _beings_, we should be accused of believing in the Platonic +self-existing ideas, or Epicurus's sensible forms--in short, of deeming +attributes substances. To fill this gap, the abstract, _entity_, was +made into a concrete, equivalent to _being_. Yet even _entity_ implies, +though not so much as _being_, the notion of substance. In fact, every +word originally connoting simply existence, gradually enlarges its +connotation to mean _separate_ existence, i.e. existence freed from the +condition of belonging to a substance, so as to exclude attributes and +feelings. Since, then, all the terms are ambiguous, that among them (and +the same principle applies to terms generally) will be employed here +which seems on each occasion to be _least_ ambiguous: and terms will be +used even in improper senses, when these by familiar association convey +the proper meaning. + +_Nameable things_ are--I. Feelings or States of Consciousness.--A +feeling, being anything of which the mind is conscious, is synonymous +with _state of consciousness_. It is commonly confined to the sensations +and emotions, or to the emotions alone; but it is properly a genus, +having for species, Sensation, Emotion, Thought, and Volition. By +thought is meant all that we are internally conscious of when we think; +e.g. the idea of the sun, and not the sun itself, is a thought; and so, +not even an imaginary thing like a ghost, but only the idea of it, is a +thought. In like manner, a sensation differs both from the object +causing it, and the attribute ascribed to the object. Yet language +(except in the case of the sensations of hearing) has seldom provided +the sensations with separate names; so that we have to name the +sensation from the object or the attribute exciting it, though we might +_conceive_ the sensation to exist, though it never actually does, +without an exciting cause. Again, another distinction has to be attended +to, viz. the difference between the sensation and the state of the +bodily organs, which is the physical agency producing it. This +distinction escapes notice partly by reason of the division of the +feelings into bodily and mental. But really there is no such division, +even sensations being states of the sentient mind, and not of the body. +The difference, in fact, between sensations, thoughts, and emotions, is +only in the different agency producing the feeling; it being, in the +case of the sensations, a bodily, and, for the other two, a mental +state. Some suppose, after the sensation, in which, they say, the mind +is passive, a distinct active process called perception, which is the +direct recognition of an external object, as the cause of the sensation. +Probably, perceptions are simply cases of belief claiming to be +intuitive, i.e. free of external evidence. But, at any rate, any +question as to their nature is irrelevant to an inquiry like the +present, viz. how we get the non-original part of our knowledge. And so +also is the distinction in German metaphysics, between the mind's _acts_ +and its passive _states_. Enough for us now that they are all states of +the mind. + +II. Substances.--Logicians think they have defined substance and +attribute, when they have shown merely what difference the use of them +respectively makes in the grammar of a sentence. They say an attribute +must be an attribute _of_ something, but that a substance is +self-existent (being followed, if a relative, by _of_, not _qua_ +substance, but _qua_ the relation). But this _of_, as distinguishing +attributes, itself needs explanation: besides, we can no more conceive a +substance independent of attributes, than an attribute independent of a +substance. Metaphysicians go deeper into the distinction than logicians. +Substances, most of them say, are either bodies or minds; and, of these, +a body is the external cause to which we ascribe sensations. Berkeley +and the Idealists, however, deny that there exists any cause of +sensations (except, indeed, a First Cause). They argue that the _whole_ +of our notion of a body consists of a number of our own or others' +sensations occurring together habitually (so that, the thought of one +being associated with the thought of the others, we get what Hartley and +Locke call a complex idea). They deny that a residuum would remain if +all the attributes were pared off; for that, though the sensations are +bound together by a law, the existence of a _substratum_ is but one of +many forms of mentally realising the connection. And they ask how it +is,--since so long as the sensations occurred in the old order, we +should not miss such a _substratum_, supposing it to have once existed +_and to have perished_--that we can know it exists even now? Their +opponents used formerly to reply, that the uniform order of sensations +implies an external cause determining the law of the order; and that the +attributes _inhere_ in this external cause or substratum, viz. matter. +But at last it was seen that the existence of matter could not be proved +by extrinsic evidence; consequently, now the answer to the idealist +argument simply is, that the belief in an external cause of sensations +is universal, and as intuitive as our knowledge of sensations +themselves. Even Kant allows this (notwithstanding his belief in the +existence of a universe of _things in themselves_, i.e. Nouemena, as +contrasted with the mental representation of them, where the sensations, +he thinks, furnish the matter, and the laws of the mind, the form). +Brown even traced up to the sensations of touch, combined with the +sensations seated in the muscular frame, those very properties, viz., +extension and figure, which Reid referred to as proving that some +qualities must exist, not in the sensations, but in the things +themselves, _since_ they cannot possibly be copies of any impression on +the senses. We have, in truth, no right to consider a thing's sensible +qualities akin to its nature, unless we suppose an absurdity, viz. that +a cause must, as such, resemble its effects. In any case, the question +whether Ontology be a possible science, concerns, not Logic, but the +nature and laws of intuitive knowledge. And the question as to the +nature of Mind is as out of place here as that about Body. As body is +the unknown exciting cause of sensations, so mind, the other kind of +substance, is the unknown recipient both of the sensations and of all +the other feelings. Though I call a something _myself_, as distinct from +the series of feelings, the 'thread of consciousness,' yet this self +shows itself only through its capacity of feeling or being conscious; +and I can, with my present faculties, conceive the gaining no new +information but about as yet unknown faculties of feeling. In short, as +body is the unsentient cause of all feelings, so mind is the sentient +_subject_ (in the German sense) of them, viz. that which feels them. +About this inner nature we know nothing, and Logic cares nothing. + +III. Attributes.--Qualities are the first class of attributes. Now, if +we know nothing about bodies but the sensations they excite, we can mean +nothing by the attributes of bodies but sensations. Against this it has +been urged that, though we know nothing of sensible objects except the +sensations, the quality which we ascribe on the _ground_ of the +sensation may yet be a real hidden power or quality in the object, of +which the sensation is only the evidence. Seemingly, this doctrine +arises only from the tendency to suppose that there must be two +different things to answer to two names when not quite synonymous. +Quality and sensation are probably names for the same thing viewed in +different lights. The doctrine of an entity _per se_, called quality, is +a relic of the scholastic _occult causes_; the only intelligible cause +of sensation being the presence of the assemblage of phenomena, called +the _object_. Why the presence of the object causes the sensation, we +know not; and, granting an _occult cause_, we are still in the dark as +to how _that_ produces the effect. However, the question belongs to +metaphysics; and it suits this doctrine, as well as the opposed one, to +say that a quality has for its _foundation_ a sensation. + +Relations form the second class of attributes. In all cases of relation +there exists some fact into which the relatives enter as parties +concerned; and this is the _fundamentum relationis_. Whenever two things +are involved in some one fact, we may ascribe to them a relation +grounded on it, however general the fact may be. As, then, a quality is +an attribute based on the fact of a sensation, so a relation is an +attribute based on a fact into which two objects enter jointly. This +fact in both is always composed entirely of states of consciousness; and +this, whether it be complicated, as in many legal relations, or simple, +as in the relations expressed by _antecedent_ and _consequent_ and by +_simultaneous_, where the fact consists merely of the two things so +related, since the consciousness either of the succession or of the +simultaneousness of the two sensations which represent the things, is a +feeling not added to, but involved in _them_, being a condition under +which we must suppose things. And so, likewise, with the relations of +likeness and unlikeness. The feeling of these sometimes cannot be +analysed, when the _fundamentum relationis_ is, as in the case of two +simple sensations, e.g. two sensations of white, only the two sensations +themselves, the consequent feeling of their resemblance being, like that +of their succession or simultaneousness, apparently involved in the +sensations themselves. Sometimes, again, the likeness or unlikeness is +complex, and therefore can be analysed into simpler cases. In any case, +likeness or unlikeness must resolve itself into likeness or unlikeness +between states of our own or some other mind; and this, whether the +feeling of the resemblance or dissimilarity relate to bodies or to +attributes, since the former we know only through the sensations they +are supposed to excite, and the latter through the sensations on which +they are grounded. And so, again, when we say that two relations are +alike (one of the many senses of analogy), we simply assert resemblance +between the facts constituting the two _fundamenta relationis_. Several +relations, called by different names, are really cases of resemblance. +Thus, equality, i.e. the exact resemblance existing between things in +respect of their quantity, is often called identity. + +The _third_ species of attributes is Quantity. The assertion of likeness +or unlikeness in quantity, as in quality, is always founded on a +likeness or unlikeness in the sensations excited. What the difference is +all who have had the sensations know, but it cannot be explained to +those who never had them. + +In fine, all the attributes classed under Quality and Quantity are the +powers bodies have of exciting certain sensations. So, Relation +generally is but the power which an object has of joining its +correlative in producing the series of sensations, which is the only +sign of the existence of the fact on which they both are grounded. The +relations of succession and simultaneousness, indeed, are not based on +any fact (i.e. any feeling) distinct from the related objects. But these +relations are themselves states of consciousness; resemblance, for +example, being nothing but our feeling of resemblance: at least, we +ascribe these relations to objects or attributes simply because they +hold between the feelings which the objects excite and on which the +attributes are grounded. And as with the attributes of bodies, so also +those of minds are grounded on states of consciousness. Considered in +itself, we can predicate of a mind only the series of its own feelings: +e.g. by _devout_ we mean that the feelings implied in that word form an +oft-recurring part of the series of feelings filling up the sentient +existence of that mind. Again, attributes may be ascribed to a mind as +to a body, as grounded on the thoughts or emotions (not the sensations, +for only bodies excite them) which it excites in others: e.g. when we +call a character admirable, we mean that it causes feelings in us of +admiration. Sometimes, under one word really two attributes are +predicated, one a state of the mind, the other of other minds affected +by thinking of it: e.g. He is generous. Sometimes, even bodies have the +attribute of producing an emotion: e.g. That statue is beautiful. + +The general result is, that there are three chief kinds of nameable +things:--1. Feelings distinct from the objects exciting and the organs +supposed to convey them, and divisible into four classes, perceptions +being only a particular case of belief, which is itself a sort of +thought, while actions are only volitions followed by an effect. 2. +Substances, i.e. the unknown cause and the unknown recipient of our +sensations. 3. Attributes, subdivisible into Quality, Relation, +Quantity. Of these ([Greek: a]) qualities, like substances, are known +only by the states of consciousness which they excite, and on which they +are based, and by which alone, though they are treated as a distinct +class, they can be described. ([Greek: b]) Relations also, with four +exceptions, are based on some fact, i.e. a series of states of +consciousness. ([Greek: g]) Quantity is, in the same way, based on our +sensations. In short, all attributes are only our sensations and other +feelings, or something involved in them. We may, then, classify nameable +things thus:--1, Feelings; 2, Minds; 3, Bodies, together with the +properties whereby they are _popularly_ (though the evidence is very +deficient) supposed to excite sensations; 4, the relations of Succession +and Coexistence, Likeness and Unlikeness, which subsist really only +between states of consciousness. + +These four classes are a substitute for Aristotle's abortive Categories. +As they comprise all nameable things, every fact is made up of them or +some of them; those that are called _subjective_ facts being composed +wholly of feelings as such, and the _objective_ facts, though composed +wholly or partly of substances and attributes, being grounded on +corresponding subjective facts. + + + + +CHAPTER IV. + +PROPOSITIONS. + + +The copula is a mere sign of predication, though it is often confounded +with _to be_, the verb of existence (and that not merely by Greeks, but +even by moderns, whose larger experience how one word in one language +often answers to several in another, should have saved them from +thinking that things with a common name must have a common nature). The +_first_ division of propositions is into Affirmative and Negative, the +copula in the latter being _is not_. Hobbes and others, by joining the +_not_ to the predicate, made the latter what they call a _negative +name_. But as a negative name is one expressing the _absence_ of an +attribute, we thus in fact merely deny its presence, and therefore the +affirmative guise these thinkers give to negative propositions is only a +fiction. Again, _modal_ propositions cannot be reduced to the common +form by joining the modality to the predicate, and turning, e.g. The sun +_did_ rise, into, The sun is a thing having risen; for the past time is +not a particular kind of rising, and it affects not the predicate, but +the predication, i.e. the applicability of the predicate to the subject. +There are, however, certain cases in which the qualification may be +detached from the copula; e.g. in such expressions as, _may be_, _is +perhaps_; for, then we really do not mean to assert anything about the +fact, but only about the state of our mind about it, so that it is not +the predication which is affected: e.g. Caesar _may be_ dead, may +properly be rendered, I am not sure that he is alive. + +The _second_ division is into Simple and Complex. Several propositions +joined by a conjunction do not make a complex proposition. The +conjunction, so far from making the two one, adds another, as being an +abbreviation generally of an additional proposition: e.g. _and_ is an +abbreviation of one additional proposition, viz. We must think of the +two together; while _but_ is an abbreviation of two additional +propositions, viz. We must think of them together, and we must recollect +there is a contrast between them. But hypothetical propositions, i.e. +both disjunctives and conditionals, are true complex propositions, since +with several terms they contain but a single assertion. Thus, in, If the +Koran comes from God, Mahomet is God's prophet, we do not assert the +truth of either of the simple propositions therein contained (viz. the +Koran comes from God, and Mahomet is God's prophet), but only the +inferribility of one from the other. The only difference, then, between +a hypothetical and a categorical proposition, is that the former is +always an assertion about an assertion (though some categoricals are so +likewise; e.g. That the whole is greater than its parts, is an axiom). +Their conspicuous place in treatises on Logic arises from this attribute +which they predicate of a proposition (for a proposition, like other +things, has attributes), viz. its being an inference from something +else, being, with reference to Logic, its chief attribute. + +The _third_ common division is into Universal, Particular, Indefinite, +and Singular. A proposition whose subject is an individual name, even if +not a proper name, is singular, e.g. The founder of Rome was killed. In +particular propositions, if the part of the class meant by the _some_ +were specified, the proposition would become either singular, or +universal with a different subject including all the part. Indefinite in +Logic is a solecism like _doubtful gender_ in grammar, for the speaker +must mean to make either a particular or a universal assertion. + + + + +CHAPTER V. + +THE IMPORT OF PROPOSITIONS. + + +The object of an inquiry into the nature of propositions must be to +analyse, either, 1, the state of mind called belief, or 2, what is +believed. Philosophers have usually, but wrongly, thought the former, +i.e. an analysis of the act of judgment, the chief duty of Logic, +considering a proposition to consist in the denying or affirming one +_idea_ of another. True, we must have the two ideas in the mind +together, in order to believe the assertion about the two _things_; but +so we must also in order to disbelieve it. True also, that besides the +putting the ideas together, there may be a mental process; but this has +nothing to do with the import of propositions, since they are assertions +about things, i.e. facts of external nature, not about the ideas of +them, i.e. facts in our mental history. Logic has suffered from stress +being laid on the relation between the ideas rather than the phenomena, +nature thus coming to be studied by logicians second-hand, that is to +say, as represented in our minds. Our present object, therefore, must +be to investigate judgments, not judgment, and to inquire what it is +which we assert when we make a proposition. + +Hobbes (though he certainly often shows his belief that all propositions +are not merely about the meaning of words, and that general names are +given to things on account of their attributes) declares that what we +assert, is our belief that the subject and predicate are names of the +same thing. This is, indeed, a property of all true propositions, and +the only one true of all. But it is not the scientific definition of +propositions; for though the mere collocation which makes a proposition +a proposition, signifies only this, yet that _form_, combined with other +_matter_, conveys much more meaning. Hobbes's principle accounts _fully_ +only for propositions where both terms are proper names. He applied it +to others, through attending, like all nominalists, to the denotation, +and not the connotation of words, holding them to be, like proper names, +mere marks put upon individuals. But when saying that, e.g. Socrates is +wise, is a true proposition, because of the conformity of import between +the terms, he should have asked himself why _Socrates_ and _wise_ are +names of the same person. He ought to have seen that they are given to +the same person, not because of the intention of the maker of each word, +but from the resemblance of their connotation, since a word means +properly certain attributes, and, only secondarily, objects denoted by +it. What we really assert, therefore, in a proposition, is, that where +we find certain attributes, we shall find a certain other one, which is +a question not of the meaning of names, but of the laws of nature. + +Another theory virtually identical with Hobbes's, is that commonly +received, which makes predication consist in referring things to a +_class_; that is (since a class is only an indefinite number of +individuals denoted by a general name), in viewing them as some of those +to be called by that general name. This view is the basis of the _dictum +de omni et nullo_, on which is supposed to rest the validity of all +reasoning. Such a theory is an example of [Greek: hysteron proteron]: it +explains the cause by the effect, since the predicate cannot be known +for a class name which includes the subject, till several propositions +having it for predicate have been first assented to. This doctrine seems +to suppose all individuals to have been made into parcels, with the +common name outside; so that, to know if a general name can be +predicated correctly of the subject, we need only search the roll so +entitled. But the truth is, that general names are marks put, not upon +definite objects, but upon collections of objects ever fluctuating. We +may frame a class without knowing a single individual belonging to it: +the individual is placed in the class because the proposition is true; +the proposition is not made true by the individual being placed there. + +Analysis of different propositions shows what is the real import of +propositions not simply verbal. Thus, we find that even a proposition +with a proper name for subject, means to assert that an individual thing +has the attributes connoted by the predicate, the name being thought of +only as means for giving information of a physical fact. This is still +more the case in propositions with connotative subjects. In these the +denoted objects are indicated by some of their attributes, and the +assertion really is, that the predicate's set of attributes constantly +accompanies the subject's set. But as every attribute is grounded on +some fact or phenomenon, a proposition, when asserting the attendance of +one or some attributes on others, really asserts simply the attendance +of one phenomenon on another; e.g. When we say Man is mortal, we mean +that where certain physical and moral facts called humanity are found, +there also will be found the physical and moral facts called death. But +analysis shows that propositions assert other things besides (although +this is indeed their ordinary import) this coexistence or sequence of +two phenomena, viz. two states of consciousness. Assertions in +propositions about those unknowable entities (_nouemena_) which are the +hidden causes of phenomena, are made, indeed, only in virtue of the +knowable _phenomena_. Still, such propositions do, besides asserting the +sequence or coexistence of the phenomena, assert further the _existence_ +of the nouemena; and, moreover, in affirming the existence of a nouemenon, +which is an unknowable _cause_, they assert _causation_ also. Lastly, +propositions sometimes assert _resemblance_ between two phenomena. It is +not true that, as some contend, every proposition whose predicate is a +general name affirms resemblance to the other members of the class; for +such propositions generally assert only the possession by the subject of +certain common peculiarities; and the assertion would be true though +there were no members of the class besides those denoted by the +subject. Nevertheless, _resemblance alone_ is _sometimes_ predicated. +Thus, when individuals are put into a class as belonging to it, not +absolutely, but rather than to any other, the assertion is, not that +they have the attributes connoted, but that they resemble those having +them more than they do other objects. So, again, _only resemblance_ is +predicated, when, though the predicate is a class name, the class is +based on general unanalysable resemblance. The classes in question are +those of the simple feelings; the names of feelings being, like all +concrete general names, connotative, but only of a mere resemblance. + +In short, one of _five_ things, viz. Existence, Coexistence (or, to be +more particular, Order in Place), Sequence (or, more particularly, Order +in Time, which comprises also the _mere fact of Coexistence_), +Causation, and Resemblance, is asserted or denied in every proposition. +This division is an exhaustive classification with respect to all things +that can be believed. Although only propositions with concrete terms +have been spoken of, it is equally the fact that, in propositions with +an abstract term or terms, we predicate one of these same _five_ things. +There cannot be any difference in the import of these two classes of +propositions, since there is none in the import of their terms, for the +real signification of a concrete term resides in its connotation (so +that in a concrete proposition we really predicate an attribute), and +what the concrete term connotes forms the whole sense of the abstract. +Thus, all propositions with abstract terms can be turned into equivalent +ones with concrete, the new terms being either the names which connote +the attributes, or names of the facts which are the _fundamenta_ of the +attributes: e.g. Thoughtlessness is danger, is equivalent to, +Thoughtless actions (the _fundamentum_) are dangerous. + +Finally, as these _five_ are the only things affirmable, so are they the +only things deniable. + + + + +CHAPTER VI. + +PROPOSITIONS MERELY VERBAL. + + +The object of Logic is to find how propositions are to be proved. As +preliminary to this, it has been already shown that the Conceptualist +view of propositions, viz. that they assert a relation between two +ideas, and the Nominalist, that they assert agreement or disagreement +between the meanings of two names, are both wrong as general theories: +for that _generally_ the import of propositions is, to affirm or deny +respecting a phenomenon, or its hidden source, one of five kinds of +facts. There is, however, a class of propositions which relate not to +matter of fact, but to the meaning of names, and which, therefore, as +names and their meanings are arbitrary, admit not of truth or falsity, +but only of agreement or disagreement with usage. These _verbal_ +propositions are not only those in which both terms are proper names, +but also some, viz. _essential_ propositions, thought to be more closely +related to things than any others. The Aristotelians' belief that +objects are made what they are called by the inherence of a certain +_general substance_ in the individuals which get from it all their +essential properties, prevented even Porphyry (though more reasonable +than the mediaeval Realists) from seeing that the only difference between +altering a non-essential (or _accidental_) property, which, he says, +makes the thing [Greek: alloion], and altering an essential one, which +makes it [Greek: allo] (i.e. a different thing), is, that the latter +change makes the object change its name. But even when it was no longer +believed that there are real entities answering to general terms, the +doctrine based upon it, viz. that a thing's essence is that without +which the thing could neither be, nor be conceived to be, was still +generally held, till Locke convinced most thinkers that the supposed +essences of classes are simply the significations of their _names_. Yet +even Locke supposed that, though the essences of classes are _nominal_, +_individuals_ have _real_ essences, which, though unknown, are the +causes of their sensible properties. + +An accidental proposition (i.e. in which a property not connoted by the +subject is predicated of it) tacitly asserts the existence of a thing +corresponding to the subject; otherwise, such a proposition, as it does +not explain the name, would assert nothing at all. But an essential +proposition (i.e. in which a property connoted by the subject is +predicated of it) is identical. The only use of such propositions is to +_define_ words by unfolding the meaning involved in a name. When, as in +mathematics, important consequences seem to follow from them, such +really follow from the tacit assumption, through the ambiguity of the +copula, of the real existence of the _object_ named. + +Accidental propositions include, 1, those with a proper name for +subject, since an individual has no essence (although the schoolmen, +and rightly, according to their view of genera and species as entities +inhering in the individuals, attributed to the individual the essence of +his class); and, 2, all general or particular propositions in which the +predicate connotes any attribute not connoted by the subject. Accidental +propositions may be called _real_; they add to our knowledge. Their +import may be expressed (according as the attention is directed mainly, +either to what the proposition means, or to the way in which it is to be +used), either, by the formula: The attributes of the subject are always +(or never) accompanied by those signified by the predicate; or, by the +formula: The attributes of the subject are evidence, or a mark, of the +presence of those of the predicate. For the purposes of reasoning, since +propositions enter into _that_, not as ultimate results, but as means +for establishing other propositions, the latter formula is preferable. + + + + +CHAPTER VII. + +THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES. + + +It is merely an accident when general names are names of classes of real +objects: e.g. The unity of God, in the Christian sense, and the +non-existence of the things called dragons, do not prevent those names +being general names. The using a name to connote attributes, turns the +things, whether real or imaginary, into a class. But, in predicating the +name, we predicate only the attributes; and even when a name (as, e.g. +those in Cuvier's system) is introduced as a means of grouping certain +objects together, and not, as usually, as a means of predication, it +still signifies nothing but the possession of certain attributes. + +Classification (as resulting from the use of general language) is the +subject of the Aristotelians' Five Predicables, viz. _Genus_, _Species_, +_Differentia_, _Proprium_, _Accidens_. These are a division of general +names, not based on a distinction in their meaning, i.e. in the +attributes connoted, but on a distinction in the class denoted. They +express, not the meaning of the predicate itself, but its relation (a +varying one) to the subject. Commonly, the names of any two classes (or, +popularly, the classes themselves), one of which includes all the other +and more, are called respectively _genus_ and _species_. But the +Aristotelians, i.e. the schoolmen, meant by _differences in kind_ +(_genere_ or _specie_) something which was in its nature (and not merely +with reference to the connotation of the name) distinct from +_differences_ in the _accidents_. Now, it is the fact that, though a +fresh class may be founded on the smallest distinction in attributes, +yet that some classes have, to separate them from other classes, no +common attributes except those connoted by the name, while others have +innumerable common qualities (from which we have to select a few samples +for connotation) not referrible to a common source. The ends of language +and of classification would be subverted if the latter (not if the +former) sorts of _difference_ were disregarded. Now, it was these only +that the Aristotelians called _kinds_ (_genera_ or _species_), holding +_differences_ made up of _certain_ and _definite_ properties to be +_differences_ in the _accidents_ of things. In conformity with this +distinction--and it is a true one--any class, e.g. negro as opposed to +white man, may, according as physiology shall show the _differences_ to +be infinite or finite, be discovered to be a distinct _kind_ or +_species_ (though not according to the naturalist's construction of +_species_, as including all descended from the same stock), or merely a +subdivision of the _kind_ or _species_, Man. Among _kinds_, a _genus_ is +a class divisible into other _kinds_, though it may be itself a species +in reference to higher _genera_; that which is not so divisible, is an +individual's _proximate kind_ or _infima species_ (_species +praedicabilis_ and also _subjicibilis_), whose common properties must +include all the common properties of every other real _kind_ to which +the individual can be referred. + +The Aristotelians said that the _differentia_ must be of the _essence_ +of the subject. They vaguely understood, indeed, by the _essence_ of a +thing, that which makes it the _kind_ of thing that it is. But, as a +_kind_ is such from innumerable qualities not flowing from a common +source, logicians selected the qualities which make the thing be what it +is called, and termed these the essence, not merely of the _species_, +but, in the case of the _infima species_, of the individual also. Hence, +the distinction between the predicables, Differentia, Proprium, and +Accidens, is founded, not on the nature of things, but on the +connotation of names. The _specific difference_ is that which must be +added to the connotation of the _genus_ to complete the connotation of +the _species_. A _species_ may have various _differences_, according to +the principle of the particular classification. A _kind_, and not +merely a class, may be founded on any one of these, if there be a host +of properties behind, of which this one is the index, and not the +source. Sometimes a name has a technical as well as an ordinary +connotation (e.g. the name Man, in the Linnaean system, connotes a +certain number of incisor and canine teeth, instead of its usual +connotation of rationality and a certain general form); and then the +word is in fact ambiguous, i.e. two names. _Genus_ and _Differentia_ are +said to be of the essence; that is, the properties signified by them are +connoted by the name denoting the _species_. But both _proprium_ and +_accidens_ are said to be predicated of the species _accidentally_. A +proprium of the species, however, is predicated of the species +necessarily being an attribute, not indeed connoted by the name, but +following from an attribute connoted by it. It follows, either by way of +demonstration as a conclusion from premisses, or by way of causation as +effect from cause; but, in either case, _necessarily_. Inseparable +accidents, on the other hand, are attributes universal, so far as we +know, to the species (e.g. blackness to crows), but not _necessary_; +i.e. neither involved in the meaning of the name of the species, nor +following from attributes which are. Separable accidents do not belong +to all, or if to all, not at all times (e.g. the fact of being born, to +man), and sometimes are not constant even in the same individual (e.g. +to be hot or cold). + + + + +CHAPTER VIII. + +DEFINITION. + + +A definition is a proposition declaring either the special or the +ordinary meaning, i.e. in the case of connotative names, the +connotation, of a word. This may be effected by stating directly the +attributes connoted; but it is more usual to predicate of the subject of +definition one name of synonymous, or several which, when combined, are +of equivalent, connotation. So that, a definition of a name being thus +generally the sum total of the essential propositions which could be +framed with that name for subject, is really, as Condillac says, an +_analysis_. Even when a name connotes only a single attribute, it (and +also the corresponding abstract name itself) can yet be defined (in this +sense of being analysed or resolved into its elements) by declaring the +connotation of that attribute, whether, if it be a union of several +attributes (e.g. Humanity), by enumerating them, or, if only one (e.g. +Eloquence), by dissecting the fact which is its foundation. Even when +the fact which is the foundation of the attribute is a simple feeling, +and therefore incapable of analysis, still, if the simple feeling have a +name, the attribute and the object possessing it may be defined by +reference to the fact: e.g. a white object is definable as one exciting +the sensation of white; and whiteness, as the power of exciting that +sensation. The only names, abstract or concrete, incapable of analysis, +and therefore of definition, are proper names, as having no meaning, and +also the names of the simple feelings themselves, since these can be +explained only by the resemblance of the feelings to former feelings +called by the same or by an exactly synonymous name, which consequently +equally needs definition. + +Though the only accurate definition is one declaring all the facts +involved in the name, i.e. its connotation, men are usually satisfied +with anything which will serve as an index to its denotation, so as to +guard them from applying it inconsistently. This was the object of +logicians when they laid down that a species must be defined _per genus +et differentiam_, meaning by the _differentia one_ attribute included in +the essence, i.e. in the connotation. And, in fact, one attribute, e.g. +in defining man, Rationality (Swift's Houyhnhms having not been as yet +discovered) often does sufficiently mark out the objects denoted. But, +besides that a definition of this kind ought, in order to be complete, +to be _per genus et differentias_, i.e. by _all_ the connoted attributes +not implied in the name of the _genus_, still, even if all were given, a +_summum genus_ could not be so defined, since it has no superior genus. +And for merely marking out the objects denoted, Description, in which +none of the connoted attributes are given, answers as well as logicians' +so-called _essential_ definition. In Description, any one or a +combination of attributes may be given, the object being to make it +exactly coextensive with the name, so as to be predicable of the same +things. Such a description may be turned into an essential definition by +a change of the connotation (not the denotation) of the name; and, in +fact, thus are manufactured almost all scientific definitions, which, +being landmarks of classification, and not meant to declare the meaning +of the name (though, in fact, they do declare it in its new use), are +ever being modified (as is the definition of a science itself) with the +advance of knowledge. Thus, a technical definition helps to expound the +artificial classification from which it grows; but ordinary definition +cannot expound, as the Aristotelians fancied it could, the natural +classification of things, i.e. explain their division into _kinds_, and +the relations among the _kinds_: for the properties of every _kind_ are +innumerable, and all that definition can do is to state the connotation +of the name. + +Both these two modes, viz. the essential but incomplete Definition, and +the accidental, or Description, are imperfect; but the Realists' +distinction between definition of names and of things is quite +erroneous. Their doctrine is now exploded; but many propositions +consistent with it alone (e.g. that the science of geometry is deduced +from definitions) have been retained by Nominalists, such as Hobbes. +Really a definition, as such, cannot explain a thing's nature, being +merely an identical proposition explaining the meaning of a word. But +definitions of names _known to be names of really existing objects_, as +in geometry, include two propositions, one a definition and another a +postulate. The latter affirms the existence of a thing answering to the +name. The science is based on the postulates (whether they rest on +intuition or proof), for the demonstration appeals to them alone, and +not on the definitions, which indeed might, though at some cost of +brevity, be dispensed with entirely. It has been argued that, at any +rate, definitions are premisses of science, _provided_ they give such +meanings to terms as suit existing things: but even so, the inference +would obviously be from the existence, not of the name which means, but +of the thing which has the properties. + +One reason for the belief that demonstrative truths follow from the +definitions, not from the postulates, was because the postulates are +never quite true (though in reality so much of them is true as is true +of the conclusions). Philosophers, therefore, searching for something +more accurately true, surmised that definitions must be statements and +analyses, neither of words nor of things, as such, but of ideas; and +they supposed the subject-matter of all demonstrative sciences to be +abstractions of the mind. But even allowing this (though, in fact, the +mind cannot so abstract one property, e.g. length, from all others; it +only _attends_ to the one exclusively), yet the conclusions would still +follow, not from the mere definitions, but from the postulates of the +real existence of the ideas. + +Definitions, in short, are of names, not things: yet they are not +therefore arbitrary; and to determine what _should be_ the meaning of a +term, it is often necessary to look at the objects. The obscurity as to +the connotation arises through the objects being named before the +attributes (though it is from the latter that the concrete general terms +get their meaning), and through the same name being popularly applied to +different objects on the ground of general resemblance, without any +distinct perception of their common qualities, especially when these are +complex. The philosopher, indeed, uses general names with a definite +connotation; but philosophers do not make language--it grows: so that, +by degrees, the same name often ceases to connote even general +resemblance. The object in remodelling language is to discover if the +things denoted have common qualities, i.e. if they form a class; and, if +they do not, to form one artificially for them. A language's rude +classifications often serve, when retouched, for philosophy. The +transitions in signification, which often go on till the different +members of the group seem to connote nought in common, indicate, at any +rate, a striking resemblance among the objects denoted, and are +frequently an index to a real connection; so that arguments turning +apparently on the double meaning of a term, may perhaps depend on the +connection of two ideas. To ascertain the link of connection, and to +procure for the name a distinct connotation, the resemblances of things +must be considered. Till the name has got a distinct connotation, it +cannot be defined. The philosopher chooses for his connotation of the +name the attributes most important, either directly, or as the +differentiae leading to the most interesting propria. The enquiry into +the more hidden agreement on which these obvious agreements depend, +often itself arises under the guise of enquiries into the definition of +a name. + + + + +BOOK II. + +REASONING. + + + + +CHAPTER I. + +INFERENCE, OR REASONING IN GENERAL. + + +The preceding book treated, not of the proper subject of logic, viz. the +nature of proof, but of assertion. Assertions (as, e.g. definitions) +which relate to the meaning of words, are, since _that_ is arbitrary, +incapable of truth or falsehood, and therefore of proof or disproof. But +there are assertions which are subjects for proof or disproof, viz. the +propositions (the real, and not the verbal) whose subject is some fact +of consciousness, or its hidden cause, about which is predicated, in the +affirmative or negative, one of five things, viz. existence, order in +place, order in time, causation, resemblance: in which, in short, it is +asserted, that some given subject does or does not possess some +attribute, or that two attributes, or sets of attributes, do or do not +(constantly or occasionally) coexist. + +A proposition not believed on its own evidence, but inferred from +another, is said to be _proved_; and this process of inferring, whether +syllogistically or not, is _reasoning_. But whenever, as in the +deduction of a particular from a universal, or, in Conversion, the +assertion in the new proposition is the same as the whole or part of +the assertion in the original proposition, the inference is only +apparent; and such processes, however useful for cultivating a habit of +detecting quickly the concealed identity of assertions, are not +reasoning. + +Reasoning, or Inference, properly so called, is, 1, Induction, when a +proposition is inferred from another, which, whether particular or +general, is less general than itself; 2, Ratiocination, or Syllogism, +when a proposition is inferred from others equally or more general; 3, a +kind which falls under neither of these descriptions, yet is the basis +of both. + + + + +CHAPTER II. + +RATIOCINATION, OR SYLLOGISM. + + +The syllogistic figures are determined by the position of the middle +term. There are four, or, if the fourth be classed under the first, +three. But syllogisms in the other figures can be reduced to the first +by conversion. Such reduction may not indeed be necessary, for different +arguments are suited to different figures; the first figure, says +Lambert, being best adapted to the discovery or proof of the properties +of things; the second, of the distinctions between things; the third, of +instances and exceptions; the fourth, to the discovery or exclusion of +the different species of a genus. Still, as the premisses of the first +figure, got by reduction, are really the same as the original ones, and +as the only arguments of great scientific importance, viz. those in +which the conclusion is a universal affirmative, can be proved in the +first figure alone, it is best to hold that the two elementary forms of +the first figure are the universal types, the one in affirmatives, the +other in negatives, of all correct ratiocination. + +The _dictum de omni et nullo_, viz. that whatever can be affirmed or +denied of a class can be affirmed or denied of everything included in +the class, which is a true account generalised of the constituent parts +of the syllogism in the first figure, was thought the basis of the +syllogistic theory. The fact is, that when universals were supposed to +have an independent objective existence, this dictum stated a supposed +law, viz. that the _substantia secunda_ formed part of the properties of +each individual substance bearing the name. But, now that we know that a +class or universal is nothing but the individuals in the class, the +dictum is nothing but the identical proposition, that whatever is true +of certain objects is true of each of them, and, to mean anything, must +be considered, not as an axiom, but as a circuitous definition of the +word _class_. + +It was the attempt to combine the nominalist view of the signification +of general terms with the retention of the dictum as the basis of all +reasoning, that led to the self-contradictory theories disguised under +the ultra-nominalism of Hobbes and Condillac, the ontology of the later +Kantians, and (in a less degree) the abstract ideas of Locke. It was +fancied that the process of inferring new truths was only the +substitution of one arbitrary sign for another; and Condillac even +described science as _une langue bien faite_. But language merely +enables us to remember and impart our thoughts; it strengthens, like an +artificial memory, our power of thought, and is thought's powerful +instrument, but not its exclusive subject. If, indeed, propositions in a +syllogism did nothing but refer something to or exclude it from a class, +then certainly syllogisms might have the dictum for their basis, and +import only that the classification is consistent with itself. But such +is not the primary object of propositions (and it is on this account, as +well as because men will never be persuaded in common discourse to +_quantify_ the predicate, that Mr. De Morgan's or Sir William Hamilton's +_quantification of the predicate_ is a device of little value). What is +asserted in every proposition which conveys real knowledge, is a fact +dependent, not on artificial classification, but on the laws of nature; +and as ratiocination is a mode of gaining real knowledge, the principle +or law of all syllogisms, with propositions not purely verbal, must be, +for affirmative syllogisms, that; Things coexisting with the same thing +coexist with one another; and for negative, that; A thing coexisting +with another, with which a third thing does not coexist, does not +coexist with that third thing. But if (see _supra_, p. 26) propositions +(and, of course, all combinations of them) be regarded, not +speculatively, as portions of our knowledge of nature, but as memoranda +for practical guidance, to enable us, when we know that a thing has one +of two attributes, to infer it has the other, these two axioms may be +translated into one, viz. Whatever has any mark has that which it is a +mark of; or, if both premisses are universal, Whatever is a mark of any +mark, is a mark of that of which this last is a mark. + + + + +CHAPTER III. + +THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM. + + +The question is, whether the syllogistic process is one of inference, +i.e. a process from the known to the unknown. Its assailants say, and +truly, that in every syllogism, considered as an argument to prove the +conclusion, there is a _petitio principii_; and Dr. Whately's defence of +it, that its object is to unfold assertions wrapped up and implied (i.e. +in fact, _asserted unconsciously_) in those with which we set out, +represents it as a sort of trap. Yet, though no reasoning from generals +to particulars can, as such, prove anything, the conclusion _is_ a _bona +fide_ inference, though not an inference from the general proposition. +The general proposition (i.e. in the first figure, the major premiss) +contains not only a record of many particular facts which we have +observed or inferred, but also instructions for making inferences in +unforeseen cases. Thus the inference is completed in the major premiss; +and the rest of the syllogism serves only to decipher, as it were, our +own notes. + +Dr. Whately fails to make out that syllogising, i.e. reasoning from +generals to particulars, is the _only_ mode of reasoning. No additional +evidence is gained by interpolating a general proposition, and therefore +we may, if we please, reason directly from the individual cases, since +it is on these alone that the general proposition, if made, would rest. +Indeed, thus are in fact drawn, as well the inferences of children and +savages, and of animals (which latter having no signs, can frame no +general propositions), as even those drawn by grown men generally, from +personal experience, and particularly the inferences of men of high +practical genius, who, not having been trained to generalise, can apply, +but not state, their principles of action. Even when we have general +propositions we need not use them. Thus Dugald Stewart showed that the +axioms need not be expressly adverted to in order to make good the +demonstrations in Euclid; though he held, inconsistently, that the +definitions must be. All general propositions, whether called axioms, or +definitions, or laws of nature, are merely abridged statements of the +particular facts, which, as occasion arises, we either think we may +proceed on as proved, or intend to assume. + +In short, all inference is from particulars to particulars; and general +propositions are both registers or memoranda of such former inferences, +and also short formulae for making more. The major premiss is such a +formula; and the conclusion is an inference drawn, not from, but +according to that formula. The _actual_ premisses are the particular +facts whence the general proposition was collected inductively; and the +syllogistic rules are to guide us in reading the register, so as to +ascertain what it was that we formerly thought might be inferred from +those facts. Even where ratiocination is independent of induction, as, +when we accept from a man of science the doctrine that all A is B; or +from a legislator, the law that all men shall do this or that, the +operation of drawing thence any particular conclusion is a process, not +of inference, but of interpretation. In fact, whether the premisses are +given by authority, or derived from our own (or predecessors') +observation, the object is always simply to interpret, by reference to +certain marks, an intention, whether that of the propounder of the +principle or enactment, or that which we or our predecessors had when we +framed the general proposition, so that we may draw no inferences that +were not _intended_ to be drawn. We assent to the conclusion in a +syllogism on account of its consistency with what we interpret to have +been the intention of the framer of the major premiss, and not, as Dr. +Whately held, because the supposition of a false conclusion from the +premisses involves a contradiction, since, in fact, the denial, e.g. +that an individual now living will die, is not _in terms_ contradictory +to the assertion that his ancestors and their contemporaries (to which +the general proposition, as a record of facts, really amounts) have all +died. + +But the syllogistic form, though the process of inference, which there +always is when a syllogism is used, lies not in this form, but in the +act of generalisation, is yet a great collateral security for the +correctness of that generalisation. When all possible inferences from a +given set of particulars are thrown into one general expression (and, if +the particulars support one inference, they always will support an +indefinite number), we are more likely both to feel the need of weighing +carefully the sufficiency of the experience, and also, through seeing +that the general proposition would equally support some conclusion which +we _know_ to be false, to detect any defect in the evidence, which, from +bias or negligence, we might otherwise have overlooked. But the +syllogistic form, besides being useful (and, when the validity of the +reasoning is doubtful, even indispensable) for verifying arguments, has +the acknowledged merit of all general language, that it enables us to +make an induction once for all. We _can_, indeed, and in simple cases +habitually _do_, reason straight from particulars; but in cases at all +complicated, all but the most sagacious of men, and they also, unless +their experience readily supplied them with parallel instances, would be +as helpless as the brutes. The only counterbalancing danger is, that +general inferences from insufficient premisses may become hardened into +general maxims, and escape being confronted with the particulars. + +The major premiss is not really part of the argument. Brown saw that +there would be a _petitio principii_ if it were. He, therefore, +contended that the conclusion in reasoning follows from the minor +premiss alone, thus suppressing the appeal to experience. He argued, +that to reason is merely to analyse our general notions or abstract +ideas, and that, _provided_ that the relation between the two ideas, +e.g. of _man_ and of _mortal_, has been first perceived, we can evolve +the one directly from the other. But (to waive the error that a +proposition relates to ideas instead of things), besides that this +_proviso_ is itself a surrender of the doctrine that an argument +consists simply of the minor and the conclusion, the perception of the +relation between two ideas, one of which is not implied in the name of +the other, must obviously be the result, not of analysis, but of +experience. In fact, both the minor premiss, and also the expression of +our former experience, must _both_ be present in our reasonings, or the +conclusion will not follow. Thus, it appears that the universal type of +the reasoning process is: Certain individuals possess (as I or others +have observed) a given attribute; An individual resembles the former in +certain other attributes: Therefore (the conclusion, however, not being +conclusive from its form, as is the conclusion in a syllogism, but +requiring to be sanctioned by the canons of induction) he resembles them +also in the given attribute. But, though this, and not the syllogistic, +is the universal type of reasoning, yet the syllogistic process is a +useful test of inferences. It is expedient, _first_, to ascertain +generally what attributes are marks of a certain other attribute, so as, +subsequently, to have to consider, _secondly_, only whether any given +individuals have those former marks. Every process, then, by which +anything is inferred respecting an unobserved case, we will consider to +consist of both these last-mentioned processes. Both are equally +induction; but the name may be conveniently confined to the process of +establishing the general formula, while the interpretation of this will +be called 'Deduction.' + + + + +CHAPTER IV. + +TRAINS OF REASONING, AND DEDUCTIVE SCIENCES. + + +The minor premiss always asserts a resemblance between a new case and +cases previously known. When this resemblance is not obvious to the +senses, or ascertainable at once by direct observation, but is itself +matter of inference, the conclusion is the result of a train of +reasoning. However, even then the conclusion is really the result of +induction, the only difference being that there are two or more +inductions instead of one. The inference is still from particulars to +particulars, though drawn in conformity, not to one, but to several +formulae. This need of several formulae arises merely from the fact that +the marks by which we perceive that an inference can be drawn (and of +which marks the formulae are records) happen to be recognisable, not +directly, but only through the medium of other marks, which were, by a +previous induction, collected to be marks of them. + +All reasoning, then, is induction: but the difficulties in sciences +often lie (as, e.g. in geometry, where the inductions are the simple +ones of which the axioms and a few definitions are the formulae) not at +all in the inductions, but only in the formation of trains of reasoning +to prove the minors; that is, in so combining a few simple inductions as +to bring a new case, by means of one induction within which it evidently +falls, within others in which it cannot be directly seen to be included. +In proportion as this is more or less completely effected (that is, in +proportion as we are able to discover marks of marks), a science, though +always remaining inductive, tends to become also _deductive_, and, to +the same extent, to cease to be one of the _experimental_ sciences, in +which, as still in chemistry, though no longer in mechanics, optics, +hydrostatics, acoustics, thermology, and astronomy, each generalisation +rests on a special induction, and the reasonings consist but of one step +each. + +An experimental science may become deductive by the mere progress of +experiment. The mere connecting together of a few detached +generalisations, or even the discovery of a great generalisation working +only in a limited sphere, as, e.g. the doctrine of chemical equivalents, +does not make a science deductive as a whole; but a science is thus +transformed when some comprehensive induction is discovered connecting +hosts of formerly isolated inductions, as, e.g. when Newton showed that +the motions of all the bodies in the solar system (though each motion +had been separately inferred and from separate marks) are all marks of +one like movement. Sciences have become deductive usually through its +being shown, either by deduction or by direct experiment, that the +varieties of some phenomenon in them uniformly attend upon those of a +better known phenomenon, e.g. every variety of sound, on a distinct +variety of oscillatory motion. The science of number has been the grand +agent in thus making sciences deductive. The truths of numbers are, +indeed, affirmable of all things only in respect of their quantity; but +since the variations of _quality_ in various classes of phenomena have +(e.g. in mechanics and in astronomy) been found to correspond regularly +to variations of _quantity_ in the same or some other phenomena, every +mathematical formula applicable to quantities so varying becomes a mark +of a corresponding general truth respecting the accompanying variations +in quality; and as the science of quantity is, so far as a science can +be, quite deductive, the theory of that special kind of qualities +becomes so likewise. It was thus that Descartes and Clairaut made +geometry, which was already partially deductive, still more so, by +pointing out the correspondence between geometrical and algebraical +properties. + + + + +CHAPTERS V. AND VI. + +DEMONSTRATION AND NECESSARY TRUTHS. + + +All sciences are based on induction; yet some, e.g. mathematics, and +commonly also those branches of natural philosophy which have been made +deductive through mathematics, are called Exact Sciences, and systems of +Necessary Truth. Now, their necessity, and even their alleged certainty, +are illusions. For the conclusions, e.g. of geometry, flow only +seemingly from the definitions (since from definitions, as such, only +propositions about the meaning of words can be deduced): really, they +flow from an implied assumption of the existence of real things +corresponding to the definitions. But, besides that the existence of +such things is not actual or possible consistently with the constitution +of the earth, neither can they even be _conceived_ as existing. In fact, +geometrical points, lines, circles, and squares, are simply copies of +those in nature, to a part alone of which we choose to _attend_; and the +definitions are merely some of our first generalisations about these +natural objects, which being, though equally true of all, not exactly +true of any one, must, actually, when extended to cases where the error +would be appreciable (e.g. to lines of perceptible breadth), be +corrected by the joining to them of new propositions about the +aberration. The exact correspondence, then, between the facts and those +first principles of geometry which are involved in the so-called +definitions, is a fiction, and is merely _supposed_. Geometry has, +indeed (what Dugald Stewart did not perceive), some first principles +which are true without any mixture of hypothesis, viz. the axioms, as +well those which are indemonstrable (e.g. Two straight lines cannot +enclose a space) as also the demonstrable ones; and so have all sciences +some exactly true general propositions: e.g. Mechanics has the first law +of motion. But, generally, the necessity of the conclusions in geometry +consists only in their following necessarily from certain _hypotheses_, +for which same reason the ancients styled the conclusions of all +deductive sciences _necessary_. That the hypotheses, which form part of +the premisses of geometry, must, as Dr. Whewell says, not be +arbitrary--that is, that in their positive part they are observed facts, +and only in their negative part hypothetical--happens simply because our +aim in geometry is to deduce conclusions which may be true of real +objects: for, when our object in reasoning is not to investigate, but to +illustrate truths, arbitrary hypotheses (e.g. the operation of British +political principles in Utopia) are quite legitimate. + +The ground of our belief in axioms is a disputed point, and one which, +through the belief arising too early to be traced by the believer's own +recollection, or by other persons' observation, cannot be settled by +reference to actual dates. The axioms are really only generalisations +from experience. Dr. Whewell, however, and others think that, though +suggested, they are not proved by experience, and that their truth is +recognised _a priori_ by the constitution of the mind as soon as the +meaning of the proposition is understood. But this assumption of an _a +priori_ recognition is gratuitous. It has never been shown that there is +anything in the facts inconsistent with the view that the recognition of +the truth of the axioms, however exceptionally complete and instant, +originates simply in experience, equally with the recognition of +ordinary physical generalisations. Thus, that we see a property of +geometrical forms to be true, without inspection of the material forms, +is fully explained by the capacity of geometrical forms of being painted +in the imagination with a distinctness equal to reality, and by the fact +that experience has informed us of that capacity; so that a conclusion +on the faith of the imaginary forms is really an induction from +observation. Then, again, there is nothing inconsistent with the theory +that we learn by experience the truth of the axioms, in the fact that +they are conceived by the mind as universally and necessarily true, that +is, that we cannot figure them to ourselves as being false. Our capacity +or incapacity of conceiving depends on our associations. Educated minds +can break up their associations more easily than the uneducated; but +even the former not entirely at will, even when, as is proved later, +they are erroneous. The Greeks, from ignorance of foreign languages, +believed in an inherent connection between names and things. Even Newton +imagined the existence of a subtle ether between the sun and bodies on +which it acts, because, like his rivals the Cartesians, he could not +conceive a body acting where it is not. Indeed, inconceivableness +depends so completely on the accident of our mental habits, that it is +the essence of scientific triumphs to make the contraries of once +inconceivable views themselves appear inconceivable. For instance, +suppositions opposed even to laws so recently discovered as those of +chemical composition appear to Dr. Whewell himself to be inconceivable. +What wonder, then, that an acquired incapacity should be mistaken for a +natural one, when not merely (as in the attempt to conceive space or +time as finite) does experience afford no model on which to shape an +opposed conception, but when, as in geometry, we are unable even to call +up the geometrical ideas (which, being impressions of form, exactly +resemble, as has been already remarked, their prototypes), e.g. of two +straight lines, in order to try to conceive them inclosing a space, +without, by the very act, repeating the scientific experiment which +establishes the contrary. + +Since, then, the axioms and the misnamed definitions are but inductions +from experience, and since the definitions are only hypothetically true, +the deductive or demonstrative sciences--of which these axioms and +definitions form together the first principles--must really be +themselves inductive and hypothetical. Indeed, it is to the fact that +the results are thus only conditionally true, that the necessity and +certainty ascribed to demonstration are due. + +It is so even with the Science of Number, i.e. arithmetic and algebra. +But here the truth has been hidden through the errors of two opposite +schools; for while many held the truths in this science to be _a +priori_, others paradoxically considered them to be merely verbal, and +every process to be simply a succession of changes in terminology, by +which equivalent expressions are substituted one for another. The excuse +for such a theory as this latter was, that in arithmetic and algebra we +carry no ideas with us (not even, as in a geometrical demonstration, a +mental diagram) from the beginning, when the premisses are translated +into signs, till the end, when the conclusion is translated back into +things. But, though this is so, yet in every step of the calculation, +there is a real inference of facts from facts: but it is disguised by +the comprehensive nature of the induction, and the consequent generality +of the language. For numbers, though they must be numbers of something, +may be numbers of anything; and therefore, as we need not, when using an +algebraical symbol (which represents all numbers without distinction), +or an arithmetical number, picture to ourselves all that it stands for, +we may picture to ourselves (and this not as a sign of things, but as +being itself a thing) the number or symbol itself as conveniently as any +other single thing. That we are conscious of the numbers or symbols, in +their character of things, and not of mere signs, is shown by the fact +that our whole process of reasoning is carried on by predicating of them +the properties of things. + +Another reason why the propositions in arithmetic and algebra have been +thought merely verbal, is that they seem to be _identical_ propositions. +But in 'Two pebbles and one pebble are equal to three pebbles,' equality +but not identity is affirmed; the subject and predicate, though names of +the same objects, being names of them in different states, that is, as +producing different impressions on the senses. It is on such inductive +truths, resting on the evidence of sense, that the Science of Number is +based; and it is, therefore, like the other deductive sciences, an +inductive science. It is also, like them, hypothetical. Its inductions +are the definitions (which, as in geometry, assert a fact as well as +explain a name) of the numbers, and two axioms, viz. The sums of equals +are equal; the differences of equals are equal. These axioms, and +so-called definitions are themselves exactly, and not merely +hypothetically, true. Yet the conclusions are true only on the +assumption that, 1 = 1, i.e. that all the numbers are numbers of the +same or equal units. Otherwise, the certainty in arithmetical processes, +as in those of geometry or mechanics, is not _mathematical_, i.e. +unconditional certainty, but only certainty of inference. It is the +enquiry (which can be gone through once for all) into the inferences +which can be drawn from assumptions, which properly constitutes all +demonstrative science. + +New conclusions may be got as well from fictitious as from real +inductions; and this is even consciously done, viz. in the _reductio ad +absurdum_, in order to show the falsity of an assumption. It has even +been argued that all ratiocination rests, in the last resort, on this +process. But as this is itself syllogistic, it is useless, as a proof of +a syllogism, against a man who denies the validity of this kind of +reasoning process itself. Such a man cannot in fact be forced to a +contradiction in terms, but only to a contradiction, or rather an +infringement, of the fundamental maxim of ratiocination, viz. 'Whatever +has a mark, has what it is a mark of;' and, since it is only by +admitting premisses, and yet rejecting a conclusion from them, that this +axiom is infringed, consequently nothing is _necessary_ except the +connection between a conclusion and premisses. + + + + +BOOK III. + +INDUCTION. + + + + +CHAPTER I. + +PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL. + + +As all knowledge not intuitive comes exclusively from inductions, +induction is the main topic of Logic; and yet neither have +metaphysicians analysed this operation with a view to practice, nor, on +the other hand, have discoverers in physics cared to generalise the +methods they employed. + +Inferences are equally _inductive_, whether, as in science, which needs +its conclusions for record, not for instant use, they pass through the +intermediate stage of a general proposition (to which class Dr. Whewell, +without sanction from facts, or from the usage of Reid and Stewart, the +founders of modern English metaphysical terminology, limits the term +induction), or are drawn direct from particulars to a supposed parallel +case. Neither does it make any difference in the _character_ of the +induction, whether the process be experiment or ratiocination, and +whether the object be to infer a general proposition or an individual +fact. That, in the latter case, the difficulty of the practical +enquiries, e.g. of a judge or an advocate, lies chiefly in selecting +from among all approved general propositions those inductions which suit +his case (just as, even in deductive sciences, the ascertaining of the +inductions is easy, their combination to solve a problem hard) is not to +the point: the legitimacy of the inductions so selected must at all +events be tried by the same test as a new general truth in science. +Induction, then, may be treated here as though it were the operation of +discovering and proving general propositions; but this is so only +because the evidence which justifies an inference respecting one unknown +case, would justify a like inference about a whole class, and is really +only another form of the same process: because, in short, the logic of +science is the universal logic applicable to all human enquiries. + + + + +CHAPTER II. + +INDUCTIONS IMPROPERLY SO CALLED. + + +Induction is the process by which what is true at certain times, or of +certain individuals, is inferred to be true in like circumstances at all +times, or of a whole class. There must be an inference from the known to +the unknown, and not merely from a less to a more general expression. +Consequently, there is no valid induction, 1, in those cases laid down +in the common works on Logic as the only perfect instances of induction, +viz. where what we affirm of the class has already been ascertained to +be true of each individual in it, and in which the seemingly general +proposition in the conclusion is simply a number of singular +propositions written in an abridged form; or, 2, when, as often in +mathematics, the conclusion, though really general, is a mere summing up +of the different propositions from which it is drawn (whether actually +ascertained, or, as in the case of the uncalculated terms of an +arithmetical series, when once its law is known, readily to be +understood); or, 3, when the several parts of a complex phenomenon, +which are only capable of being observed separately, have been pieced +together by one conception, and made, as it were, one fact represented +in a single proposition. + +Dr. Whewell sets out this last operation, which he terms the +_colligation of facts_, as induction, and even as the type of induction +generally. But, though induction is always colligation, or (as we may, +with equal accuracy, characterise such a general expression obtained by +abstraction simply connecting observed facts by means of common +characters) _description_, colligation, or description, as such, though +a necessary preparation for induction, is not induction. Induction +explains and predicts (and, as an incident of these powers, describes). +Different explanations collected by real induction from supposed +parallel cases (e.g. the Newtonian and the _Impact_ doctrines as to the +motions of the heavenly bodies), or different predictions, i.e. +different determinations of the conditions under which similar facts may +be expected again to occur (e.g. the stating that the position of one +planet or satellite so as to overshadow another, and, on the other hand, +that the impending over mankind of some great calamity, is the condition +of an eclipse), cannot be true together. But, for a colligation to be +correct, it is enough that it enables the mind to represent to itself as +a whole all the separate facts ascertained at a given time, so that +successive tentative descriptions of a phenomenon, got by guessing till +a guess is found which tallies with the facts, may, though conflicting +(e.g. the theories respecting the motions of the heavenly bodies), be +_all_ correct _so far as they go_. Induction is proof, the inferring +something unobserved from something observed; and to provide a proper +test of proof is the special purpose of inductive logic. But colligation +simply sums up the facts observed, as seen under a new point of view. +Dr. Whewell contends that, besides the sum of the facts, colligation +introduces, as a principle of connection, a conception of the mind not +existing in the facts. But, in fact, it is only because this conception +is a copy of something in the facts, although our senses are too weak to +recognise it directly, that the facts are rightly classed under the +conception. The conception is often even got by abstraction from the +facts which it colligates; but also when it is a hypothesis, borrowed +from strange phenomena, it still is accepted as true only because found +actually, and as a fact, whatever the origin of the knowledge of the +fact, to fit and to describe as a whole the separate observations. Thus, +though Kepler's consequent inference that, _because_ the orbit of a +planet is an ellipse, the planet would _continue_ to revolve in that +same ellipse, was an induction, his previous application of the +conception of an ellipse, abstracted from other phenomena, to sum up his +direct observations of the successive positions occupied by the +different planets, and thus to describe their orbits, was no induction. +It altered only the _predicate_, changing--The successive places of, +e.g. Mars, are A, B, C, and so forth, into--The successive places of, +e.g. Mars, are points in an ellipse: whereas induction always widens the +_subject_. + + + + +CHAPTER III. + +THE GROUND OF INDUCTION. + + +Induction is generalisation from experience. It assumes, that whatever +is true in any one case, is true in all cases of a certain description, +whether past, present, or future (and not merely in future cases, as is +wrongly implied in the statement by Reid's and Stewart's school, that +the principle of induction is 'our intuitive conviction that the future +will resemble the past'). It assumes, in short, that the course of +nature is uniform, that is, that all things take place according to +general laws. But this general axiom of induction, though by it were +discovered the obscure laws of nature, is no explanation of the +inductive process, but is itself an induction (not, as some think, an +intuitive principle which experience _verifies_ only), and is arrived at +after many separate phenomena have been first observed to take place +according to general laws. It does not, then, _prove_ all other +inductions. But it is a _condition_ of their proof. For any induction +can be turned into a syllogism by supplying a major premiss, viz. What +is true of this, that, &c. is true of the whole class; and the process +by which we arrive at this immediate major may be itself represented by +another syllogism or train of syllogisms, the major of the ultimate +syllogism, and which therefore is the warrant for the immediate major, +being this axiom, viz. that there is uniformity, at all events, in the +class of phenomena to which the induction relates, and a uniformity +which, if not foreknown, may now be known. + +But though the course of nature is uniform, it is also infinitely +various. Hence there is no certainty in the induction in use with the +ancients, and all non-scientific men, and which Bacon attacked, viz. +'Inductio per enumerationem simplicem, ubi non reperitur instantia +contradictoria'--_unless_, as in a few cases, we must have known of the +contradictory instances if existing. The scientific theory of induction +alone can show why a general law of nature may sometimes, as when the +chemist first discovers the existence and properties of a before unknown +substance, be inferred from a single instance, and sometimes (e.g. the +blackness of all crows) not from a million. + + + + +CHAPTER IV. + +LAWS OF NATURE. + + +The uniformity of the course of nature is a complex fact made up of all +the separate uniformities in respect to single phenomena. Each of these +separate uniformities, if it be not a mere case of and result from +others, is a law of nature; for, though _law_ is used for any general +proposition expressing a uniformity, _law of nature_ is restricted to +cases where it has been thought that a separate act of creative will is +necessary to account for the uniformity. Laws of nature, in the +aggregate, are the fewest general propositions from which all the +uniformities in the universe might be deducted. Science is ever tending +to resolve one law into a higher. Thus, Kepler's three propositions, +since having been resolved by Newton into, and shown to be cases of the +three laws of motion, may be indeed called laws, but not laws of nature. + +Since every correct inductive generalisation is either a law of nature, +or a result from one, the problem of inductive logic is to unravel the +web of nature, tracing each thread separately, with the view, 1, of +ascertaining what are the _several_ laws of nature, and, 2, of following +them into their results. But it is impossible to frame a scientific +method of induction, or test of inductions, unless, unlike Descartes, we +start with the hypothesis that some trustworthy inductions have been +already ascertained by man's involuntary observation. These spontaneous +generalisations must be revised; and the same principle which common +sense has employed to revise them, correcting the narrower by the wider +(for, in the end, experience must be its own test), serves also, only +made more precise, as the real type of scientific induction. As +preliminary to the employment of this test, nature must be surveyed, +that we may discover which are respectively the invariable and the +variable inductions at which man has already arrived unscientifically. +Then, by connecting these different ascertained inductions with one +another through ratiocination, they become mutually confirmative, the +strongest being made still stronger when bound up with the weaker, and +the weakest at least as strong as the weakest of those from which they +are deduced (as in the case of the Torricellian experiment) while those +leading deductively to incompatible consequences become each other's +test, showing that one must be given up (e.g. the old farmers' bad +induction that seed never throve if not sown during the increase of the +moon). It is because a survey of the uniformities ascertained to exist +in nature makes it clear that there are certain and universal +uniformities serving as premisses whence crowds of lower inductions may +be deduced, and so be raised to the same degree of certainty, that a +logic of induction is possible. + + + + +CHAPTER V. + +THE LAW OF UNIVERSAL CAUSATION. + + +Phenomena in nature stand to each other in two relations, that of +simultaneity, and that of succession. On a knowledge of the truths +respecting the succession of facts depends our power of predicting and +influencing the future. The object, therefore, must be to find some law +of succession not liable to be defeated or suspended by any change of +circumstances, by being tested by, and deduced from which law, all other +uniformities of succession may be raised to equal certainty. Such a law +is not to be found in the class of laws of number or of space; for +though these are certain and universal, no laws except those of space +and number can be deduced from them by themselves (however important +_elements_ they may be in the ascertainment of uniformities of +succession). But causation is such a law; and of this, moreover, all +cases of succession whatever are examples. + +This _Law of Causation_ implies no particular theory as to the ultimate +production of effects by _efficient_ causes, but simply implies the +existence of an invariable order of succession (on our assurance of +which the validity of the canons of inductive logic depends) found by +observation, or, when not yet observed, believed, to obtain between an +invariable antecedent, i.e. the _physical_ cause, and an invariable +consequent, the effect. This sequence is generally between a consequent +and the _sum_ of several antecedents. The cause is really the sum total +of the conditions, positive and negative; the negative being stated as +one condition, the same always, viz. the absence of counteracting causes +(since one cause generally counteracts another by the same law whereby +it produces its own effects, and, therefore, the particular mode in +which it counteracts another may be classed under the positive causes). +But it is usual, even with men of science, to reserve the name _cause_ +for an antecedent _event_ which completes the assemblage of conditions, +and begins to exist immediately before the effect (e.g. in the case of +death from a fall, the slipping of the foot, and not the weight of the +body), and to style the permanent facts or _states_, which, though +existing immediately before, have also existed long previously, the +_conditions_. But indeed, popularly, any condition which the hearer is +least likely to be aware of, or which needs to be dwelt upon with +reference to the particular occasion, will be selected as the cause, +even a negative condition (e.g. the sentinel's absence from his post, as +the cause of a surprise), though from a mere negation no consequence can +really proceed. On the other hand, the object which is popularly +regarded as standing in the relation of _patient_, and as being the mere +theatre of the effect, is never styled _cause_, being included in the +phrase describing the effect, viz. as the object, of which the effect is +_a state_. But really these so-called _patients_ are themselves agents, +and their properties are positive conditions of the effect. Thus, the +death of a man who has taken prussic acid is as directly the effect of +the organic properties of the man, i.e. the _patient_, as of the poison, +i.e. the _agent_. + +To be a cause, it is not enough that the sequence _has been_ invariable. +Otherwise, night might be called the cause of day; whereas it is not +even a condition of it. Such relations of succession or coexistence, as +the succession of day and night (which Dr. Whewell contrasts as _laws of +phenomena_ with _causes_, though, indeed, the latter also are laws of +phenomena, only more universal ones), result from the coexistence of +real causes. The causes themselves are followed by their effects, not +only invariably, but also _necessarily_, i.e. _unconditionally_, or +subject to none but negative conditions. _This_ is material to the +notion of a cause. But another question is not material, viz. whether +causes _must_ precede, or may, at times, be simultaneous with (they +certainly are never preceded by) their effects. In some, though not in +all cases, the causes do invariably continue _together with_ their +effects, in accordance with the schools' dogma, _Cessante causa, cessat +et effectus_; and the hypothesis that, in such cases, the effects are +produced _afresh_ at each instant by their cause, is only a verbal +explanation. But the question does not affect the theory of causation, +which remains intact, even if (in order to take in cases of simultaneity +of cause and effect) we have to define a cause, as the assemblage of +phenomena, which occurring, some other phenomenon invariably and +unconditionally commences, or has its origin. + +There exist certain original natural agents, called permanent causes +(some being objects, e.g. the earth, air, and sun; others, cycles of +events, e.g. the rotation of the earth), which together make up nature. +All other phenomena are immediate or remote effects of these causes. +Consequently, as the state of the universe at one instant is the +consequence of its state at the previous instant, a person (but only if +of more than human powers of calculation, and subject also to the +possibility of the order being changed by a new volition of a supreme +power) might predict the whole future order of the universe, if he knew +the original distribution of all the permanent causes, with the laws of +the succession between each of them and its different mutually +independent effects. But, in fact, the distribution of these permanent +causes, with the reason for the proportions in which they coexist, has +not been reduced to a law; and this is why the sequences or coexistences +among the effects of several of them together cannot rank as laws of +nature, though they are invariable while the causes coexist. For this +same reason (since the proximate causes are traceable ultimately to +permanent causes) there are no original and independent uniformities of +coexistence between effects of different (proximate) causes, though +there may be such between different effects of the same cause. + +Some, and particularly Reid, have regarded man's voluntary agency as +the true type of causation and the exclusive source of the idea. The +facts of inanimate nature, they argue, exhibit only antecedence and +sequence, while in volition (and this would distinguish it from physical +causes) we are conscious, prior to experience, of power to produce +effects: volition, therefore, whether of men or of God, must be, they +contend, an efficient cause, and the only one, of all phenomena. But, in +fact, they bring no positive evidence to show that we could have known, +apart from experience, that the effect, e.g. the motion of the limbs, +would follow from the volition, or that a volition is more than a +physical cause. In lieu of positive evidence, they appeal to the +supposed conceivableness of the direct action of will on matter, and +inconceivableness of the direct action of matter on matter. But there is +no inherent law, to this effect, of the conceptive faculty: it is only +because our voluntary acts are, from the first, the most direct and +familiar to us of all cases of causation, that men, as is seen from the +structure of languages (e.g. their active and passive voices, and +impersonations of inanimate objects), get the _habit_ of borrowing them +to explain other phenomena by a sort of original Fetichism. Even Reid +allows that there is a tendency to assume volition where it does not +exist, and that the belief in it has its sphere gradually limited, in +proportion as fixed laws of succession among external objects are +discovered. + +This proneness to require the appearance of some necessary and natural +connection between the cause and its effect, i.e. some reason _per se_ +why the one should produce the other, has infected most theories of +causation. But the selection of the particular agency which is to make +the connection between the physical antecedent and its consequent seem +_conceivable_, has perpetually varied, since it depends on a person's +special habits of thought. Thus, the Greeks, Thales, Anaximenes, and +Pythagoras, thought respectively that water, air, or number is such an +agency explaining the production of physical effects. Many moderns, +again, have been unable to _conceive_ the production of effects by +volition itself, without some intervening agency to connect it with +them. This medium, Leibnitz thought, was some _per se_ efficient +physical antecedent; while the Cartesians imagined for the purpose the +theory of Occasional Causes, that is, supposed that God, not _qua_ mind, +or _qua_ volition, but _qua_ omnipotent, intervenes to connect the +volition and the motion: so far is the mind from being forced to think +the action of mind on matter more _natural_ than that of matter on +matter. Those who believe volition to be an efficient cause are guilty +of exactly the same error as the Greeks, or Leibnitz or Descartes; that +is, of requiring an _explanation_ of physical sequences by something +[Greek: aneu hou to aition ouk an pot' eie aition]. But they are guilty +of another error also, in inferring that volition, even if it is an +_efficient_ cause of so peculiar a phenomenon as nervous action, must +therefore be the efficient cause of all other phenomena, though having +scarcely a single circumstance in common with them. + + + + +CHAPTER VI. + +THE COMPOSITION OF CAUSES. + + +An effect is almost always the result of the concurrence of several +causes. When all have their full effect, precisely as if they had +operated _successively_, the joint effect (and it is not inconsistent to +give the name of _joint effect_ even to the mutual obliteration of the +separate ones) may be _deduced_ from the laws which govern the causes +when acting separately. Sciences in which, as in mechanics, this +principle, viz. the _composition of causes_, prevails, are deductive and +demonstrative. Phenomena, in effect, do generally follow this principle. +But in some classes, e.g. chemical, vital, and mental phenomena, the +laws of the elements when called on to work together, cease and give +place to others, so that the joint effect is not the sum of the separate +effects. Yet even here the more general principle is exemplified. For +the new _heteropathic_ laws, besides that they never supersede _all_ the +old laws (thus, The weight of a chemical compound is equal to the sum of +the weight of the elements), have been often found, especially in the +case of vital and mental phenomena, to enter _unaltered_ into +composition with one another, so that complex facts may thus be +_deducible_ from comparatively simple laws. It is even possible that, as +has been already partly effected by Dalton's law of definite +proportions, and the law of isomorphism, chemistry itself, which is now +the least deductive of sciences, may be made deductive, through the laws +of the combinations being ascertained to be, though not compounded of +the laws of the separate agencies, yet derived from them according to a +fixed principle. + +The proposition, that effects are proportional to their causes, is +sometimes laid down as an independent axiom of causation: it is really +only a particular case of the composition of causes; and it fails at the +same point as the latter principle, viz. when an addition does not +become compounded with the original cause, but the two together generate +a new phenomenon. + + + + +CHAPTER VII. + +OBSERVATION AND EXPERIMENT. + + +Since the whole of the present facts are the infallible result of the +whole of the past, so that if the prior state of the entire universe +could recur it would be followed by the present, the process of +ascertaining the relations of cause and effect is an analysis or +resolution of this complex uniformity into the simpler uniformities +which make it up. We must first mentally analyse the facts, not making +this analysis minuter than is needed for our object at the time, but at +the same time not regarding (as did the Greeks their verbal +classifications) a mental decomposition of facts as ultimate. When we +have thus succeeded in looking at any two successive chaotic masses (for +such nature keeps at each instant presenting to us) as so many distinct +antecedents and consequents, we must analyse the facts themselves, and +try, by varying the circumstances, to discover which of the antecedents +and consequents (for many are always present together) are related to +each other. + +Experiment and observation are the two instruments for thus varying the +circumstances. When the enquiry is, What are the effects of a given +cause? experiment is far the superior, since it enables us not merely to +produce many more and more opportune variations than nature, which is +not arranged on the plan of facilitating our studies, offers +spontaneously, but, what is a greater advantage, though one less +attended to, also to insulate the phenomenon by placing it among known +circumstances, which can be then infinitely varied by introducing a +succession of well-defined new ones. + +Observation cannot ascertain the effects of a given cause, because it +cannot, except in the simplest cases, discover what are the concomitant +circumstances; and therefore sciences in which experiment cannot be +used, either at all, as in astronomy, or commonly, as in mental and +social science, must be mainly deductive, not inductive. When, however, +the object is to discover causes by means of their effects, observation +alone is primarily available, since new effects could be artificially +produced only through their causes, and these are, in the supposed case, +unknown. But even then observation by itself cannot directly discover +causes, as appears from the case of zoology, which yet contains many +recognised uniformities. We have, indeed, ascertained a real uniformity +when we observe some one antecedent to be invariably found along with +the effects presented by nature. But it is only by reversing the +process, and experimentally producing the effects by means of that +antecedent, that we can prove it to be unconditional, i.e. the cause. + + + + +CHAPTER VIII. AND NOTE TO CHAPTER IX.[1] + +THE FOUR METHODS OF EXPERIMENTAL ENQUIRY. + + +Five canons may be laid down as the principles of experimental enquiry. +The first is that of the Method of Agreement, viz.: _If two or more +instances of the phenomenon under investigation have only one +circumstance in common, the circumstance in which alone all the +circumstances agree is the cause or the effect of the given phenomenon._ +The second canon is that of the Method of Difference, viz.: _If an +instance in which the phenomenon occurs and an instance in which it does +not occur have every circumstance in common, save one, and that one +occurs only in the former, that one circumstance is the effect, or the +cause, or a necessary part of the cause, of the phenomenon._ + +These two are the simplest modes of singling out from the facts which +precede or follow a phenomenon, those with which it is connected by an +invariable law. Both are methods of elimination, their basis being, for +the method of agreement, that whatever can be eliminated _is not_, and +for that of difference, that whatever cannot be eliminated _is_ +connected with the given phenomenon by a law. It is only, however, by +the method of difference, which is a method of artificial experiment +(and by experiment we can introduce into the pre-existing facts a change +perfectly definite), that we can, at least by direct experience, arrive +with certainty at causes. The method of agreement is chiefly useful as +preliminary to and suggestive of applications of the method of +difference, or as an inferior resource in its stead, when, as in the +case of many spontaneous operations of nature, we have no power of +producing the phenomenon. + +When we have power to produce the phenomenon, but only by the agency, +not of a single antecedent, but of a combination, the method of +agreement can be improved (though it is even then inferior to the direct +method of difference) by a double process being used, each proof being +independent and corroborative of the other. This may be called the +Indirect Method of Difference, or the Joint Method of Agreement and +Difference, and its canon will be: _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 a +necessary part of the cause, of the phenomenon._ + +The fourth canon is that of the Method of Residues, viz.: _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._ This method is a modification of +the method of difference, from which it differs in obtaining, of the +two required instances, only the positive instance, by observation or +experiment, but the negative, by deduction. Its certainty, therefore, in +any given case, is conditional on the previous inductions having been +obtained by the method of difference, and on there being in reality no +remaining antecedents _besides_ those given as such. + +The fifth canon is that of the Method of Concomitant Variations, viz.: +_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_ (since they may be effects of a common cause) _is +connected with it through some fact of causation._ Through this method +alone can we find the laws of the permanent causes. For, though those of +the permanent causes whose influence is local may be escaped from by +changing the scene of the observation or experiment, many can neither be +excluded nor even kept isolated from each other; and, therefore, in such +cases, the method of difference, which requires a negative instance, and +that of agreement, which requires the different instances to agree only +in one circumstance, in order to prove causation, are (together with the +methods which are merely forms of these) equally inapplicable. But, +though many permanent antecedents insist on being always present, and +never present alone, yet we have the resource of making or finding +instances in which (the accompanying antecedents remaining unchanged) +their influence is _varied_ and _modified_. This method can be used most +effectually when the variations of the cause are variations of +quantity; and then, if we know the absolute quantities of the cause and +the effect, we may affirm generally that, at least within our limits of +observation, the variations of the cause will be attended by similar +variations of the effect; it being a corollary from the principle of the +composition of causes, that more of the cause is followed by more of the +effect. This method is employed usually when the method of difference is +impossible; but it is also of use to determine according to what law the +quantity or different relations of an effect ascertained by the method +of difference follow those of the cause. + +These four methods are the only possible modes of experimental enquiry. +Dr. Whewell attacks them, first, on the ground (and the canon of +ratiocination was attacked on the same) that they assume the reduction +of an argument to formulae, which (with the procuring the evidence) is +itself the chief difficulty. And this is in truth the case: but, to +reduce an argument to a particular form, we must first know what the +form is; and in showing us this, Inductive Logic does a service the +value of which is tested by the number of faulty inductions in vogue. +Dr. Whewell next implies a complaint that no discoveries have ever been +made by these four methods. But, as the analogous argument against the +syllogism was invalidated by applying equally as against all reasoning, +which must be reducible to syllogism, so this also falls by its own +generality, since, if true against these methods, it must be true +against all observation and experiment, since these must ever proceed by +one of the four. And, moreover, even if the four methods were not +methods of discovery, as they are, they would yet be subjects for logic, +as being, at all events, the sole methods of Proof, which (unless Dr. +Whewell be correct in his view that inductions are simply conceptions +consistent with the facts they colligate) is the principal topic of +logic. + +FOOTNOTE: + +[1] Chap. IX. consists of 'Miscellaneous Examples of the Four Methods,' +which cannot be well represented in an abridged form. + + + + +CHAPTER X. + +PLURALITY OF CAUSES, AND INTERMIXTURE OF EFFECTS. + + +The difficulty in tracing the laws of nature arises chiefly from the +Intermixture of Effects, and from the Plurality of Causes. The +possibility of the latter in any given case--that is, the possibility +that the same effect may have been produced by different causes--makes +the Method of Agreement (when applied to positive instances) +inconclusive, if the instances are few; for that Method involves a tacit +supposition, that the same effect in different instances, which have +_one_ common antecedent, must follow in all from the same cause, viz. +from their common antecedent. When the instances are varied and very +many (how many, it is for the Theory of Probability to consider), the +supposition, that the presence in all of the common antecedent may be +simply a coincidence, is rebutted; and this is the sole reason why mere +_number_ of instances, differing only in immaterial points, is of any +value. As applied, indeed, to negative instances, i.e. to those +resembling each other in the absence of a certain circumstance, the +Method of Agreement is not vitiated by Plurality of Causes. But the +negative premiss cannot generally be worked unless an affirmative be +joined with it: and then the Method is the Joint Method of Agreement and +Difference. Thus, to find the cause of Transparency, we do not enquire +in what circumstance the numberless _non_-transparent objects agree; but +we enquire, first, in what the few transparent ones agree; and then, +whether all the opaque do not agree in the _absence_ of this +circumstance. + +Not only may there be Plurality of Causes, the whole of the effect being +produced now by one, now by another antecedent; but there may also be +Intermixture of Effects, through the interference of different causes +with each other, so that part of the total effect is due to one, and +part to another cause. This latter contingency, which, more than all +else, complicates, the study of nature, does not affect the enquiry into +those (the exceptional) cases, where, as in chemistry, the total effect +is something quite different to the separate effects, and governed by +different laws. There the great problem is to discover, not the +properties, but the cause of the new phenomenon, i.e. the particular +conjunction of agents whence it results; which could indeed never be +ascertained by specific enquiry, were it not for the peculiarity, not of +all these cases (e.g. not of mental phenomena), but of many, viz. that +the heterogeneous effects of combined causes often reproduce, i.e. are +_transformed into_ their causes (as, e.g. water into its components, +hydrogen and oxygen). The great difficulty is _not_ there to discover +the properties of the new phenomenon itself, for these can be found by +experiment like the _simple_ effects of any other cause; since, in this +class of cases the effects of the separate causes give place to a new +effect, and thereby cease to need consideration as separate effects. But +in the far larger class of cases, viz. when the total effect is the +exact sum of the separate effects of all the causes (the case of the +Composition of Causes), at no point may it be overlooked that the effect +is not simple but complex, the result of various separate causes, all of +which are always tending to produce the whole of their several natural +effects; having, it may be, their _effects_ modified, disturbed, or even +prevented by each other, but always preserving their _action_, since +laws of causation cannot have exceptions. + +These complex effects must be investigated by _deducing_ the law of the +effect from the laws of the separate causes on the combination of which +it depends. No inductive method is conclusive in such cases (e.g. in +physiology, or _a fortiori_, in politics and history), whether it be the +method of simple observation, which compares instances, whether positive +or negative, to see if they agree in the presence or the absence of one +common antecedent, or the empirical method, which proceeds by directly +trying different combinations (either made or found) of causes, and +watching what is the effect. Both are inconclusive; the former, because +an effect may be due to the concurrence of many causes, and the latter, +because we can rarely know what all the coexisting causes are; and still +more rarely whether a certain portion (if not all) of the total effect +is not due to these other causes, and not to the combination of causes +which we are observing. + + + + +CHAPTER XI. + +THE DEDUCTIVE METHOD. + + +The deductive method is the main source of our knowledge of complex +phenomena, and the sole source of all the theories through which vast +and complicated facts have been embraced under a few simple laws. It +consists of processes of Induction, Ratiocination, and Verification. +First, by one of the four inductive methods, the simple laws (whence may +be _deduced_ the complex) of each separate cause which shares in +producing the effect, must be first ascertained. This is difficult, when +the causes or rather tendencies cannot be observed singly. Such is the +case in physiology, since the different agencies which make up an +organized body cannot be separated without destroying the phenomenon; +consequently there our sole resource is to produce experimentally, or +find (as in the case of diseases), pathological instances in which only +one organ at a time is affected. Secondly, when the laws of the causes +have been found, we calculate the effect of any given combination of +them by ratiocination, which may have (though not necessarily) among its +premisses the theorems of the sciences of number and geometry. Lastly, +as it might happen that some of the many concurring agencies have been +unknown or overlooked, the conclusions of ratiocination must be +_verified_; that is, it must be explained why they do not, or shown that +they do, accord with _observed_ cases of at least equal complexity, and +(which is the most effectual test) that the empirical laws and +uniformities, if any, arrived at by direct observation, can be deduced +from and so accounted for by them, as, e.g. Kepler's laws of the +celestial motions by Newton's theory. + + + + +CHAPTERS XII. AND XIII. + +THE EXPLANATION AND EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE. + + +The aim, in the deductive method, is either to discover the law of the +effect, or to account for it by _explaining_ it, that is, by pointing +out some more general phenomenon (though often less familiar to us) of +which this is a case and a partial exemplification, or some laws of +causation which produce it by their joint or successive action. This +explanation may be made, either--1. By resolving the laws of the complex +effect into its elements, which consist as well of the separate laws of +the causes which share in producing it, as also of their collocation, +i.e. the fact that these separate laws have been so combined; or--2. By +resolving the law which connects two links, not proximate, in a chain of +causation, into the laws which connect each link with the intermediate +links; or--3. By the _subsumption_ or gathering up of several laws under +one which amounts to the sum of them all, and which is the recognition +of the same sequence in different sets of instances. In the first two of +the processes, laws are resolved into others, which both extend to more +cases, i.e. are more _general_, and also, as being laws of nature, of +which the complex laws are but results, are more _certain_, i.e. more +_unconditional_ and more _universally true_. In the third process, laws +are resolved into others which are indeed more _general_, but not more +_certain_, since they are in fact the same laws, and therefore, subject +to the same exceptions. + +Liebig's researches, e.g. into the Contagious Influence of Chemical +Action, and his Theory of Respiration, are among the finest examples, +since Newton's exposition of the law of gravitation, of the use of the +deductive method for _explanation_.[2] But the method is as available +for explaining mental as physical facts. It is destined to predominate +in philosophy. Before Bacon's time deductions were accepted as +sufficient, when neither had the premisses been established by proper +canons of experimental enquiry, nor the results tested by verification +by specific experience. He therefore changed the method of the sciences +from deductive to experimental. But, now that the principles of +deduction are better understood, it is rapidly reverting from +experimental to deductive. Only it must not be supposed that the +inductive part of the process is yet complete. Probably, few of the +great generalisations fitted to be the premisses for future deductions +will be found among truths now known. Some, doubtless, are yet unthought +of; others known only as laws of some limited class of facts, as +electricity once was. They will probably appear first in the shape of +hypotheses, needing to be tested by canons of legitimate induction. + +FOOTNOTE: + +[2] These, and other illustrations in chap. xiii., cannot be usefully +represented in an abridged form. + + + + +CHAPTER XIV. + +THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE. HYPOTHESES. + + +The constant tendency of science, operating by the Deductive Method, is +to resolve all laws, even those which once seemed ultimate and not +derivative, into others still more general. But no process of +_resolving_ will ever reduce the number of ultimate laws below the +number of those varieties of our feelings which are distinguishable in +quality, and not merely in quantity or degree. The _ideal_ limit of the +explanation of natural phenomena is to show that each of these ultimate +facts has (since the differences in the different cases of it affect our +sensations as differences in degree only, and not in quality) only one +sort of cause or mode of production; and that all the seemingly +different modes of production or causes of it are resolvable into one. +But _practically_ this limit is never attained. Thus, though various +laws of Causes of Motion have been resolved into others (e.g. the fall +of bodies to the earth, and the motions of the planets, into the one law +of mutual attraction), many causes of it remain still unresolved and +distinct. + +Hypotheses are made for the sake of this resolving and explaining of +laws. When we do not _know_ of any more general laws into which to +resolve an uniformity, we then (either on no or on insufficient +evidence) _suppose_ some, imagining either causes (as, e.g. Descartes +did the Vortices), or the laws of their operation (as did Newton +respecting the planetary central force); but we never feign both cause +and law. The use of a hypothesis is to enable us to apply the Deductive +Method before the laws of the causes have been ascertained by Induction. +In those cases where a false law could not have led to a true result (as +was the case with Newton's hypothesis as to the law of the Attractive +force) the third part of the process in the Deductive Method, viz. +Verification, which shows that the results deduced are true, amounts to +a complete induction, and one conforming to the canon of the Method of +Difference. But this is the case only when either the cause is known to +be one given agent (and only its law is unknown), or to be one of +several given agents. + +An assumed cause, on the other hand, cannot be accepted as true simply +_because_ it explains the phenomena (since two conflicting hypotheses +often do this even originally, or, as Dr. Whewell himself allows, may at +any rate by modifications be made to do it); nor _because_ it moreover +leads to the prediction of other results which turn out true (since this +shows only what was indeed apparent already from its agreement with the +old facts, viz. that the phenomena are governed by laws partially +identical with the laws of other causes); nor _because_ we cannot +imagine any other hypothesis which will account for the facts (since +there may be causes unknown to our present experience which will equally +account for them). The utility of such assumptions _of causes_ depends +on their being, in their own nature, _capable_ (as Descartes' Vortices +were not, though possibly the Luminiferous Ether may be) of being, at +some time or other, proved directly by independent evidence to be the +causes. And this was, perhaps, all that Newton meant by his _verae +causae_, which alone, he said, may be assigned as causes of phenomena. +Assumptions of causes, which fulfil this condition, are, in science, +even indispensable, with a view both to experimental inquiry, and still +more to the application of the Deductive Method. They may be accepted, +not indeed, as Dr. Whewell thinks they may be, as proof, but as +suggesting a line of experiment and observation which may result in +proof. And this is actually the method used by practical men for +eliciting the truth from involved statements. They first extemporise, +from a few of the particulars, a rude theory of the mode in which the +event happened; and then keep altering it to square with the rest of the +facts, which they review one by one. + +The attempting, as in Geology, to conjecture, in conformity with known +laws, in what former collocations of known agents (though _not_ known to +have been formerly present) individual existing facts may have +originated, is not Hypothesis but Induction; for then we do not +_suppose_ causes, but legitimately infer from known effects to unknown +causes. Of this nature was Laplace's theory, whether weak or not, as to +the origin of the earth and planets. + + + + +CHAPTER XV. + +PROGRESSIVE EFFECTS, AND CONTINUED ACTION OF CAUSES. + + +Sometimes a complex effect results, not (as has been supposed in the +last four chapters) from several, but from _one_ law. The following is +the way. + +Some effects are instantaneous (e.g. some sensations), and are +prolonged only by the prolongation of the causes; others are in their +own nature permanent. In some cases of the latter class, the original is +also the proximate cause (e.g. Exposure to moist air is both the +original and the proximate cause of iron rust). But in others of the +same class, the permanency of the effect is only the permanency of a +series of changes. Thus, e.g. in cases of Motion, the original force is +only the _remote_ cause of any link (after the very first) in the +series; and the motion immediately preceding it, being itself a compound +of the original force and any retarding agent, is its _proximate_ cause. +When the original cause is permanent as well as the effect (e.g. Suppose +a continuance of the iron's exposure to moist air), we get a progressive +series of effects arising from the cause's accumulating influence; and +the sum of these effects amounts exactly to what a number of +successively introduced similar causes would have produced. Such cases +fall under the head of Composition of Causes, with this peculiarity, +that, as the causes (to regard them as plural) do not come into play all +at once, the effect at each instant is the sum of the effects only of +the then acting causes, and the result will appear as an ascending +series. Each addition in such case takes place according to a fixed law +(equal quantities in equal times); and therefore it can be computed +deductively. Even when, as is sometimes the case, a cause is at once +permanent and progressive (as, e.g. the sun, by its position becoming +more vertical, increases the heat in summer) so that the quantities +added are unequal, the effect is still progressive, resulting from its +cause's continuance and progressiveness combined. + +In _all_ cases whatever of progressive effects, the succession not +merely between the cause and the effect, but also between the first and +latter stages of the effect, is uniform. Hence, from the invariable +sequence of two terms (e.g. Spring and Summer) in a series going through +any continued and uniform process of variation, we do not presume that +one is the cause and the others the effect, but rather that the whole +series is an effect. + + + + +CHAPTER XVI. + +EMPIRICAL LAWS. + + +Empirical laws are derivative laws, of which the derivation is not +known. They are observed uniformities, which we compare with the result +of any deduction to verify it; but of which the _why_, and also the +limits, are unrevealed, through their being, though resolvable, not yet +resolved into the simpler laws. They depend usually, not solely on the +ultimate laws into which they are resolvable; but on those, together +with an ultimate fact, viz. the mode of coexistence of some of the +component elements of the universe. Hence their untrustworthiness for +scientific purposes; for, till they have been resolved (and then a +derivative law ceases to be empirical), we cannot know whether they +result from the different effects of one cause, or from effects of +different causes; that is, whether they depend on laws, or on laws and a +collocation. And if they thus depend on a collocation, they can be +received as true only within the limits of time and space, and also +circumstance, in which they have been observed, since the mode of the +collocation of the permanent causes is not reducible to a law, there +being no principle known to us as governing the distribution and +relative proportions of the primaeval natural agents. + +Uniformities cannot be proved by the Method of Agreement alone to be +laws of causation; they must be tested by the Method of Difference, or +explained deductively. But laws of causation themselves are either +ultimate or derivative. Signs, previous to actual proof by _resolution_ +of them, of their being derivative, are, either that we can _surmise_ +the existence of a link between the known antecedent and the consequent, +as e.g. in the laws of chemical action; or, that the antecedent is some +very complex fact, the effects of which are probably (since most complex +cases fall under the Composition of Causes) compounded of the effects of +its different elements. But the laws which, though laws of causation, +are thus presumably derivative laws only, need, equally with the +uniformities which are not known to be laws of causation at all, to be +explained by deduction (which they then in turn verify), and are less +_certain_ than when they have been resolved into the ultimate laws. +Consequently they come under the definition of Empirical Laws, equally +with uniformities not known to be laws of causation. However, the latter +are far more _uncertain_; for as, till they are resolved, we cannot tell +on how many collocations, as well as laws, they may not depend, we must +not rely on them beyond the exact limits in which the observations were +made. Therefore, the name _Empirical Laws_ will generally be confined +here to these. + + + + +CHAPTER XVII. + +CHANCE, AND ITS ELIMINATION. + + +Empirical laws are certain only in those limits within which they have +been _observed_ to be true. But, even within those limits, the +connection of two phenomena may, as the same effect may be produced by +several different causes, be due to Chance; that is, it may, though +being, as all facts must be, the result of some law, be a coincidence +whence, simply because we do not know all the circumstances, _we_ have +no ground to infer an uniformity. When neither Deduction, nor the Method +of Difference, can be applied, the only way of inferring that +coincidences are not casual, is by observing the frequency of their +occurrence, not their absolute frequency, but whether they occur _more_ +often than chance would (that is, more often than the positive frequency +of the phenomena would) account for. If, in such cases, we could ascend +to the causes of the two phenomena, we should find at some stage some +cause or causes common to both. Till we can do this, the fact of the +connection between them is only an empirical law; but still it is a law. + +Sometimes an effect is the result partly of chance, and partly of law: +viz. when the total effect is the result partly of the effects of casual +conjunctions of causes, and partly of the effects of some constant cause +which they blend with and modify. This is a case of Composition of +Causes. The object being to find _how much_ of the result is +attributable to a given constant cause, the only resource, when the +variable causes cannot be wholly excluded from the experiment, is to +ascertain what is the effect of all of _them_ taken together, and then +to eliminate this, which is the casual part of the effect, in reckoning +up the results. If the results of frequent experiments, in which the +constant cause is kept invariable, oscillate round one point, that +average or middle point is due to the constant cause, and the variable +remainder to chance; that is, to causes the coexistence of which with +the constant cause was merely casual. The test of the sufficiency of +such an induction is, whether or not an increase in the number of +experiments materially alters the average. + +We can thus discover not merely _how much_ of the effect, but even +whether _any_ part of it whatever is due to a constant cause, when this +latter is so uninfluential as otherwise to escape notice (e.g. the +loading of dice). This case of the Elimination of Chance is called _The +discovery of a residual phenomenon by eliminating the effects of +chance._ + +The mathematical doctrine of chances, or Theory of Probabilities, +considers what deviation from the average chance by itself can possibly +occasion in some number of instances smaller than is required for a fair +average. + + + + +CHAPTER XVIII. + +THE CALCULATION OF CHANCES. + + +In order to calculate chances, we must know that of several events one, +and no more, must happen, and also not know, or have any reason to +suspect, which of them that one will be. Thus, with the simple knowledge +that the issue must be one of a certain number of possibilities, we +_may_ conclude that one supposition is most probable _to us_. For this +purpose it is not _necessary_ that specific experience or reason should +have also proved the occurrence of each of the several events to be, as +a fact, equally frequent. For, the probability of an event is not a +quality of the event (since every event is in itself certain), but is +merely a name for the degree of ground _we_ have, with our present +evidence, for expecting it. Thus, if we know that a box contains red, +white, and black balls, though we do not know in what proportions they +are mingled, we have numerically appreciable grounds for considering the +probability to be two to one against any one colour. Our judgment may +indeed be said in this case to rest on the experience we have of the +laws governing the frequency of occurrence of the different cases; but +such experience is universal and axiomatic, and not specific experience +about a particular event. Except, however, in games of chance, the +purpose of which requires ignorance, such specific experience can +generally be, and should be gained. And a slight improvement in the data +profits more than the most elaborate application of the calculus of +probabilities to the bare original data, e.g. to such data, when we are +calculating the credibility of a witness, as the proportion, even if it +could be verified, between the number of true and of erroneous +statements a man, _qua_ man, may be supposed to make during his life. +Before applying the Doctrine of Chance, therefore, we should lay a +foundation for an evaluation of the chances by gaining positive +knowledge of the facts. Hence, though not a _necessary_, yet a most +usual condition for calculating the probability of a fact is, that we +should possess a _specific_ knowledge of the proportion which the cases +in which facts of the particular sort occur bear to the cases in which +they do not occur. + +Inferences drawn correctly according to the Doctrine of Chances depend +ultimately on causation. This is clearest, when, as sometimes, the +probability of an event is deduced from the frequency of the occurrence +of the causes. When its probability is calculated by merely counting and +comparing the number of cases in which it has occurred with those in +which it has not, the law, being arrived at by the Method of Agreement, +is only empirical. But even when, as indeed generally, the numerical +data are obtained in the latter way (since usually we can judge of the +frequency of the causes only through the medium of the empirical law, +which is based on the frequency of the effects), still then, too, the +inference really depends on causation alone. Thus, an actuary infers +from his tables that, of any hundred living persons under like +conditions, five will reach a given age, not simply because that +proportion have reached it in times past, but because that fact shows +the existence there of a particular proportion between the _causes_ +which shorten and the causes which prolong life to the given extent. + + + + +CHAPTER XIX. + +THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES. + + +Derivative laws are inferior to ultimate laws, both in the extent of the +propositions, and in their degree of certainty within that extent. In +particular, the uniformities of coexistence and sequence which obtain +between effects depending on different primaeval causes, vary along with +any variation in the collocation of these causes. Even when the +derivative uniformity is between different effects of the same cause, it +cannot be trusted to, since one or more of the effects may be producible +by another cause also. The effects, even, of derivative laws of +_causation_ (resulting, i.e. the laws, from the combination of several +causes) are not independent of collocations; for, though laws of +causation, whether ultimate or derivative, are themselves universal, +being fulfilled even when counteracted, the peculiar probability of the +latter kind of laws of causation being counteracted (as compared with +ultimate laws, which are liable to frustration only from one set of +counteracting causes) is fatal to the universality of the derivative +uniformities made up of the sequences or coexistences of their effects; +and, therefore, such derivative uniformities as the latter are to be +relied on only when the collocations are known not to have changed. + +Derivative laws, not causative, may certainly be extended beyond the +limits of observation, but only to cases _adjacent_ in time. Thus, we +may not predict that the sun will rise this day 20,000 years, but we can +predict that it will rise to-morrow, on the ground that it has risen +every day for the last 5,000 years. The latter prediction is lawful, +_because_, while we know the causes on which its rising depends, we +know, also, that there has existed hitherto no perceptible cause to +counteract them; and that it is opposed to experience that a cause +imperceptible for so long should start into immensity in a day. If the +uniformity is empirical only, that is, if we do not know the causes, and +if we infer that they remain uncounteracted from their effects alone, we +still can extend the law to adjacent cases, but only to cases still more +closely adjacent in time; since we can know neither whether changes in +these unknown causes may not have occurred, nor whether there may not +exist now an adverse cause capable after a time of counteracting them. + +An empirical law cannot generally be extended, in reference to _Place_, +even to adjacent cases (since there is no uniformity in the collocations +of primaeval causes). Such an extension is lawful only if the new cases +are _presumably_ within the influence of the same individual causes, +even though unknown. When, however, the causes are known, and the +conjunction of the effects is deducible from laws of the causes, the +derivative uniformity may be extended over a wider space, and with less +abatement for the chance of counteracting causes. + + + + +CHAPTER XX. + +ANALOGY. + + +One of the many meanings of _Analogy_ is, Resemblance of Relations. The +value of an analogical argument in this sense depends on the showing +that, on the common circumstance which is the _fundamentum relationis_, +the rest of the circumstances of the case depend. But, generally, _to +argue from analogy_ signifies to infer from resemblance in some points +(not necessarily in _relations_) resemblance in others. Induction does +the same: but analogy differs from induction in not requiring the +previous proof, by comparison of instances, of the invariable +conjunction between the known and the unknown properties; though it +requires that the latter should not have been ascertained to be +_unconnected_ with the common properties. + +If a fair proportion of the properties of the two cases are known, every +resemblance affords ground for expecting an indefinite number of other +resemblances, among which the property in question may perhaps be found. +On the other hand, every dissimilarity will lead us to expect that the +two cases differ in an indefinite number of properties, including, +perhaps, the one in question. These dissimilarities may even be such as +would, in regard to one of the two cases, imply the absence of that +property; and then every resemblance, as showing that the two cases have +a similar nature, is even a reason for presuming against the presence of +that property. Hence, the value of an analogical argument depends on +the extent of ascertained resemblance as compared, first, with the +amount of ascertained difference, and next, with the extent of the +unexplored region of unascertained properties. + +The conclusions of analogy are not of direct use, unless when the case +to which we reason is a case _adjacent_, not, as before, in time or +place, but in _circumstances_. Even then a complete induction should be +sought after. But the great value of analogy, even when faint, in +science, is that it may suggest observations and experiments, with a +view to establishing positive scientific truths, for which, however, the +hypotheses based on analogies must never be mistaken. + + + + +CHAPTER XXI. + +THE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION. + + +The validity of all the four inductive methods depends on our assuming +that there is a cause for every event. The belief in this, i.e. in the +law of universal causation, some affirm, is an instinct which needs no +warrant other than all men's disposition to believe it; and they argue +that to demand evidence of it is to appeal to the intellect from the +intellect. But, though there is no appeal from the faculties all +together, there may be from one to another: and, as belief is not proof +(for it may be generated by association of ideas as well as by +evidence), a case of belief does require to be proved by an appeal to +something else, viz. to the faculties of sense and consciousness. + +The law of universal causation is, in fact, a generalisation from many +partial uniformities of sequence. Consequently, like these, which cannot +have been arrived at by any strict inductive method (for all such +methods presuppose the law of causation itself), it must itself be based +on inductions _per simplicem enumerationem_, that is, generalisations of +observed facts, from the mere absence of any known instances to the +contrary. This unscientific process is, it is true, usually delusive; +but only because, and in proportion as, the subject-matter of the +observation is limited in extent. Its results, whenever the number of +coincidences is too large for chance to explain, are empirical laws. +These are ordinarily true only within certain limits of time, place, and +circumstance, since, beyond these, there may be different collocations +or counteracting agencies. But the subject-matter of the law of +universal causation is so diffused that there is no time, place, or set +of circumstances, at least within the portion of the universe within our +observation, and adjacent cases, but must prove the law to be either +true or false. It has, in fact, never been found to be false, but in +ever increasing multitudes of cases to be true; and phenomena, even +when, from their rarity or inaccessibility, or the number of modifying +causes, they are not reducible _universally_ to any law, yet _in some +instances_ do conform to this. Thus, it may be regarded as coextensive +with all human experience, at which point the distinction between +empirical laws and laws of nature vanishes. Formerly, indeed, it was +only a very high probability; but, with our modern experience, it is, +practically, absolutely certain, and it confirms the particular laws of +causation, whence itself was drawn, when there seem to be exceptions to +them. All narrower inductions got by simple enumeration are unsafe, +till, by the application to them of the four methods, the supposition of +their falsity is shown to contradict _this_ law, though it was itself +arrived at by simple enumeration. + + + + +CHAPTER XXII. + +UNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION. + + +Besides uniformities of succession, which always depend on causation, +there are uniformities of coexistence. These also, whenever the +coexisting phenomena are effects of causes, whether of one common cause +or of several different causes, depend on the laws of their cause or +causes; and, till resolved into these laws, are mere empirical laws. But +there are some uniformities of coexistence, viz. those between the +ultimate properties of _kinds_, which do not depend on causation, and +therefore seem entitled to be classed as a peculiar sort of laws of +nature. As, however, the presumption always is (except in the case of +those _kinds_ which are called _simple substances_ or elementary natural +agents), that a thing's properties really depend on causes though not +traced, and we _never_ can be certain that they do not; we cannot safely +claim (though it _may_ be an ultimate truth) higher certainty than that +of an empirical law for any generalisation about coexistence, that is to +say (since _kinds_ are known to us only by their properties, and, +consequently, all assertions about them are assertions about the +coexistence of something with those properties), about the properties of +_kinds_. + +Besides, no rigorous inductive system can be applied to the uniformities +of coexistence, since there is no general axiom related to them, as is +the law of causation to those of succession, to serve as a basis for +such a system. Thus, Bacon's practical applications of his method +failed, from his supposing that we can have previous certainty that a +property must have an invariable coexistent (as it must have an +invariable antecedent), which he called its form. He ought to have seen +that his great logical instrument, elimination, is inapplicable to +coexistences, since things, which agree in having certain apparently +ultimate properties, often agree in nothing else; even the properties +which (e.g. Hotness) are effects of causes, generally being not +connected with the ultimate resemblances or diversities in the objects, +but depending on some outward circumstance. + +Our only substitute for an universal law of coexistence is the ancients' +induction _per enumerationem simplicem ubi non reperitur instantia +contradictoria_, that is, the improbability that an exception, if any +existed, could have hitherto remained unobserved. But the certainty thus +arrived at can be only that of an empirical law, true within the limits +of the observations. For the coexistent property must be either a +property of the _kind_, or an accident, that is, something due to an +extrinsic cause, and not to the _kind_ (whose own indigenous properties +are always the same). And the ancients' class of induction can only +prove that _within given limits_, either (in the latter case) one +common, though unknown, cause has always been operating, or (in the +former case) that no new _kind_ of the object has _as yet_ or _by us_ +been discovered. + +The evidence is, of course (with respect both to the derivative and the +ultimate uniformities of coexistence), stronger in proportion as the law +is more general; for the greater the amount of experience from which it +is derived, the more probable is it that counteracting causes, or that +exceptions, if any, would have presented themselves. Consequently, it +needs more evidence to establish an exception to a very general, than to +a special, empirical law. And common usage agrees with this principle. +Still, even the greater generalisations, when not based on connection by +causation, are delusive, unless grounded on a separate examination of +_each_ of the included _infimae species_, though certainly there is a +probability (no more) that a sort of parallelism will be found in the +properties of different kinds; and that their degree of unlikeness in +one respect bears some proportion to their unlikeness in others. + + + + +CHAPTER XXIII. + +APPROXIMATE GENERALISATIONS, AND PROBABLE EVIDENCE. + + +The inferences called _probable_ rest on approximate generalisations. +Such generalisations, besides the inferior assurance with which they +can be applied to individual cases, are _generally_ almost useless as +premisses in a deduction; and therefore in _Science_ they are valuable +chiefly as steps towards universal truths, the discovery of which is its +proper end. But in _practice_ we are forced to use them--1, when we have +no others, in consequence of not knowing what general property +distinguishes the portion of the class which have the attribute +predicated, from the portion which have it not (though it is true that +we can, in such a case, usually obtain a collection of exactly true +propositions by subdividing the class into smaller classes); and, 2, +when we _do_ know this, but cannot examine whether that general property +is present or not in the individual case; that is, when (as usually in +_moral_ inquiries) we could get universal majors, but not minors to +correspond to them. In any case an approximate generalisation can never +be more than an empirical law. Its authority, however, is less when it +composes the whole of our knowledge of the subject, than when it is +merely the most available form of our knowledge for practical guidance, +and the causes, or some certain mark of the attribute predicated, being +known to us as well as the effects, the proposition can be tested by our +trying to deduce it from the causes or mark. Thus, our belief that most +Scotchmen can read, rests on our knowledge, not merely that most +Scotchmen that we have known about could read, but also that most have +been at efficient schools. + +Either a single approximate generalisation may be applied to an +individual instance, or several to the same instance. In the former +case, the proposition, as stating a general average, must be applied +only to average cases; it is, therefore, generally useless for guidance +in affairs which do not concern large numbers, and simply supplies, as +it were, the first term in a series of approximations. In the latter +case, when two or more approximations (not connected with each other) +are _separately_ applicable to the instance, it is said that two (or +more) _probabilities are joined by addition_, or, that there is a +_self-corroborative chain_ of evidence. Its type is: Most A are B; most +C are B; this is both an A and a C; therefore it is probably a B. On the +other hand, when the subsequent approximation or approximations is or +are applicable only by virtue of the application of the first, this is +joining two (or more) probabilities, _by way of Deduction_, which +produces a _self-infirmative chain_; and the type is: Most A are B; most +C are A; this is a C; therefore it is probably an A; therefore it is +probably a B. As, in the former case, the probability increases at each +step, so, in the latter, it progressively dwindles. It is measured by +the probability arising from the first of the propositions, abated in +the ratio of that arising from the subsequent; and the error of the +conclusion amounts to the aggregate of the errors of all the premisses. + +In two classes of cases (exceptions which prove the rule) approximate +can be employed in deduction as usefully as complete generalisations. +Thus, first, we stop at them sometimes, from the inconvenience, not the +impossibility, of going further; and, by adding provisos, we might +change the approximate into an universal proposition; the sum of the +provisos being then the sum of the errors liable to affect the +conclusion. Secondly, they are used in Social Science with reference to +masses with _absolute_ certainty, even without the addition of such +provisos. Although the premisses in the Moral and Social Sciences are +only probable, these sciences differ from the exact only in that we +cannot decipher so many of the laws, and not in the conclusions that we +do arrive at being less scientific or trustworthy. + + + + +CHAPTER XXIV. + +THE REMAINING LAWS OF NATURE. + + +There are, we have seen, five facts, one of which every proposition must +assert, viz. Existence, Order in Place, Order in Time, Causation, and +Resemblance. Causation is not fundamentally different from Coexistence +and Sequence, which are the two modes of Order in Time. They have been +already discussed. Of the rest, Existence, if of things in themselves, +is a topic for Metaphysics, Logic regarding the existence of _phenomena_ +only; and as this, when it is not perceived directly, is proved by +proving that the unknown phenomenon is connected by _succession or +coexistence_ with some known phenomenon, the fact of Existence is not +amenable to any _peculiar_ inductive principles. There remain +Resemblance and Order in Place. + +As for Resemblance, Locke indeed, and, in a more unqualified way, his +school, asserted that all reasoning is simply a comparison of two ideas +by means of a third, and that knowledge is only the perception of the +agreement or disagreement, that is, the resemblance or dissimilarity, of +two ideas: they did not perceive, besides erring in supposing ideas, and +not the phenomena themselves, to be the subjects of reasoning, that it +is only sometimes (as, particularly, in the sciences of Quantity and +Extension) that the agreement or disagreement of two things is the one +thing to be established. Reasonings, however, about _Resemblances_, +whenever the two things cannot be directly compared by the virtually +simultaneous application of our faculties to each, do agree with Locke's +account of reasoning; being, in fact, simply such a comparison of two +things through the medium of a third. There are laws or formulae for +guiding the comparison; but the only ones which do not come under the +principles of Induction already discussed, are the mathematical axioms +of Equality, Inequality, and Proportionality, and the theorems based on +them. For these, which are true of all phenomena, or, at least, without +distinction of origin, have no connection with laws of Causation, +whereas all other theorems asserting resemblance have, being true only +of special phenomena originating in a certain way, and the resemblances +between which phenomena must be derived from, or be identical with, the +laws of their causes. + +In respect to Order in Place, as well as in respect to Resemblance, some +mathematical truths are the only general propositions which, as being +independent of Causation, require separate consideration. Such are +certain geometrical laws, through which, from the position of certain +points, lines, or spaces, we infer the position of others, without any +reference to their physical causes, or to their special nature, except +as regards position or magnitude. There is no other peculiarity as +respects Order in Place. For, the Order in Place of effects is of course +a mere consequence of the laws of their causes; and, as for primaeval +causes, in _their_ Order in Place, called their _collocation_, no +uniformities are traceable. + +Hence, only the methods of Mathematics remain to be investigated; and +they are partly discussed in the Second Book. The directly inductive +truths of Mathematics are few: being, first, certain propositions about +existence, tacitly involved in the so-called definitions; and secondly, +the axioms, to which latter, though resting only on induction, _per +simplicem enumerationem_, there could never have been even any apparent +exceptions. Thus, every arithmetical calculation rests (and this is what +makes Arithmetic the type of a deductive science) on the evidence of the +axiom: The sums of equals are equals (which is coextensive with nature +itself)--combined with the definitions of the numbers, which are +severally made up of the explanation of the name, which connotes the way +in which the particular agglomeration is composed, and of the assertion +of a fact, viz. the physical property so connoted. + +The propositions of Arithmetic affirm the modes of formation of given +numbers, and are true of all things under the condition of being divided +in a particular way. Algebraical propositions, on the other hand, affirm +the equivalence of different modes of formation of numbers generally, +and are true of all things under condition of being divided in _any_ +way. + +Though the laws of Extension are not, like those of Number, remote from +visual and tactual imagination, Geometry has not commonly been +recognised as a strictly physical science. The reason is, first, the +possibility of collecting its facts as effectually from the ideas as +from the objects; and secondly, the illusion that its ideal data are not +mere hypotheses, like those in now deductive physical sciences, but a +peculiar class of realities, and that therefore its conclusions are +_exceptionally_ demonstrative. Really, all geometrical theorems are laws +of external nature. They might have been got by generalising from actual +comparison and measurement; only, that it was found practicable to +deduce them from a few obviously true general laws, viz. The sums of +equals are equals; things equal to the same thing are equal to one +another (which two belong to the Science of Number also); and, thirdly +(what is no merely verbal definition, though it has been so called): +Lines, surfaces, solid spaces, which can be so applied to one another as +to coincide, are equal. The rest of the premisses of Geometry consist of +the so-called definitions, which assert, together with one or more +properties, the real existence of objects corresponding to the names to +be defined. The reason why the premisses are so few, and why Geometry is +thus almost entirely deductive, is, that all questions of position and +figure, that is, of quality, may be resolved into questions of quantity +or magnitude, and so Geometry may be reduced to the one problem of the +measurement of magnitudes; that is, to the finding the equalities +between them. + +Mathematical principles can be applied to other sciences. All causes +operate according to mathematical laws; an effect being ever dependent +on the quantity or a function of the agent, and generally on its +position too. Mathematical principles cannot, indeed, as M. Comte has +well explained, be usefully applied to physical questions, whenever the +causes are either too inaccessible for their numerical laws to be +ascertained, or are too complex for _us_ to compute the effect, or are +ever fluctuating. And, in proportion as physical questions cease to be +abstract and hypothetical, mathematical solutions of them become +imperfect. But the great value of mathematical training is, that we +learn to use its _method_ (which is the most perfect type of the +Deductive Method), that is, we learn to employ the laws of simpler +phenomena to explain and predict those of the more complex. + + + + +CHAPTER XXV. + +THE GROUNDS OF DISBELIEF. + + +The result of examining evidence is not always belief, or even +suspension of judgment, but is sometimes positive disbelief. This can +ensue only when the affirmative evidence does not amount to full proof, +but is based on some approximate generalisation. In such cases, if the +negative evidence consist of a stronger, though still only an +approximate, generalisation, we think the fact improbable, and +disbelieve it provisionally; but if of a complete generalisation based +on a rigorous induction, it is disbelieved by us totally, and thought +impossible. Hence, Hume declared miracles incredible, as being, he +considered, contrary to a complete induction. Now, it is true that _in +the absence of any adequate counteracting cause_, a fact contrary to a +complete induction is incredible, whatever evidence it may be grounded +on; unless, indeed, the evidence go to prove the supposed law +inconsistent with some better established one. But when a miracle is +asserted, the presence of an adequate counteracting cause _is_ asserted, +viz. a direct interposition of an act of the will of a Being having +power over nature. Therefore, all that Hume proved is, that we cannot +believe in a miracle unless we believe in the power, and _the will_, of +the Deity to interfere with existing causes by introducing new ones; and +that, in default of such belief, not the most satisfactory evidence of +our senses or of testimony can hinder us from holding a seeming miracle +to be merely the result of some unknown natural cause. The argument of +Dr. Campbell and others against Hume, however, is untenable, viz. that, +as we do not disbelieve an alleged fact (which may be something +conforming to the uniform course of experience) merely because the +chances are against it, therefore we need never disbelieve any fact +supported by credible testimony (even if contrary to the uniform course +of experience). But this is to confound _improbability before the fact_, +which is _not_ always a ground for disbelief, with _improbability after +the fact_, which always is. + +Facts which conflict with special laws of causation are only improbable +before the fact; that is, our disbelief depends on the improbability +that there could have been present, without our knowledge, at the time +and place of the event, an adequate counteracting cause. So, too, with +facts which conflict with the properties of _kinds_ (which are +uniformities of mere coexistence not proved to be dependent on +causation), that is, facts which assert the existence of a new _kind_; +such facts we disbelieve only if, the generalisation being sufficiently +comprehensive, some properties are said to have been found in the +supposed new _kind_ disjoined from others which always have been known +to accompany them. When the assertion would amount, if admitted, only to +the existence of an unknown cause or an anomalous _kind_, +_unconformable_, but, as Hume puts it, _not contrary_ to experience, in +circumstances so little explored, that it is credible hitherto unknown +things may there be found, and when prejudice cannot have tempted to the +assertion, one ought neither to admit nor to reject the testimony, but +to suspend judgment till it be confirmed or disproved from other +sources. Only facts, then, which are contradictory to the laws of +Number, Extension, and Universal Causation (since these know no +counteraction or anomaly), or to laws nearly as general, are improbable +after, as well as before the fact, and only these we should term +_absolutely impossible_, calling other facts _improbable_ only, or, at +most, _impossible in the circumstances of the case_. + +Between these two species of improbabilities lie _coincidences_; that +is, combinations of chances presenting some unexpected regularity +assimilating them in so far to the results of law. It was thought by +d'Alembert that, though regular combinations are as probable as others +according to the mathematical theory, some physical law prevents them +from occurring so often. Now, stronger testimony may indeed be needed +to support the assertion of such a combination as, e.g. ten successive +throws of sixes at dice, because such a regular series is more likely +than an irregular series to be the result of design; and because even +the desire to excite wonder is likely to tempt men to assert the +occurrence falsely, though this probability must be estimated afresh in +every instance. But though such a series _seems_ peculiarly improbable, +it is only because the comparison is tacitly made, not between it and +any one particular previously fixed series of throws, but between all +regular and all irregular successions taken together. The fact is not in +itself more improbable; and no stronger evidence is needed to give it +credibility, apart from the reasons above mentioned, than in the case of +ordinary events. + + + + +BOOK IV. + +OPERATIONS SUBSIDIARY TO INDUCTION. + + + + +CHAPTER I. + +OBSERVATION AND DESCRIPTION. + + +The mental process which Logic deals with, viz. the investigation of +truth by means of evidence, is always a process of Induction. Since +Induction is simply the extension to a class of something observed to be +true of certain members of it, Observation is the first preliminary to +it. It is, therefore, right to consider, not indeed how or what to +observe (for this belongs to the art of Education), but under what +conditions observation is to be relied on. The sole condition is, that +the supposed observation should really be an observation, and not an +inference, whereas it is usually a compound of both, there being, in our +propositions, besides observation which relates only to the sensations, +an inference from the sensations to the objects themselves. Thus +so-called errors of sense are only erroneous inferences from sense. The +sensations themselves must be genuine; but, as they generally arise on a +certain arrangement of outward objects being present to the organs, we, +as though by instinct, infer this arrangement even when not existing. +The sole object, then, of the logic of observation, is to separate the +inferences from observation from the observations themselves, the only +thing really observed by the mind (to waive the metaphysical problem as +to the _perception_ of objects) being its own feelings or states of +consciousness, outward, viz. Sensations, and inward, viz. Thoughts, +Emotions, and Volitions. + +As in the simplest observation much is inference, so, in describing an +observed fact, we not merely describe the fact, but are always forced to +class it, affirming the resemblance, in regard of whatever is the ground +of the name being given, between it and all other things denoted by the +name. The resemblance is sometimes perceived by direct comparison of the +objects together; sometimes (as, e.g. in the description of the earth's +figure as globular and so forth) it is inferred through intermediate +marks, i.e. deductively. When a hypothesis is made (e.g. by Kepler, as +to the figure of the earth's orbit), and then verified by comparison +with actual observations, Dr. Whewell calls the process Colligation of +Facts by appropriate Conceptions, and affirms it to be the whole of +Induction. But this also is only description, being really the ordinary +process of ascertaining resemblance by a comparison of phenomena; and, +though subsidiary to Induction, it is not itself Induction at all. + + + + +CHAPTER II. + +ABSTRACTION, OR THE FORMATION OF CONCEPTIONS. + +_This Chapter is a digression._ + + +Abstract Ideas, that is, General Conceptions, certainly do exist, +however Metaphysics may decide as to their composition. They +_represent_ in our minds the whole classes of things called by the +general names; and, being implied in the mental operation whereby +classes are formed, viz. in the comparison of phenomena, to ascertain in +what they agree, cannot be dispensed with in induction, since such a +comparison is a necessary preliminary to an induction, and more than two +objects cannot well be compared without a type, in which capacity +conceptions serve. + +But, though implied in the comparison, it does not follow that, as Dr. +Whewell supposes, they must have existed in the mind prior to +comparison. Sometimes, but only sometimes, they are pre-existent to the +comparison of the particular facts in question, being, as was Kepler's +hypothesis of an ellipse, familiar conceptions borrowed from different +facts, and _superinduced_, to use Dr. Whewell's expression, on the facts +in question. But even such conceptions are the results of former +comparisons of individual facts. And much more commonly (and these are +the more difficult cases in science) conceptions are not pre-existent +even in this sense; but they have to be got (e.g. the Idea of Polarity) +by abstraction, that is, by comparison, from among the very phenomena +which they afterwards serve to arrange, or, as Dr. Whewell says, to +_connect_. They seem to be pre-existent; but this is only because the +mind keeps ever forming conceptions from the facts, which at the time +are before it, and then tentatively applies these conceptions (which it +is always remodelling, dropping some which are found not to suit +after-found facts, and generalising others by a further effort of +abstraction) as types of comparison for phenomena subsequently +presented to it; so that, being found in these later stages of the +comparison already in the mind, they appear in the character simply of +types, and not as being also themselves results of comparison. Really +they are always both; and the term _comparison_ expresses as well their +origin as (and this far more exactly than to _connect_ or to +_superinduce_) their function. + +Dr. Whewell says that conceptions must be _appropriate_ and _clear_. +They must, indeed, be appropriate relatively to the purpose in view (for +appropriateness is only relative); but they cannot avoid being +appropriate (though one may be more so than another) if our comparison +of the objects has led to a conception corresponding to any real +agreement in the facts: the ancients' and schoolmen's conceptions were +often absolutely inappropriate, because grounded on only apparent +agreement. So, again, they must be _clear_ in the following sense; that +is to say, a _sufficient number_ of facts must have been _carefully +observed_, and accurately _remembered_. It is also a condition (and one +implied in the latter qualities) of clearness, that the conception +should be _determinate_, that is, that we should know precisely what +agreements we include in it, and never vary the connotation except +consciously. + +Activity, carefulness, and accuracy in the observing and comparing +faculties are therefore needed; the first quality to produce +appropriateness, and the latter two, clearness. Moreover, _scientific +imagination_, i.e. the faculty of mentally arranging known elements into +new combinations, is necessary for forming true conceptions; and the +mind should be stored with previously acquired conceptions, kindred to +the subject of inquiry, since a comparison of the facts themselves often +fails to suggest the principle of their agreement; just as, in seeking +for anything lost, we often have to ask ourselves in what places it may +be hid, that we may search for it there. + + + + +CHAPTER III. + +NAMING AS SUBSIDIARY TO INDUCTION. + + +As reasoning is from particulars to particulars, and consists simply in +recognising one fact as a mark of another, or a mark of a mark of +another, the only necessary conditions of the exertion of the reasoning +power are senses, to perceive that two facts are conjoined; and +association, as the law by which one of the two facts raises up the idea +of the other. The existence of artificial signs is not a third +_necessary_ condition. It is only, however, the rudest inductions (and +of such even brutes are capable) that can be made without language or +other artificial signs. Without such we could avail ourselves but little +of the experience of others; and (except in cases involving our intenser +sensations or emotions) of none of our own long past experience. It is +only through the medium of such permanent signs that we can register +uniformities; and the existence of uniformities is necessary to justify +an inference, even in a single case, and they can be ascertained once +for all. + +General names are not, as some have argued, a mere contrivance to +economise words. For, if there were a name for every individual object, +but no general names, we could not record one uniformity, or the result +of a single comparison. To effect this, all indeed, that are +_indispensable_, are the abstract names of attributes; but, in fact, men +have always given general names to objects also. + + + + +CHAPTER IV. + +THE REQUISITES OF A PHILOSOPHICAL LANGUAGE, AND THE PRINCIPLES OF +DEFINITION. + + +Concrete general names (and the meaning of abstract names depends on the +concrete) should have a fixed and knowable connotation. This is easy +enough when, as in the case of new technical names, we choose the +connotation for ourselves; but it is hard when, as generally happens +with names in common use, the same name has been applied to different +objects, from only a vague feeling of resemblance. For, then, after a +time, general propositions are made, in which predicates are applied to +those names; and these propositions make up a loose connotation for the +class name, which, and the abstract at about this same period formed +from it, are consequently never understood by two people, or by the same +person at different times, in the same way. The logician has to fix this +fluctuating connotation, but so that the name may, if possible, still +_denote_ the things of which it is currently affirmed. To effect this +double object (which is called, though improperly, defining _not the +name but the thing_), he must select from the attributes in which the +denoted objects agree, choosing, as the common properties are always +many, and, in a _kind_, innumerable, those which are familiarly +predicated of the class, and out of them, if possible, or otherwise, +even in preference to them, the ones on which depend, or which are the +best marks of, those thus familiarly predicated. To do this +successfully, presumes a knowledge of all the common properties of the +class, and the relations between them of causation and dependence. Hence +the discussion of non-verbal definitions (which Dr. Whewell calls the +Explication of Conceptions) is part of the business of discovery. Hence, +too, disputes in science have often assumed the form of a battle of +definitions; such definitions being not arbitrary, but made with a view +to some tacitly assumed principle needing expression. + +We ought, if possible, to define in consonance with the denotation. But +sometimes this is impossible, through the name having accumulated +_transitive_ applications, in its gradual extension from one object, in +relation to which it connotes one property, to another which resembles +the former, but in quite a different attribute. These _transitive_ +applications, even when found to correspond in different languages, may +have arisen, not from any common quality in the objects, but from some +association of ideas founded on the common nature and condition of +mankind. When the association is so natural and habitual as to become +virtually indissoluble, the _transitive_ meanings are apt to coalesce in +one complex conception; and every new transition becomes a more +comprehensive generalisation of the term in question. In such cases the +ancients and schoolmen did not suspect, what otherwise they carefully +watched for, viz. ambiguities: not Plato, though his Comparisons and +Abstractions preparatory to Induction are perfect; not even Bacon, in +his speculations on Heat. Hence have sprung the various vain attempts to +trace a common idea in all the uses of a word, such as _Cause_ +(Efficient, Material, Formal, and Final _Cause_), _the Good_, _the Fit_. + +When a term is applied to many different objects agreeing _all_ only in +_one_ quality (e.g. things _beautiful_, in _agreeableness_), though +_most_ agree in something besides, it is better to exclude part of the +denotation than of the connotation, however indistinct: else language +ceases to keep alive old experience, alien perhaps to present +tendencies. In any case, words are always in danger of losing part of +their connotation. For, just one or two out of a complex cluster of +ideas, and sometimes merely the look or sound of the word itself, is +often all that is absolutely necessary for the suggesting another set of +ideas to continue the process of thought; and consequently, some +metaphysicians have even fancied that all reasoning is but the +mechanical use of terms according to a certain form. If persons be not +of active imaginations, the only antidote against the propensity to let +slip the connotation of names, is the habit of predicating of them the +properties connoted; though even the propositions themselves, as may be +seen from the way in which maxims of Religion, Ethics, and Politics are +used, are often repeated merely mechanically, not being questioned, but +also not being felt. Much of our knowledge recorded in words is ever +oscillating between its tendency, in consequence of different +generations attending exclusively to different properties in names, to +become partially dormant, and the counter-efforts of individuals, at +times, to revive it by tracing the forgotten properties historically in +the almost mechanically repeated formulas of propositions; and, when +they have been there rediscovered, promulgating them, not as +discoveries, but with authority as what men still profess to believe. +The danger is, lest the formula itself be dismissed by clear-headed +narrow-minded logicians, and the connotation fixed by them (in order +that the denotation may be extended) in accordance with the present use +of the term. Then, if the truths be at any time rediscovered, the +prejudice is against them as novelties. The _selfish_ theory of morals +partly fell because the inconsistency of received formulas with it +prompted a reconsideration of its basis. What would have been the result +if the formulas attaching odium to selfishness, praise to +self-sacrifice, had been dismissed, if this indeed had been possible! +Language, in short, is the depositary of all experience, which, being +the inheritance of posterity, we have a right to vary, but none to +curtail. We may improve the conclusions of our ancestors; we should not +let drop any of their premisses; we may alter a word's connotation; but +we must not destroy part of it. + + + + +CHAPTER V. + +THE NATURAL HISTORY OF THE VARIATION IN THE MEANING OF TERMS. + + +The connotation of names shifts not only by reason of gradual +inattention to some of the common properties, which, if language were +ruled by convention alone, would be in their entirety both the perpetual +and the sole constituents of the connotation; but also from the +incorporation in the connotation, in addition to these, and often, +finally, to the _exclusion_ of them altogether, of other circumstances +at first only casually associated with it. These collateral associations +are the cause why there are so few exact synonymes; and why the +dictionary meaning, or Definition, is so bad a guide to its uses, as +compared with its history, since the latter explains the law of the +succession by showing the causes which determined the successive uses. + +Two counter-movements are always going on in language. One is +generalisation, by which words are ever losing part of their +connotation, and becoming more general. This arises, partly from men, +such as historians and travellers, using words, especially those +expressing complicated mental and social facts strange to them, in a +loose sense, in ignorance of the true connotation; partly, from known +things multiplying faster than names for them; partly, also, from the +wish to give people some notion of a new object by reference to a known +thing resembling it however slightly. The other movement is +specialisation; and by it words (even the same words which, as, e.g. +_pagan_ and _villain_, later get generalised in a new direction) are +ever taking a fresh connotation, through their denotation being +diminished. Specialisations often occur even in scientific nomenclature, +a word which expressed general characters becoming confined to a +specific substance in which these characters are predominant. So it is +when any set of persons has to think of one species oftener than of any +other contained in the genus: e.g. some sportsmen mean partridges by the +term _birds_. But, as ideas of our pleasures and pains and their +supposed causes, cling, most of all, by association to what they have +been once connected with, the great source of specialisation is the +addition of the ideas of agreeableness or painfulness, and approbation +or censure, to the connotation. And hence arises the fallacy of +_question-begging_ names referred to later on. + +It is the business of logicians not to ignore, for they cannot prevent, +transformations of terms in common use, but to trace and embody them, +and men's half unconscious reasons for them, in distinct definitions. + + + + +CHAPTER VI. + +TERMINOLOGY AND NOMENCLATURE. + + +Not only must words have a fixed and knowable meaning; but also, no +important meaning should be without its word: that is, there should be a +name for everything which we have often to make assertions about. There +should be, therefore, first, names suited to describe all the individual +facts; secondly, a name for every important common property detected by +comparing those facts; and, thirdly, a name for every _kind_. + +First, it conduces to brevity and clearness to have separate names for +the oft-recurring combinations of feelings; but, as these can be defined +without reference back to the feelings themselves, it is _enough_ for a +_descriptive_ terminology, if there be a name for every variety of +elementary feeling, since none of these can be defined, or indicated to +a person, except either by his having the sensation itself, or being +referred through a known mark to his remembrance of it. The meaning of +the name when given to a feeling is fixed, in the first instance, by +convention, and must be associated _immediately_, not through the usage +of ordinary language, with the feeling, so that it may at once recall +the latter. But even among the elementary feelings, those purely mental, +and also sensations, such as those from disease, the identity of which +in different persons cannot be determined, cannot be exactly +_described_. It is only the impressions on the outward senses, or those +inward feelings connected uniformly with outward objects (and, +consequently, sciences, such as botany, conversant with outward +objects), which are susceptible of an exact descriptive language. + +Secondly, there must also be a separate name for every important common +property recognised through that comparison of observed instances which +is preparatory to induction (including names for the classes which we +artificially construct in virtue of those properties). For, although a +definition would often convey the meaning, both time and space are +saved, perspicuity promoted, and the attention excited and concentrated, +by giving a brief and compact name to each of the new _general +conceptions_, as Dr. Whewell calls them, that is, the new results of +abstraction. Thenceforward the name nails down and clenches the +unfamiliar combination of ideas, and suggests its own definition. + +Thirdly, as, besides the artificial classes which are marked out from +neighbouring classes by definite properties to be arrived at by +abstraction, there are classes, viz. _kinds_, distinguished severally by +an unknown multitude of independent properties (and about which classes +therefore many assertions will be made), there must be a name for every +_kind_. That is, besides a terminology, there must be a nomenclature, +i.e. a collection of the names of all the lowest _kinds_, or _infimae +species_. The Linnaean arrangements of plants and animals, and the French +of chemistry, are nomenclatures. The peculiarity of a name which belongs +to a nomenclature is, not that its meaning resides in its denotation +instead of its connotation (for it resides in its connotation, like that +of other concrete general names); but that, besides connoting certain +attributes which its definition explains, it also connotes that these +attributes are distinctive of a _kind_; and this fact its definition +cannot explain. + +A philosophical language, then, must possess, first, precision, and next +(the subject of the present chapter), completeness. Some have argued +that, in addition, names are fitted for the purposes of thought in +proportion as they approximate to mere symbols in compactness, through +meaninglessness, and capability of use as counters without reference to +the various objects which, though utterly different, they may thus at +different times equally well represent. Such are, indeed, the qualities +enabling us to employ the figures of arithmetic and the symbols of +algebra perfectly mechanically according to general technical rules. +But, in the first place, in our direct inductions, at all events, +depending as they do on our perception of the particulars of the +agreement and difference of the phenomena, we could never dispense with +a distinct mental image of the latter. Further, even in deduction, +though a syllogism is conclusive from its mere form, if the terms are +unambiguous, yet the _practical_ validity of the reasoning depends on +the hypothesis that no counteracting cause has interfered with the truth +of the premisses. We can assure ourselves of this only by studying the +phenomena at every step. For it is only in geometry and algebra that +there is no danger from the Composition of Causes, or the superseding of +one set of laws by another; and that, therefore, the propositions are +categorically true. In sciences in general, then, the object should be, +so far from keeping individualising peculiarities out of sight, to +contrive the greatest possible obstacles to a merely mechanical use of +language: we should carefully keep alive a consciousness of its meaning, +by referring, by aid of derivation and the analogies between the ideas +of the roots and the derivatives, to the origin of words; and as words, +however philosophically constructed, are always tending, like coins, to +have their inscription worn off, we should be ever stamping them afresh. +This we shall effect, if we contemplate habitually, not the _formulas_ +which record the laws of the phenomena (for, if so, the formulas will +themselves progressively lose their meaning), but the phenomena whence +the laws were collected; and we must conceive these phenomena in the +concrete, and clothe them in circumstances. + + + + +CHAPTER VII. + +CLASSIFICATION, AS SUBSIDIARY TO INDUCTION. + + +Every name which connotes an attribute thereby divides, but only +incidentally, all things, known and unknown, real and imagined, into two +classes, viz. those which have, and those which have not the attribute. +But sometimes the naming itself is but the secondary and subsidiary, and +the classification, the primary object. The general problem of such +classification is, to provide that things shall be thought of in such +groups, and the groups in such an order, as will best promote the +remembrance and ascertainment of their laws. Its subjects are _real +things_ exclusively, but _all_ real things, since, to place one object +in a group, we ought to know the divisions of nature at large. + +Any property may be the basis for a classification; but those best +suited are properties which are causes, or, next, as the cause of a +class's chief peculiarities seldom serves as its diagnostic, any effect +which is a sure mark both of the cause and of the other effects. Only a +classification so grounded is scientific; the same also is not technical +or artificial, but natural, and emphatically _natural_ (as compared with +classifications in an inferior degree also _natural_, which are based on +properties important with reference to the reasoner's special practical +objects), when the classification is based on those properties which +would most impress one who knew all the properties, but was not +interested particularly in any one. Further, it is a great +recommendation of a classification, that it groups together things of +like general aspect; but this is not a _sine qua non_: a group may be +_natural_ even if based on very _unobvious_ properties, provided these +are marks of many other properties, though certainly then there should +be also some more obvious property to act as a mark of the unobvious +ones which form the real basis. + +As the first principle of _natural_ classification is that the classes +must be so formed that the objects composing each may have as many +properties in common as possible to serve as predicates, all _kinds_ +should have places among the _natural_ groups, since the common +properties of _kinds_, and, therefore, the general assertions that can +be made about them, are innumerable. But _kinds_ are too few to make up +the whole of a classification: other classes also may be eminently +_natural_, though marked out from each other only by a definite number +of properties. Of neither sort of _natural_ groups is Dr. Whewell's +theory _strictly_ true, viz. that every _natural_ group is not +determined by definition, that is, by definite characters which can be +expressed in words, but is fixed by Type. He explains that a type is an +example of any class, for instance, a species of a genus, which +possesses all the characters and properties of the genus in a marked +way; that round this type-species are grouped all the other species, +which, though deviating from it in various directions and degrees, yet +are of closer affinity to it than to the centre of any other group; and +that this is the reason why propositions about _natural_ groups so often +state matters as being true not in all cases, but only in most. Now, +there is a truth, but only a partial truth, in this doctrine. It is +this: in forming _natural_ groups, species which want certain of the +class-characters, some one, and others another, are classed with those +(the majority) that have them all, because they are more like (that is, +in fact, have more of the common characters of) that particular group +than of any other. On account of the feeling of vagueness hence +engendered, we certainly, in deciding if an object belong to the group, +do generally (and _must_, when the classification is made expressly with +a view to a special inductive enquiry) refer mentally, not as a +substitute for, but in illustration of the definition of the group, to +some standard specimen which has _all_ the characters well developed. +But not the less, therefore, are all _natural_, equally with all +artificial, groups framed with distinct reference to certain definite +characters. In the case of _kinds_, a few characters are chosen as marks +of the rest. In the case of other _natural_ groups, the formation of the +larger groups, into which we collect the _infimae species_, is suggested +indeed by resemblance to types (since we form each such larger group +round a selected _kind_ which serves as its exemplar); but the group +itself, when formed, is determined by definite characters. + +Class names should by the mode of their construction help those who have +learnt about the thing, to remember it, and those who have not learnt, +now to learn, by being merely told the name. This is best effected, in +the case of _kinds_, when the word indicates by its very formation the +properties it connotes. But this is seldom possible. For, though a +_kind_-name connotes not all the _kind_-properties, but some only which +serve as sure marks of the rest, even these have been found too many to +be included conveniently in a name (except in Elementary Chemistry, +where every compound substance has one distinctive index-property, viz. +the chemical composition). A subsidiary resource is to point out the +_kind's_ nearest natural affinities. For instance, in the binary +Nomenclature of Botany and of Zoology, the name of every species +consists of the name of the _natural_ group next above, with a word +added expressive of some quality in the nature or mode of discovery, or +what not, of the particular species itself. By this device (obtaining at +present only in Botany and Zoology), as well is the expression, in the +name, of many of the _kind's characters_ secured, as the use of names +economised, and the memory relieved. Except for some such plan, what +hope of naming the 60,000 known species of Plants? + + + + +CHAPTER VIII. + +CLASSIFICATION BY SERIES. + + +The object of Classification generally is to bring our ideas of objects +into the order best fitted for prosecuting inductive enquiries into the +laws of the phenomena generally. But a Classification which aims at +facilitating an inductive enquiry into the laws of some special +phenomenon, must be based on that phenomenon itself. The requisites of +such a classification are, first, the bringing into one class all +_kinds_ of things which exhibit the phenomenon; next, the arranging +them in a _series_, according to the degrees in which they exhibit it. +Such a classification has been largely applied in Comparative Anatomy +and Physiology (and these alone), since there has been found a +recognisable difference in the degree in which animals possess one main +phenomenon, viz. Animal Life. + +This arrangement of the instances, whence the law is to be collected, in +a series, is that which is always implied in and is a condition of _any_ +application of the method, viz. that of Concomitant Variations, which +must be used when conjoined circumstances cannot easily be separated by +experiment. But sometimes (and it is so in Zoology) the law of the +subject of the special enquiry (e.g. Animal Life) has such influence +over the general character of the objects, that all other differences +among them seem mere modifications of it; and then the classification +required for the special purpose becomes the determining principle of +the classification of the same objects for general purposes. + +To recognise the identity of phenomena which thus differ only in degree, +we must assume a type-species. This will be that _kind_ which has the +class-properties in their greatest intensity (and, therefore, most +easily studied with all their effects); and we must conceive the other +varieties as instances of degeneracy from that type. + +The divisions of the series must be determined by the principles of +_natural_ grouping in general (that is, in effect, by natural affinity); +in subordination, however, to the principle of a natural series; that +is, in the same group must not be placed things which ought to occupy +different points of the general scale. + +Zoology affords the only _complete_ example of the true principles of +rational classification, whether as to the formation of groups or of +series. Yet the same principles are applicable to all cases (to art and +business as well as science) where the various parts of a wide subject +have to be brought into mental co-ordination. + + + + +BOOK V. + +FALLACIES. + + + + +CHAPTER I. + +FALLACIES IN GENERAL. + + +The habit of reasoning well is the only complete safeguard against +reasoning ill, that is, against drawing conclusions with insufficient +evidence, a practice which the various contradictory opinions, +particularly about the phenomena relating to Man, show to be even now +common, and that too among the most enlightened. But, to be able to +explain an error is a necessary condition of seeing the truth; for, +'Contrariorum eadem est Scientia.' Consequently, a work on Logic must +classify Fallacies, that is, the varieties of Apparent Evidence; for +they _can_ be classified, though not in respect of their negative +quality of being either not evidence at all, or inconclusive, yet in +respect of the positive property they have of _appearing_ to be +evidence. + +As Logic has been here treated as embracing the whole reasoning process, +so it must notice the fallacies incident to any part of it (not to +Ratiocination merely), whether arising from faulty Induction, or from +faulty Ratiocination, or from dispensing wholly with either or both of +them. It does not treat of errors from negligence, or from inexpertness +in using right methods, nor does it treat of errors from moral causes, +viz. Indifference to truth, or Bias by our wishes or our fears; for the +moral causes are but the _remote_ and _predisposing_, not the _exciting_ +causes of opinions; and therefore inferences from them, since they must +always involve the intellectual operation of admitting insufficient +evidence as sufficient, really come under a classification of the things +which wrongly _appear_ evidence to the _understanding_. + +Fallacies may be arranged, with reference either to the cause which +makes them (erroneously) appear evidence, or to the particular kind of +evidence they simulate. The following classification is grounded on both +these considerations jointly. + + + + +CHAPTER II. + +CLASSIFICATION OF FALLACIES. + + +The business of Logic is, not to enumerate false opinions, but to +enquire what property in the facts led to them, that is, what +peculiarity of relation between two facts made us suppose them +habitually conjoined or disjoined, and thus regard the presence or +absence of the one as evidence of that of the other. For every such +property in the facts, or our mode of considering them, there is a +corresponding class of Fallacies. + +As the supposed habitual connexion or repugnance of two facts may be +admitted, either as a self-evident and axiomatic truth, or as itself an +inference, the first great division is into Fallacies of Simple +Inspection or _a priori_ Fallacies, and Fallacies, of Inference. But +there is also an intermediate class. For, sometimes an inference is +erroneous through our not conceiving what our premisses precisely are, +and from our therefore substituting new premisses for the old, or a new +conclusion for the one we undertook to prove; and this is called the +Fallacy of Confusion. Under this head, indeed, of Fallacies of +Confusion, might strictly be brought almost any fallacy, though falling +also under some other head: for, some of the links in an argument, +especially if sophistical, are sure to be suppressed; and, it being left +doubtful which is the proposition to be supplied, we can seldom tell +with certainty under _which_ class the fallacy absolutely comes. It is, +however, convenient to reserve the name _Fallacy of Confusion_ for cases +where Confusion is the _sole_ cause of the error. + +Cases, then, where there is more or less ground for the error in _the +nature of the apparent evidence itself_, the evidence being assumed to +be of a certain sort, and a false conclusion being drawn from it, may be +classed as Fallacies of Inference. According as the apparent evidence +consists of particular facts, or of foregone generalisations, we call +the errors Fallacies of Induction or of Deduction. Each of these +classes, again, may be subdivided into two species, according as the +apparent evidence is either false, or, though true, inconclusive. Such +subdivisions of the Fallacy of Induction are respectively called, in the +former case, Fallacies of Observation (including cases where the facts +are not directly observed, but inferred), and, in the latter, Fallacies +of Generalisation. Among Fallacies of Deduction, those which proceed on +false premisses have no specific name, for they must fall under one of +the other heads of Fallacies; but those, the premisses of which, though +true, do not support the conclusion, compose a subdivision, which may be +specified as Fallacies of Ratiocination. + + + + +CHAPTER III. + +FALLACIES OF SIMPLE INSPECTION; OR, A PRIORI FALLACIES. + + +There must be some _a priori_ knowledge, some propositions to be +received without proof; for there cannot be a chain suspended from +nothing. What these are is disputed, one school recognising as ultimate +premisses only the facts of our subjective consciousness, e.g. +Sensations, while Ontologists hold that the mind intuitively, and not +through experience, recognises as realities other existences, e.g. +Substances, which are suggested by, though not inferrible from, those +facts of consciousness. But, as both schools, in fact, allow that the +mind infers the _reality_ from the _idea_ of a thing, and that it may do +this unduly, there results a class of Fallacies resting on the tacit +assumption that the objects in nature have the same order as our ideas +of them. Hence not only arose the vulgar belief that facts which make us +think of an event are omens foreboding (e.g. lucky or unlucky names), or +even causing its occurrence; but even men of science both did and do +fall into this Fallacy. The following dogmas express the different forms +of this error:-- + +1. [Greek: a]. _Things which we cannot help thinking of together must +coexist_; thus Descartes held that, because existence is involved +(though really only by the thinker himself) in the idea of a geometrical +figure, a thing like the idea must exist. [Greek: b]. _Whatever is +inconceivable is false._ The latter proposition has been defended by +drawing a distinction between the principle, and its possibly wrong +application to facts, e.g. to Antipodes; but how can we ever know that +it has been rightly applied? Coleridge, again, has distinguished between +the unimaginable, which he thinks may possibly be true, and the +inconceivable, which he thinks cannot be; but Antipodes were imaginable +at the same period when they were inconceivable. In fact, as even to +Newton it seemed inconceivable, that a thing should act where it is not +(e.g. that the sun should act upon the earth without the medium of an +ether), simply because his mind was not familiar with the idea, so it +_may_ be with _our_ incapability (if not, indeed, resulting merely from +our limited faculties) of _conceiving_, e.g. that matter cannot think; +that space is infinite; that _ex nihilo nihil fit_. Leibnitz's tenet +that all _natural_ phenomena must be explicable _a priori_, and the +further assumption by some that Nature always acts by the simplest, i.e. +by the most easily conceivable means (and that, therefore, e.g. the +heavenly bodies have a circular movement), exhibit vividly this Fallacy +of Simple Inspection. + +2. _Whatever can be thought of apart, or has a separate name, exists +apart as a separate entity_, e.g. Nature, Time, qualities, as e.g. +Whiteness, and, worst of all, the Substantiae Secundae. Mysticism is this +habit of ascribing objective existence to the subjective creations of +the mind, and reasoning from them to the things themselves. + +3. _A fact must follow a certain law, because we see no reason for its +deviating from it in one way rather than in another._ This, which is the +same as the Principle of the Sufficient Reason, has been used to prove +the Law of Inertia (the very point to be proved, viz. that only external +force can be a sufficient reason for motion _in a particular direction_, +being assumed), and also the First Law of Motion, the argument being, in +the latter case, that a moving body, if it do _not_ continue of itself +to move uniformly in a straight line, must deviate right or left, and +that there is _no reason_ for its going one way more than the other: to +which the answer is, that, apart from experience, we could not know +whether or not there were a reason. Geometers often fall into this +Fallacy. + +4. _The differences in nature must correspond to our received +distinctions_ (in names and classifications). Thus, the Greeks thought +that, by determining the meanings of words, they ascertained facts. +Aristotle usually starts with 'We say thus or thus.' So, with the +_Doctrine of Contrarieties_, in which the Pythagoreans and others +assumed that oppositions in language imply similar ones in nature. +Hence, too, the ancient belief in the essential difference between the +laws of things terrestrial and things celestial, and in man's +incapability of imitating nature's works. Bacon's error (which vitiates +his inductive system) was analogous, in looking (either through his +eagerness for practical results, or a lingering belief that causes were +the sole object of philosophy) for the cause of given effects rather +than the effects of a given cause. Hence sprang his tacit assumption +(and that in enquiries into the causes of a thing's sensible qualities, +where it was especially fatal), that in all cases, e.g. of heat or cold, +the _forma_, or set of conditions, is _one_ thing. A similar notion, +viz. that each property of gold, as of other things, has its one +_forma_, produced the belief in Alchemy. + +5. The conditions of a phenomenon often do resemble the phenomenon +itself, e.g. in cases of Motion, Contagion, Feelings; but it is a +Fallacy to suppose that _they must or probably will_. By this fancied +law men guided their conjectures. Thus, the _Doctrine of Signatures_ +was, that substances showed their uses as medicines by external +resemblance, either to their supposed effect, or to the disease. So, the +Cartesians, and even Leibnitz, argued, that nothing physical but +previous motion could account for motion, explaining the human body's +voluntary motions by Nervous Vibrations or by Animal Spirits. Hence, +too, the inference that there is a correspondence between the physical +qualities of the cause, and like or like-named ones, either of the +phenomenon (e.g. between sharp particles and a sharp taste), or of its +effects (e.g. between the redness of Mars, and fire and slaughter as +results of that planet's influence). In metaphysics, the Epicureans' +doctrine of _species sensibiles_, and the moderns' of _perception +through ideas_, arose from this fallacy (combined with another, viz. +that a thing cannot act where it is not). Again, the conditions of a +thing are sometimes spoken of even as though they were the thing itself. +Thus, in the Novum Organon, heat (i.e. really the conditions of the +feeling of it) is called a kind of motion; and Darwin, in his Zoonomia, +after describing _idea_ as a kind of _notion of external things_, +defines it as _a motion of the fibres_. Cousin says: 'Tout ce qui est +vrai de l'effet est vrai de la cause,' though, the reverse _might_ be +true; and Coleridge affirms, as _an evident truth_, that mind and +matter, as having no common property, cannot act on each other. The same +fallacy led Leibnitz to his _pre-established harmony_, and Malebranche +to his _occasional causes_. So, Cicero argues that mental pleasures, if +arising from the bodily, could not, as they do, exceed their cause; and +Descartes, that the Efficient Cause must have all the perfections of the +effect. Conversely Descartes, too, and persons who assail, e.g. the +Principle of Population by reference to Divine benevolence (thus +implying that, because God is perfect, therefore what _they_ think +perfection must obtain in nature), assume that effects must resemble +their causes. + + + + +CHAPTER IV. + +FALLACIES OF OBSERVATION. + + +A fallacy of Observation (the first of the three fallacies of Proof) may +be either negative or positive. + +1. The former, which is called Non-observation, is a case, not of a +positive mis-estimate of evidence, or of the proper faculties (whether +the senses or reason) not having been employed, but simply of the +non-employment of any of the faculties. It arises ([Greek: a]) from +neglect of instances. Sometimes this is when there is a stronger motive +to remember the instances on the one side, and the observers have +neglected the principle of the Elimination of Chance. Hence (the mind, +as Bacon says, being more moved by affirmative than by negative +instances) the belief in predictions, e.g. about the weather, because +they occasionally turn out correct; and the credit of the proverb, that +'Fortune favours fools,' since the cases of a wise man's success through +luck are forgotten in his more numerous successes through genius. But a +preconceived opinion is the _chief_ cause why opposing instances are +overlooked. Hence originate the errors about physical facts (e.g. of +Copernicus's foes, and friends, too, about the falling stone), and _a +fortiori_, on moral, social, and religious subjects, where yet stronger +feelings are involved. + +The fallacy of Non-observation may occur ([Greek: b]) from neglect, not +of the material instances wholly, but of some material facts in them, +e.g. in cases of cures by quack remedies (such as Kenelm Digby's +'sympathetic powder'), of some attendant fact (as exclusion of air from +a wound, rest, regimen, and the like) which really worked the cure. +Sometimes the neglected fact is one ascertainable, not by the senses, +but by reasoning, which has been overlooked. Thus, Cousin's argument +that, if the sole end of punishment were to prevent crime by +intimidating intending criminals, the punishment of the innocent, +indiscriminately with the guilty, would have the same effect, ignores +the fact that the innocent would then be equally intimidated, and so the +punishment would be of no use as an example to criminals. So, in +Political Economy, where the effects of a cause often consist of two +sets of phenomena, the one obvious, the other deeper under the surface, +and exactly contrary, the latter is often neglected. This was why the +rapidly spent capital of the prodigal was supposed formerly to employ +more labour than the invested savings of the parsimonious, and the +purchase of native goods to encourage native industry more than the +purchase of foreign. + +2. The error in Mal-observation, which is the _positive_ kind of +Mis-observation, is not the overlooking facts, but the seeing them +wrong. It arises from mistaking what is in fact inference (as much +_must_ be, whenever we try to observe or to describe) for perception, +which is infallible evidence of what is really perceived. The +Anti-Copernicans, when they appealed to common sense, made this mistake. +So do untrained persons generally in describing facts, especially +natural phenomena (e.g. apothecaries and nurses in stating symptoms), +and that, too, in proportion to their ignorance. We might expect this, +since usually the actual perceptions of the senses (e.g. the colour and +extension) are not of interest, except as marks whence to draw +inferences about something else (e.g. about the body, to which these +qualities belong). Painters, therefore, to know what the sensation +actually was, have to go through a special training. But this confusion +of inference with perception is still more likely in highly abstract +subjects; and, consequently, in these, mere, and often false inferences, +have continually been regarded as intuitive judgments. + + + + +CHAPTER V. + +FALLACIES OF GENERALISATION. + + +This class includes whatever errors of generalisation are not mere +blunders, but arise from some wrong general conception of the inductive +process. Only a few kinds can be noted. 1. Under this Fallacy come +generalisations which _cannot_ be established by experience, e.g. +inferences from the order in the Solar System to other and unknown parts +of the universe; and also, except when a particular effect would +contradict either the laws of number and extension, or the universal law +of causality, all inferences from the fact that _we_ have never known of +a particular effect to its impossibility. 2. Those generalisations also +are fallacious which resolve, either, as in early Greece, all things +into one element, or, as often in modern times, impressions on the +senses, differing in quality, and not merely in degree, into the same; +e.g. heat, light, and (through vibrations) sensation, into motion; +mental, into nervous states; and vital phenomena, into mechanical or +chemical processes. In these theories, one fact has its laws applied to +another. It may possibly be a condition of that other; but even then the +mode in which the new fact is actually produced would have to be +explained by its own law, and not by that of the condition. 3. Again, +generalisations got by Simple Enumeration, fall under this Fallacy. That +sort of Induction 'precario concludit,' says Bacon, 'et periculo +exponitur ab instantia contradictoria, ... ex his tantummodo quae praesto +sunt pronuncians.' The ancients used it; and in questions relating to +man and society, it is still employed by _practical_ men. By it men +arrived at the various examples of the formula, _Whatsoever has never +been_ (e.g. a State without artificial distinctions of rank; negroes as +civilised as the white race) _will never be_; which, being inductions +without elimination, could at most form the ground only of the lowest +empirical laws. Higher empirical laws can be got, when a phenomenon +presents (as no negation can) a series of regular gradations, since +something may then be inferred from the observed as to the unobservable +terms of the series. Such is the law of man's necessary progression, in +contradiction to the above formula. But even this better generalisation +is similarly, though not as grossly, fallacious as the preceding, when, +though not itself a cause, but only a summary expression for the general +result of all the causes, it is accepted as _the_ law of human changes, +past and even future. So, empirical generalisations, from present to +past time, and from the character of one nation to that of another, are +similarly fallacious when employed as causal laws. 4. This Fallacy +occurs, not only when an empirical is confounded with a causal law, but +when causation is inferred improperly. The mistake sometimes lies in +inferring _a posteriori_ that one fact must be the cause of another +(e.g. the National Debt, or some special institution, of England's +prosperity), because of their casual conjunction; at other times, in +assuming _a priori_ that one of several coexisting agents is the sole +cause, and then deducing the effects from it exclusively. The latter is +properly False Theory. It has been exemplified in medicine by the +tracing of all diseases by one school, to viscidity of the blood, by +another, to the presence of some acid or alkali, and, in politics, by +the assumption that some special form of government or society is +absolutely good. 5. In False Analogies (which fall under this Fallacy) +there is no pretence of a conclusive induction. The argument from +Analogy is the inferring, in the absence of evidence either way, that an +object resembles a second object in one point, because it is seen to +resemble it in another point, which either is not known to be connected +with the first by causation (as, that the planets must be inhabited +because they obey the same astronomical laws with the earth, which is), +or which is known to be, not, indeed, its cause or its effect, but +either one of a set of conditions, which together are its cause, or an +occasional effect of its cause. Now, persons (usually from poverty, not +from luxuriance, of imagination) often overrate the weight of true +analogies; but the fallacy specially consists in inferring resemblance +in one point from resemblance in another, when the evidence is not only +not in favour of, but even positively against the connection of the two +by way of causation. It is so in the argument in favour of absolutism, +on the ground of its resemblance to paternal government in the one point +of irresponsibility, as though the assumed benefits of paternal rule +flowed from this quality. Similarly fallacious are the inferences, +through analogies, from the liability to decay of bodies natural to that +of bodies politic; from the supposed need of a _primum mobile_ in nature +to that of an irresponsible power in a state; and from the effects of a +decrease of a country's corn to the effects of a decrease of its gold +(the utility of which, but not of corn, depends on its value, and its +value on its scarcity). Such, also, were the Pythagorean inferences that +there is a music of the spheres, because the intervals between the +planets have the same proportion as the divisions of the monochord; and, +again, that the movements of the stars as being _divine_ must be +regular, because so are those even of orderly _men_. So, Aristotle and +other ancients supposed perfection to obtain in all natural facts, +because it appeared to exist in some; and so, the Stoics tried to prove +the equality of all crimes by reference to various similes and metaphors +(as, that the man held half an inch below the surface will be drowned as +certainly as the man at the bottom of the sea; and that want of skill is +shown as much in steering a straw-laden boat as a treasure galleon on to +the rocks). But, in fact, the connection by causation between the known +and the inferred resemblance, which is _assumed_ by these metaphors, is +the very thing which they are brought to prove. The real use of such +cases of analogy as metaphors is that they serve, not as an argument, +but as an assertion that one exists. Though they cannot prove, they +sometimes suggest the proof, and point to a case in which the same +grounds for a conclusion have been found adequate. Such are d'Alembert's +classification of successful politicians as either eagles or serpents; +and the statement, as an argument for education, that, in waste land +weeds will spring up; and such is _not_ Bacon's inference from the +levity of floating straw to the worthlessness of the _extant_ scientific +works of the ancients. + +The great source of fallacious generalisation is bad classification, by +which things with no, or no important, common properties, are grouped +together. Worst is it, when a word which commonly signifies some +definite fact is applied to other facts only slightly similar. Bacon +(who has himself thus erred in his enquiries into heat) specifies, as +examples of this, the various applications (got, by unscientific +abstraction, from the original sense) of the word 'wet,' to flame, air, +dust, and glass, as well as to water. The application by Plato, +Aristotle, and other ancients, of the terms Generation, Corruption, and +[Greek: kinesis] to many heterogeneous phenomena, with a mixture of the +ideas belonging to them severally, caused many perplexities, which may +be noticed under Fallacies of Confusion. + + + + +CHAPTER VI. + +FALLACIES OF RATIOCINATION. + + +These fallacies (to which the name _Fallacy_ is commonly applied +exclusively) would generally be detected if the arguments were set out +formally; and the value of the syllogistic rules is, that they force the +reasoner to be aware what it is that he is really asserting. The +frequent errors in processes such as Conversion and Opposition, which +are in appearance, though not in reality, inferences from premisses, may +for convenience be here referred to. Such are the simple conversion of +an universal affirmative; the corresponding error in a hypothetical +proposition of inferring the truth of the antecedent from that of the +consequent; and the confusing of a contrary with a contradictory, which +amounts, in practice, to mistaking the reverse of wrong for right. But +fallacies of Ratiocination properly lie in syllogisms. They commonly +resolve themselves, when in a single syllogism, into the having more +than three terms, whether covertly, as through an undistributed middle, +or an illicit process, or avowedly. But the most dangerous and the +commonest of these fallacies arise in a chain of argument from _changing +the premisses_. One of the obscurer forms of this is the fallacy _a +dicto secundum quid_ (i.e. with a qualification, or condition, +expressed, or, more usually, understood) _ad dictum simpliciter_. Thus, +the Mercantile Theory was in favour of prohibiting all trade which tends +to carry out more money than it brings in, on the ground that money is +riches, though it is so only if the money can be _freely_ spent. Such, +too, was the argument (used to support the doctrine that tithes fall on +the landlord) that, because now the rent of tithe-free land exceeds that +of tithed land, the rent from the latter would be increased by the +abolition of all tithes. There was a similar fallacy in the use of the +maxim, that individuals are the best judges of their pecuniary +interests, against Mr. Wakefield's scheme for concentrating settlers. +Cases in which the condition of _time_ is dropped, fall under this same +particular fallacy, as, when the maxim that prices always find their +level, is construed as meaning that they are always _at_ their level. It +is the same with the reasoning (especially in political and social +subjects), upon principles, which are true in the absence of all +modifying causes, as though no such causes _could_ exist. Other +analogous fallacies are those _a dicto simpliciter ad dictum secundum +quid_ (the converse of the preceding), and _a dicto secundum quid ad +dictum secundum alterum quid_. + + + + +CHAPTER VII. + +FALLACIES OF CONFUSION. + + +Under this head come all fallacies which arise, not so much from a false +estimate of the probative force of known evidence, as from an indistinct +conception what the evidence is. + +1. Thus, where there is an ambiguous middle, or a term used in different +senses in the premisses and in the conclusion, the argument proceeds as +though there were evidence to the point, when, in fact, there is none. +This error does not occur much in direct inductions, since the things +themselves are there present to the senses or memory; but chiefly, in +Ratiocination, where we are deciphering our own or others' notes. The +ambiguity arises very often from assuming that a word corresponds +precisely in meaning with the root itself (e.g. _representative_), or +with cognate words from the same root, called _paronymous_ words (as, +_artful_, with _art_). Other examples of ambiguities are; 'Money,' +which, meaning both the currency and also capital seeking investment, is +often thought to be scarce in the former sense, because scarce in the +latter; 'Influence of Property,' which, signifying equally the influence +of respect for the power for good, and of fear of the power for evil, +which is possessed by the rich, is represented as being assailed under +its former form when attacked really only under the latter; 'Theory,' +which, because applied popularly to the accounting for an effect apart +from facts, is ridiculed, even when expressing, as it properly does, the +result of philosophical induction from experience; 'The Church,' which +refers (as in the question of the inviolability of _Church_ property) +sometimes to the clergy alone, sometimes to all its members; 'Good,' in +the Stoic argument that virtue, as alone _good_ (in the Stoic sense), +must therefore include freedom and beauty, because these are _good_ (in +the popular sense). So, the meaning of 'I' shifts from _the laws of my +nature_ to _my will_, in Descartes' _a priori_ argument for the being of +a God, viz. that there must be an external archetype whence I got the +conception, for if _I_ (i.e. _the laws of my nature_) made it, _I_ (i.e. +_my will_, and not, as it should consistently be, _the laws of my +nature_) could unmake it; but _I_ (i.e. _my will_) cannot. In the +Free-Will controversy, 'I' is used ambiguously for volitions, actions, +and mental dispositions, and 'Necessity' both for _Certainty_ and for +_Compulsion_. From the application of 'same,' 'one,' 'identical,' which +primarily refer to a single object, to several objects because +_similar_, grew up (for the purpose of accounting for the supposed +_oneness_ in things said to have the _same_ nature or qualities) both +the Platonic _Ideas_, and also the _Substantial Forms_ and _Second +Substances_ of the Aristotelians, even though the latter did see the +distinction between things differing both _specie_ and _numero_, and +those differing _numero_ only. And thence, too, sprang Berkeley's proof +of the existence of a Universal Mind from the supposed need of such a +Being to harbour, in the interval, the idea, which, one and the same +(really, only two _similar_ ideas), a man's mind has entertained at two +distinct times. The difficulty in _Achilles and the Tortoise_ arises +from the use of _infinity_, or, _for ever_, in the premisses, to +signify a finite time which is infinitely divisible, and, in the +conclusion, to signify an infinite time. Thus, again, 'right' is used to +express, both what others have no right to stop a man from doing, and +also what it is not against his own duty to do; both what people are +entitled to expect from, and also what they may enforce from others. The +Fallacy of Composition and Division, i.e. the use of the same term in a +syllogism, at one time in a collective, at another in a distributive +sense, is one of the Fallacies of Ambiguous Terms. Examples of it are +the arguments, that _great men_ (collectively) could be dispensed with, +because the place of any particular great man might have been supplied +(i.e., in fact, by some other great man); and, that a high prize in a +lottery may be reasonably expected (by _a certain individual_, viz. +oneself), because a high prize is commonly gained (_by some one or +other_). + +2. In Petitio Principii, the premisses are not even verbally sufficient +for the conclusion, since one premiss is either clearly the same as the +conclusion, or actually proved from it, or not susceptible of any other +proof. Men commonly fall into it, through believing that the premiss +_was_ verified, though they have forgotten how. But the variety, termed +Reasoning in a Circle, implies a conscious attempt to prove two +propositions reciprocally from each other. This formal proof is not +often attempted, except under the pressure of controversy; but, from +mistaking mutual coherency for truth, propositions, which cannot be +proved except from each other, are often _admitted_, when expressed in +different language, without other proof. Frequently a proposition is +presented in abstract terms as a proof of the same in concrete, as, in +Moliere's parody, 'L'opium endormit parcequ'il a une vertu soporifique.' +So, some qualities of a thing selected arbitrarily are termed its nature +or essence, and then reasoned from as though not able to be counteracted +by any of the rest. 'Question-begging appellatives,' particularly, are +cases of Petitio Principii, e.g. the styling any reform an _innovation_, +which it really is, only that _innovation_ conveys, besides its +dictionary meaning, a covert sense of something extreme. Thus, in +Cicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to +express certain desires the moral character of which is the point in +question. Again, the infinite divisibility of matter was assumed by the +argument which was used to prove it, viz. that the least portion of +matter must have both an upper and an under surface (which, as every +other Fallacy of Confusion, when cleared up, appears as a fallacy of a +different sort, under shelter of which, as indeed in ratiocinative +fallacies generally, the mere verbal juggle at first escapes detection). +Such, again, was Euler's argument, that _minus_ multiplied by _minus_ +gives _plus_, _because_ it could not give the same as _minus_ multiplied +by _plus_, which gives _minus_. So, some ethical writers begin by +assuming, that certain general sentiments are the _natural_ sentiments +of mankind, and thence argue that any which differ are morbid and +_unnatural_. Thus, lastly, Hobbes and Rousseau rested the existence of +government and law on a supposed social compact, and not on men's +perception of the interests of society, which, however, could be the +only ground for their abiding by such compact if a fact. + +3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the +error lies not either in mistaking the import of the premisses, or in +forgetting what they are, but in mistaking what is the conclusion to be +proved. Sometimes, a particular is substituted for the universal as the +proposition needing proof, and sometimes, a proposition with different +terms. Under this fallacy come the cases, not only of proving what was +not denied, but of disproving what was not asserted; e.g. the argument +used against Malthus (whose own position was, that population increases +only _in so far as not kept down_ by prudence, or by poverty and +disease), that, at times, population has been nearly stationary; or +again, that, in some country or other, population and comfort are +increasing together, Malthus himself having asserted that this might be +so, if capital has increased. Similarly, even Reid, Stewart, and Brown +(not merely Dr. Johnson) urged that Berkeley ought, if consistent, to +have run his head against a post, as though the non-recognition of an +occult _cause_ of sensations implies disbelief in any _fixed order among +them_. + + + + +BOOK VI. + +ON THE LOGIC OF THE MORAL SCIENCES. + + + + +CHAPTER I. + +INTRODUCTORY REMARKS. + + +Many complex problems have been resolved through the use of the +Scientific Methods, and thus only. The most complex of all problems are +the problems relating to Man himself; and of them those concerned with +the Mind and Society have never been scientifically resolved. They can +be rescued from empiricism, if at all, only by being submitted to some +of the methods already characterised as applicable to science in +general. Which of these methods must be selected, and why; what are the +causes of previous failures; and what degree of success now is possible +or probable, will be considered in this book, when a preliminary +objection (_based on the theory of free will_), that men's actions are +not, like other natural events, subject to invariable laws, has been +first removed. + + + + +CHAPTER II. + +LIBERTY AND NECESSITY. + + +The theory of _free will_, viz. that the will is determined by itself, +and not by antecedents, was invented as being more in accordance with +the dignity of human nature and our consciousness of freedom, than +_philosophical necessity_. The latter doctrine, in laying down simply +that our volitions and actions are invariable consequents of our +antecedent states of mind, and that, given our motives, character, and +disposition, other men could predict our conduct as certainly as any +physical event, states indeed nothing which is in itself either +contradicted by our consciousness, or degrading; yet the doctrine of +causation, as applied to volition, is supposed, from the natural +tendency of the mind to imagine falsely that a mysterious constraint is +exercised by _any_ antecedent over the consequent, to imply some state +of dependence which our consciousness does contradict. Moreover, the +erroneous notion that something more than uniformity of order and +capability of being predicted is meant, has been favoured by the use of +the ambiguous term _necessity_ (which, it is true, commonly implies +irresistibleness), to signify simply that the given cause will be +followed by the effect subject to all possibilities of counteraction by +other causes. Most necessarians have been themselves deceived by the +expression: they are apt to be partially fatalists as to their own +actions, with a weaker spirit of self-culture than the believers in +free-will, and to fail to see that the fact of their character being +formed _for_ them, that is, by their circumstances, including their own +organisation, is consistent with its being formed _by_ themselves, as +intermediate agents, moulding it in any particular way which they may +_wish_. The belief that the _wishing_ is excited by external causes, +e.g. by education, casual aspirations, and experience of ills resulting +from our previous character, can be of no practical harm, and does not +conflict with our feeling of moral freedom, that is, of power, _if we +wish_, to modify or conquer our own character. + +The ambiguity of the word _motive_ has also caused confusion. A motive, +when used to signify that which determines the will, means not always or +only the anticipation of a pleasure or a pain, but often the desire of +the action itself. The action having finally become by association in +itself desirable, we may get the habit of willing it (that is, get a +_purpose_) without reference to its being pleasurable. We are then said +to have a confirmed character. + + + + +CHAPTER III. + +THERE IS, OR MAY BE, A SCIENCE OF HUMAN NATURE. + + +Any facts may be a subject of science, if they follow one another +according to constant laws; and this, whether, although the ultimate +laws are known, yet, of the derivative laws on which a phenomenon +directly depends, either _none_, as in Meteorology, or, as in Tidology, +_only_ the laws of the greater causes on which the chief part of a +phenomenon directly depends, have been ascertained, and not those of all +the minor modifying causes; or, as in Astronomy (which is therefore +called an _exact_ science), both the ultimate laws are known, and also +the derivative laws as well of the greater as of all the minor causes. +The science of Human Nature cannot be exact, the causes of human conduct +being only approximately known. Hence it is impossible to predict _with +scientific accuracy_ any one man's acts, resulting as they do partly +from his circumstances, which, in the future, cannot be precisely +foreseen, and, partly, from his character, which can never be exactly +calculated, because the causes which have determined it are sure, in the +aggregate, not to be entirely like those which have determined any other +man's. But approximate generalisations, though only probably true as to +the acts and characters of individuals, will be certainly true as to +those of masses, whose conduct is determined by general causes chiefly; +and they are therefore sufficient for political and social science. They +must, however, be connected deductively with the universal laws of human +nature on which they rest, or they will be only low empirical laws. This +is the text of the next two chapters. + + + + +CHAPTER IV. + +THE LAWS OF MIND. + + +By the laws of mind (i.e. as considered in this treatise, the laws of +mental phenomena) are meant the laws according to which one state of +mind is produced by another. If M. Comte and others be right in saying +that, in like manner with the mental phenomena called sensations, all +the other states of mind have for their proximate causes nervous states, +there would be no original laws of mind, and Psychology would be a mere +branch of Physiology. But at present, this tenet is not proved, however +highly probable; and, at all events, the characteristics of those +nervous states are quite unknown; consequently the uniformities of +succession among the mental phenomena, which undoubtedly do exist, and +which are not proved to result from more general laws, must be +considered as the subject of a distinct science called Psychology. We +can ascertain only by experiment the simple laws of Mind, such as--1. +That a state of consciousness can be reproduced in the absence of the +cause which first excited it (i.e. that every mental impression has its +idea), and--2. That these secondary mental states themselves are +produced according to the three laws of ideas. But the complex laws are +got from these simple laws, according either to the Composition of +Causes, when the complex idea is said to _consist of_ the Simple Ideas, +or to chemical combination, when it is said to be _generated by_ them. +Hartley and Mr. James Mill indeed hold _all_ the mental phenomena to be +generated by chemical combination from simple ideas of _sensation_, +however unlike to the alleged results; but even though they had proved +their theory, employing the Method of Difference, and not only the +Method of Agreement (which latter itself they have used only partially), +we should still have to study the complex ideas themselves inductively, +before we could ascertain their sequences. + +The analytical enquiry (neglected alike by the German metaphysical +school, and by M. Comte) into the general laws of mind, will show that +the mental differences of individuals are not ultimate facts, but may be +referred generally to their particular mental history, their education +and circumstances, but sometimes also to organic differences influencing +the mental phenomena, not directly, but through the medium of the +psychological causes of the latter. Men's animal instincts, however, are +probably, equally with the mere sensations, connected directly with +physical conditions of the brain and nerves. Whether or not there be any +direct relation between organic causes and any other mental phenomena, +Physiology is likely in time to show; but at least Phrenology does not +embody the principles of the relation. + + + + +CHAPTER V. + +ETHOLOGY, OR THE SCIENCE OF THE FORMATION OF CHARACTER. + + +Till the Empirical laws of Mind, i.e. the truths of common experience, +are _explained_ by being resolved into the causal laws (the subject of +the last chapter), they are mere approximate generalisations which +cannot be safely applied beyond the limits in which they were collected +by observation. But this does not prove aught against the universality +and simplicity of the ultimate mental laws; for the same is the case +with the empirical laws even in astronomy, where each effect results +from but few causes; _a fortiori_, therefore, will it be so in regard to +man's character, which is influenced by each of his circumstances, which +differ in the case of each nation, generation, and individual. But +though mankind have not one universal character, yet there exist +universal laws of the formation of character. These universal laws +cannot be discovered experimentally, i.e. either by artificial +experiment, since we can seldom vary the experiment sufficiently, and +exclude all but known circumstances, or by observation, since, even in +the most favourable instances for the latter, viz. National acts, only +the Method of Agreement can be applied. Observation has its uses in +relation to this subject; but only as verification of the results +arrived at by the Deductive Method. The Deductive Method must be +employed to obtain the laws of the formation of character. They are got +by supposing any given circumstances, and then considering how these +will, according to the general laws of mind, influence the formation of +character. So, contrary to Bacon's rule, laid down wrongly as universal, +for the discovery of principles, the highest generalisations must be +first ascertained by the experimental science of Psychology; and then +will come what is in fact a system of corollaries from the latter +science, viz. Ethology, i.e. (as dealing only with tendencies) the +_exact_ science of human character, or of education both national and +individual, and which has for its principles the middle principles +(_axiomata media_) of mental science. It does not yet, but it will soon, +exist as a science. Its object must be to determine, from the general +laws of mind, combined with man's general position in the universe, what +circumstances will aid or check the growth of good or bad qualities, so +that the Art of Education will be merely the transformation of these +middle principles into precepts and their adaptation to the special +cases. But at every step these middle principles, got by deduction, must +be verified _a posteriori_ by empirical laws, and by specific experience +respecting the assumed circumstances. + + + + +CHAPTER VI. + +GENERAL CONSIDERATIONS ON THE SOCIAL SCIENCE. + + +Political and social phenomena have been thought too complex for +scientific treatment. Practitioners hitherto have been the only +students; and so, as in medicine, before the rise of Physiology and +Natural History, _experimenta fructifera_, and not _lucifera_, have been +sought. The scheme of such a science has even been thought quackery, +through the vain attempts of some theorists to frame universal precepts, +as though their failure (arising from the variety of human +circumstances) proved that the phenomena do not conform to universal +laws. Social phenomena, however, being phenomena of human nature in +masses, must, as human nature is itself subject to fixed laws, obey +fixed laws resulting from the fixed laws of human nature. The number and +changefulness of the data (unlike those of Astronomy) will prevent our +ever predicting the far future of society. But, when general laws have +been ascertained, an application of them to the individual circumstances +of a given age and country will show us the causes and tendencies of, +and the means of modifying, its actual condition. A consideration of two +methods, erroneously used for this science, viz. the Experimental or +Chemical, and the Abstract or Geometrical, will introduce us to the true +one. + + + + +CHAPTER VII. + +THE CHEMICAL, OR EXPERIMENTAL, METHOD IN THE SOCIAL SCIENCE. + + +The followers of this method do not recognise the laws of social +phenomena as merely a composition of the laws of individual human +nature. They demand specific experience in all cases; and they attempt +to make effects, which depend on the greatest possible complication of +causes, the subject of induction by observation and experiment. The +attempt must fail; for, we can neither get by experiment appropriate +_artificial_ instances, nor, by observation, _spontaneous_ instances +(from history), with the circumstances enough varied for a true +induction. Neither the _direct_ nor the _indirect_ Method of Difference +can be applied, for we cannot find either two single instances differing +in nothing but the presence or absence of a given circumstance (the +_direct_), or two classes respectively agreeing in nothing but the +presence of a circumstance on one side and its absence on the other (the +_indirect_). Then, again, the Method of Agreement is of small value, +because social phenomena admit the widest plurality of causes; and so +also is that of Concomitant Variations, on account of the mutual action +of the coexisting elements of society being such that what affects one +affects all. The Method of Residues is better suited to social enquiries +than the other three. But _it_ is not a method of pure observation and +experiment. It presupposes that we know, by previous deduction from +principles of human nature, the causes of part of the effect. But if +thus part of the truths are, why may not all be, ascertained by +Deduction, and the experimental argument be confined to the verifying of +the deductions? + + + + +CHAPTER VIII. + +THE GEOMETRICAL, OR ABSTRACT, METHOD. + + +The Methods of Elementary Chemistry are applied to social phenomena from +carelessness as to, or ignorance of, any of the higher physical +sciences: the Geometrical Method, from the belief that Geometry, that +is, a science of coexistent, not successive facts, where there are no +conflicting forces, is, and that the now deductive physical sciences of +Causation, where there are conflicting forces, are _not_, the type of +deductive science. Thus, it seems to have been supposed by many +philosophers, that each social phenomenon results from only one force, +one single property of human nature. For instance, Hobbes assumed (eking +out his assumption by the fiction of an original contract), that +government is founded on fear. Even the scientific Bentham School based +a general theory on one premiss, viz. that men's actions are always +determined by their interests, meaning probably thereby, that the bulk +of the conduct of any succession, or of the majority of any body of men, +is determined by their private or worldly interests. They inferred +thence, that those rulers alone will govern according to the interest of +the governed, whose selfish interests are identified with it (forgetting +that, apart from the philanthropy and sense of duty of many, the +conduct of _all_ rulers must be influenced by the habits of mind, both +of the whole community, and also of their own class in it, and by the +maxims of their predecessors). Lastly, they laid down that this sense of +identity of interest with the governed is producible only by +responsibility (whereas the personal interest of rulers often prompts +them to acts, e.g. for the suppression of anarchy, which are also for +the interest of the governed). In fact, this school was pleading for +parliamentary reform, and saw truly, that it is against the selfish +interests of rulers that constitutional checks are needed, and that, in +modern Europe, a feeling in the governors of identity of interest, when +not active enough, can be roused only by responsibility to the governed. +Their mistake was, that they based on just these few premisses a general +theory of government, in forgetfulness that such should proceed by +deduction from _the whole_ of the laws of human nature, since each +effect is an aggregate result of many causes operating now through the +same ones, now through different ones, of these laws. + + + + +CHAPTER IX. + +THE PHYSICAL, OR CONCRETE DEDUCTIVE, METHOD. + + +The complexity in social effects arises from the number, not of the +laws, but of the data. Therefore, Sociology, i.e. Social Science, must +use the Concrete Deductive Method, compounding with one another the laws +of all the causes on which any one effect depends, and inferring its law +from them all. As in the easiest case to which the Method of Deduction +applies, so in this, the most difficult, the conclusions of +ratiocination must be _verified_ by collation with the concrete +phenomena, or, if possible, with their empirical laws; and then the only +effect of an increase in the complication of the subject will be a +tendency to a disturbance, and sometimes even to an inversion (which, +indeed, M. Comte thinks inseparable from all Sociological enquiries) in +the order of the two processes, obliging us, first, to conjecture the +conclusions by specific experience, and then verify them by _a priori_ +reasonings showing their connection with the principles of human nature. + +Sociology is a system not of positive predictions, but of tendencies. Of +tendencies themselves, not many can be laid down as true of all +societies alike. Even in the case of any single feature of society, the +_consensus_ which exists in the body politic, as in the body natural, +makes it uncertain whether a cause with a special tendency in one age or +country will have quite the same in another. General propositions, +therefore, in this deductive science, as, to be true, they must be +hypothetical, and state the operation of a given cause in _given +circumstances_, so, to be of any utility, should be limited to those +classes of facts, which, though influenced by all sociological agents, +are yet influenced _immediately_ by a few only, certain fixed +combinations of which are likely to recur often. Thus, Political +Economy, taking the one psychological law that men prefer a greater gain +to a smaller, and ignoring every other motive, except what are +perpetually adverse principles to this, viz. men's aversion to labour +and desire of present costly pleasures, assumes, in enquiring what acts +this desire of gain will produce, that, within the department of human +affairs, where it is actually the main end, it is the _sole_ end. Yet +its general propositions are of great practical use, even though it thus +provisionally overlooks as well miscellaneous concurrent causes (with +some exceptions, as e.g. the principle of population), as also the fact +of the non-existence elsewhere of the conditions of any one particular +country (e.g. the peculiarly British mode of distribution of the produce +of industry among three classes). Another hypothetical or abstract +science, which can be carved out of Sociology, is the as yet unexplored +Political Ethology, i.e. the theory of the causes which determine a +people's, or age's, type of character, which collective character, +besides being the most interesting phenomenon in the particular state of +society, is the _main_ cause of the social state which follows, and +moulds _entirely_ customs and laws. The neglect of national diversities +sometimes (as e.g. the assumption by our political economists, that in +commercial populations everywhere, equally as in Great Britain and +America, all motives yield to the desire of gain) vitiates only the +practical application of a proposition; but when the national character +is mixed up at every step with the phenomena (as is the case in +questions respecting the tendencies of forms of government), the +phenomena cannot properly be insulated in a separate branch of +Sociology. + +As in Ethology and other deductive sciences, so in Statistics and +History there are empirical laws. The immediate causes of social facts +are often not open to direct observation; and the deductive science can +determine only what causes produce a given effect, and not the frequency +and quantities of them; in such cases, the empirical law of the causes +(which, however, can be applied to new cases only if we know that the +remoter causes, on which these latter causes depend, remain unchanged) +must be found through that of the effects, the Deductive Science relying +then for its data on indirect observation. But, in the separate branches +of Sociology, we cannot obtain empirical laws by specific experience. It +is so particularly (on account both of the number of the causes, and +also the fewness of the instances to be compared with the one in point) +when the effect of any one (e.g. Corn Laws) of many simultaneous social +causes has to be determined. We can, however, in such cases, verify +_indirectly_ a theory as to the influence of a particular cause in given +circumstances, by seeing if the same theory accounts for the _existing_ +state of actual social facts which that cause has a tendency to +influence. + + + + +CHAPTER X. + +THE INVERSE DEDUCTIVE, OR HISTORICAL, METHOD. + + +The _general_ Science of Society, as contrasted with the branches, +shows, not what effect will follow from a given cause under given +circumstances, but what are the causes and characteristic phenomena of +States of Society generally. A _State of Society_ is the simultaneous +state of all the chief social facts (e.g. employments, beliefs, laws). +It is a condition of the whole organism; and, when analysed, it +exhibits uniformities of coexistence between its different elements. +But, as this correlation between the phenomena is itself a law resulting +from the laws which regulate the succession between one state of society +and another, the fundamental problem of Social Science is to find these +latter laws. The form of this succession, by which (on account of the +exceptionally constant reaction, in social facts, of the effects, i.e. +human character, on their causes, i.e. human circumstances) one social +state is ever in process of changing into a different one, is now +allowed to be, not, as in the solar system, a cycle, but a _progress_ +(by which is not here _necessarily_ meant _improvement_, whatever the +fact may be). In France it has been thought, that a law of progress, to +be found by an analysis of the course of history, would enable us to +predict the whole future. But such a law would be empirical, and not +true beyond its own facts; for the succession of mental and social +states cannot have an independent law. Empirical laws must indeed be +found; or a _general_ Science of Society would be impossible: for, the +character of any one generation is so much the result of the characters +of all prior ones, that _men_ could not compute so long a series from +the elementary laws producing it. But the empirical laws, when found (as +they can be, since the series of the effects as a whole is ever growing +in uniformity), must be shown by deductions to be, if not the only +possible, or even the most probable, at least possible, consequences of +the laws of human nature. + +The empirical laws of society are uniformities, either of coexistence, +or of succession. The former are ascertained and verified by Social +Statics (which is the theory of the _consensus_, i.e. the mutual actions +and reactions, of contemporaneous social elements); the latter, by +Social Dynamics (the theory of Society considered as in a state of +progress). As to Social Statics--there is, M. Comte thinks, a perpetual +reciprocity of influence between all aspects of the same organism, and +to such an extent, that the condition of any one which we cannot +directly observe can be estimated by that of another which we can. There +is, he considers, such an interdependence, not only between the +different sciences and arts among themselves, but between the sciences +in general and the arts in general, even between the condition of +different nations of the same age, and between a form of government and +the civilisation of the period. Social Statics will ascertain for us the +requisites of stable political union: it will enquire what special +circumstances have always attended on such union, increasing and +decreasing in proportion to its completeness; and will then verify these +facts as requisites by deducing them from general laws of human nature. +Thus, history indicates as such requisites and conditions of free +political union: 1. A system of educational discipline checking man's +tendency to anarchy; 2. Loyalty, i.e. a feeling of there being +something, whether persons, institutions, or individual freedom and +political and social equality, which is not to be, at least in practice, +called in question; 3. That which the Roman Empire, notwithstanding all +its tyranny, established, viz. a strong sense of common interest among +fellow-citizens (a very different feeling, by the bye, to mere +antipathy to foreigners). + +Social Dynamics regards sequences. But the _consensus_ in social facts +prevents our tracing the leading facts in one generation to separate +causes in a prior one. Therefore, we must find the law of the +correspondence not only between the simultaneous states, but between the +simultaneous changes of the elements of society. To find this law, +which, when duly verified, will be the scientific derivative law of the +development of humanity, we must combine the statical view of the +phenomena with the dynamical. Fortunately, the state of mankind's +speculative faculties and beliefs, being the prime agent of the social +movement, furnishes a clue in the maze of social elements, since the +order of human progression in all respects will mainly depend on the +order of progression of this prime agent. That the other dispositions +which aid in social progress (e.g. the desire for increased material +comfort) owe their means of working to this (however relatively weak a +propensity it may be) is a conclusion from the laws of human nature; and +this conclusion is in accordance also with the course of history, in +which internal social changes have ever been preceded by proportionate +intellectual changes. To determine the law of the successive +transformations of opinions all past time must be searched, since such +changes appear definitely only at long intervals. M. Comte alone has +followed out this conception of the Historical Method; and his +generalisation, to the effect that speculation has, on all subjects, +three successive stages, has high scientific value. + +The Historical Method will trace the derivative laws of social order +and progress. It will enable us both to predict the future, and (thus +founding the noblest part of the Political Art) partly to shape it. At +present, both the Science and the Art are in the rudiments; but they are +progressing. + + + + +CHAPTER XI. + +THE LOGIC OF PRACTICE, OR ART; INCLUDING MORALITY AND POLICY. + + +Practical Ethics, i.e. Morality, is an art; and therefore its Method +must be that of Art in general. Now, Art from the major premiss, +supplied by itself, viz. that the end is desirable, and from the +theorem, lent by Science, of the combinations of circumstances by which +the end can be reached, concludes that to secure this combination of +circumstances is desirable; if it also appear practicable, it turns the +theorem into a rule. Unless Science's report as to the circumstances is +a full one, the rule may fail; and as, in any case, rules of conduct +cannot comprise more than the ordinary conditions of the effect (or they +would be too cumbrous for use), they must, at least in moral subjects, +be considered, till confronted with the theorems, which are the reasons +of them, provisional only. Practical maxims, therefore, till so +confronted, are not universally true even for a given end, much less for +conduct generally, and must not be used, as they are by the +_geometrical_ school, as ultimate premisses. + +Any particular art consists of its rules, _together with_ the theorems +on which they depend; and Art in general consists of the truths of +Science; only these must be arranged in the order most convenient, not, +as in Science (which is an enquiry into the course of nature), for +thought, but for practice. Intermediate scientific truths must be framed +to serve as first principles of the various arts: and through them the +end or purpose of an art will be connected with the means for realising +the conditions of its attainment. The end itself, however, is defined by +the art, not by the science. Each art has one first principle or major +premiss which does not, as the propositions of Science, assert that a +thing _is_ or _will be_, but recommends it as what _ought to be_. A +scientific theory, however complete, of the history and tendencies of +society does not show us (without Teleology, i.e. the Doctrine of Ends) +what are the preferable ends. Art itself has its Philosophia Prima, for +ascertaining the standard of ends. There can be but one such standard or +general principle to which all rules of practice should conform; for, if +there were several, a higher yet would be needed, as umpire when they +disagreed. In Morality the felt need of a standard has been sometimes +supplied by the hypothesis of intuitive moral principles: but a standard +would still be wanted for the other two branches of the Art of Life, +viz. Prudence or Policy, and Taste; and _their_ standard when found +would serve for Morality as well. The true standard, or general +principle, is, _the promotion of the happiness of_ ALL _sentient +beings_. This is not the _sole_ end; for instance, ideal nobleness of +will or conduct should be pursued in preference to the _specific_ +pursuit of happiness; but all ends whatsoever must be justified and +should be controlled by it. + + +LONDON +PRINTED BY SPOTTISWOODE AND CO. +NEW-STREET SQUARE + + + + + +End of the Project Gutenberg EBook of Analysis of Mr. Mill's System of Logic, by +William Stebbing + +*** END OF THIS PROJECT GUTENBERG EBOOK MILL'S LOGIC *** + +***** This file should be named 30866.txt or 30866.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/0/8/6/30866/ + +Produced by David Clarke, Martin Pettit and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive/Million Book Project) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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